publicationDate,title,abstract,id
2015-06-25,Ground-state densities from the Rayleigh--Ritz variation principle and from density-functional theory,"The relationship between the densities of ground-state wave functions (i.e.,
the minimizers of the Rayleigh--Ritz (RR) variation principle) and the
ground-state densities in density-functional theory (i.e., the minimizers of
the Hohenberg--Kohn (HK) variation principle) is studied within the framework
of convex conjugation, in a generic setting covering molecular systems,
solid-state systems, and more. Having introduced admissible density functionals
as functionals that produce the exact ground ground-state energy for a given
external potential by minimizing over densities in the HK variation principle,
necessary sufficient conditions on such functionals are established to ensure
that the RR ground-state densities and the HK ground-state densities are
identical. We apply the results to molecular systems in the BO-approximation.
For any given potential $v \in L^{3/2}(\mathbb{R}^3) +
L^{\infty}(\mathbb{R}^3)$, we establish a one-to-one correspondence between the
mixed ground-state densities of the RR variation principle and the mixed
ground-state densities of the HK variation principle when the Lieb
density-matrix constrained-search universal density functional is taken as the
admissible functional. A similar one-to-one correspondence is established
between the pure ground-state densities of the RR variation principle and the
pure ground-state densities obtained using the HK variation principle with the
Levy--Lieb pure-state constrained-search functional. In other words, all
physical ground-state densities (pure or mixed) are recovered with these
functionals and no false densities (i.e., minimizing densities that are not
physical) exist. The importance of topology (i.e., choice of Banach space of
densities and potentials) is emphasized and illustrated. The relevance of these
results for current-density-functional theory is examined.",1506.07740v1
2004-07-05,Local density approximation for exchange in excited-state density functional theory,"Local density approximation for the exchange energy is made for treatment of
excited-states in density-functional theory. It is shown that taking care of
the state-dependence of the LDA exchange energy functional leads to accurate
excitation energies.",0407099v1
2023-05-12,Density of states of a 2D system of soft--sphere fermions by path integral Monte Carlo simulations,"The Wigner formulation of quantum mechanics is used to derive a new path
integral representation of quantum density of states. A path integral Monte
Carlo approach is developed for the numerical investigation of density of
states, internal energy and spin--resolved radial distribution functions for a
2D system of strongly correlated soft--sphere fermions. The peculiarities of
the density of states and internal energy distributions depending on the
hardness of the soft--sphere potential and particle density are investigated
and explained. In particular, at high enough densities the density of states
rapidly tends to a constant value, as for an ideal system of 2D fermions.",2305.07601v2
2018-11-13,Quantum states and knowledge: Between pure states and density matrices,"In this note I will present a subtle interplay between density matrices and
the knowledge about their preparation, and I will argue that there is a need to
consider a new type of quantum state, in between pure states and density
matrices.",1811.05472v1
2011-12-09,Stabilizer States as a Basis for Density Matrices,"We show that the space of density matrices for n-qubit states, considered as
a (2^n)^2 dimensional real vector space, has a basis consisting of density
matrices of stabilizer states. We describe an application of this result to
automated verification of quantum protocols.",1112.2156v1
2022-02-05,Many body density of states in the edge of the spectrum: non-interacting limit,"In noninteracting limit, the density of states of a many body system can be
expressed as the convolution of single body density of states of its subunits.
Here we use the formulation to derive the ensemble averaged many body density
of states for the cases in which subunits can be modelled by Gaussian or
Wishart random matrix ensembles.",2202.02605v1
2010-08-27,Lifshitz tails estimate for the density of states of the Anderson model,"We prove an upper bound for the (differentiated) density of states of the
Anderson model at the bottom of the spectrum. The density of states is shown to
exhibit the same Lifshitz tails upper bound as the integrated density of
states.",1008.4817v1
1997-10-15,The state space of short-range Ising spin glasses: the density of states,"The state space of finite square and cubic Ising spin glass models is
analysed in terms of the global and the local density of states. Systems with
uniform and gaussian probability distribution of interactions are compared.
Different measures for the local state density are presented and discussed. In
particular the question whether the local density of states grows exponentially
or not is considered. The direct comparison of global and local densities leads
to consequences for the structure of the state space.",9710146v1
2015-10-27,Long range interaction induced density modulated state in a Bose-Einstein condensate,"We consider a Gross-Pitaevskii model of BEC with non-local s-wave scattering
to study the density modulated state in 1D. We resort to a perturbative Taylor
series expansion for the order parameter. By perturbative calculations, we show
that under long range s-wave scattering a density modulated state is
energetically favourable as compared to the uniform density state. We obtain
density modulated state as a solution to the perturbative non-local GP
equation, rather than the conventional approach of introducing amplitude
modulations on top of the uniform density state and lowering the roton minimum.",1510.07843v1
2001-12-18,Charge densities and charge noise in mesoscopic conductors,"We introduce a hierarchy of density of states to characterize the charge
distribution in a mesoscopic conductor. At the bottom of this hierarchy are the
partial density of states which represent the contribution to the local density
of states if both the incident and the out-going scattering channel is
prescribed. The partial density of states play a prominent role in measurements
with a scanning tunneling microscope on multiprobe conductors in the presence
of current flow. The partial density of states determine the degree of
dephasing generated by a weakly coupled voltage probe. In addition the partial
density of states determine the frequency-dependent response of mesoscopic
conductors in the presence of slowly oscillating voltages applied to the
contacts of the sample. The partial density of states permit the formulation of
a Friedel sum rule which can be applied locally. We introduce the off-diagonal
elements of the partial density of states matrix to describe charge fluctuation
processes. This generalization leads to a local Wigner-Smith life-time matrix.",0112330v1
2001-07-30,The low-energy nuclear density of states and the saddle point approximation,"The nuclear density of states plays an important role in nuclear reactions.
At high energies, above a few MeV, the nuclear density of states is well
described by a formula that depends on the smooth single particle density of
states at the Fermi surface, the nuclear shell correction and the pairing
energy. In this paper we present an analysis of the low energy behaviour of the
nuclear density of states using the saddle point approximation and extensions
to it. Furthermore, we prescribe a simple parabolic form for excitation energy,
in the low energy limit, which may facilitate an easy computation of level
densities.",0107074v1
2003-02-16,New Zero-Resistance States in Heterostructures: Anderson-Brinkman-Phillips Charge Density Waves and New States,"Recently, observed zero-resistance states are interpreted by
Anderson-Brinkman and Phillips as charge density waves. We point out the
existence of charge-density waves, superconducting states and new states
including a state of zero charge and finite spin.",0302320v1
2022-05-14,Electronic excited states in extreme limits via ensemble density functionals,"Density functional theory (DFT) has greatly expanded our ability to
affordably compute and understand electronic ground states, by replacing
intractable {\em ab initio} calculations by models based on paradigmatic
physics from high- and low-density limits. But, a comparable treatment of
excited states lags behind. Here, we solve this outstanding problem by
employing a generalization of density functional theory to ensemble states
(EDFT). We thus address important paradigmatic cases of all electronic systems
in strongly (low-density) and weakly (high-density) correlated regimes. We show
that the high-density limit connects to recent, exactly-solvable EDFT results.
The low-density limit reveals an unnoticed and most unexpected result --
density functionals for strictly correlated {\em ground} states can be reused
{\em directly} for excited states. Non-trivial dependence on excitation
structure only shows up at third leading order. Overall, our results provide
foundations for effective models of excited states that interpolate between
exact low- and high-density limits, which we illustrate on the cases of
singlet-singlet excitations in H$_2$ and a ring of quantum wells.",2205.07136v3
2015-03-30,Strong and weak separability conditions for two-qubits density matrices,"Explicit separable density matrices, for mixed two qubits states, are derived
by the use of Hilbert Schmidt decompositions and Peres Horodecki criterion. A
strongly separable two qubits mixed state is defined by multiplications of two
density matrices given with pure states while weakly separable two qubits state
is defined by multiplications of two density matrices which includes non-pure
states. We find the sufficient and necessary condition for separability of
two-qubits density matrices and show that under this condition the two-qubit
density matrices are strongly separable.",1503.08643v2
2001-03-30,"The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics","The local Larmor clock is used to derive a hierarchy of local densities of
states. At the bottom of this hierarchy are the partial density of states for
which represent the contribution to the local density of states if both the
incident and outgoing scattering channel are prescribed. On the next higher
level is the injectivity which represents the contribution to the local density
of states if only the incident channel is prescribed regardless of the final
scattering channel. The injectivity is related by reciprocity to the emissivity
of a point into a quantum channel. The sum of all partial density of states or
the sum of all injectivities or the sum of all emissivities is equal to the
local density of states. The use of the partial density of states is
illustrated for a number of different electron transport problems in mesoscopic
physics: The transmission from a tunneling tip into a mesoscopic conductor, the
discussion of inelastic or phase breaking scattering with a voltage probe, and
the ac-conductance of mesoscopic conductors. The transition from a capacitive
response (positive time-delay) to an inductive response (negative time-delay)
for a quantum point contact is used to illustrate the difficulty in associating
time-scales with a linear response analysis. A brief discussion of the
off-diagonal elements of a partial density of states matrix is presented. The
off-diagonal elements permit to investigate carrier fluctuations away from the
average carrier density. The work concludes with a discussion of the relation
between the partial density of states matrix and the Wigner-Smith delay time
matrix.",0103164v1
2022-07-06,"On atomic state purity operator, degree of state purity and concurrence in the JC and anti-JC models","The state of an atom in a bipartite qubit, Jaynes-Cummings (JC) or
anti-Jaynes-Cummings (aJC) interaction is described by a reduced density
operator. The purity of the state has been measured by taking the trace of the
square of the reduced density operator. In this article, we define the square
of the reduced density operator as the state purity operator, composed of a
completely pure state part and a completely mixed state part. The coefficient
of the completely mixed state part is the mixed state measure, formally
obtained as the determinant of the reduced density operator and it is therefore
directly related to tangle, the square of concurrence of the bipartite system.
Expressed in various equivalent forms, the mixed state measure provides all the
characteristic elements of state purity or entanglement, such as eigenvalues of
the reduced density operator, nonclassicality measures and a state purity
complex amplitude. The argument of the state purity complex amplitude in polar
form is the phase of the state purity measure, which defines the degree of
purity of the state. We find that the degree of purity and concurrence are
complementary quantifiers satisfying a complementarity relation.",2207.02730v1
2004-09-16,Cavity broadcasting via Raman scattering,"The notion of broadcasting is extended to include the case where an arbitrary
input density state of a two-mode radiation field gives rise to an output state
with identical marginal states for the respective modes, albeit different from
the input state. The initial unknown input density state is unitarily related
to the output state but is not equal to the two identical output marginal
states. This extended notion of broadcasting suggests a possible way of
discriminating between two noncommuting quantum states.",0409105v1
2011-01-11,On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder,"We establish new results on the dimension of density of states for the
Anderson-Bernoulli model at small disorder",1101.2148v1
2004-10-14,An accurate exchange energy functional in excited-state density functional theory,"An exchange energy functional is proposed and tested for obtaining a class of
excited-state energies using density-functional formalism. The functional is
the excited-state counterpart of the local-density approximation functional for
the ground-state. It takes care of the state-dependence of the energy
functional and leads to highly accurate excitation energies.",0410361v1
2024-03-07,Foundation for the ΔSCF Approach in Density Functional Theory,"We extend ground-state density-functional theory to excited states and
provide the theoretical formulation for the widely used $\Delta SCF$ method for
calculating excited-state energies and densities. As the electron density alone
is insufficient to characterize excited states, we formulate excited-state
theory using the defining variables of a noninteracting reference system,
namely (1) the excitation quantum number $n_{s}$ and the potential
$w_{s}(\mathbf{r})$ (excited-state potential-functional theory, $n$PFT), (2)
the noninteracting wavefunction $\Phi$ ($\Phi$-functional theory, $\Phi$FT), or
(3) the noninteracting one-electron reduced density matrix
$\gamma_{s}(\mathbf{r},\mathbf{r}')$ (density-matrix-functional theory,
$\gamma_{s}$FT). We show the equivalence of these three sets of variables and
their corresponding energy functionals. Importantly, the ground and
excited-state exchange-correlation energy use the \textit{same} universal
functional, regardless of whether $\left(n_{s},w_{s}(\boldsymbol{r})\right)$,
$\Phi$, or $\gamma_{s}(\mathbf{r},\mathbf{r}')$ is selected as the fundamental
descriptor of the system. We derive the excited-state (generalized) Kohn-Sham
equations. The minimum of all three functionals is the ground-state energy and,
for ground states, they are all equivalent to the Hohenberg-Kohn-Sham method.
The other stationary points of the functionals provide the excited-state
energies and electron densities, establishing the foundation for the $\Delta
SCF$ method.",2403.04604v1
2021-03-18,Nuclear energy density functionals from empirical ground-state densities,"A model is developed, based on the density functional perturbation theory and
the inverse Kohn-Sham method, that can be used to improve relativistic nuclear
energy density functionals towards an exact but unknown Kohn-Sham
exchange-correlation functional. The improved functional is determined by
empirical exact ground-state densities of finite systems. A test of the model
and an illustrative calculation are performed, starting from two different
approximate functionals, to reproduce the parameters and density dependence of
a target functional, using exact ground-state densities of symmetric N=Z
systems.",2103.10096v1
2023-02-16,Learning Density-Based Correlated Equilibria for Markov Games,"Correlated Equilibrium (CE) is a well-established solution concept that
captures coordination among agents and enjoys good algorithmic properties. In
real-world multi-agent systems, in addition to being in an equilibrium, agents'
policies are often expected to meet requirements with respect to safety, and
fairness. Such additional requirements can often be expressed in terms of the
state density which measures the state-visitation frequencies during the course
of a game. However, existing CE notions or CE-finding approaches cannot
explicitly specify a CE with particular properties concerning state density;
they do so implicitly by either modifying reward functions or using value
functions as the selection criteria. The resulting CE may thus not fully fulfil
the state-density requirements. In this paper, we propose Density-Based
Correlated Equilibria (DBCE), a new notion of CE that explicitly takes state
density as selection criterion. Concretely, we instantiate DBCE by specifying
different state-density requirements motivated by real-world applications. To
compute DBCE, we put forward the Density Based Correlated Policy Iteration
algorithm for the underlying control problem. We perform experiments on various
games where results demonstrate the advantage of our CE-finding approach over
existing methods in scenarios with state-density concerns.",2302.08001v1
1998-08-18,Spin-density-functional theory of circular and elliptical quantum dots,"Using spin-density-functional theory, we study the electronic states of a
two-dimensional parabolic quantum dot with up to N=58 electrons. We observe a
shell structure for the filling of the dot with electrons. Hund's rule
determines the spin configuration of the ground state, but only up to 22
electrons. At specific N, the ground state is degenerate, and a small
elliptical deformation of the external potential induces a rotational
charge-density-wave (CDW) state. Previously identified spin-density-wave (SDW)
states are shown to be artifacts of broken spin symmetry in density-functional
theory.",9808193v1
2013-01-11,Spin polarization of electrons in quantum wires,"The total energy of a quasi-one-dimensional electron system is calculated
using density functional theory. It is shown that spontaneous ferromagnetic
state in quantum wire occurs at low one-dimensional electron density. The
critical electron density below which electrons are in spin-polarized state is
estimated analytically.",1301.2544v1
2018-08-30,Nuclear kinetic density from ab initio theory,"Background: The nuclear kinetic density is one of many fundamental quantities
in density functional theory (DFT) dependent on the nonlocal nuclear density.
Often, approximations may be made when computing the density that may result in
spurious contributions in other DFT quantities. With the ability to compute the
nonlocal nuclear density from ab initio wave functions, it is now possible to
estimate effects of such spurious contributions. Purpose: We derive the kinetic
density using ab initio nonlocal scalar one-body nuclear densities computed
within the no-core shell model (NCSM) approach, utilizing two- and
three-nucleon chiral interactions as the sole input. With the ability to
compute translationally invariant nonlocal densities, it is possible to
directly gauge the impact of the spurious center-of-mass (COM) contributions in
DFT quantities such as the kinetic density. Methods: The nonlocal nuclear
densities are derived from the NCSM one-body densities calculated in second
quantization. We present a review of COM contaminated and translationally
invariant nuclear densities. We then derive an analytic expression for the
kinetic density using these nonlocal densities, producing an ab initio kinetic
density. Results: The ground state nonlocal densities of
\textsuperscript{4,6,8}He, \textsuperscript{12}C, and \textsuperscript{16}O are
used to compute the kinetic densities of the aforementioned nuclei. The impact
of the COM removal technique in the densities is discussed. The results of this
work can be extended to other fundamental quantities in DFT. Conclusions: The
use of a general nonlocal density allows for the calculation of fundamental
quantities taken as input in theories such as DFT. This allows benchmarking of
procedures for COM removal in different many-body techniques.",1808.10537v2
2010-04-18,Subgraph densities in signed graphons and the local Sidorenko conjecture,"We prove inequalities between the densities of various bipartite subgraphs in
signed graphs and graphons. One of the main inequalities is that the density of
any bipartite graph with girth r cannot exceed the density of the r-cycle. This
study is motivated by Sidorenko's conjecture, which states that the density of
a bipartite graph F with m edges in any graph G is at least the m-th power of
the edge density of G. Another way of stating this is that the graph G with
given edge density minimizing the number of copies of F is, asymptotically, a
random graph. We prove that this is true locally, i.e., for graphs G that are
""close"" to a random graph.",1004.3026v1
2000-02-11,Coexistent State of Charge Density Wave and Spin Density Wave in One-Dimensional Quarter Filled Band Systems under Magnetic Fields,"We theoretically study how the coexistent state of the charge density wave
and the spin density wave in the one-dimensional quarter filled band is
enhanced by magnetic fields. We found that when the correlation between
electrons is strong the spin density wave state is suppressed under high
magnetic fields, whereas the charge density wave state still remains. This will
be observed in experiments such as the X-ray measurement.",0002165v3
2006-02-03,Exploring Foundations of Time-Independent Density Functional Theory for Excited-States,"Based on the work of Gorling and that of Levy and Nagy, density-functional
formalism for many Fermionic excited-states is explored through a careful and
rigorous analysis of the excited-state density to external potential mapping.
It is shown that the knowledge of the ground-state density is a must to fix the
mapping from an excited-state density to the external potential. This is the
excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the
ground-state density the density of the excited-state gives the true many-body
wavefunctions of the system. Further, the excited-state Kohn-Sham system is
defined by comparing it's non-interacting kinetic energy with the true kinetic
energy. The theory is demonstrated by studying a large number of atomic
systems.",0602067v1
2004-06-13,N-representability of two-electron densities and density matrices and the application to the few-body problem,"We have found a (dense) basis for the N-representable, two-electron
densities, in which all N-representable two-electron densities can be expanded,
using positive coefficients. The inverse problem of finding a representative
wavefunction, giving a prescribed two-electron density, has also been solved.
The two-electron densities are found to lie in a convex set in a vector space.
We show that density matrices are more complicated objects than densities, and
density matrices do not seem to lie in a convex set. An algorithm to compute
the ground-state energy of a few-particle system is proposed, based on the
obtained results, where the correlation is treated exactly.",0406300v1
2011-11-28,Local density of states of the one-dimensional spinless fermion model,"We investigate the local density of states of the one-dimensional half-filled
spinless fermion model with nearest-neighbor hopping t>0 and interaction V in
its Luttinger liquid phase -2t < V <= 2t. The bulk density of states and the
local density of states in open chains are calculated over the full band width
4t with an energy resolution <= 0.08t using the dynamical density-matrix
renormalization group (DDMRG) method. We also perform DDMRG simulations with a
resolution of 0.01t around the Fermi energy to reveal the power-law behaviour
predicted by the Luttinger liquid theory for bulk and boundary density of
states. The exponents are determined using a finite-size scaling analysis of
DDMRG data for lattices with up to 3200 sites. The results agree with the exact
exponents given by the Luttinger liquid theory combined with the Bethe Ansatz
solution. The crossover from boundary to bulk density of states is analyzed. We
have found that boundary effects can be seen in the local density of states at
all energies even far away from the chain edges.",1111.6545v2
2023-07-26,DFR-Net: Density Feature Refinement Network for Image Dehazing Utilizing Haze Density Difference,"In image dehazing task, haze density is a key feature and affects the
performance of dehazing methods. However, some of the existing methods lack a
comparative image to measure densities, and others create intermediate results
but lack the exploitation of their density differences, which can facilitate
perception of density. To address these deficiencies, we propose a
density-aware dehazing method named Density Feature Refinement Network
(DFR-Net) that extracts haze density features from density differences and
leverages density differences to refine density features. In DFR-Net, we first
generate a proposal image that has lower overall density than the hazy input,
bringing in global density differences. Additionally, the dehazing residual of
the proposal image reflects the level of dehazing performance and provides
local density differences that indicate localized hard dehazing or high density
areas. Subsequently, we introduce a Global Branch (GB) and a Local Branch (LB)
to achieve density-awareness. In GB, we use Siamese networks for feature
extraction of hazy inputs and proposal images, and we propose a Global Density
Feature Refinement (GDFR) module that can refine features by pushing features
with different global densities further away. In LB, we explore local density
features from the dehazing residuals between hazy inputs and proposal images
and introduce an Intermediate Dehazing Residual Feedforward (IDRF) module to
update local features and pull them closer to clear image features. Sufficient
experiments demonstrate that the proposed method achieves results beyond the
state-of-the-art methods on various datasets.",2307.13927v1
2017-11-08,Effect of density of states peculiarities on Hund's metal behavior,"We investigate a possibility of Hund's metal behavior in the Hubbard model
with asymmetric density of states having peak(s). Specifically, we consider the
degenerate two-band model and compare its results to the five-band model with
realistic density of states of iron and nickel, showing that the obtained
results are more general, provided that the hybridization between states of
different symmetry is sufficiently small. We find that quasiparticle damping
and the formation of local magnetic moments due to Hund's exchange interaction
are enhanced by both, the density of states asymmetry, which yields stronger
correlated electron or hole excitations, and the larger density of states at
the Fermi level, increasing the number of virtual electron-hole excitations.
For realistic densities of states these two factors are often interrelated
because the Fermi level is attracted towards peaks of the density of states. We
discuss the implication of the obtained results to various substances and
compounds, such as transition metals, iron pnictides, and cuprates.",1711.02991v3
2010-04-28,The scaling of the density of states in systems with resonance states,"Resonance states of a two-electron quantum dot are studied using a
variational expansion with both real basis-set functions and complex scaling
methods. We present numerical evidence about the critical behavior of the
density of states in the region where there are resonances. The critical
behavior is signaled by a strong dependence of some features of the density of
states with the basis-set size used to calculate it. The resonance energy and
lifetime are obtained using the scaling properties of the density of states",1004.5054v1
2013-10-04,Fermion $N$-representability for prescribed density and paramagnetic current density,"The $N$-representability problem is the problem of determining whether or not
there exists $N$-particle states with some prescribed property. Here we report
an affirmative solution to the fermion $N$-representability problem when both
the density and paramagnetic current density are prescribed. This problem
arises in current-density functional theory and is a generalization of the
well-studied corresponding problem (only the density prescribed) in density
functional theory. Given any density and paramagnetic current density
satisfying a minimal regularity condition (essentially that a von
Weiz\""acker-like the canonical kinetic energy density is locally integrable),
we prove that there exist a corresponding $N$-particle state. We prove this by
constructing an explicit one-particle reduced density matrix in the form of a
position-space kernel, i.e.\ a function of two continuous position variables.
In order to make minimal assumptions, we also address mathematical subtleties
regarding the diagonal of, and how to rigorously extract paramagnetic current
densities from, one-particle reduced density matrices in kernel form.",1310.1246v2
2003-06-17,Interplay of disorder and magnetic field in the superconducting vortex state,"We calculate the density of states of an inhomogeneous superconductor in a
magnetic field where the positions of vortices are distributed completely at
random. We consider both the cases of s-wave and d-wave pairing. For both
pairing symmetries either the presence of disorder or increasing the density of
vortices enhances the low energy density of states. In the s-wave case the gap
is filled and the density of states is a power law at low energies. In the
d-wave case the density of states is finite at zero energy and it rises
linearly at very low energies in the Dirac isotropic case
(\alpha_D=t/\Delta_0=1, where t is the hopping integral and \Delta_0 is the
amplitude of the order parameter). For slightly higher energies the density of
states crosses over to a quadratic behavior. As the Dirac anisotropy increases
(as \Delta_0 decreases with respect to the hopping term) the linear region
decreases in width. Neglecting this small region the density of states
interpolates between quadratic and back to linear as \alpha_D increases. The
low energy states are strongly peaked near the vortex cores.",0306448v1
2014-12-02,Phenomenological QCD equation of state for massive neutron stars,"We construct an equation of state for massive neutron stars based on quantum
chromodynamics phenomenology. Our primary purpose is to delineate the relevant
ingredients of equations of state that simultaneously have the required
stiffness and satisfy constraints from thermodynamics and causality. These
ingredients are: (i) a repulsive density-density interaction, universal for all
flavors; (ii) the color-magnetic interaction active from low to high densities;
(iii) confining effects, which become increasingly important as the baryon
density decreases; (iv) non-perturbative gluons, which are not very sensitive
to changes of the quark density. We use the following ""3-window"" description:
At baryon densities below about twice normal nuclear density, 2n_0, we use the
Akmal-Pandharipande-Ravenhall (APR) equation of state, and at high densities, >
(4-7)n_0, we use the three-flavor Nambu-Jona-Lasinio (NJL) model supplemented
by vector and diquark interactions. In the transition density region, we
smoothly interpolate the hadronic and quark equations of state in the chemical
potential-pressure plane. Requiring that the equation of state approach APR at
low densities, we find that the quark pressure in non-confining models can be
larger than the hadronic pressure, unlike in conventional equations of state.
We show that consistent equations of state of stiffness sufficient to allow
massive neutron stars are reasonably tightly constrained, suggesting that gluon
dynamics remains non-perturbative even at baryon densities ~10n_0.",1412.1108v2
2003-04-25,Tunneling Density of States of the Interacting Two-Dimensional Electron Gas,"We investigate the influence of electron--electron interactions on the
density of states of a ballistic two--dimensional electron gas. The density of
states is determined nonperturbatively by means of path integral techniques
allowing for reliable results near the Fermi surface, where perturbation theory
breaks down. We find that the density of states is suppressed at the Fermi
level to a finite value. This suppression factor grows with decreasing electron
density and is weakened by the presence of gates.",0304592v2
2018-12-30,Van der Waals equation of state and PVT properties of real fluid,"It is shown that: in the case when two parameters of the Van der Waals
equation of state are defined from the critical temperature and pressure the
exact parametrical solution of the equations of the liquid-vapor phase
equilibrium of the Van der Waals fluid quantitatively describes the
experimental dependencies of the saturated pressure of argon on the temperature
and reduced vapor density, and it gives the quantitative description of the
temperature dependencies of the reduced densities near critical point. When the
parameters are defined from the critical pressure and density the parametric
solution describes quantitatively the experimental dependencies of the
saturated pressure of argon on the density and reduced temperature, it can
describe qualitatively the dependencies of the vapor and liquid densities on
the reduced temperature, and it gives the quantitative description of the
dependencies of the densities on the reduced temperature near critical point.
If the parameters are defined from the critical temperature and density then
the exact solution describes quantitatively the experimental dependencies of
the reduced saturated pressure of argon on the density and temperature, it
describes qualitatively the temperature dependencies of the vapor and liquid
densities of argon, and it gives the quantitative description of the
temperature dependencies of the vapor and liquid densities near critical point.
It is also shown that the Van der Waals equation of state describes
quantitatively the reference experimental PVT- data for the gas and
supercritical fluid states for the under-critical densities of argon, the
dependencies of the saturation pressure on the temperature and vapor density,
and the dependence of the vapor density of argon on temperature if the
parameters are defined from the critical pressure and temperature.",1812.11572v1
2011-12-07,"Bounds on the density of states for Schr\"" odinger operators","We establish bounds on the density of states measure for Schr\""odinger
operators. These are deterministic results that do not require the existence of
the density of states measure, or, equivalently, of the integrated density of
states. The results are stated in terms of a ""density of states outer-measure""
that always exists, and provides an upper bound for the density of states
measure when it exists. We prove log-H\""older continuity for this density of
states outer-measure in one, two, and three dimensions for Schr\""odinger
operators, and in any dimension for discrete Schr\""odinger operators.",1112.1716v3
2018-01-29,Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory,"We show that the particle density, $\rho(\mathbf{r})$, and the paramagnetic
current density, $\mathbf{j}^{p}(\mathbf{r})$, are not sufficient to determine
the set of degenerate ground-state wave functions. This is a general feature of
degenerate systems where the degenerate states have different angular momenta.
We provide a general strategy for constructing Hamiltonians that share the same
ground state density, yet differ in degree of degeneracy. We then provide a
fully analytical example for a noninteracting system subject to electrostatic
potentials and uniform magnetic fields. Moreover, we prove that when
$(\rho,\mathbf{j}^p)$ is ensemble $(v,\mathbf{A})$-representable by a mixed
state formed from $r$ degenerate ground states, then any Hamiltonian
$H(v',\mathbf{A}')$ that shares this ground state density pair must have at
least $r$ degenerate ground states in common with $H(v,\mathbf{A})$. Thus, any
set of Hamiltonians that shares a ground-state density pair
$(\rho,\mathbf{j}^p)$ by necessity has at least have one joint ground state.",1801.09606v1
2001-09-26,Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State,"We examine the long wave length limit of the self-consistent Hartree-Fock
approximation irreducible static density-density response function by
evaluating the charge induced by an external charge. Our results are consistent
with the compressibility sum rule and inconsistent with earlier work that did
not account for consistency between the exchange-local-field and the disorder
potential. We conclude that the thermodynamic density of states is finite, in
spite of the vanishing tunneling density of states at the critical energy of
the integer quantum Hall transition.",0109501v2
2004-03-15,Relation between the High Density Phase and the Very-High Density Phase of Amorphous Solid Water,"It has been suggested that high-density amorphous (HDA) ice is a structurally
arrested form of high-density liquid (HDL) water, while low-density amorphous
(LDA) ice is a structurally arrested form of low-density liquid (LDL) water.
Recent experiments and simulations have been interpreted to support the
possibility of a second ""distinct"" high-density structural state, named very
high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test
this interpretation using extensive computer simulations, and find that VHDA is
a more stable form of HDA and that in fact VHDA should be considered as the
amorphous ice of the quenched HDL.",0403365v1
2011-04-27,Topological density wave states of non-zero angular momentum,"The pseudogap state of high temperature superconductors is a profound
mystery. It has tantalizing evidence of a number of broken symmetry states, not
necessarily conventional charge and spin density waves. Here we explore a class
of more exotic density wave states characterized by topological properties
observed in recently discovered topological insulators. We suggest that these
rich topological density wave states deserve closer attention in not only high
temperature superconductors but in other correlated electron states, as in
heavy fermions.",1104.5053v2
2007-11-14,Density operators and selective measurements,"It is widely believed that statistical interpretation of quantum mechanics
requires that density operators representing quantum states be normalized. We
present a description of selective measurements in terms of density operators.
The description is inspired by Schwinger's Algebra of Microscopic Measurements.
Density operators used are not normalized. We do not know applications of
density operators requiring normalization.",0711.2258v1
2019-12-11,Emergence and spectral-weight transfer of electronic states in the Hubbard ladder,"The number of electronic bands is usually considered invariant regardless of
the electron density in a band picture. However, in interacting systems, the
spectral-weight distribution generally changes depending on the electron
density, and electronic states can even emerge or disappear as the electron
density changes. Here, to clarify how electronic states emerge and become
dominant as the electron density changes, the spectral function of the Hubbard
ladder with strong repulsion and strong intrarung hopping is studied using the
non-Abelian dynamical density-matrix renormalization-group method. A mode
emerging in the low-electron-density limit gains spectral weight as the
electron density increases and governs the dimer Mott physics at
quarter-filling. In contrast, the antibonding band, which is dominant in the
low-electron-density regime, loses spectral weight and disappears at the Mott
transition at half-filling, exhibiting the momentum-shifted magnetic dispersion
relation in the small-doping limit. This paper identifies the origin of the
electronic states responsible for the Mott transition and brings a new
perspective to electronic bands by revealing the overall nature of electronic
states over a wide energy and electron-density regime.",1912.05080v2
2022-03-30,Mixed state representability of entropy-density pairs,"In this note, we show the representability of density-entropy pairs with
canonical and grand-canonical states, and we provide bounds on the kinetic
energy of the representing states.",2203.16441v1
1998-06-15,Negative Energy Density States for the Dirac Field in Flat Spacetime,"Negative energy densities in the Dirac field produced by state vectors that
are the superposition of two single particle electron states are examined. I
show that for such states the energy density of the field is not bounded from
below and that the quantum inequalities derived for scalar fields are
satisfied. I also show that it is not possible to produce negative energy
densities in a scalar field using state vectors that are arbitrary
superpositions of single particle states.",9806064v1
2003-06-06,Neutrons transition densities for the $2^+-8^+$ multiplet of states in $^{90}$Zr,"The neutron transition densities of the $2^+-8^+$ levels in $^{90}$Zr were
extracted in the process of analysing ({\bf p},p') scattering at 400 Mev. Its
comparison with the proton transition densities for these levels was
undertaken. The radial shapes of the experimental neutron and proton transition
densities for each state were found to be different.",0306010v1
2011-07-24,Doping of epitaxial graphene on SiC intercalated with hydrogen and its magneto-oscillations,"We study the charge transfer between a quasi-free-standing monolayer
graphene, produced by hydrogen intercalation, and surface acceptor states. We
consider two models of acceptor density of states to explain the high hole
densities observed in graphene and find the density responsivity to the gate
voltage. By studying magneto-oscillations of the carrier density we provide an
experimental way to determine the relevant model.",1107.4769v1
1994-11-10,Two-Dimensional t-J Model at Low Electron Density,"The phase diagram of the two-dimensional t-J model is determined accurately
at low electron density by a combination of analytic and numerical techniques.
The ground state exhibits three phases in the limit of zero electron density:
an unpaired state at small J/t, a gas of s-wave pairs for 2 < J/t < 3.4367, and
a phase separated state at larger interaction strengths. Bound states of larger
clusters are never realized, and the instabilities present at small densities
are discussed.",9411042v2
2010-08-05,The integrated density of states of the random graph Laplacian,"We analyse the density of states of the random graph Laplacian in the
percolating regime. A symmetry argument and knowledge of the density of states
in the nonpercolating regime allows us to isolate the density of states of the
percolating cluster (DSPC) alone, thereby eliminating trivially localised
states due to finite subgraphs. We derive a nonlinear integral equation for the
integrated DSPC and solve it with a population dynamics algorithm. We discuss
the possible existence of a mobility edge and give strong evidence for the
existence of discrete eigenvalues in the whole range of the spectrum.",1008.1087v1
2021-07-14,Multifractal correlations of the local density of states in dirty superconducting films,"Mesoscopic fluctuations of the local density of states encode multifractal
correlations in disorderedelectron systems. We study fluctuations of the local
density of states in a superconducting state of weakly disordered films. We
perform numerical computations in the framework of the disordered attractive
Hubbard model on two-dimensional square lattices. Our numerical results are
explained by an analytical theory. The numerical data and the theory together
form a coherent picture of multifractal correlations of local density of states
in weakly disordered superconducting films.",2107.06728v1
2015-05-19,Many-Body Localization of Symmetry Protected Topological States,"We address the following question: Which kinds of symmetry protected
topological (SPT) Hamiltonians can be many-body localized? That is, which
Hamiltonians with an SPT ground state have finite energy density excited states
which are all localized by disorder? Based on the observation that a finite
energy density state, if localized, can be viewed as the ground state of a
local Hamiltonian, we propose a simple (though possibly incomplete) rule for
many-body localization of SPT Hamiltonians: If the ground state and top state
(highest energy state) belong to the same SPT phase, then it is possible to
localize all the finite energy density states; If the ground and top state
belong to different SPT phases, then most likely there are some finite energy
density states which can not be fully localized. We will give concrete examples
of both scenarios. In some of these examples, we argue that interaction can
actually ""assist"" localization of finite energy density states, which is
counter-intuitive to what is usually expected.",1505.05147v2
1997-12-02,Density-Density Correlators in Infinite Random Matrices,"Using the BRM theory developed recently by Fyodorov and Mirlin we calculate
the density-density correlators for Banded Random Matrix of infinite size.
Within the accuracy of $1/b^2$ ($b$ is the matrix bandwidth) it appears to be
the same in both cases of orthogonal and unitary symmetry. Moreover, its form
coincides exactly with the formula obtained long ago by Gogolin for electron
density-density correlator in strictly 1D disordered metals.
  In addition to the ``fixed energy'' density-density correlator considered in
the solid state physics we calculate also the ``time averaged'' one, which has
different properties at small separations. Our predictions are compared with
the existing numerical data.",9712001v1
2015-12-23,Exact Maps in Density Functional Theory for Lattice Models,"In the present work, we employ exact diagonalization for model systems on a
real-space lattice to explicitly construct the exact density-to-potential and
for the first time the exact density-to-wavefunction map that underly the
Hohenberg-Kohn theorem in density functional theory. Having the explicit
wavefunction-to- density map at hand, we are able to construct arbitrary
observables as functionals of the ground-state density. We analyze the
density-to-potential map as the distance between the fragments of a system
increases and the correlation in the system grows. We observe a feature that
gradually develops in the density-to-potential map as well as in the
density-to-wavefunction map. This feature is inherited by arbitrary expectation
values as functional of the ground-state density. We explicitly show the
excited-state energies, the excited-state densities, and the correlation
entropy as functionals of the ground-state density. All of them show this exact
feature that sharpens as the coupling of the fragments decreases and the
correlation grows. We denominate this feature as intra-system steepening. We
show that for fully decoupled subsystems the intra-system steepening transforms
into the well-known inter-system derivative discontinuity. An important
conclusion is that for e.g. charge transfer processes between localized
fragments within the same system it is not the usual inter-system derivative
discontinuity that is missing in common ground-state functionals, but rather
the differentiable intra-system steepening that we illustrate in the present
work.",1512.07456v1
2002-05-28,Boson ground state fields in electroweak theory with non-zero charge densities,"The ""non-linear"" self-consistent theory of classical fields in the
electroweak model is proposed. Homogeneous boson ground state solutions in the
GSW model at the presence of a non-zero extended fermionic charge densities are
reviewed and fully reinterpreted to make the theory with non-zero charge
densities fruitful. Consequences of charge density fluctuations are proposed.",0205313v1
2003-07-16,Effect of anisotropic impurity scattering on a density of states of a d-wave superconductor,"We discuss the effect of an anisotropic impurity potential on the critical
temperature, local density of states in the vicinity of a single impurity, and
the quasiparticle density of states for a finite impurity concentration in a
d-wave superconductor. Different scattering regimes are concerned.",0307399v1
2003-07-17,Local density of states induced by anisotropic impurity scattering in a d-wave superconductor,"We study a single impurity effect on the local density of states in a d-wave
superconductor accounting for the momentum-dependent impurity potential. We
show that the anisotropy of the scattering potential can alter significantly
the spatial dependence of the quasiparticle density of states in the vicinity
of the impurity.",0307427v1
2005-09-13,Local superconducting density of states of ErNi2B2C,"We present local tunnelling microscopy and spectroscopy measurements at low
temperatures in single crystalline samples of the magnetic superconductor
ErNi2B2C. The electronic local density of states shows a striking departure
from s-wave BCS theory with a finite value at the Fermi level, which amounts to
half of the normal phase density of states.",0509339v1
2003-10-17,The integrated density of states for an interacting multielectron homogeneous model,"For a system of n interacting electrons moving in the background of a
""homogeneous"" potential, we show that, if the single electron Hamiltonian
admits a density of states, so does the interacting Hamiltonian. Moreover this
integrated density of states coincides with that of the free electron
Hamiltonian.",0310031v1
2007-10-11,On the low-energy density of states in disordered d-wave superconductor,"We study the low-energy density of states of Dirac fermions in disordered
d-wave superconductor. At zero energy, a finite density of states is obtained
via the mechanism of dynamical mass generation in an effective
(1+1)-dimensional relativistic field theory.",0710.2270v3
2016-04-06,Constraining the supersaturation density equation of state from core-collapse supernova simulations - Excluded volume extension of the baryons,"In this article the role of the supersaturation density equation of state
(EOS) is explored in simulations of failed core-collapse supernova explosions.
Therefore the nuclear EOS is extended via a one-parameter excluded volume
description for baryons, taking into account their finite and increasing volume
with increasing density in excess of saturation density. Parameters are
selected such that the resulting supernova EOS represent extreme cases, with
high pressure variations at supersaturation density which feature extreme stiff
and soft EOS variants of the reference case, i.e. without excluded volume
corrections. Unlike in the interior of neutron stars with central densities in
excess of several times saturation density, central densities of core-collapse
supernovae reach only slightly above saturation density. Hence, the impact of
the supersaturation density EOS on the supernova dynamics as well as the
neutrino signal is found to be negligible. It is mainly determined from the
low- and intermediate-density domain, which is left unmodified within this
generalized excluded volume approach.",1604.01629v1
2008-05-26,Stability of the density-wave state of a dipolar condensate in a pancake trap,"We study a dipolar boson-fermion mixture in a pancake geometry at absolute
zero temperature, generalizing our previous work on the stability of polar
condensates and the formation of a density-wave state in cylindrical traps.
After examining the dependence of the polar condensate stability on the
strength of the fermion-induced interaction, we determine the transition point
from a ground-state Gaussian to a hexagonal density-wave state. We use a
variational principle to analyze the stability properties of those density-wave
state.",0805.3870v1
2024-02-01,Density fluctuations for Squeezed Number State and Coherent Squeezed Number State in Flat FRW Universe,"We study the density fluctuations for Coherent Squeezed Number State (CSNS)
and Squeezed Number States (SNS) formalism in Semiclassical theory of grav ity
in flat FRW universe. We used Number state evolution of oscillatory phase of
inflaton for coherent squeezed number state and squeezed number states for
malisms. We analyzed that density fluctuations for SNS depends upon squeezing
parameter and number state while for CSNS density fluctuations depends upon
squeezing parameter, number state and coherent state parameter. These param
eters plays an important role for quantum consideration of SNS and CSNS. The
results of the analysis shows that increase in density fluctuations for both
SNS and CSNS, demonstrate quantum behavior of SCEE as well as production of
various kind of particles in these states.",2402.00432v1
2004-05-13,Hadronic property at finite density,"We report on three topics on finite density simulations: (i) the derivative
method for hadronic quantities, (ii) phase fluctuations in the vicinity of the
critical temperature and (iii) the density of states method at finite isospin
density.",0405010v2
2008-01-06,Statistics of local density of states in the Falicov-Kimball model with local disorder,"Statistics of the local density of states in the two-dimensional
Falicov-Kimball model with local disorder is studied by employing the
statistical dynamical mean-field theory. Within the theory the local density of
states and its distributions are calculated through stochastic self-consistent
equations. The most probable value of the local density of states is used to
monitor the metal-insulator transition driven by correlation and disorder.
Nonvanishing of the most probable value of the local density of states at the
Fermi energy indicates the existence of extended states in the two-dimensional
disordered interacting system. It is also found that the most probable value of
the local density of states exhibits a discontinuity when the system crosses
from extended states to the Anderson localization. A phase diagram is also
presented.",0801.0852v1
2001-11-29,Density of states for Random Band Matrix,"By applying the supersymmetric approach we rigorously prove smoothness of the
averaged density of states for a three dimensional random band matrix ensemble,
in the limit of infinite volume and fixed band width. We also prove that the
resulting expression for the density of states coincides with the Wigner
semicircle with a precision $1/W^2$, for $W$ large but finite.",0111047v1
2002-10-16,Dependence of Nuclear Level Density on Vibrational State Damping,"The response function approach is proposed to include vibrational state in
calculation of level density. The calculations show rather strong dependence of
level density on the relaxation times of collective state damping.",0210048v1
1996-09-17,Topological Dislocations and Mixed State of Charge Density Waves,"We discuss the possibility of the ``mixed state'' in incommensurate charge
density waves with three-dimensional order. It is shown that the mixed state
can be created by applying an electric field perpendicular to the chains. This
state consists of topological dislocations induced by the external field and is
therefore similar to the mixed states of superfluids (type-II superconductor or
liquid Helium II). However, the peculiar coupling of charge density waves with
the electric field strongly modifies the nature of the mixed state compared to
the conventional superfluids. The field and temperature dependence of the
properties of the mixed state are studied, and some experimental aspects are
discussed.",9609148v1
2004-06-25,Conditional Density Matrix in the Context of Noncontextuality,"Conditional density matrix represents a quantum state of subsystem in
different schemes of quantum communication. Here we discuss some properties of
conditional density matrix and its place in general scheme of quantum
mechanics.",0406187v1
2009-06-19,Overhauser's spin-density wave in exact-exchange spin density functional theory,"The spin density wave (SDW) state of the uniform electron gas is investigated
in the exact exchange approximation of noncollinear spin density functional
theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic
state of the electron gas is unstable against formation of the spin density
wave for all densities, in exact-exchange spin-DFT this instability occurs only
for densities lower than a critical value. It is also shown that, although in a
suitable density range it is possible to find a non-interacting SDW ground
state Slater determinant with energy lower than the corresponding paramagnetic
state, this Slater determinant is not a self-consistent solution of the
Optimized Effective Potential (OEP) integral equations of noncollinear
spin-DFT. A selfconsistent solution of the OEP equations which gives an even
lower energy can be found using an excited-state Slater determinant where only
orbitals with single-particle energies in the lower of two bands are occupied
while orbitals in the second band remain unoccupied even if their energies are
below the Fermi energy.",0906.3721v2
2007-02-07,Classification of two-particle quantum channels of information transfer,"Classification of states of two-particle quantum channels of information
transfer is built on the basis of irreducible representations of qubit state
space group of symmetry and properties of density matrix spectrum. It is shown
that the reason of state disentanglement can be in degeneration of non-zero
density matrix eigenvalues. Among the states with non-degenerate density matrix
disentangled states form two-dimensional surface of special states.",0702076v2
2003-12-01,Equation of state for nuclear matter based on density dependent effective interaction,"An interesting method of obtaining equation of state for nuclear matter, from
a density dependent M3Y interaction, by minimizing the energy per nucleon is
described. The density dependence parameters of the interaction are obtained by
reproducing the saturation energy per nucleon and the saturation density of
spin and isospin symmetric cold infinite nuclear matter. The nuclear matter
equation of state thus obtained is then used to calculate the pressure, the
energy density, the nuclear incompressibility and the velocity of sound in
nuclear medium. The results obtained are in good agreement with experimental
data and provide a unified description of radioactivity, scattering and nuclear
matter.",0312002v2
2000-01-21,Density Wave States of Non-Zero Angular Momentum,"We study the properties of states in which particle-hole pairs of non-zero
angular momentum condense. These states generalize charge- and
spin-density-wave states, in which s-wave particle-hole pairs condense. We show
that the p-wave spin-singlet state of this type has Peierls ordering, while the
d-wave spin-singlet state is the staggered flux state. We discuss model
Hamiltonians which favor p-wave and d-wave density wave order. There are
analogous orderings for pure spin models, which generalize spin-Peierls order.
The spin-triplet density wave states are accompanied by spin-1 Goldstone
bosons, but these excitations do not contribute to the spin-spin correlation
function. Hence, they must be detected with NQR or Raman scattering
experiments. Depending on the geometry and topology of the Fermi surface, these
states may admit gapless fermionic excitations. As the Fermi surface geometry
is changed, these excitations disappear at a transition which is third-order in
mean-field theory. The singlet d-wave and triplet p-wave density wave states
are separated from the corresponding superconducting states by zero-temperature
O(4)-symmetric critical points",0001303v1
1998-04-29,Particle-hole state densities with non-equidistant single-particle levels,"The correct use of energy-dependent single-particle level (s.p.l.) densities
within particle-hole state densities based on the equidistant spacing model
(ESM) is analysed. First, an analytical expression is obtained following the
convolution of energy-dependent excited-particle and hole densities. Next, a
comparison is made with results of the ESM formula using average s.p.l.
densities for the excited particles and holes, respectively. The Fermi-gas
model (FGM) s.p.l. densities calculated at the corresponding average excitation
energies are used in both cases. The analysis concerns also the density of
particle-hole bound states. The pairing correlations are taken into account
while the comparison of various effects includes the exact correction for the
Pauli exclusion principle. Quantum-mechanical s.p.l. densities and the
continuum effect can also match a corresponding FGM formula, suitable for use
within the average energy-dependent partial state density in multistep reaction
models.",9804074v1
2020-01-05,On Operators Generated by Density Matrix,"In this survey the possible approaches to the description of the evolution of
states of quantum many-particle systems by means of the possible modifications
of the density operator which kernel known as density matrix are considered. In
addition, an approach to the description of the evolution of states by means of
the state of a typical particle of a quantum system of many particles is
discussed or in other words, the foundations of describing the evolution of
states by kinetic equations are considered.",2001.01180v1
1997-07-05,Density of States in Superconductor - Normal Metal - Superconductor Junctions,"We consider the chi_0 dependence of the density of states inside the normal
metal of a superconductor - normal metal - superconductor (SNS) junction.Here
chi_0 is the phase difference of two superconductors of the junction. It is
shown that in the absence of electron-electron interaction the energy
dependence of the density of states has a gap which decreases as chi_0
increases and closes at chi_0= pi. Both the analytical expressions for the
chi_0 dependence of the density of states and the results of numerical
simulations are presented.",9707056v2
2003-11-12,Hartree-Fock energy of a density wave in a spin polarized two-dimensional electron gas,"We calculate the Hartree-Fock energy of a density-wave in a spin polarized
two-dimensional electron gas using a short-range repulsive interaction. We find
that the stable ground state for a short-range potential is always either the
paramagnetic state or the uniform ferromagnetic state. The energy of a
density-wave state is, however, reduced by a factor proportional to (1 -
zeta^2), where zeta is the polarization of the electron gas. Since this
situation occurs in the most unfavorable conditions (short-range repulsive
interaction) it is therefore conceivable that by including higher order
many-body corrections to the interaction a density-wave ground state is indeed
found to be stable.",0311292v1
2006-02-03,Local-density approximation for exchange energy functional in excited-state density functional theory,"An exchange energy functional is proposed and tested for obtaining a class of
excited-state energies using density functional formalism. The functional is
the excited-state counterpart of the local-density approximation functional for
the ground state. It takes care of the state dependence of the energy
functional and leads to highly accurate excitation energies.",0602064v1
2018-02-12,Quantum oscillations in a biaxial pair density wave state,"There has been growing speculation that a pair density wave state is a key
component of the phenomenology of the pseudogap phase in the cuprates.
Recently, direct evidence for such a state has emerged from an analysis of
scanning tunneling microscopy data in halos around the vortex cores. By
extrapolation, these vortex halos would then overlap at a magnetic field scale
where quantum oscillations have been observed. Here, we show that a biaxial
pair density wave state gives a unique description of the quantum oscillation
data, bolstering the case that the pseudogap phase in the cuprates may be a
pair density wave state.",1802.04333v1
2016-09-13,Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with particle nonconservation,"We study asymmetric exclusion processes (TASEP) on a nonuniform
one-dimensional ring consisting of two segments having unequal hopping rates,
or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics
(LK), that are parameterised by generic unequal attachment and detachment
rates. For an extended defect, in the thermodynamic limit the system
generically displays inhomogeneous density profiles in the steady state - the
faster segment is either in a phase with spatially varying density having no
density discontinuity, or a phase with a discontinuous density changes.
Nonequilibrium phase transitions between them are controlled by the
inhomogeneity and LK. The slower segment displays only macroscopically uniform
bulk density profiles in the steady states, reminiscent of the maximal current
phase of TASEP but with a bulk density generally different from half. With a
point defect, there are low and high density spatially uniform phases as well,
in addition to the inhomogeneous density profiles observed for an extended
defect. In all the cases, it is argued that the the mean particle density in
the steady state is controlled only by the ratio of the LK attachment and
detachment rates.",1609.03814v1
2012-11-20,Critical densities in sandpile models with quenched or annealed disorder,"We discuss various critical densities in sandpile models. The stationary
density is the average expected height in the stationary state of a
finite-volume model; the transition density is the critical point in the
infinite-volume counterpart. These two critical densities were generally
assumed to be equal, but this has turned out to be wrong for deterministic
sandpile models. We show they are not equal in a quenched version of the Manna
sandpile model either.
  In the literature, when the transition density is simulated, it is implicitly
or explicitly assumed to be equal to either the so-called threshold density or
the so-called critical activity density. We properly define these auxiliary
densities, and prove that in certain cases, the threshold density is equal to
the transition density. We extend the definition of the critical activity
density to infinite volume, and prove that in the standard infinite volume
sandpile, it is equal to 1. Our results should bring some order in the precise
relations between the various densities.",1211.4760v1
2018-11-07,PaDNet: Pan-Density Crowd Counting,"The problem of counting crowds in varying density scenes or in different
density regions of the same scene, named as pan-density crowd counting, is
highly challenging. Previous methods are designed for single density scenes or
do not fully utilize pan-density information. We propose a novel framework, the
Pan-Density Network (PaDNet), for pan-density crowd counting. In order to
effectively capture pan-density information, PaDNet has a novel module, the
Density-Aware Network (DAN), that contains multiple sub-networks pretrained on
scenarios with different densities. Further, a module named the Feature
Enhancement Layer (FEL) is proposed to aggregate the feature maps learned by
DAN. It learns an enhancement rate or a weight for each feature map to boost
these feature maps. Further, we propose two refined metrics, Patch MAE (PMAE)
and Patch RMSE (PRMSE), for better evaluating the model performance on
pan-density scenarios. Extensive experiments on four crowd counting benchmark
datasets indicate that PaDNet achieves state-of-the-art recognition performance
and high robustness in pan-density crowd counting.",1811.02805v3
2021-10-31,Density of Bloch states inside a one dimensional photonic crystal,"The density of Bloch electromagnetic states inside a one dimensional photonic
crystal (1D PC) is formulated based on its dispersion relations. The
formulation applied to any anisotropic medium with known dispersion relations
and iso-frequency surfaces. Using a practical 1D PC parameters in the visible
range, the density of Bloch states for different modes are calculated.",2111.00564v1
2007-05-21,Negative Energy in Superposition and Entangled States,"We examine the maximum negative energy density which can be attained in
various quantum states of a massless scalar field. We consider states in which
either one or two modes are excited, and show that the energy density can be
given in terms of a small number of parameters. We calculate these parameters
for several examples of superposition states for one mode, and entangled states
for two modes, and find the maximum magnitude of the negative energy density in
these states. We consider several states which have been, or potentially will
be, generated in quantum optics experiments.",0705.3003v1
2013-04-16,Recursive calculation of the microcanonical density of states,"For a classical system of noninteracting particles we establish recursive
integral equations for the density of states on the microcanonical ensemble.
The recursion can be either on the number of particles or on the dimension of
the system. The solution of the integral equations is particularly simple when
the single-particle density of states in one dimension follows a power law.
Otherwise it can be obtained using a Laplace transform method. Since the
Laplace transform of the microcanonical density of states is the canonical
partition function, it factorizes for a system of noninteracting particles and
the solution of the problem is straightforward. The results are illustrated on
several classical examples.",1304.4349v2
2016-09-30,Extremal Density Matrices for Qudit States,"An algebraic procedure to find extremal density matrices for any Hamiltonian
of a qudit system is established. The extremal density matrices for pure states
provide a complete description of the system, that is, the energy spectra of
the Hamiltonian and their corresponding projectors. For extremal density
matrices representing mixed states, one gets mean values of the energy in
between the maximum and minimum energies associated to the pure case. These
extremal densities give also the corresponding mixture of eigenstates that
yields the corresponding mean value of the energy. We enhance that the method
can be extended to any hermitian operator.",1609.09835v1
1997-12-11,"Acoustic Peak Spacing, Cosmological Density, and Equation of State","The spacing of the acoustic peaks in the cosmic microwave background
radiation anisotropy multipole spectrum has been claimed to provide the value
of the total cosmological density overtly, ``written on the sky.'' Through a
semianalytic analysis of the cosmological evolution of the sound horizon and
the physics of decoupling we address the robustness of the relation between the
peak spacing and the cosmological density. In fact, the asymptotic distance and
horizon scalings often used are not good approximations, and the individual
densities and equations of state of different components do enter the problem.
An observed spacing could be fit by models with different total densities. We
investigate the different regions of density-equation of state parameter space
and also provide accurate fitting formulas for the peak spacing as a function
of matter density, total density, and additional component equation of state
(e.g. cosmological constant or cosmic strings). Limits provided by peak spacing
measurements on the number of neutrino species and the baryon-photon ratio are
also addressed.",9712159v1
2008-07-30,"Negative density of states: screening, Einstein relation, and negative diffusion","In strongly interacting electron systems with low density and at low
temperature the thermodynamic density of states is negative. It creates
difficulties with understanding of the Einstein relation between conductivity
and diffusion coefficient. Using the expression for electrochemical potential
that takes into account the long range part of the Coulomb interaction it is
shown that at negative density of states Einstein relation gives a negative
sign of the diffusion coefficient D, but under this condition there is no
thermodynamic limitation on the sign of D. It happens because the unipolar
relaxation of inhomogeneous electron density is not described by the diffusion
equation. The relaxation goes much faster due to electric forces caused by
electron density and by neutralizing background. Diffusion coefficient is
irrelevant in this case and it is not necessarily positive because process of
diffusion does not contribute to the positive production of entropy. In the
case of bipolar diffusion negative D results in a global absolute instability
that leads to formation of neutral excitons. Graphene is considered as an
example of a system, where the density relaxation is expected to be due to
electric force rather than diffusion. It may also have a negative density of
states.",0807.4962v2
1999-05-13,Quasiparticle spectrum of a type-II superconductor in a high magnetic field with randomly pinned vortices,"We show that gapless superconductivity of a strongly type-II superconductor
in a high magnetic field prevails in the presence of disorder, suggesting a
topological nature. We calculate the density of states of the Bogoliubov-de
Gennes quasiparticles for a two-dimensional inhomogeneous system in both cases
of weak and strong disorder. In the limit of very weak disorder, the effect is
very small and the density of states is not appreciably changed. As the
disorder increases, the density of states at low energies increases and the
ratio of the low-energy density of states to its maximum increases
significantly.",9905180v1
2006-11-02,Density of states of a two dimensional XY model from Wang-Landau algorithm,"Using Wang-landau algorithm combined with analytic method, the density of
states of two dimensional XY model on square lattices of sizes $16\times16$,
$24\times24$ and $32\times32$ is accurately calculated. Thermodynamic
quantities, such as internal energy, free energy, entropy and specific heat are
obtained from the resulted density of states by numerical integration. From the
entropy curve symptoms of phase transition is observed. A general method of
calculation of the density of states of continuous models by simulation
combined with analytical method is proposed.",0611039v1
2017-04-27,A Lee-Yang--inspired functional with a density--dependent neutron-neutron scattering length,"Inspired by the low--density Lee-Yang expansion for the energy of a dilute
Fermi gas of density $\rho$ and momentum $k_F$, we introduce here a
Skyrme--type functional that contains only $s$-wave terms and provides, at the
mean--field level, (i) a satisfactory equation of state for neutron matter from
extremely low densities up to densities close to the equilibrium point, and
(ii) a good--quality equation of state for symmetric matter at density scales
around the saturation point. This is achieved by using a density--dependent
neutron-neutron scattering length $a(\rho$) which satisfies the low--density
limit (for Fermi momenta going to zero) and has a density dependence tuned in
such a way that the low--density constraint $|a(\rho) k_F| \le 1$ is satisfied
at all density scales.",1704.08510v1
2014-08-29,Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization,"We assume that a finite set of moments of a random vector is given. Its
underlying density is unknown. An algorithm is proposed for efficiently
calculating Dirac mixture densities maintaining these moments while providing a
homogeneous coverage of the state space.",1408.7083v1
2013-11-08,Generalized coherent states,"In the coherent state of the harmonic oscillator, the probability density is
that of the ground state subjected to an oscillation along a classical
trajectory. Senitzky and others pointed out that there are states of the
harmonic oscillator corresponding to an identical oscillatory displacement of
the probability density of any energy eigenstate. These generalizations of the
coherent state are rarely discussed, yet they furnish an interesting set of
quantum states of light that combine features of number states and coherent
states. Here we give an elementary account of the quantum optics of generalized
coherent states.",1311.1920v2
2012-08-16,alpha-cluster correlations and symmetry breaking in light nuclei,"$\alpha$-cluster correlations in the ground states of $^{12}$C and $^{16}$O
are studied. Because of the $\alpha$ correlations, the intrinsic states of
$^{12}$C and $^{16}$O have triangle and tetrahedral shapes, respectively. The
deformations are regarded as spontaneous symmetry breaking of rotational
invariance, and the resultant oscillating surface density is associated with a
density wave (DW) state caused by the instability of Fermi surface with respect
to a kind of $1p$-$1h$ correlations. To discuss the symmetry breaking between
uniform density states and the oscillating density state, a schematic model of
a few clusters on a Fermi gas core in a one-dimensional finite box was
introduced. The model analysis suggests structure transitions from a Fermi gas
state to a DW-like state via a BCS-like state, and to a Bose Einstein
condensation (BEC)-like state depending on the cluster size relative to the box
size. It was found that the oscillating density in the DW-like state originates
in Pauli blocking effects.",1208.3275v1
2014-03-24,Gedanken Densities and Exact Constraints in Density Functional Theory,"Approximations to the exact density functional for the exchange-correlation
energy of a many-electron ground state can be constructed by satisfying
constraints that are universal, i.e., valid for all electron densities.
Gedanken densities are designed for the purpose of this construction, but need
not be realistic. The uniform electron gas is an old gedanken density. Here, we
propose a spherical two-electron gedanken density in which the dimensionless
density gradient can be an arbitrary positive constant wherever the density is
non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied
within a generalized gradient approximation (GGA) by bounding its enhancement
factor or simplest GGA exchange-energy density. This enhancement-factor bound
is well known to be sufficient, but our gedanken density shows that it is also
necessary. The conventional exact exchange-energy density satisfies no such
local bound, but energy densities are not unique, and the simplest GGA
exchange-energy density is not an approximation to it. We further derive a
strongly and optimally tightened bound on the exchange enhancement factor of a
two-electron density, which is satisfied by the local density approximation but
is violated by all published GGA's or meta-GGA's. Finally, some consequences of
the non-uniform density-scaling behavior for the asymptotics of the exchange
enhancement factor of a GGA or meta-GGA are given.",1403.5832v2
2022-06-03,MCD: Marginal Contrastive Discrimination for conditional density estimation,"We consider the problem of conditional density estimation, which is a major
topic of interest in the fields of statistical and machine learning. Our
method, called Marginal Contrastive Discrimination, MCD, reformulates the
conditional density function into two factors, the marginal density function of
the target variable and a ratio of density functions which can be estimated
through binary classification. Like noise-contrastive methods, MCD can leverage
state-of-the-art supervised learning techniques to perform conditional density
estimation, including neural networks. Our benchmark reveals that our method
significantly outperforms in practice existing methods on most density models
and regression datasets.",2206.01592v1
1995-09-18,Random Magnetic Impurities and the Landau Problem,"The 2-dimensional density of states of an electron is studied for a
Poissonian random distribution of point vortices carrying $\alpha$ flux in unit
of the quantum of flux. It is shown that, for any given density of impurities,
there is a transition, when $\alpha\simeq 0.3-0.4$, from an ""almost free""
density of state -with only a depletion of states at the bottom of the spectrum
characterized by a Lifschitz tail- to a Landau density of state with sharp
Landau level oscillations. Several evidences and arguments for this transition
-numerical and analytical- are presented.",9509105v1
2004-11-19,The Integrated Density of States for 1D Nanostructures at Zero Bias Limit,"By methods of quasiclassical asymptotics the behaviour of the integrated
density of states for 1D periodic nanostructures at the zero bias limit is
studied. It is shown that the density of states at the zero bias limit has no
regular limit while the integrated density of states has. The rigorous proof of
this phenomenon given in the paper is based on a novel approach for the
quasiclassical asymptotics on the spectrum of the Stark-Wannier operators. A
connection of this phenomenon with the zero bias limits of the current through
the nanostructures and their conductivity is briefly discussed.",0411510v1
2000-11-11,Regularity of the Density of Surface States,"We prove that the integrated density of surface states of continuous or
discrete Anderson-type random Schroedinger operators is a measurable locally
integrable function rather than a signed measure or a distribution. This
generalize our recent results on the existence of the integrated density of
surface states in the continuous case and those of A. Chahrour in the discrete
case. The proof uses the new $L^p$-bound on the spectral shift function
recently obtained by Combes, Hislop, and Nakamura. Also we provide a simple
proof of their result on the Hoelder continuity of the integrated density of
bulk states.",0011019v1
2008-06-12,Statistical Characterization of a 1D Random Potential Problem - with applications in score statistics of MS-based peptide sequencing,"We provide a complete thermodynamic solution of a 1D hopping model in the
presence of a random potential by obtaining the density of states. Since the
partition function is related to the density of states by a Laplace transform,
the density of states determines completely the thermodynamic behavior of the
system. We have also shown that the transfer matrix technique, or the so-called
dynamic programming, used to obtain the density of states in the 1D hopping
model may be generalized to tackle a long-standing problem in statistical
significance assessment for one of the most important proteomic tasks - peptide
sequencing using tandem mass spectrometry data.",0806.1988v1
2021-07-29,Purcell effect with extended sources: The role of the cross density of states,"We analyze the change in the spontaneous decay rate, or Purcell effect, of an
extended quantum emitter in a structured photonic environment. Based on a
simple theory, we show that the cross-density of states is the central quantity
driving interferences in the emission process. Using numerical simulations in
realistic photonic cavity geometries, we demonstrate that a structured
cross-density of states can induce subradiance or superradiance, and change
subtantially the emission spectrum. Interestingly, the spectral lineshape of
the Purcell effect of an extended source cannot be predicted from the sole
knowledge of the spectral dependence of the local density of states.",2107.13980v3
2015-03-02,The density of states approach for the simulation of finite density quantum field theories,"Finite density quantum field theories have evaded first principle Monte-Carlo
simulations due to the notorious sign-problem. The partition function of such
theories appears as the Fourier transform of the generalised density-of-states,
which is the probability distribution of the imaginary part of the action. With
the advent of Wang-Landau type simulation techniques and recent advances, the
density-of-states can be calculated over many hundreds of orders of magnitude.
Current research addresses the question whether the achieved precision is high
enough to reliably extract the finite density partition function, which is
exponentially suppressed with the volume. In my talk, I review the
state-of-play for the high precision calculations of the density-of-states as
well as the recent progress for obtaining reliable results from highly
oscillating integrals. I will review recent progress for the $Z_3$ quantum
field theory for which results can be obtained from the simulation of the dual
theory, which appears to free of a sign problem.",1503.00450v1
2001-01-29,Exact expression of the ground state energy of quantum many-particle systems as a functional of the particle density,"By introducing a phase field and solving the eigen-functional equation of
particles, we obtain the exact expressions of the ground state energy as a
functional of the particle density for interacting electron/boson systems, and
a two-dimensional electron gas under an external magnetic field, respectively.
With the eigen-functionals of the particles, we can construct the ground state
wave-function of the systems. Moreover, with the expressions of the ground
state energy, we can exactly determine the ground state energy and the ground
state particle density of the systems by taking $% \delta E_g[\rho ]/\delta
\rho (x)=0$.",0101428v1
2014-06-27,Calculating and visualizing the density of states for simple quantum mechanical systems,"We present a graphical approach to understanding the degeneracy, density of
states, and cumulative state number for some simple quantum systems. By taking
advantage of basic computing operations we define a straightforward procedure
for determining the relationship between discrete quantum energy levels and the
corresponding density of states and cumulative level number. The density of
states for a particle in a rigid box of various shapes and dimensions is
examined and graphed. It is seen that the dimension of the box, rather than its
shape, is the most important feature. In addition, we look at the density of
states for a multi-particle system of identical bosons built on the
single-particle spectra of those boxes. A simple model is used to explain how
the $N$-particle density of states arises from the single particle system it is
based on.",1406.7216v1
2015-12-17,Multi-$Q$ hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave,"We study hexagonal spin-channel (""triplet"") density waves with commensurate
$M$-point propagation vectors. We first show that the three $Q=M$ components of
the singlet charge density and charge-current density waves can be mapped to
multi-component $Q=0$ nonzero angular momentum order in three dimensions ($3D$)
with cubic crystal symmetry. This one-to-one correspondence is exploited to
define a symmetry classification for triplet $M$-point density waves using the
standard classification of spin-orbit coupled electronic liquid crystal phases
of a cubic crystal. Through this classification we naturally identify a set of
non-coplanar spin density and spin-current density waves: the chiral spin
density wave and its time-reversal invariant analog. These can be thought of as
$3D$ $L=2$ and $L=4$ spin-orbit coupled isotropic $\beta$-phase orders. In
contrast, uniaxial spin density waves are shown to correspond to
$\alpha$-phases. The non-coplanar triple-$M$ spin-current density wave realizes
a novel $2D$ semimetal state with three flavors of four-component spin-momentum
locked Dirac cones, protected by a crystal symmetry akin to non-symmorphic
symmetry, and sits at the boundary between a trivial and topological insulator.
In addition, we point out that a special class of classical spin states,
defined as classical spin states respecting all lattice symmetries up to global
spin rotation, are naturally obtained from the symmetry classification of
electronic triplet density waves. These symmetric classical spin states are the
classical long-range ordered limits of chiral spin liquids.",1512.05673v3
2016-09-08,Exact-dimensional property of density of states measure of Sturm Hamiltonian,"For frequency $\alpha$ of bounded type and coupling $\lambda>20$, we show
that the density of states measure $\NN_{\alpha,\lambda}$ of the related Sturm
Hamiltonian is exact upper and lower dimensional, however, in general it is not
exact-dimensional.",1609.02347v1
2021-09-14,Learning Density Distribution of Reachable States for Autonomous Systems,"State density distribution, in contrast to worst-case reachability, can be
leveraged for safety-related problems to better quantify the likelihood of the
risk for potentially hazardous situations. In this work, we propose a
data-driven method to compute the density distribution of reachable states for
nonlinear and even black-box systems. Our semi-supervised approach learns
system dynamics and the state density jointly from trajectory data, guided by
the fact that the state density evolution follows the Liouville partial
differential equation. With the help of neural network reachability tools, our
approach can estimate the set of all possible future states as well as their
density. Moreover, we could perform online safety verification with probability
ranges for unsafe behaviors to occur. We use an extensive set of experiments to
show that our learned solution can produce a much more accurate estimate on
density distribution, and can quantify risks less conservatively and flexibly
comparing with worst-case analysis.",2109.06728v1
2019-11-13,Estimation of Cooper pair density and its relation to the critical current density in hole doped high-Tc cuprate superconductors,"Hole concentration in the CuO2 plane largely controls all the properties in
the normal and superconducting states of high-Tc cuprates. The critical current
density, Jc, is no exception. Previous hole content dependent studies have
demonstrated that the role of intrinsic depairing current density in
determining the observed critical current density in copper oxide
superconductors. It is also widely agreed upon that the temperature and
magnetic field dependent vortex pinning energy plays a major role the Jc of a
system.This pinning energy depends directly on the superconducting condensation
energy. Superconducting condensation energy, on the other hand, is proportional
to the Cooper pair density (superpair density), which is found to be highly
dependent on the hole concentration, p, within the CuO2 plane. We have
calculated the Cooper pair density, rho_s, of YBCO (Y123), a typical hole doped
cuprate, as a function of p, in this study. A triangular pseudogap (PG), pinned
at the Fermi level, in the quasiparticle spectral density has been considered.
The low-temperature critical current density of a number of Y(Ca)BCO
superconductors over wide range of compositions and hole concentrations have
been explored. The normalized values of the superpair density and the critical
current density exhibit a clear correspondence as the in-plane hole content is
varied. This systematic behavior provides us with strong evidence that the
critical current density of hole doped cuprates is primarily dependent on the
superpair density, which in turn depends on the magnitude of the PG energy.The
agreement between the estimated p-dependent superpair density and the
previously experimentally determined superfluid density of Y(Ca)BCO is quite
remarkable.",1911.05237v1
2005-03-31,The density of states of classical spin systems with continuous degrees of freedom,"In the last years different studies have revealed the usefulness of a
microcanonical analysis of finite systems when dealing with phase transitions.
In this approach the quantities of interest are exclusively expressed as
derivatives of the entropy $S = \ln \Omega$ where $\Omega$ is the density of
states. Obviously, the density of states has to be known with very high
accuracy for this kind of analysis. Important progress has been achieved
recently in the computation of the density of states of classical systems, as
new types of algorithms have been developed. Here we extend one of these
methods, originally formulated for systems with discrete degrees of freedom, to
systems with continuous degrees of freedoms. As an application we compute the
density of states of the three-dimensional XY model and demonstrate that
critical quantities can directly be determined from the density of states of
finite systems in cases where the degrees of freedom take continuous values.",0503733v1
2000-12-15,Conductance and density of states as the Kramers-Kronig dispersion relation,"By applying the Kramers-Kronig dispersion relation to the transmission
amplitude a direct connection of the conductance with the density of states is
given in quantum scattering systems connected to two one-channel leads.
  Using this method we show that in the Fano resonance the peak position of the
density of states is generally different from the position of the corresponding
conductance peak, whereas in the Breit-Wigner resonance those peak positions
coincide.
  The lineshapes of the density of states are well described by a Lorentz type
in the both resonances.
  These results are verified by another approach using a specific form of the
scattering matrix to describe scattering resonances.",0012282v1
2005-09-13,Wang-Landau algorithm for continuous models and joint density of states,"We present modified Wang-Landau algorithm for models with continuous degrees
of freedom. We demonstrate this algorithm with the calculation of the joint
density of states $g(M,E)$ of ferromagnet Heisenberg models. The joint density
of states contains more information than the density of states of a single
variable--energy, but is also much more time-consuming to calculate. We discuss
the strategies to perform this calculation efficiently for models with several
thousand degrees of freedom, much larger than other continuous models studied
previously with the Wang-Landau algorithm.",0509335v1
2007-01-26,Fast Algorithm to Calculate Density of States,"An algorithm to calculate the density of states, based on the well-known
Wang-Landau method, is introduced. Independent random walks are performed in
different restricted ranges of energy, and the resultant density of states is
modified by a function of time, F(t)=1/t, for large time. As a consequence, the
calculated density of state, gm(E,t), approaches asymptotically the exact value
gex(E) as 1/sqrt(t), avoiding the saturation of the error. It is also shown
that the growth of the interface of the energy histogram belongs to the random
deposition universality class.",0701672v2
2008-09-05,Comparison of Raman spectra and vibrational density of states between graphene nanoribbons with different edges,"Vibrational properties of graphene nanoribbons are examined with density
functional based tight-binding method and non-resonant bond polarization
theory. We show that the recently discovered reconstructed zigzag edge can be
identified from the emergence of high-energy vibrational mode due to strong
triple bonds at the edges. This mode is visible also in the Raman spectrum.
Total vibrational density of states of the reconstructed zigzag edge is
observed to resemble the vibrational density of states of armchair, rather than
zigzag, graphene nanoribbon. Edge-related vibrational states increase in energy
which corroborates increased ridigity of the reconstructed zigzag edge.",0809.0976v1
2023-08-07,Analytic density of states of two-dimensional Chern insulator,"We present analytic expressions for the density of states and its consistent
derivation for the two-dimensional Qi-Wu-Zhang (QWZ) Hamiltonian, a generic
model for the Chern topological insulators of class A. This density of states
is expressed in terms of elliptical integrals. We discuss and plot special
cases of the dispersion relations and the corresponding densities of states.
Spectral moments are also presented. The exact formulae ought to be useful in
determining physical properties of the non-interacting Chern insulators and
within the dynamical mean-field theory for interacting fermions with the QWZ
Hamiltonian in the non-interacting limit.",2308.03681v2
2005-06-12,Expressions for the Exchange Correlation Potential and Exchange Correlation Functional of Kohn--Sham Density Functional Theory,"The State--Specific Kohn--Sham Density Functional Theory
[arXiv:physics/0506037] is used to derive the Kohn-Sham exchange-correlation
potential $\vxc$ and exchange-correlation energy $\Eco$ as explicit functionals
of $v_s$ and $\phi_1$, where $v_s$ is the local, one-body potential from the
Kohn--Sham equations, and $\phi_1$ is the spinless one-particle density matrix
from the Kohn--Sham noninteracting state, say $|\phi_1\ran$. In other words,
$|\phi_1\ran$ is the ground state eigenfunction of the noninteracting
Schr\""odinger equation with the one-body potential $v_s$. For simplicity, we
only consider noninteracting states that are closed-shell states and
interacting states that are nondegenerate, singlet ground-states.",0506109v1
2021-10-01,Constraints on high density equation of state from maximum neutron star mass,"The low density nuclear matter equation of state is strongly constrained by
nuclear properties, however, for constraining the high density equation of
state it is necessary to resort to indirect information obtained from the
observation of neutron stars, compact objects that may have a central density
several times nuclear matter saturation density, $n_0$. Taking a meta-modelling
approach to generate a huge set of equation of state that satisfy nuclear
matter properties close to $n_0$ and that do not contain a first order phase
transition, the possibility of constraining the high density equation of state
was investigated. The entire information obtained from the GW170817 event for
the probability distribution of $\tilde{\Lambda}$ was used to make a
probabilistic inference of the EOS, which goes beyond the constraints imposed
by nuclear matter properties. Nuclear matter properties close to saturation,
below $2n_0$, do not allow us to distinguish between equations of state that
predict different neutron star (NS) maximum masses. This is, however, not true
if the equation of state is constrained at low densities by the tidal
deformability of the NS merger associated to GW170817. Above $3n_0$,
differences may be large, for both approaches, and, in particular, the pressure
and speed of sound of the sets studied do not overlap, showing that the
knowledge of the NS maximum mass may give important information on the high
density EOS. Narrowing the maximum mass uncertainty interval will have a
sizeable effect on constraining the high density EOS.",2110.00305v1
2014-03-29,Nonlinear channels of Werner states,"The nonlinear positive map of density matrix of two-qubit Werner state called
nonlinear channel is studied. The map of density matrix is realized by rational
function. The influence of the map onto the entanglement properties of the
transformed density matrix is discussed. The violation of Bell inequality (CHSH
inequality) for the two-qubit state is investigated. The nonlinear channels
under discussion create the entangled state from separable Werner state. The
quantum spin-tomograms of the states are studied.",1403.7612v1
2005-05-11,Molecular dynamics simulation for baryon-quark phase transition at finite temperature and density,"We study the baryon-quark phase transition in a molecular dynamics (MD) of
quark degrees of freedom at finite temperature and density. The baryon state at
low density and temperature, and the deconfined quark state at high density and
temperature are reproduced. We investigate the equations of state of matters
with different $u$-$d$-$s$ compositions. Then we draw phase diagrams in the
temperature-density plane by this simulation. It is found that the baryon-quark
transition is sensitive to the quark width.",0505029v2
2013-10-22,Intrinsic exchange-correlation magnetic fields in exact current-density functional theory for degenerate systems,"We calculate the exact Kohn-Sham (KS) scalar and vector potentials that
reproduce, within current-density functional theory, the steady-state density
and current density corresponding to an electron quasiparticle added to the
ground state of a model quantum wire. Our results show that, even in the
absence of an external magnetic field, a KS description of a steady-state
system in general requires a non-zero exchange-correlation magnetic field that
is purely mechanical in origin. The KS paramagnetic current density is not, in
general, that of the interacting system in any gauge.",1310.5887v1
2024-02-27,Sequential transport maps using SoS density estimation and $α$-divergences,"Transport-based density estimation methods are receiving growing interest
because of their ability to efficiently generate samples from the approximated
density. We further invertigate the sequential transport maps framework
proposed from arXiv:2106.04170 arXiv:2303.02554, which builds on a sequence of
composed Knothe-Rosenblatt (KR) maps. Each of those maps are built by first
estimating an intermediate density of moderate complexity, and then by
computing the exact KR map from a reference density to the precomputed
approximate density. In our work, we explore the use of Sum-of-Squares (SoS)
densities and $\alpha$-divergences for approximating the intermediate
densities. Combining SoS densities with $\alpha$-divergence interestingly
yields convex optimization problems which can be efficiently solved using
semidefinite programming. The main advantage of $\alpha$-divergences is to
enable working with unnormalized densities, which provides benefits both
numerically and theoretically. In particular, we provide two new convergence
analyses of the sequential transport maps: one based on a triangle-like
inequality and the second on information geometric properties of
$\alpha$-divergences for unnormalizied densities. The choice of intermediate
densities is also crucial for the efficiency of the method. While tempered (or
annealed) densities are the state-of-the-art, we introduce diffusion-based
intermediate densities which permits to approximate densities known from
samples only. Such intermediate densities are well-established in machine
learning for generative modeling. Finally we propose and try different
low-dimensional maps (or lazy maps) for dealing with high-dimensional problems
and numerically demonstrate our methods on several benchmarks, including
Bayesian inference problems and unsupervised learning task.",2402.17943v1
2019-12-23,Empirical constraints on the high-density equation of state from multi-messenger observables,"We search for possible correlations between neutron star observables and
thermodynamic quantities that characterize high density nuclear matter. We
generate a set of model-independent equations of state describing stellar
matter from a Taylor expansion around saturation density. Each equation of
state which is a functional of the nuclear matter parameters is
thermodynamically consistent, causal and compatible with astrophysical
observations. We find that the neutron star tidal deformability and radius are
strongly correlated with the pressure, the energy density and the sound
velocity at different densities. Similar correlations are also exhibited by a
large set of mean-field models based on non-relativistic and relativistic
nuclear energy density functionals. These model independent correlations can be
employed to constrain the equation of state at different densities above
saturation from measurements of NS properties with multi-messenger
observations. In particular, precise constraints on the radius of PSR
J0030+0451 thanks to NICER observations would allow to better infer the
properties of matter around two times the nuclear saturation density.",1912.11131v1
2005-06-04,State-Specific Kohn-Sham Density Functional Theory,"A generalization of the Kohn--Sham approach is derived where the
correlation-energy functional depends on the one-particle density matrix of
noninteracting states and on the external potential from the interacting
target-state. The one-particle equations contain the exact exchange potential,
a nonlocal correlation potential, and an additional operator involving the
correlation density. The electronic-energy functional has multiple solutions:
Any one-particle density matrix delivering the target-state density yields a
solution. In order to obtain the Kohn--Sham solution, the nonlocal operators
are converted into local ones using an approach developed by Sala and Gorling.
Since the exact exchange-potential is used, and the N--representability problem
does not arise--in contrast to the Kohn--Sham approach--errors from Coulomb
self-interactions do not occur, nor the need to introduce functionals defined
by a constraint search. Furthermore, the approach does not use the
Hohenberg-Kohn theorem. A density functional formalism is also derived that
assumes that the one-particle density matrices of interest have v-representable
(non-interacting) densities and that these density matrices can be written as
an explicit functional of the electron density. For simplicity, we only
consider noninteracting closed-shell states and target states that are
nondegenerate, singlet ground-states.",0506037v2
2010-12-04,Photonic density of states maps for design of photonic crystal devices,"In this work, it has been investigated whether photonic density of states
maps can be applied to the design of photonic crystal-based devices. For this
reason, comparison between photonic density of states maps and transmittance
maps was carried out. Results of comparison show full correspondence between
these characteristics. Photonic density of states maps appear to be preferable
for the design of photonic crystal devices, than photonic band gap maps
presented earlier and than transmittance maps shown in the paper.",1012.0921v1
2013-06-25,High-frequency vibrational density of states of a disordered solid,"We investigate the high-frequency behavior of the density of vibrational
states in three-dimensional elasticity theory with spatially fluctuating
elastic moduli. At frequencies well above the mobility edge, instanton
solutions yield an exponentially decaying density of states. The instanton
solutions describe excitations, which become localized due to the
disorder-induced fluctuations, which lower the sound velocity in a finite
region compared to its average value. The exponentially decaying density of
states (known in electronic systems as the Lifshitz tail) is governed by the
statistics of a fluctuating-elasticity landscape, capable of trapping the
vibrational excitations.",1306.5894v1
2004-03-20,Spin polarized states in nuclear matter with Skyrme effective interaction,"The possibility of appearance of spin polarized states in symmetric and
strongly asymmetric nuclear matter is analyzed within the framework of a Fermi
liquid theory with the Skyrme effective interaction. The zero temperature
dependence of the neutron and proton spin polarization parameters as functions
of density is found for SkM$^*$, SGII (symmetric case) and SLy4, SLy5 (strongly
asymmetric case) effective forces. By comparing free energy densities, it is
shown that in symmetric nuclear matter ferromagnetic spin state (parallel
orientation of neutron and proton spins) is more preferable than
antiferromagnetic one (antiparallel orientation of spins). Strongly asymmetric
nuclear matter undergoes at some critical density a phase transition to the
state with the oppositely directed spins of neutrons and protons while the
state with the same direction of spins does not appear. In comparison with
neutron matter, even small admixture of protons strongly decreases the
threshold density of spin instability. It is clarified that protons become
totally polarized within a very narrow density domain while the density profile
of the neutron spin polarization parameter is characterized by the appearance
of long tails near the transition density.",0403059v1
2019-02-20,On the Probability Density of the Nuclei in a Vibrationally Excited Molecule,"For localized and oriented vibrationally excited molecules, the one-body
probability density of the nuclei (one-nucleus density) is studied. Like the
familiar and widely used one-electron density that represents the probability
of finding an electron at a given location in space, the one-nucleus density
represents the probability of finding a nucleus at a given position in space
independent of the location of the other nuclei. In contrast to the full
many-dimensional nuclear probability density, the one-nucleus density contains
less information and may thus be better accessible by experiment, especially
for large molecules. It also provides a quantum-mechanical view of molecular
vibrations that can easily be visualized. We study how the nodal structure of
the wavefunctions of vibrationally excited states translates to the one-nucleus
density. It is found that nodes are not necessarily visible: Already for
relatively small molecules, only certain vibrational excitations change the
one-nucleus density qualitatively compared to the ground state. It turns out
that there are some simple rules for predicting the shape of the one-nucleus
density from the normal mode coordinates, and thus for predicting if a
vibrational excitation is visible in a corresponding experiment.",1902.07469v1
2017-10-28,Universality of Quantum Information in Chaotic CFTs,"We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal
field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute
the reduced density matrix of a ball-shaped subsystem of finite size in the
infinite volume limit when the full system is an energy eigenstate. This
reduced density matrix is close in trace distance to a density matrix, to which
we refer as the ETH density matrix, that is independent of all the details of
an eigenstate except its energy and charges under global symmetries. In two
dimensions, the ETH density matrix is universal for all theories with the same
value of central charge. We argue that the ETH density matrix is close in trace
distance to the reduced density matrix of the (micro)canonical ensemble. We
support the argument in higher dimensions by comparing the Von Neumann entropy
of the ETH density matrix with the entropy of a black hole in holographic
systems in the low temperature limit. Finally, we generalize our analysis to
the coherent states with energy density that varies slowly in space, and show
that locally such states are well described by the ETH density matrix.",1710.10458v2
2009-06-17,Optimality of log Hölder continuity of the integrated density of states,"We construct examples, that log H\""older continuity of the integrated density
of states cannot be improved. Our examples are limit-periodic.",0906.3300v1
2005-09-09,Quasi-stationary States of Two-Dimensional Electron Plasma Trapped in Magnetic Field,"We have performed numerical simulations on a pure electron plasma system
under a strong magnetic field, in order to examine quasi-stationary states that
the system eventually evolves into. We use ring states as the initial states,
changing the width, and find that the system evolves into a vortex crystal
state from a thinner-ring state while a state with a single-peaked density
distribution is obtained from a thicker-ring initial state. For those
quasi-stationary states, density distribution and macroscopic observables are
defined on the basis of a coarse-grained density field. We compare our results
with experiments and some statistical theories, which include the
Gibbs-Boltzmann statistics, Tsallis statistics, the fluid entropy theory, and
the minimum enstrophy state. From some of those initial states, we obtain the
quasi-stationary states which are close to the minimum enstrophy state, but we
also find that the quasi-stationary states depend upon initial states, even if
the initial states have the same energy and angular momentum, which means the
ergodicity does not hold.",0509239v2
2000-06-01,Non-spiky density of states of an icosahedral quasicrystal,"The density of states of the ideal three-dimensional Penrose tiling, a
quasicrystalline model, is calculated with a resolution of 10 meV. It is not
spiky. This falsifies theoretical predictions so far, that spikes of width
10-20 meV are generic for the density of states of quasicrystals, and it
confirms recent experimental findings. The qualitative difference between our
results and previous calculations is partly explained by the small number of k
points that has usually been included in the evaluation of the density of
states of periodic approximants of quasicrystals. It is also shown that both
the density of states of a small approximant of the three-dimensional Penrose
tiling and the density of states of the ideal two-dimensional Penrose tiling do
have spiky features, which also partly explains earlier predictions.",0006018v2
2023-04-08,Quantum dynamics as a pseudo-density matrix,"While in relativity theory space evolves over time into a single entity known
as spacetime, quantum theory lacks a standard notion of how to encapsulate the
dynamical evolution of a quantum state into a single ""state over time"".
Recently it was emphasized in the work of Fitzsimons, Jones and Vedral that if
such a state over time is to encode not only spatial but also temporal
correlations which exist within a quantum dynamical process, then it should be
represented not by a density matrix, but rather, by a pseudo-density matrix. A
pseudo-density matrix is a hermitian matrix of unit trace whose marginals are
density matrices, and in this work, we make use a factorization system for
quantum channels to associate a pseudo-density matrix with a quantum system
which is to evolve according to a finite sequence of quantum channels. We then
view such a pseudo-density matrix as the quantum analog of a local patch of
spacetime, and we make an in-depth mathematical analysis of such quantum
dynamical pseudo-density matrices and the properties they satisfy. We also show
how to explicitly extract quantum dynamics from a given pseudo-density matrix,
thus solving an open problem posed in the literature.",2304.03954v3
2020-08-31,State densities of heavy nuclei in the static-path plus random-phase approximation,"Nuclear state densities are important inputs to statistical models of
compound-nucleus reactions. State densities are often calculated with
self-consistent mean-field approximations that do not include important
correlations and have to be augmented with empirical collective enhancement
factors. Here, we benchmark the static-path plus random-phase approximation
(SPA+RPA) to the state density in a chain of samarium isotopes $^{148-155}$Sm
against exact results (up to statistical errors) obtained with the shell model
Monte Carlo (SMMC) method. The SPA+RPA method incorporates all static
fluctuations beyond the mean field together with small-amplitude quantal
fluctuations around each static fluctuation. Using a pairing plus quadrupole
interaction, we show that the SPA+RPA state densities agree well with the exact
SMMC densities for both the even- and odd-mass isotopes. For the even-mass
isotopes, we also compare our results with mean-field state densities
calculated with the finite-temperature Hartree-Fock-Bogoliubov (HFB)
approximation. We find that the SPA+RPA repairs the deficiencies of the
mean-field approximation associated with broken rotational symmetry in deformed
nuclei and the violation of particle-number conservation in the pairing
condensate. In particular, in deformed nuclei the SPA+RPA reproduces the
rotational enhancement of the state density relative to the mean-field state
density.",2008.13722v1
2020-06-20,PDE-based Dynamic Density Estimation for Large-scale Agent Systems,"Large-scale agent systems have foreseeable applications in the near future.
Estimating their macroscopic density is critical for many density-based
optimization and control tasks, such as sensor deployment and city traffic
scheduling. In this paper, we study the problem of estimating their dynamically
varying probability density, given the agents' individual dynamics (which can
be nonlinear and time-varying) and their states observed in real-time. The
density evolution is shown to satisfy a linear partial differential equation
uniquely determined by the agents' dynamics. We present a density filter which
takes advantage of the system dynamics to gradually improve its estimation and
is scalable to the agents' population. Specifically, we use kernel density
estimators (KDE) to construct a noisy measurement and show that, when the
agents' population is large, the measurement noise is approximately
``Gaussian''. With this important property, infinite-dimensional Kalman filters
are used to design density filters. It turns out that the covariance of
measurement noise depends on the true density. This state-dependence makes it
necessary to approximate the covariance in the associated operator Riccati
equation, rendering the density filter suboptimal. The notion of input-to-state
stability is used to prove that the performance of the suboptimal density
filter remains close to the optimal one. Simulation results suggest that the
proposed density filter is able to quickly recognize the underlying modes of
the unknown density and automatically ignore outliers, and is robust to
different choices of kernel bandwidth of KDE.",2006.11461v1
2012-03-30,Density functional theory with adaptive pair density,"We propose a density functional to find the ground state energy and density
of interacting particles, where both the density and the pair density can
adjust in the presence of an inhomogeneous potential. As a proof of principle
we formulate an a priori exact functional for the inhomogeneous Hubbard model.
The functional has the same form as the Gutzwiller approximation but with an
unknown kinetic energy reduction factor. An approximation to the functional
based on the exact solution of the uniform problem leads to a substantial
improvement over the local density approximation.",1203.6873v1
2016-04-22,From dilute matter to the equilibrium point in the energy--density--functional theory,"Due to the large value of the scattering length in nuclear systems, standard
density--functional theories based on effective interactions usually fail to
reproduce the nuclear Fermi liquid behavior both at very low densities and
close to equilibrium. Guided on one side by the success of the Skyrme density
functional and, on the other side, by resummation techniques used in Effective
Field Theories for systems with large scattering lengths, a new energy--density
functional is proposed. This functional, adjusted on microscopic calculations,
reproduces the nuclear equations of state of neutron and symmetric matter at
various densities. Furthermore, it provides reasonable saturation properties as
well as an appropriate density dependence for the symmetry energy.",1604.06587v1
2014-09-21,The role of fluctuations across a density interface,"A statistical mechanics theory for a fluid stratified in density is
presented. The predicted statistical equilibrium state is the most probable
outcome of turbulent stirring. The slow temporal evolution of the vertical
density profile is related to the presence of irreversible mixing, which alters
the global distribution of density levels. We propose a model in which the
vertical density profile evolves through a sequence of statistical equilibrium
states. The theory is then tested with laboratory experiments in a two-layer
stably stratified fluid forced from below by an oscillating grid. Quantitative
measurements of density fluctuations across the interface are made by planar
laser induced fluorescence. These fluctuations are splitted in a ""wave"" part
and a ""turbulent"" part. The wave part of the density field is well described by
a previous theory due to Phillips. We argue that statistical mechanics
predictions apply for the turbulent part of the density field sufficiently
close to the interface. However inside the mixed layer density fluctuations are
instead controlled by a balance between eddy flux downward and dissipation by
cascade to small scales. We report exponential tails for the density pdf in
this region.",1409.6010v1
2017-07-25,Order-disorder transition in active nematic: A lattice model study,"We introduce a lattice model for active nematic composed of self-propelled
apolar particles,study its different ordering states in the density-temperature
parameter space, and compare with the corresponding equilibrium model. The
active particles interact with their neighbours within the framework of the
Lebwohl-Lasher model, and move anisotropically along their orientation to an
unoccupied nearest neighbour lattice site. An interplay of the activity,
thermal fluctuations and density gives rise distinct states in the system. For
a fixed temperature, the active nematic shows a disordered isotropic state, a
locally ordered inhomogeneous mixed state, and bistability between the
inhomogeneous mixed and a homogeneous globally ordered state in different
density regime. In the low temperature regime, the isotropic to the
inhomogeneous mixed state transition occurs with a jump in the order parameter
at a density less than the corresponding equilibrium disorder-order transition
density. Our analytical calculations justify the shift in the transition
density and the jump in the order parameter. We construct the phase diagram of
the active nematic in the density-temperature plane.",1707.07850v1
2008-11-21,Superfluid-density of the ultra-cold Fermi gas in optical lattices,"In this paper we study the superfluid density of the two component Fermi gas
in optical lattices with population imbalance. Three different type of phases,
the BCS-state (Bardeen, Cooper, and Schrieffer), the FFLO-state (Fulde, Ferrel,
Larkin, and Ovchinnikov), and the Sarma state, are considered. We show that the
FFLO superfluid density differs from the BCS/Sarma superfluid density in an
important way. Although there are dynamical instabilities in the FFLO phase,
when the interaction is strong or densities are high, on the weak coupling
limit the FFLO phase is found to be stable.",0811.3623v3
2016-06-30,Negative-parity nucleon excited state in nuclear matter,"Spectral functions of the nucleon and its negative parity excited state in
nuclear matter are studied using QCD sum rules and the maximum entropy method
(MEM). It is found that in-medium modifications of the spectral functions are
attributed mainly to density dependencies of the $\langle \bar{q}q \rangle $
and $\langle q^{\dagger}q \rangle $ condensates. The MEM reproduces the
lowest-energy peaks of both the positive and negative parity nucleon states at
finite density up to $\rho \sim \rho_N$ (normal nuclear matter density). As the
density grows, the residue of the nucleon ground state decreases gradually
while the residue of the lowest negative parity excited state increases
slightly. On the other hand, the positions of the peaks, which correspond to
the total energies of these states, are almost density independent for both
parity states. The density dependencies of the effective masses and vector
self-energies are also extracted by assuming the mean-field green functions for
the peak states. We find that, as the density increases, the nucleon effective
mass decreases while the vector self-energy increases. The density dependence
of these quantities for the negative parity state on the other hand turns out
to be relatively weak.",1606.09434v2
2001-05-03,Construction of a dispersion relation from an arbitrary density of states,"The dispersion relations of energy bands in solids are characterized by their
density of states, but a given density of states may originate from various
band structures. We show how a spherically symmetric dispersion can be
constructed for any one-band density of states. This method is applied to one-,
two- and three-dimensional systems. It also serves to establish that any
one-band spectrum with finite bandwidth can be obtained from a properly scaled
dispersion relation in the limit of infinite dimensions.",0105068v2
2006-11-14,Ground state energy of the low density Hubbard model. An upper bound,"We derive an upper bound on the ground state energy of the three-dimensional
(3D) repulsive Hubbard model on the cubic lattice agreeing in the low density
limit with the known asymptotic expression of the ground state energy of the
dilute Fermi gas in the continuum. As a corollary, we prove an old conjecture
on the low density behavior of the 3D Hubbard model, i.e., that the total spin
of the ground state vanishes as the density goes to zero.",0611034v2
2011-09-16,Probing the quantum state of a 1D Bose gas using off-resonant light scattering,"We present a theoretical treatment of coherent light scattering from an
interacting 1D Bose gas at finite temperatures. We show how this can provide a
nondestructive measurement of the atomic system states. The equilibrium states
are determined by the temperature and interaction strength, and are
characterized by the spatial density-density correlation function. We show how
this correlation function is encoded in the angular distribution of the
fluctuations of the scattered light intensity, thus providing a sensitive,
quantitative probe of the density-density correlation function and therefore
the quantum state of the gas.",1109.3727v1
2015-11-30,Dimensional Effects on the Density of States in Systems with Quasi-Relativistic Dispersion Relations and Potential Wells,"Motivated by the recent discoveries of materials with quasi-relativistic
dispersion relations, we determine densities of states in materials with low
dimensional substructures and relativistic dispersion relations. We find that
these dimensionally hybrid systems yield quasi-relativistic densities of states
that are a superposition of the corresponding two- and three-dimensional
densities of states.",1511.09421v2
2000-10-26,Initial-state dependence in time-dependent density functional theory,"Time-dependent density functionals in principle depend on the initial state
of the system, but this is ignored in functional approximations presently in
use. For one electron it is shown there is no initial-state dependence: for any
density, only one initial state produces a well-behaved potential. For two
non-interacting electrons with the same spin in one-dimension, an initial
potential that makes an alternative initial wavefunction evolve with the same
density and current as a ground state is calculated. This potential is
well-behaved and can be made arbitrarily different from the original potential.",0010432v1
2010-04-29,Ground state at high density,"Weak limits as the density tends to infinity of classical ground states of
integrable pair potentials are shown to minimize the mean-field energy
functional. By studying the latter we derive global properties of high-density
ground state configurations in bounded domains and in infinite space. Our main
result is a theorem stating that for interactions having a strictly positive
Fourier transform the distribution of particles tends to be uniform as the
density increases, while high-density ground states show some pattern if the
Fourier transform is partially negative. The latter confirms the conclusion of
earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and
Likos et al. (2007). Other results include the proof that there is no Bravais
lattice among high-density ground states of interactions whose Fourier
transform has a negative part and the potential diverges or has a cusp at zero.
We also show that in the ground state configurations of the penetrable sphere
model particles are superposed on the sites of a close-packed lattice.",1004.5260v2
2022-04-21,Honing in on a topological zero-bias conductance peak,"A popular signature of Majorana bound states in topological superconductors
is the zero-energy conductance peak with a height of $2e^2/h$. However, a
similar zero energy conductance peak with almost the same height can also arise
due to non-topological reasons. Here we show that these trivial and topological
zero energy conductance peaks can be distinguished via the zero energy local
density of states and local magnetization density of states. We find that the
zero-energy local density of states exhibits oscillations with a finite period
for a trivial zero-bias conductance peak. In contrast, these oscillations
disappear for the topological zero-bias conductance peak. On the other hand,
zero energy local magnetization density of states shows a periodic oscillation
for trivial zero-bias conductance peak, while for topological ZBCP, they
vanish. Our results suggest that zero-energy local density of states and local
magnetization density of states can be used as an experimental probe to
distinguish trivial zero energy conductance peak from topological zero energy
conductance peak.",2204.09925v2
1999-02-28,Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron,"A formula is derived that relates the ground-state dispersion of a many-body
system with the end-to-end distribution of paths with open boundary conditions
in imaginary time. The formula does not involve the energy estimator. It allows
direct measurement of the ground-state dispersion by quantum Monte Carlo
methods without analytical continuation or auxiliary fitting. The formula is
applied to the lattice polaron problem. The exact polaron spectrum and density
of states are calculated for several models in one, two, and three dimensions.
In the adiabatic regime of the Holstein model, the polaron density of states
deviates spectacularly from the free-particle shape.",9903011v1
1997-05-09,On the Lifshitz tail in the density of states of a superconductor with magnetic impurities,"We argue that any superconductor with magnetic impurities is gapless due to a
Lifshitz tail in the density of states extending to zero energy. At low energy
the density of states $\nu(E \to 0)$ remains finite. We show that fluctuations
in the impurity distribution produce regions of suppressed superconductivity,
which are responsible for the low energy density of states.",9705093v1
1998-07-29,Density of states in the non-hermitian Lloyd model,"We reconsider the recently proposed connection between density of states in
the so-called ``non-hermitian quantum mechanics'' and the localization length
for a particle moving in random potential. We argue that it is indeed possible
to find the localization length from the density of states of a non-hermitian
random ``Hamiltonian''. However, finding the density of states of a
non-hermitian random ``Hamiltonian'' remains an open problem, contrary to
previous findings in the literature.",9807391v1
2020-12-23,Revisiting density-functional theory of the total current density,"Density-functional theory requires an extra variable besides the electron
density in order to properly incorporate magnetic-field effects. In a
time-dependent setting, the gauge-invariant, total current density takes that
role. A peculiar feature of the static ground-state setting is, however, that
the gauge-dependent paramagnetic current density appears as the additional
variable instead. An alternative, exact reformulation in terms of the total
current density has long been sought but to date a work by Diener is the only
available candidate. In that work, an unorthodox variational principle was used
to establish a ground-state density-functional theory of the total current
density as well as an accompanying Hohenberg-Kohn-like result. We here
reinterpret and clarify Diener's formulation based on a maximin variational
principle. Using simple facts about convexity implied by the resulting
variational expressions, we prove that Diener's formulation is unfortunately
not capable of reproducing the correct ground-state energy and, furthermore,
that the suggested construction of a Hohenberg-Kohn map contains an irreparable
mistake.",2012.12661v2
2007-06-21,Series expansion for the density of states of the Ising and Potts models,"An approximation of the density of states for the Ising and Potts models
based on the high- and low-temperature series are developed.",0706.3116v1
2020-06-29,Analyticity of density of states for the Cauchy distribution,"We compute the density of states for the Cauchy distribution for a large
class of random operators and show it is analytic in a strip about the real
axis.",2006.15840v1
2018-04-23,Head-on collision of multi-state ultralight BEC dark matter configurations,"Density profiles of ultralight Bose-Condensate dark matter inferred from
numerical simulations of structure formation, ruled by the
Gross-Pitaevskii-Poisson (GPP) system of equations, have a core-tail structure.
Multi-state equilibrium configurations of the GPP system on the other hand,
have a similar core-tail density profile. We now submit these multi-state
configurations to highly dynamical scenarios and show their potential as
providers of appropriate density profiles of structures. What we do is to
present the simulation of head-on collisions between two equilibrium
configurations of the GPP system of equations, including the collision of
ground state with multi-state configurations. We study the regimes of solitonic
and merger behavior, and show generic properties of the dynamics of the system,
including the relaxation process and attractor density profiles. We show the
merger of multi-state configurations have the potential to produce core-tail
density profiles, with the core dominated by the ground state and a halo
dominated by an additional states.",1804.08670v2
2020-03-21,Magnetic breakdown and charge density wave formation: a quantum oscillation study of the rare-earth tritellurides,"The rare-earth tritellurides ($R$Te$_3$, where $R$ = La, Ce, Pr, Nd, Sm, Gd,
Tb, Dy, Ho, Er, Tm, Y) form a charge density wave state consisting of a single
unidirectional charge density wave for lighter $R$, with a second
unidirectional charge density wave, perpendicular and in addition to the first,
also present at low temperatures for heavier $R$. We present a quantum
oscillation study in magnetic fields up to 65T that compares the single charge
density wave state with the double charge density wave state both above and
below the magnetic breakdown field of the second charge density wave. In the
double charge density wave state it is observed that there remain several
small, light pockets with the largest occupying around 0.5% of the Brillouin
zone. By applying magnetic fields above the independently determined magnetic
breakown field, the quantum oscillation frequencies of the single charge
density wave state are recovered, as expected in a magnetic breakdown scenario.
Measurements of the electronic effective mass do not show any divergence or
significant increase on the pockets of Fermi surface observed here as the
putative quantum phase transition between the single and double charge density
wave states is approached.",2003.09657v2
2018-12-05,Managing uncertainty in data-derived densities to accelerate density functional theory,"Faithful representations of atomic environments and general models for
regression can be harnessed to learn electron densities that are close to the
ground state. One of the applications of data-derived electron densities is to
orbital-free density functional theory. However, extrapolations of densities
learned from a training set to dissimilar structures could result in inaccurate
results, which would limit the applicability of the method. Here, we show that
a non-Bayesian approach can produce estimates of uncertainty which can
successfully distinguish accurate from inaccurate predictions of electron
density. We apply our approach to density functional theory where we initialise
calculations with data-derived densities only when we are confident about their
quality. This results in a guaranteed acceleration to self-consistency for
configurations that are similar to those seen during training and could be
useful for sampling based methods, where previous ground state densities cannot
be used to initialise subsequent calculations.",1812.01966v2
2020-08-04,Electrically induced charge-density waves in a two-dimensional electron channel: Beyond the Local Density Approximation,"In a previous paper we suggested that a macroscopic force field applied
across a two-dimensional electron gas channel could induce a microscopic charge
density wave as soon as the proper compressibility becomes negative, which
happens at densities much higher than the critical density for the Wigner
crystal transition. The suggestion was based on a calculation of the ground
state energy in the local density approximation. In this paper we refine our
calculation of the energy by including a self-consistent gradient correction to
the kinetic energy. Due to the increased energy cost of rapid density
variations, we find a much lower critical density for the onset of the charge
density wave. This critical density coincides with the result of a linear
stability analysis of the uniform ground state in the absence of the electric
field.",2008.01324v2
2015-09-17,Density Induced Phases in Active Nematic,"We introduce a minimal model for a collection of self-propelled apolar active
particles, also called as `active nematic', on a two-dimensional substrate and
study the order-disorder transition with the variation of density. The
particles interact with their neighbours within the framework of the
Lebwohl-Lasher model and move asymmetrically, along their orientation, to
unoccupied nearest neighbour lattice sites. At a density lower than the
equilibrium isotropic-nematic transition density, the active nematic shows a
first order transition from the isotropic state to a banded state. The banded
state extends over a range of density, and the scalar order parameter of the
system shows a plateau like behaviour, similar to that of the magnetic systems.
In the large density limit the active nematic shows a bistable behaviour
between a homogeneous ordered state with global ordering and an inhomogeneous
mixed state with local ordering. The study of the above phases with density
variation is scant and gives significant insight of complex behaviours of many
biological systems.",1509.05166v1
2023-01-18,What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates,"We use a suite of 3D simulations of star-forming molecular clouds, with and
without stellar feedback, magnetic fields, and driven turbulence, to study the
compression and expansion rates of the gas as functions of density. We show
that, around the mean density, supersonic turbulence promotes rough equilibrium
between the amounts of compressing and expanding gas, consistent with
continuous gas cycling between high and low density states. We find that the
inclusion of protostellar jets produces rapidly expanding and compressing
low-density gas. We find that the gas mass flux peaks at the transition between
the lognormal and power-law forms of the density probability distribution
function (PDF). This is consistent with the transition density tracking the
post-shock density, which promotes an enhancement of mass at this density
(i.e., shock compression and filament formation). At high densities, the gas
dynamics are dominated by self-gravity: the compression rate in all of our runs
matches the rate of the run with only gravity, suggesting that processes other
than self-gravity have little effect at these densities. The net gas mass flux
becomes constant at a density below the sink formation threshold, where it
equals the star formation rate. The density at which the net gas mass flux
equals the star formation rate is one order of magnitude lower than our sink
threshold density, corresponds to the formation of the second power-law tail in
the density PDF, and sets the overall star formation rates of these
simulations.",2301.07723v1
2009-10-05,Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group,"A useful concept for finding numerically the dominant correlations of a given
ground state in an interacting quantum lattice system in an unbiased way is the
correlation density matrix. For two disjoint, separated clusters, it is defined
to be the density matrix of their union minus the direct product of their
individual density matrices and contains all correlations between the two
clusters. We show how to extract from the correlation density matrix a general
overview of the correlations as well as detailed information on the operators
carrying long-range correlations and the spatial dependence of their
correlation functions. To determine the correlation density matrix, we
calculate the ground state for a class of spinless extended Hubbard models
using the density matrix renormalization group. This numerical method is based
on matrix product states for which the correlation density matrix can be
obtained straightforwardly. In an appendix, we give a detailed tutorial
introduction to our variational matrix product state approach for ground state
calculations for 1- dimensional quantum chain models. We show in detail how
matrix product states overcome the problem of large Hilbert space dimensions in
these models and describe all techniques which are needed for handling them in
practice.",0910.0753v1
2001-09-07,Numerical study of the density of states for the bag model,"The density of states for an extended MIT bag model is studied numerically by
using a parameterized smooth representation which provides the best fit to the
numerical data. It is found that the mass dependence of the surface term in the
density of states agrees with that derived from multi-reflection theory
calculation. The mass dependence of the curvature term in the density of states
is extracted for finite values of the quark mass. The scaling properties of the
data, assumed in the parameterization, are studied. The difference between the
parameterized smooth representation determined by a best fit and the results
derived from direct smoothing of the numerical data are discussed. The
fluctuations in the density of states are also discussed. We provide a smooth
representation of the density of states of a spherical cavity for
non-relativistic particles.",0109020v1
2002-06-27,Generalized two-leg Hubbard ladder at half-filling: Phase diagram and quantum criticalities,"The ground-state phase diagram of the half-filled two-leg Hubbard ladder with
inter-site Coulomb repulsions and exchange coupling is studied by using the
strong-coupling perturbation theory and the weak-coupling bosonization method.
Considered here as possible ground states of the ladder model are four types of
density-wave states with different angular momentum (s-density-wave state,
p-density-wave state, d-density-wave state, and f-density-wave state) and four
types of quantum disordered states, i.e., Mott insulating states (S-Mott,
D-Mott, S'-Mott, and D'-Mott states, where S and D stand for s- and d-wave
symmetry). The s-density-wave state, the d-density-wave state, and the D-Mott
state are also known as the charge-density-wave (CDW) state, the staggered-flux
(SF) state, and the rung-singlet state, respectively. Strong-coupling approach
naturally leads to the Ising model in a transverse field as an effective theory
for the quantum phase transitions between the SF state and the D-Mott state and
between the CDW state and the S-Mott state, where the Ising ordered states
correspond to doubly degenerate ground states in the staggered-flux or the
charge-density-wave state. From the weak-coupling bosonization approach it is
shown that there are three cases in the quantum phase transitions between a
density-wave state and a Mott state: the Ising (Z_2) criticality, the SU(2)_2
criticality, and a first-order transition. The quantum phase transitions
between Mott states and between density-wave states are found to be the U(1)
Gaussian criticality. The ground-state phase diagram is determined by
integrating perturbative renormalization-group equations. It is shown that the
S-Mott state and the SF state exist in the region sandwiched by the CDW phase
and the D-Mott phase.",0206539v2
2010-06-23,"Density functional theory calculation of ground state energy, dipole polarizability and hyperpolarizability of a confined helium atom","We calculate ground-state energies and densities of a helium atom confined in
an impenetrable spherical box within density functional theory. These
calculations are performed by variationally solving Kohn-Sham equation with the
ground-state orbital expanded in terms of Slater-type orbitals. Using the
ground-state densities we then calculate static linear polarizability and
nonlinear hyperpolarizability and study their variation with the radius of
confinement. We find that polarizability decreases monotonically with
decreasing confinement radius and the hyperpolarizability not only decreases
but also undergoes a change in sign in the strong confinement regime.",1006.4503v1
2020-07-23,Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories,"Strong correlations within a symmetry-unbroken ground-state wavefunction can
show up in approximate density functional theory as symmetry-broken
spin-densities or total densities, which are sometimes observable. They can
arise from soft modes of fluctuations (sometimes collective excitations) such
as spin-density or charge-density waves at non-zero wavevector. In this sense,
an approximate density functional for exchange and correlation that breaks
symmetry can be more revealing (albeit less accurate) than an exact functional
that does not. The examples discussed here include the stretched H$_2$
molecule, antiferromagnetic solids, and the static charge-density wave/Wigner
crystal phase of a low-density jellium. It is shown that (and in what sense)
the static charge density wave is a soft plasmon.",2007.12052v1
2018-04-01,The impossibility of expanding the square root of the electron density as a linear combination of elements of a complete set of basis functions,"In orbital-free density functional theory (OFDFT), an equation exists for
$\psi = \sqrt n$, the square root of the ground state electron density $n$. We
show that $\psi$ cannot be expanded as a linear combination of elements of a
complete set of basis functions except in the case of one or two electron
systems. This is unlike the case for the ground state of a system of identical
bosons in which the square root of the ground state bosonic density can have an
expansion as a linear combination of elements of a complete set of basis
functions.",1804.00252v1
2012-03-30,Propagation of Initially Excited States in Time-Dependent Density Functional Theory,"Many recent applications of time-dependent density functional theory begin in
an initially excited state, and propagate it using an adiabatic approximation
for the exchange-correlation potential. This however inserts the excited-state
density into a ground-state approximation. By studying a series of model
calculations, we highlight the relevance of initial-state dependence of the
exact functional when starting in an excited state, and explore the errors
inherent in the adiabatic approximation that neglect this dependence.",1203.6856v1
2022-11-08,Scaling of the Non-Phononic Spectrum of Two-Dimensional Glasses,"Low-frequency vibrational harmonic modes of glasses are frequently used to
understand their universal low-temperature properties. One well studied feature
is the excess low-frequency density of states over the Debye model prediction.
Here we examine the system size dependence of the density of states for
two-dimensional glasses. For systems of fewer than 100 particles, the density
of states scales with the system size as if all the modes were plane-wave-like.
However, for systems greater than 100 particles we find a different system-size
scaling of the cumulative density of states below the first transverse sound
mode frequency, which can be derived from the assumption that these modes are
quasi-localized. Moreover, for systems greater than 100 particles, we find that
the cumulative density of states scales with frequency as a power law with the
exponent that leads to the exponent $\beta=3.5$ for the density of states
independent of system size.",2211.07543v1
2000-06-16,"Some Fundamental Properties of the Integer-States in Open-System, Ensemble Energy-Density Functional Theories","Ensemble averages are an approximation technique for connecting macroscopic
and microscopic properties of a system. For systems open with respect to
exchange of particles with a bath, the microscopic states are those with
integer numbers of particles. When a property of the open system is represented
as an ensemble average over these microscopic states, self-consistency dictates
several implications for the properties of both for open-system energy density
functionals and the integer-state functionals describing the microscopic
states. The first is that each integer-state energy density functional is a
functional of the original type discovered by Levy. Another is that the
dependence of the open-system functional on the ensemble density is linear
whereas the dependence of the integer-state functional is decidedly nonlinear.
Finally, the derivative discontinuity behavior with respect to particle number
of some open-system density functionals appears to be connected to the
long-range behavior of the effective external potentials of the integer-state
functionals governing the interactions among subsystems in the ensemble.",0006270v2
2004-12-20,State estimation on correlated copies,"State estimation is usually analyzed in the situation when copies are in a
product state, either mixed or pure. We investigate here the concept of state
estimation on correlated copies. We analyze state estimation on correlated N
qubit states, which are permutationally invariant. Using a correlated state we
try to estimate as good as possible the direction of the Bloch vector of a
single particle reduced density matrix. We derive the optimal fidelity for all
permutation invariant states. We find the optimal state, which yields the
highest estimation fidelity among the states with the same reduced density
matrix. Interestingly this state is not a product state. We also point out that
states produced by optimal universal cloning machines are the worst form the
point of view of estimating the reduced density matrix.",0412155v3
2009-05-11,On the density matrix for the kink ground state of higher spin XXZ chain,"The exact expression for the density matrix of the kink ground state of
higher spin XXZ chain is obtained.",0905.1442v1
2010-11-20,Fractional occupation in Kohn-Sham density-functional theory and the treatment of non-pure-state v-representable densities,"In the framework of Kohn-Sham density-functional theory, systems with
ground-state densities that are not pure-state v-representable in the
non-interacting reference system (PSVR) occur frequently. In the present
contribution, a new algorithm, which allows the solution of such systems, is
proposed. It is shown that the use of densities which do not correspond to a
ground state of their non-interacting reference system is forbidden. As a
consequence, the proposed algorithm considers only non-interacting ensemble
v-representable densities. The Fe atom, a well-known non-PSVR system, is used
as an illustration. Finally, the problem is analyzed within finite temperature
density-functional theory, where the physical significance of fractional
occupations is exposed and the question of why degenerate states can be
unequally occupied is resolved.",1011.4564v1
2010-06-16,Signature of pseudogap formation in the density of states of underdoped cuprates,"The resonating valence bond spin liquid model for the underdoped cuprates has
as an essential element, the emergence of a pseudogap.
  This new energy scale introduces asymmetry in the quasiparticle density of
states because it is associated with the antiferromagnetic Brillouin zone. By
contrast, superconductivity develops on the Fermi surface and this largely
restores the particle-hole symmetry for energies below the superconducting
energy gap scale. In the highly underdoped regime, these two scales can be
separately identified in the density of states and also partial density of
states for each fixed angle in the Brillouin zone. From the total density of
states, we find that the pseudogap energy scale manifests itself differently as
a function of doping for positive and negative bias. Furthermore, we find
evidence from recent scanning tunneling spectroscopy data for asymmetry in the
positive and negative bias of the extracted $\Delta(\theta)$ which is in
qualitative agreement with this model. Likewise, the slope of the linear low
energy density of states is nearly constant in the underdoped regime while it
increases significantly with overdoping in agreement with the data.",1006.3232v1
2013-10-28,Simulations of imaging of the local density of states by charged probe technique for resonant cavities,"We simulate scanning probe imaging of the local density of states related to
scattering Fermi level wave functions inside a resonant cavity. We calculate
potential landscape within the cavity taking into account the Coulomb charge of
the probe and its screening by deformation of the two-dimensional electron gas
using the local density approximation. Approximation of the tip potential by a
Lorentz function is discussed. The electron transfer problem is solved with a
finite difference approach. We look for stable work points for the extraction
of the local density of states from conductance maps. We find that conductance
maps are highly correlated with the local density of states when the Fermi
energy level enters into Fano resonance with states localized within the
cavity. Generally outside resonances the correlation between the local density
of states and conductance maps is low.",1310.7019v1
2017-10-11,Real State Transfer,"A continuous quantum walk on a graph $X$ with adjacency matrix $A$ is
specified by the 1-parameter family of unitary matrices $U(t)=\exp(itA)$. These
matrices act on the state space of a quantum system, the states of which we may
represent by density matrices, positive semidefinite matrices with rows and
columns indexed by $V(X)$ and with trace $1$. The square of the absolute values
of the entries of a column of $U(t)$ define a probability density on $V(X)$,
and it is precisely these densities that predict the outcomes of measurements.
There are two special cases of physical interest: when the column density is
supported on a vertex, and when it is uniform. In the first case we have
perfect state transfer; in the second, uniform mixing.
  There are many results concerning state transfer and uniform mixing. In this
paper we show that these results on perfect state transfer hold largely because
at the time it occurs, the density matrix is real. We also show that the
results on uniform mixing obtained so far hold because the entries of the
density matrix are algebraic numbers. As a consequence of these we derive
strong restrictions on the occurence of uniform mixing on bipartite graphs and
on oriented graphs.",1710.04042v1
2023-01-16,Non-phononic density of states of two-dimensional glasses revealed by random pinning,"The vibrational density of states of glasses is considerably different from
that of crystals. In particular, there exist spatially localized vibrational
modes in glasses. The density of states of these non-phononic modes has been
observed to follow $g(\omega) \propto \omega^4$, where $\omega$ is the
frequency. However, in two-dimensional systems, the abundance of phonons makes
it difficult to accurately determine this non-phononic density of states
because they are strongly coupled to non-phononic modes and yield strong
system-size and preparation-protocol dependencies. In this article, we utilize
the random pinning method to suppress phonons and disentangle their coupling
with non-phononic modes and successfully calculate their density of states as
$g(\omega) \propto \omega^4$. We also study their localization properties and
confirm that low-frequency non-phononic modes in pinned systems are truly
localized without far-field contributions. We finally discuss the excess
density of states over the Debye value that results from the hybridization of
phonons and non-phononic modes.",2301.06225v1
2014-06-23,New inequality for density matrices of single qudit states,"Using the monotonity of relative entropy of composite quantum systems we
obtain new entropic inequalities for arbitrary density matrices of single qudit
states. Example of qutrit state inequalities and the ""qubit portrait"" bound for
the distance between the qutrit states are considered in explicit form.",1406.5838v1
2014-04-03,Density Functionals in the Presence of Magnetic Field,"In this paper density functionals for Coulomb systems subjected to electric
and magnetic fields are developed. The density functionals depend on the
particle density, $\rho$, and paramagnetic current density, $j^p$. This
approach is motivated by an adapted version of the Vignale and Rasolt
formulation of Current Density Functional Theory (CDFT), which establishes a
one-to-one correspondence between the non-degenerate ground-state and the
particle and paramagnetic current density. Definition of $N$-representable
density pairs $(\rho,j^p)$ is given and it is proven that the set of
$v$-representable densities constitutes a proper subset of the set of
$N$-representable densities. For a Levy-Lieb type functional $Q(\rho,j^p)$, it
is demonstrated that (i) it is a proper extension of the universal
Hohenberg-Kohn functional, $F_{HK}(\rho,j^p)$, to $N$-representable densities,
(ii) there exists a wavefunction $\psi_0$ such that
$Q(\rho,j^p)=(\psi_0,H_0\psi_0)_{L^2}$, where $H_0$ is the Hamiltonian without
external potential terms, and (iii) it is not convex. Furthermore, a convex and
universal functional $F(\rho,j^p)$ is studied and proven to be equal the convex
envelope of $Q(\rho,j^p)$. For both $Q$ and $F$, we give upper and lower
bounds.",1404.0825v1
2023-10-25,Transformer-based Atmospheric Density Forecasting,"As the peak of the solar cycle approaches in 2025 and the ability of a single
geomagnetic storm to significantly alter the orbit of Resident Space Objects
(RSOs), techniques for atmospheric density forecasting are vital for space
situational awareness. While linear data-driven methods, such as dynamic mode
decomposition with control (DMDc), have been used previously for forecasting
atmospheric density, deep learning-based forecasting has the ability to capture
nonlinearities in data. By learning multiple layer weights from historical
atmospheric density data, long-term dependencies in the dataset are captured in
the mapping between the current atmospheric density state and control input to
the atmospheric density state at the next timestep. This work improves upon
previous linear propagation methods for atmospheric density forecasting, by
developing a nonlinear transformer-based architecture for atmospheric density
forecasting. Empirical NRLMSISE-00 and JB2008, as well as physics-based TIEGCM
atmospheric density models are compared for forecasting with DMDc and with the
transformer-based propagator.",2310.16912v1
2012-06-21,Theoretical method for the study of the excited states of a system,"A novel, exact, theoretical method for the study of the excited states of a
system is presented. It is demonstrated how to transform the excited state
problem of one Hamiltonian into the ground state problem of an auxiliary one.
From this, a new exact density functional suitable for excited states is
constructed. These results make the excited states of a system accessible
through all ground state theoretical techniques.",1206.4872v1
2017-03-24,Spin-polarized local density of states in the vortex state of helical p-wave superconductors,"Properties of the vortex state in helical p-wave superconductor are studied
by the quasi-classical Eilenberger theory. We confirm the instability of the
helical p-wave state at high fields and that the spin-polarized local density
of states M(E,r) appears even when Knight shift does not change. This is
because the vorticity couples to the chirality of up-spin pair or down-spin
pair of the helical state. In order to identify the helical p-wave state at low
fields, we investigate the structure of the zero-energy M (E = 0, r) in the
vortex states, and also the energy spectra of M (E, r).",1703.08328v1
2019-07-10,Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model,"The ground-state density of states of the half-filled Falicov-Kimball model
contains a charge-density-wave gap. At finite temperature, this gap is not
immediately closed, but is rather filled in by subgap states. For a specific
combination of parameters, this leads to a stable phase where the system is in
an ordered charge-density-wave phase, but there is high density of states at
the Fermi level. We show that this property can be, in finite dimensions,
traced to a crossing of sharp states resulting from the single particle
excitations of the localized subsystem. The analysis of the inverse
participation ratio points to a strong localization in the discussed regime.
However, the pronounced subgap density of states can still lead to a notable
increase of charge transport through a finite size system. We show this by
focusing on the transmission in heterostructures where a Falicov-Kimball system
is sandwiched between two metallic leads.",1907.04697v2
2000-06-20,Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry,"We consider the statistical properties of the local density of states of a
one-dimensional Dirac equation in the presence of various types of disorder
with Gaussian white-noise distribution. It is shown how either the replica
trick or supersymmetry can be used to calculate exactly all the moments of the
local density of states. Careful attention is paid to how the results change if
the local density of states is averaged over atomic length scales. For both the
replica trick and supersymmetry the problem is reduced to finding the ground
state of a zero-dimensional Hamiltonian which is written solely in terms of a
pair of coupled ``spins'' which are elements of u(1,1). This ground state is
explicitly found for the particular case of the Dirac equation corresponding to
an infinite metallic quantum wire with a single conduction channel. The
calculated moments of the local density of states agree with those found
previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a
technique based on recursion relations for Feynman diagrams.",0006291v1
2000-05-16,Coexistent States of Charge Density Wave and Spin Density Wave in One-Dimensional Systems with the Inter-site Coulomb Interaction under the Electron Filling Control,"The coexistent state of the spin density wave (SDW) and the charge density
wave (CDW) in the one-dimensional systems is studied by the mean field
approximation at T=0 in various electron-filling cases. We find that the
coexistent state of SDW and CDW is stabilized when the on-site and the
inter-site Coulomb interactions have the values estimated for the organic
conductors. The ground state energies have cusp-like minima at 1/4, 3/8, 5/12,
7/16, 7/20 and 9/20-fillings.",0005256v1
1997-01-20,Induced Magnetic Field in a Finite Fermion Density Maxwell QED$_{2+1}$,"We are studying finite fermion density states in Maxwell QED$_{2+1}$ with
external magnetic field. It is shown that at any fermion density the energy of
some magnetized states may be less than that of the state with the same
density, but no magnetic field. Magnetized states are described by the
effective Maxwell-Chern-Simons QED$_{2+1}$ Lagrangian with gauge field mass
proportional to the number of filled Landau levels.",9701100v2
2011-11-23,Observation of reentrant quantum Hall states in the lowest Landau level,"Measurements in very low disorder two-dimensional electrons confined to
relatively wide GaAs quantum well samples with tunable density reveal reentrant
$\nu=1$ integer quantum Hall states in the lowest Landau level near filling
factors $\nu=4/5$ and 6/5. These states are not seen at low densities and
become more prominent with increasing density and in wider wells. Our data
suggest a close competition between different types of Wigner crystal states
near these fillings. We also observe an intriguing disappearance and
reemergence of the $\nu=4/5$ fractional quantum Hall effect with increasing
density.",1111.5384v1
2014-06-18,Quench between a Mott insulator and a Lieb-Liniger liquid,"In this work we study a quench between a Mott insulator and a repulsive
Lieb-Liniger liquid. We find explicitly the stationary state when a long time
has passed after the quench. It is given by a GGE density matrix which we
completely characterize, calculating the quasiparticle density describing the
system after the quench. In the long time limit we find an explicit form for
the local three body density density density correlation function and the
asymptotic long distance limit of the density density correlation function. The
later is shown to have a Gaussian decay at large distances.",1406.4902v1
1998-10-20,Quasiparticle density of states in dirty high-T_c superconductors,"We study the density of quasiparticle states of dirty d-wave superconductors.
We show the existence of singular corrections to the density of states due to
quantum interference effects. We then argue that the density of states actually
vanishes in the localized phase as $|E|$ or $E^2$ depending on whether time
reversal is a good symmetry or not. We verify this result for systems without
time reversal symmetry in one dimension using supersymmetry techniques. This
simple, instructive calculation also provides the exact universal scaling
function for the density of states for the crossover from ballistic to
localized behaviour in one dimension. Above two dimensions, we argue that in
contrast to the conventional Anderson localization transition, the density of
states has critical singularities which we calculate in a $2+\epsilon$
expansion. We discuss consequences of our results for various experiments on
dirty high-$T_c$ materials.",9810238v1
2007-07-30,Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices,"The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their
local unitary equivalents are the only states of n qubits that are not uniquely
determined among pure states by their reduced density matrices of n-1 qubits.
Thus, among pure states, the generalized GHZ states are the only ones
containing information at the n-party level. We point out a connection between
local unitary stabilizer subgroups and the property of being determined by
reduced density matrices.",0707.4428v2
2007-12-07,The Hartree-Fock ground state of the three-dimensional electron gas,"In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is
unstable to a spin density wave (SDW) instability. Determining the true HF
ground state has remained a challenge. Using numerical calculations for finite
systems and analytic techniques, we study the HF ground state of the 3D
electron gas. At high density, we find broken spin symmetry states with a
nearly constant charge density. Unlike previously discussed spin wave states,
the observed wave vector of the SDW is smaller than $2 k_F$. The
broken-symmetry state originates from pairing instabilities at the Fermi
surface, a model for which is proposed.",0712.1194v1
2008-03-06,Ultimate Energy Densities for Electromagnetic Pulses,"The ultimate electric and magnetic energy densities that can be attained by
bandlimited electromagnetic pulses in free space are calculated using an ab
initio quantized treatment, and the quantum states of electromagnetic fields
that achieve the ultimate energy densities are derived. The ultimate energy
densities also provide an experimentally accessible metric for the degree of
localization of polychromatic photons.",0803.0779v1
1994-10-01,Current density functional theory of quantum dots in a magnetic field,"We present a study of ground state energies and densities of quantum dots in
a magnetic field, which takes into account correlation effects through the
Current-density functional theory (CDFT). The method is first tested against
exact results for the energy and density of 2 and 3 electrons quantum dots, and
it is found to yield an accuracy better than $ 3 \%. $ Then we extend the study
to larger dots and compare the results with available experimental data. The
orbital and spin angular momenta of the ground state, and the evolution of the
density profile as a function of the magnetic field are calculated.
Quantitative evidence of edge reconstruction at high magnetic field is
presented.",9409122v1
1998-06-22,Density of State in a Complex Random Matrix Theory with External Source,"The density of state for a complex $N\times N$ random matrix coupled to an
external deterministic source is considered for a finite N, and a compact
expression in an integral representation is obtained.",9806254v1
2024-01-26,Ground state energy of Bogoliubov energy functional in the high density limit,"We consider the Bogoliubov energy functional proposed by Napi\'orkowski,
Reuvers and Solovej and analize it in the high density regime. We derive a two
term asymptotic expansion of the ground state energy.",2401.14809v1
1999-05-21,Broken-Symmetry Ground States of Halogen-Bridged Binuclear Metal Complexes,"Based on a symmetry argument, we study ground states of what we call
MMX-chain compounds, which are the new class of halogen-bridged metal
complexes. Commensurate density-wave solutions of a relevant multi-band
Peierls-Hubbard model are systematically revealed within the Hartree-Fock
approximation. We numerically draw ground-state phase diagrams, where various
novel density-wave states appear.",9905312v1
2004-12-22,Bound states in the phase diagram of the extended Hubbard model,"The papaer shows how the known, exact results for the two electron bound
states can modify the ground state phase diagram of extended Hubbard model
(EHM) for on-site attraction, intersite repulsion and arbitrary electron
density. The main result is suppression of the superconducting state in favor
of normal phase for small charge densities.",0412627v1
2005-06-08,Conditional probabilities and density operators in quantum modeling,"Based on a recent proof of free choices in linking equations to the
experiments they describe, I clarify relations among some purely mathematical
entities featured in quantum mechanics (probabilities, density operators,
partial traces, and operator-valued measures), thereby allowing applications of
these entities to the modeling of a wider variety of physical situations.
Conditional probabilities associated with projection-valued measures are
expressed by introducing conditional density operators, identical in some but
not all cases to the usual reduced density operators. By lifting density
operators to the extended Hilbert space featured in Neumark's theorem, I show
an obstacle to extending conditional density operators to arbitrary positive
operator-valued measures (POVMs); however, tensor products of POVMs are
compatible with conditional density operators. By way of application,
conditional density operators together with the free choice of probe particles
allow the so-called postulate of state reductions to be replaced by a theorem.
A second application demonstrates an equivalence between one form of quantum
key distribution and another, allowing a formulation of individual
eavesdropping attacks against transmitted-state BB84 to work also for
entangled-state BB84.",0506068v1
2020-07-21,Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity,"We study the effect of the boundary on a system of weakly interacting bosons
in one dimension. It strongly influences the boson density which is completely
suppressed at the boundary position. Away from it, the density is depleted over
the distances on the order of the healing length at the mean-field level.
Quantum fluctuations modify the density profile considerably. The local density
approaches the average one as an inverse square of the distance from the
boundary. We calculate an analytic expression for the density profile at
arbitrary separations from the boundary. We then consider the problem of
localization of a foreign quantum particle (impurity) in the potential created
by the inhomogeneous boson density. At the mean-field level, we find exact
results for the energy spectrum of the bound states, the corresponding wave
functions, and the condition for interaction-induced localization. The quantum
contribution to the boson density gives rise to small corrections of the bound
state energy levels. However, it is fundamentally important for the existence
of a long-range Casimir-like interaction between the impurity and the boundary.",2007.10771v2
2005-06-17,Nonanalytical equation of state of the hard sphere fluid,"An equation of state of the hard sphere fluid which is not analytical at the
freezing density is proposed and tested. The nonanalytical term is based on the
the classical nucleation theory and is able to capture the observed ``anomalous
increase'' of pressure at high densities. It is combined with the virial
expansion at low densities.",0506449v1
2007-09-13,Density of states of helium droplets,"Accurate analytical expressions for the state densities of liquid He-4
droplets are derived, incorporating the ripplon and phonon degrees of freedom.
The microcanonical temperature and the ripplon angular momentum level density
are also evaluated. The approach is based on inversions and systematic
expansions of canonical thermodynamic properties.",0709.1973v1
2018-09-20,Optimal mass transport and kernel density estimation for state-dependent networked dynamic systems,"State-dependent networked dynamical systems are ones where the
interconnections between agents change as a function of the states of the
agents. Such systems are highly nonlinear, and a cohesive strategy for their
control is lacking in the literature. In this paper, we present two techniques
pertaining to the density control of such systems. Agent states are initially
distributed according to some density, and a feedback law is designed to move
the agents to a target density profile. We use optimal mass transport to design
a feedforward control law propelling the agents towards this target density.
Kernel density estimation, with constraints imposed by the state-dependent
dynamics, is then used to allow each agent to estimate the local density of the
agents.",1809.07496v1
2014-05-19,Zero-energy Majorana states in a one-dimensional quantum wire with charge density wave instability,"One-dimensional lattice with strong spin-orbit interactions (SOI) and Zeeman
magnetic field is shown to lead to the formation of a helical charge-density
wave (CDW) state near half-filling. Interplay of the magnetic field, SOI
constants and the CDW gap seems to support Majorana bound states under
appropriate value of the external parameters. Explicit calculation of the
quasi-particles' wave functions supports a formation of the localized
zero-energy state, bounded to the sample end-points. Symmetry classification of
the system is provided. Relative value of the density of states shows a precise
zero-energy peak at the center of the band in the non-trivial topological
regime.",1405.4815v1
2013-05-24,Mean field limit of bosonic systems in partially factorized states and their linear combinations,"We study the mean field limit of one-particle reduced density matrices, for a
bosonic system in an initial state with a fixed number of particles, only a
fraction of which occupies the same state, and for linear combinations of such
states. In the mean field limit, the time-evolved reduced density matrix is
proved to converge: in trace norm, towards a rank one projection (on the state
solution of Hartree equation) for a single state; in Hilbert-Schmidt norm
towards a mixed state, combination of projections on different solutions
(corresponding to each initial datum), for states that are a linear
superposition.",1305.5699v1
2018-06-28,Non collinear Magnetism and Phonon Dispersion Relation in Vacancy Induced Phosphorene Monolayer,"We have studied the electronic, magnetic and linear phonon dispersion
behavior of Phosphorene monolayer using rst principle based ab initio method.
Phosphorene monolayer is a semiconducting system with a dimensional dependent
variable range of band gap. Vacancy has been done to study the geometry and
physical behavior of the monolayer system. Pristine, vacancy induced monolayer
and vacancy induced doped monolayer are included in the calculation. Dopant
concentration has been well checked via optimization algorithm to maintain the
dilute magnetic semiconducting behavior of the monolayer system. Density of
states and partial density of state indicates the contribution of individual
orbitals in the system. Band closing nature in observed in vacancy and doped
vacancy states indicating closed dense states and metallic behavior of the
perturbed phases. Both antiferromagnetic and ferromagnetic ordering is included
in our calculation to get a charm of both ordering in the physical properties
of the system. Landau energy level distribution is mapped via Fermi surface
with linear dispersion relation in terms of phonon vibrational density of
states and linear dispersion relations. The results of linear phonon density of
states corroborating with electronic density of states.",1806.10885v1
2023-05-10,Fulde-Ferrell-Larkin-Ovchinnikov state in a superconducting thin film attached to a ferromagnetic cluster,"We study theoretically the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states
appearing locally in a superconducting thin film with a small circular magnetic
cluster. The pair potential, the pairing correlations, the free-energy density,
and the quasiparticle density of states are calculated for several cluster
sizes and the exchange potentials by solving the Eilenberger equation in two
dimensions. The number of nodes in the pair potential increases with increasing
the exchange potential and cluster size. The local FFLO states are stabilized
by the superconducting condensate away from the magnetic cluster even though
the free-energy density beneath the ferromagnet exceeds locally the
normal-state value. The analysis of the pairing-correlation functions shows
that the spatial variation of the spin-singlet $s$-wave pair potential
generates $p$-wave Cooper pairs, and that odd-frequency Cooper pairs govern the
inhomogeneous subgap spectra in the local density of states. We also discuss a
way of detecting the local FFLO states based on the calculated quasiparticle
density of states.",2305.06015v2
2019-09-17,Majorana representation for mixed states,"We generalize the Majorana stellar representation of spin-$s$ pure states to
mixed states, and in general to any hermitian operator, defining a bijective
correspondence between three spaces: the spin density-matrices, a projective
space of homogeneous polynomials of four variables, and a set of equivalence
classes of points (constellations) on spheres of different radii. The
representation behaves well under rotations by construction, and also under
partial traces where the reduced density matrices inherit their constellation
classes from the original state $\rho$. We express several concepts and
operations related to density matrices in terms of the corresponding
polynomials, such as the anticoherence criterion and the tensor representation
of spin-$s$ states described in [1].",1909.07740v1
2021-06-09,Distributed Mean-Field Density Estimation for Large-Scale Systems,"This work studies how to estimate the mean-field density of large-scale
systems in a distributed manner. Such problems are motivated by the recent
swarm control technique that uses mean-field approximations to represent the
collective effect of the swarm, wherein the mean-field density (especially its
gradient) is usually used in feedback control design. In the first part, we
formulate the density estimation problem as a filtering problem of the
associated mean-field partial differential equation (PDE), for which we employ
kernel density estimation (KDE) to construct noisy observations and use
filtering theory of PDE systems to design an optimal (centralized) density
filter. It turns out that the covariance operator of observation noise depends
on the unknown density. Hence, we use approximations for the covariance
operator to obtain a suboptimal density filter, and prove that both the density
estimates and their gradient are convergent and remain close to the optimal one
using the notion of input-to-state stability (ISS). In the second part, we
continue to study how to decentralize the density filter such that each agent
can estimate the mean-field density based on only its own position and local
information exchange with neighbors. We prove that the local density filter is
also convergent and remains close to the centralized one in the sense of ISS.
Simulation results suggest that the centralized suboptimal density filter is
able to generate convergent density estimates, and the local density filter is
able to converge and remain close to the centralized filter.",2106.05318v2
2010-04-26,Spin density matrices for nuclear density functionals with parity violations,"The spin density matrix (SDM) used in atomic and molecular physics is
revisited for nuclear physics, in the context of the radial density functional
theory. The vector part of the SDM defines a ""hedgehog"" situation, which exists
only if nuclear states contain some amount of parity violation.",1004.4542v1
2007-05-15,Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor,"The electronic density of states of graphene is equivalent to that of
relativistic electrons. In the absence of disorder or external doping the Fermi
energy lies at the Dirac point where the density of states vanishes. Although
transport measurements at high carrier densities indicate rather high
mobilities, many questions pertaining to disorder remain unanswered. In
particular, it has been argued theoretically, that when the average carrier
density is zero, the inescapable presence of disorder will lead to electron and
hole puddles with equal probability. In this work, we use a scanning single
electron transistor to image the carrier density landscape of graphene in the
vicinity of the neutrality point. Our results clearly show the electron-hole
puddles expected theoretically. In addition, our measurement technique enables
to determine locally the density of states in graphene. In contrast to
previously studied massive two dimensional electron systems, the kinetic
contribution to the density of states accounts quantitatively for the measured
signal. Our results suggests that exchange and correlation effects are either
weak or have canceling contributions.",0705.2180v1
2019-01-07,High Density Reflection Spectroscopy I. A case study of GX~339-4,"We present a broad band spectral analysis of the black hole binary GX~339-4
with NuSTAR and Swift using high density reflection model. The observations
were taken when the source was in low flux hard states (LF) during the
outbursts in 2013 and 2015, and in a very high flux soft state (HF) in 2015.
The high density reflection model can explain its LF spectra with no
requirement for an additional low temperature thermal component. This model
enables us to constrain the density in the disc surface of GX~339-4 in
different flux states. The disc density in the LF state is $\log(n_{\rm e}/$
cm$^{-3})\approx21$, 100 times higher than the density in the HF state
($\log(n_{\rm e}/$ cm$^{-3})=18.93^{+0.12}_{-0.16}$). A close-to-solar iron
abundance is obtained by modelling the LF and HF broad band spectra with
variable density reflection model ($Z_{\rm Fe}=1.50^{+0.12}_{-0.04}Z_{\odot}$
and $Z_{\rm Fe}=1.05^{+0.17}_{-0.15}Z_{\odot}$ respectively).",1901.01739v1
2018-01-06,Ground-state properties of light kaonic nuclei signaling symmetry energy at high densities,"A sensitive correlation between the ground-state properties of light kaonic
nuclei and the symmetry energy at high densities is constructed under the
framework of relativistic mean-field theory. Taking oxygen isotopes as an
example, we see that a high-density core is produced in kaonic oxygen nuclei,
due to the strongly attractive antikaon-nucleon interaction. It is found that
the $1S_{1/2}$ state energy in the high-density core of kaonic nuclei can
directly probe the variation of the symmetry energy at supranormal nuclear
density, and a sensitive correlation between the neutron skin thickness and the
symmetry energy at supranormal density is established directly. Meanwhile, the
sensitivity of the neutron skin thickness to the low-density slope of the
symmetry energy is greatly increased in the corresponding kaonic nuclei. These
sensitive relationships are established upon the fact that the isovector
potential in the central region of kaonic nuclei becomes very sensitive to the
variation of the symmetry energy. These findings might provide another
perspective to constrain high-density symmetry energy, and await experimental
verification in the future.",1801.01946v1
2015-06-22,Reassessing nuclear matter incompressibility and its density dependence,"Experimental giant monopole resonance energies are now known to constrain
nuclear incompressibility of symmetric nuclear matter $K$ and its density slope
$M$ at a particular value of sub-saturation density, the crossing density
$\rho_c$. Consistent with these constraints, we propose a reasonable way to
construct a plausible equation of state of symmetric nuclear matter in a broad
density region around the saturation density $\rho_0$. Help of two additional
empirical inputs, the value of $\rho_0$ and that of the energy per nucleon
$e(\rho_0)$ are needed. The value of $K(\rho_0)$ comes out to be $211.9\pm
24.5$ MeV.",1506.06461v1
2012-04-10,Superfluid Local Density Approximation: A Density Functional Theory Approach to the Nuclear Pairing Problem,"I describe the foundation of a Density Functional Theory approach to include
pairing correlations, which was applied to a variety of systems ranging from
dilute fermions, to neutron stars and finite nuclei. Ground state properties as
well as properties of excited states and time-dependent phenomena can be
achieved in this manner within a formalism based on microscopic input.",1204.2207v1
2005-08-27,Need for fully unintegrated parton densities,"Associated with the use of conventional integrated parton densities are
kinematic approximations on parton momenta which result in unphysical
differential distributions for final-state particles. We argue that it is
important to reformulate perturbative QCD results in terms of fully
unintegrated parton densities, differential in all components of the parton
momentum.",0508280v1
2014-07-18,Roles of Hund's rule coupling in excitonic density-wave states,"Excitonic density-wave states realized by the quantum condensation of
electron-hole pairs (or excitons) are studied in the two-band Hubbard model
with Hund's rule coupling and the pair hopping term. Using the variational
cluster approximation, we calculate the grand potential of the system and
demonstrate that Hund's rule coupling always stabilizes the excitonic
spin-density-wave state and destabilizes the excitonic charge-density-wave
state and that the pair hopping term enhances these effects. The
characteristics of these excitonic density-wave states are discussed using the
calculated single-particle spectral function, density of states, condensation
amplitude, and pair coherence length. Implications of our results in the
materials' aspects are also discussed.",1407.4872v2
2014-07-17,Quantum State Tomography of a Single Qubit: Comparison of Methods,"The tomographic reconstruction of the state of a quantum-mechanical system is
an essential component in the development of quantum technologies. We present
an overview of different tomographic methods for determining the
quantum-mechanical density matrix of a single qubit: (scaled) direct inversion,
maximum likelihood estimation (MLE), minimum Fisher information distance, and
Bayesian mean estimation (BME). We discuss the different prior densities in the
space of density matrices, on which both MLE and BME depend, as well as ways of
including experimental errors and of estimating tomography errors. As a measure
of the accuracy of these methods we average the trace distance between a given
density matrix and the tomographic density matrices it can give rise to through
experimental measurements. We find that the BME provides the most accurate
estimate of the density matrix, and suggest using either the pure-state prior,
if the system is known to be in a rather pure state, or the Bures prior if any
state is possible. The MLE is found to be slightly less accurate. We comment on
the extrapolation of these results to larger systems.",1407.4759v3
2024-02-11,Extended $N$-centered ensemble density functional theory of double electronic excitations,"A recent work [arXiv:2401.04685] has merged $N$-centered ensembles of neutral
and charged electronic ground states with ensembles of neutral ground and
excited states, thus providing a general and in-principle exact (so-called
extended $N$-centered) ensemble density functional theory of neutral and
charged electronic excitations. This formalism made it possible to revisit the
concept of density-functional derivative discontinuity, in the particular case
of single excitations from the highest occupied Kohn-Sham (KS) molecular
orbital, without invoking the usual ""asymptotic behavior of the density""
argument. In this work, we address a broader class of excitations, with a
particular focus on double excitations. An exact implementation of the theory
is presented for the two-electron Hubbard dimer model. A thorough comparison of
the true physical ground- and excited-state electronic structures with that of
the fictitious ensemble density-functional KS system is also presented.
Depending on the choice of the density-functional ensemble as well as the
asymmetry of the dimer and the correlation strength, an inversion of states can
be observed. In some other cases, the strong mixture of KS states within the
true physical system makes the assignment ""single excitation"" or ""double
excitation"" irrelevant.",2402.07161v1
2003-03-20,Density of States and Thouless Formula for Random Unitary Band Matrices,"We study the density of states measure for some class of random unitary band
matrices and prove a Thouless formula relating it to the associated Lyapunov
exponent. This class of random matrices appears in the study of the dynamical
stability of certain quantum systems and can also be considered as a unitary
version of the Anderson model. We further determine the support of the density
of states measure and provide a condition ensuring it possesses an analytic
density.",0303047v1
2010-10-15,Computational Difficulty of Computing the Density of States,"We study the computational difficulty of computing the ground state
degeneracy and the density of states for local Hamiltonians. We show that the
difficulty of both problems is exactly captured by a class which we call #BQP,
which is the counting version of the quantum complexity class QMA. We show that
#BQP is not harder than its classical counting counterpart #P, which in turn
implies that computing the ground state degeneracy or the density of states for
classical Hamiltonians is just as hard as it is for quantum Hamiltonians.",1010.3060v2
2015-10-30,Density of states in gapped superconductors with pairing-potential impurities,"We study the density of states in disordered s-wave superconductors with a
small gap anisotropy. Disorder comes in the form of common nonmagnetic
scatterers and pairing-potential impurities, which interact with electrons via
an electric potential and a local distortion of the superconducting gap. A set
of equations for the quasiclassical Green functions is derived and solved.
Within one spin sector, pairing-potential impurities and weak spin-polarized
magnetic impurities have essentially the same effect on the density of states.
We show that if the gap is isotropic, an isolated impurity with suppressed
pairing supports an infinite number of Andreev states. With growing impurity
concentration, the energy-dependent density of states evolves from a sharp gap
edge with an impurity band below it to a smeared BCS singularity in the
so-called universal limit. If a gap anisotropy is present, the density of
states becomes sensitive to ordinary potential disorder, and the existence of
of Andreev states localized at pairing-potential impurities requires special
conditions. An unusual feature related to the anisotropy is a nonmonotonic
dependence of the gap edge smearing on impurity concentration.",1510.09172v1
1998-08-19,Intrinsic Density Matrices of the Nuclear Shell Model,"A new method for calculation of shell model intrinsic density matrices,
defined as two-particle density matrices integrated over the centre-of-mass
position vector of two last particles and complemented with isospin variables,
has been developed. The intrinsic density matrices obtained are completely
antisymmetric, translation-invariant, and do not employ a group-theoretical
classification of antisymmetric states. They are used for exact realistic
density matrix expansion within the framework of the reduced Hamiltonian
method. The procedures based on precise arithmetic for calculation of the
intrinsic density matrices that involve no numerical diagonalization or
orthogonalization have been developed and implemented in the computer code.",9808054v1
2010-02-09,Probability distribution of the vacuum energy density,"As the vacuum state of a quantum field is not an eigenstate of the
Hamiltonian density, the vacuum energy density can be represented as a random
variable. We present an analytical calculation of the probability distribution
of the vacuum energy density for real and complex massless scalar fields in
Minkowski space. The obtained probability distributions are broad and the
vacuum expectation value of the Hamiltonian density is not fully representative
of the vacuum energy density.",1002.1846v2
2012-12-14,Nuclear density probed by Kaon-Nucleus systems and Kaon-Nucleus interaction,"Effective nuclear densities probed by kaon- and anti-kaon-nucleus systems are
studied theoretically both for bound and low energy scattering states. As for
the anti-kaon bound states, we investigate kaonic atoms. We find that the
effective density depends on the atomic states significantly and we have the
possibility to obtain the anti-kaon properties at various nuclear densities by
observing the several kaonic atom states. We also find the energy dependence of
the probed density by kaon and anti-kaon scattering states. We find that the
study of the effective nuclear density will help to find the proper systems to
investigate the meson properties at various nuclear densities.",1212.3383v1
2023-10-25,DECWA : Density-Based Clustering using Wasserstein Distance,"Clustering is a data analysis method for extracting knowledge by discovering
groups of data called clusters. Among these methods, state-of-the-art
density-based clustering methods have proven to be effective for
arbitrary-shaped clusters. Despite their encouraging results, they suffer to
find low-density clusters, near clusters with similar densities, and
high-dimensional data. Our proposals are a new characterization of clusters and
a new clustering algorithm based on spatial density and probabilistic approach.
First of all, sub-clusters are built using spatial density represented as
probability density function ($p.d.f$) of pairwise distances between points. A
method is then proposed to agglomerate similar sub-clusters by using both their
density ($p.d.f$) and their spatial distance. The key idea we propose is to use
the Wasserstein metric, a powerful tool to measure the distance between $p.d.f$
of sub-clusters. We show that our approach outperforms other state-of-the-art
density-based clustering methods on a wide variety of datasets.",2310.16552v1
2013-11-15,Equation of state in the generalized density scaling regime studied from ambient to ultra-high pressure conditions,"In this paper, based on the effective intermolecular potential with well
separated density and configuration contributions and the definition of the
isothermal bulk modulus, we derive two similar equations of state dedicated to
describe volumetric data of supercooled liquids studied in the extremely wide
pressure range related to the extremely wide density range. Both the equations
comply with the generalized density scaling law of molecular dynamics versus
$h(\rho ) / T$ at different densities $\rho $ and temperatures $T$, where the
scaling exponent can be in general only a density function $\gamma(\rho ) =
\it{d} \rm{ln} \it{h / d} \rm{ln}\rho $ as recently argued by the theory of
isomorphs. We successfully verify these equations of state by using data
obtained from molecular dynamics simulations of the Kob-Andersen binary
Lennard-Jones liquid. As a very important result, we find that the
one-parameter density function $h(\rho )$ analytically formulated in the case
of this prototypical model of supercooled liquid, which implies the
one-parameter density function $\gamma(\rho )$, is able to scale the structural
relaxation times with the value of this function parameter determined by
fitting the volumetric simulation data to the equations of state. We also show
that these equations of state properly describe the pressure dependences of the
isothermal bulk modulus and the configurational isothermal bulk modulus in the
extremely wide pressure range investigated by the computer simulations.
Moreover, we discuss the possible forms of the density functions $h(\rho )$ and
$\gamma(\rho )$ for real glass formers, which are suggested to be different
from those valid for the model of supercooled liquid based on the Lennard-Jones
intermolecular potential.",1311.3910v1
1997-05-23,Quantum Molecular Dynamics Approach to the Nuclear Matter Below the Saturation Density,"Quantum molecular dynamics is applied to study the ground state properties of
nuclear matter at subsaturation densities. Clustering effects are observed as
to soften the equation of state at these densities. The structure of nuclear
matter at subsaturation density shows some exotic shapes with variation of the
density.",9705039v1
2011-10-10,Bound States in Coulomb Systems - Old Problems and New Solutions,"We analyze the quantum statistical treatment of bound states in Hydrogen
considered as a system of electrons and protons. Within this physical picture
we calculate isotherms of pressure for Hydrogen in a broad density region and
compare to some results from the chemical picture. First we resume in detail
the two transitions along isotherms : (i) the formation of bound states
occurring by increasing the density from low to moderate values, (ii) the
destruction of bound states in the high density region, modelled here by
Pauli-Fock effects. Avoiding chemical models we will show, why bound states
according to a discrete part of the spectra occur only in a valley in the T-p
plane. First we study virial expansions in the canonical ensemble and then in
the grand canonical ensemble. We show that in fugacity representations the
population of bound states saturates at higher density and that a combination
of both representations provides quickly converging equations of state. In the
case of degenerate systems we calculated first the density-dependent energy
levels, and find the pressure in Hartree-Fock-Wigner approximation showing the
prominent role of Pauli blocking and Fock effects in the selfenergy.",1110.1962v1
2023-01-28,Density of states for the Unitary Fermi gas and the Schwarzschild black hole,"The density of states of a quantum system can be calculated from its
definition but, in some cases, this approach is quite cumbersome.
Alternatively, the density of states can be deduced from the microcanonical
entropy or from the canonical partition function. After discussing the
relationship among these procedures, we suggest a simple numerical method,
which is equivalent in the thermodynamic limit to perform a Legendre
transformation, to obtain the density of states from the Helmholtz free energy.
We apply this method to determine the many-body density of states of the
unitary Fermi gas, a very dilute system of identical fermions interacting with
divergent scattering length. The unitary Fermi gas is highy symmetric due to
the absence of any internal scale except for the average distance between two
particles and, for this reason, its equation of state is called universal. In
the last part of the paper, by using the same thermodynamical techniques, we
review some properties of} the density of states of a Schwarzschild black hole,
which shares with the unitary Fermi gas the problem of finding the density of
states directly from its definition.",2301.12190v1
2003-06-10,A density functional perspective for one-particle systems,"Density functional theory is discussed in the context of one-particle
systems. We show that the ground state density $\rho_0(x)$ and energy $E_0$ are
simply related to a family of external potential energy functions with ground
state wave functions $\psi_n(x) \propto \rho_0(x)^n$ and energies $E_n=2nE_0$
for certain integer values of $n$.",0306070v1
1999-09-30,A Droplet State in an Interacting Two-Dimensional Electron System,"It is well known that the dielectric constant of two-dimensional (2D)
electron system goes negative at low electron densities. A consequence of the
negative dielectric constant could be the formation of the droplet state. The
droplet state is a two-phase coexistence region of high density liquid and low
density ""gas"". In this paper, we carry out energetic calculations to study the
stability of the droplet ground state. The possible relevance of the droplet
state to recently observed 2D metal-insulator transition is also discussed.",9909450v1
2003-07-22,Exchange-correlation energy densities for two-dimensional systems from quantum dot ground-states,"In this paper we present a new approach how to extract polarization-dependent
exchange-correlation energy densities for two-dimensional systems from
reference densities and energies of quantum dots provided by exact
diagonalization. Compared with results from literature we find systematic
corrections for all polarizations in the regime of high densities.",0307529v2
2009-07-29,Quantum measures for density correlations in optical lattices,"The density-density correlation profiles obtained superimposing absorption
images from atomic clouds freely expanding after the release of the confining
optical lattice can be theoretically described in terms of a generalized
quantum measure based on coherent-like states. We show that the corresponding
density patterns differ in a testable way from those computed using standard
many-body mean values, usually adopted in fitting experimental data.",0907.5129v1
2014-04-28,Density matrix form of Gross-Pitaevskii equation,"We consider the generalized pure state density matrix which depends on
different time moments. The evolution equation for this density matrix is
obtained in case where the density matrix corresponds to the solutions of
Gross-Pitaevskii equation.",1404.7089v1
2019-08-28,Prethermalization of density-density correlations after an interaction quench in the Hubbard model,"In weakly perturbed systems that are close to integrability, thermalization
can be delayed by the formation of prethermalization plateaus. We study the
build-up of density-density correlations after a weak interaction quench in the
Hubbard model in $d > 1$ dimensions using unitary perturbation theory. Starting
from a pre-quench state at temperature $T$, we show that the prethermalization
values of the post-quench correlations are equal to the equilibrium values of
the interacting model at the same temperature $T$. This is explained by the
local character of density-density correlations.",1908.10685v1
2016-03-21,Systematic construction of density functionals based on matrix product state computations,"We propose a systematic procedure for the approximation of density
functionals in density functional theory that consists of two parts. First, for
the efficient approximation of a general density functional, we introduce an
efficient ansatz whose non-locality can be increased systematically. Second, we
present a fitting strategy that is based on systematically increasing a
reasonably chosen set of training densities. We investigate our procedure in
the context of strongly correlated fermions on a one-dimensional lattice in
which we compute accurate training densities with the help of matrix product
states. Focusing on the exchange-correlation energy, we demonstrate how an
efficient approximation can be found that includes and systematically improves
beyond the local density approximation. Importantly, this systematic
improvement is shown for target densities that are quite different from the
training densities.",1603.06565v2
2013-09-10,Algebraic and Geometric Mean Density of States in Topological Anderson Insulators,"Algebraic and geometric mean density of states in disordered systems may
reveal properties of electronic localization. In order to understand the
topological phases with disorder in two dimensions, we present the calculated
density of states for disordered Bernevig-Hughes-Zhang model. The topological
phase is characterized by a perfectly quantized conducting plateau, carried by
helical edge states, in a two-terminal setup. In the presence of disorder, the
bulk of the topological phase is either a band insulator or an Anderson
insulator. Both of them can protect edge states from backscattering. The
topological phases are explicitly distinguished as topological band insulator
or topological Anderson insulator from the ratio of the algebraic mean density
of states to the geometric mean density of states. The calculation reveals that
topological Anderson insulator can be induced by disorders from either a
topologically trivial band insulator or a topologically nontrivial band
insulator.",1309.2468v1
2005-03-07,Local density of states of a strongly type-II d-wave superconductor: The binary alloy model in a magnetic field,"We calculate self-consistently the local density of states (LDOS) of a d-wave
superconductor considering the scattering of the quasiparticles off randomly
distributed impurities and off externally induced vortices. The impurities and
the vortices are randomly distributed but the vortices are preferably located
near the impurities. The increase of either the impurity repulsive potential or
the mpurity density only affects the density of states (DOS) slightly. The
dominant effect is due to the vortex scattering. The results for the LDOS agree
qualitatively with experimental results considering that most vortices are
pinned at the impurities.",0503164v1
2003-06-16,Density-functional calculation of ionization energies of current-carrying atomic states,"Current-density-functional theory is used to calculate ionization energies of
current-carrying atomic states. A perturbative approximation to full
current-density-functional theory is implemented for the first time, and found
to be numerically feasible. Different parametrizations for the
current-dependence of the density functional are critically compared. Orbital
currents in open-shell atoms turn out to produce a small shift in the
ionization energies. We find that modern density functionals have reached an
accuracy at which small current-related terms appearing in open-shell
configurations are not negligible anymore compared to the remaining difference
to experiment.",0306413v1
2019-07-10,The role of topological defects in the two-stage melting and elastic behavior of active Brownian particles,"We find that crystalline states of repulsive active Brownian particles at
high activity melt into a hexatic state but this transition is not driven by an
unbinding of bound dislocation pairs as suggested by the
Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. Upon reducing the
density, the crystalline state melts into a high-density hexatic state devoid
of any defects. Decreasing the density further, the dislocations proliferate
and introduce plasticity in the system, nevertheless maintaining the hexatic
state, but eventually melting into a fluid state. Remarkably, the elastic
constants of active solids are equal to those of their passive counterparts, as
the swim contribution to the stress tensor is negligible in the solid state.
The sole effect of activity is that the stable solid regime shifts to higher
densities. Furthermore, discontinuities in the elastic constants as a function
of density correspond to changes in the defect concentrations rather than to
the solid-hexatic transition.",1907.04767v1
2009-02-11,Local density of states of electron-crystal phases in graphene in the quantum Hall regime,"We calculate, within a self-consistent Hartree-Fock approximation, the local
density of states for different electron crystals in graphene subject to a
strong magnetic field. We investigate both the Wigner crystal and bubble
crystals with M_e electrons per lattice site. The total density of states
consists of several pronounced peaks, the number of which in the negative
energy range coincides with the number of electrons M_e per lattice site, as
for the case of electron-solid phases in the conventional two-dimensional
electron gas. Analyzing the local density of states at the peak energies, we
find particular scaling properties of the density patterns if one fixes the
ratio nu_N/M_e between the filling factor nu_N of the last partially filled
Landau level and the number of electrons per bubble. Although the total density
profile depends explicitly on M_e, the local density of states of the lowest
peaks turns out to be identical regardless the number of electrons M_e. Whereas
these electron-solid phases are reminiscent to those expected in the
conventional two-dimensional electron gas in GaAs heterostructures in the
quantum Hall regime, the local density of states and the scaling relations we
highlight in this paper may be, in graphene, directly measured by spectroscopic
means, such as e.g. scanning tunneling microscopy.",0902.1902v2
2020-05-06,Efficient Learning of a One-dimensional Density Functional Theory,"Density functional theory underlies the most successful and widely used
numerical methods for electronic structure prediction of solids. However, it
has the fundamental shortcoming that the universal density functional is
unknown. In addition, the computational result---energy and charge density
distribution of the ground state---is useful for electronic properties of
solids mostly when reduced to a band structure interpretation based on the
Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can
help to free density functional theory from these limitations. We study a
theory of spinless fermions on a one-dimensional lattice. The density
functional is implicitly represented by a neural network, which predicts,
besides the ground-state energy and density distribution, density-density
correlation functions. At no point do we require a band structure
interpretation. The training data, obtained via exact diagonalization, feeds
into a learning scheme inspired by active learning, which minimizes the
computational costs for data generation. We show that the network results are
of high quantitative accuracy and, despite learning on random potentials,
capture both symmetry-breaking and topological phase transitions correctly.",2005.03014v2
2009-09-12,Quantum Hall effect in dual-gated graphene bilayers with tunable layer density imbalance,"We study the magnetotransport properties of dual-gated graphene bilayers, in
which the total density and layer density imbalance are independently
controlled. As the bilayer is imbalanced we observe the emergence of a quantum
Hall state (QHS) at filling factor $\nu=0$ evinced by a plateau in the Hall
conductivity, consistent with the opening of a gap between the electron and
hole bands. By varying the layer density imbalance at fixed total density, we
observe a suppression of the QHS at filling factors $\nu=8$ and $\nu=12$ when
the layer densities are balanced, an observation at variance with theoretical
expectations in the absence of electron-electron interaction and disorder.",0909.2288v1
2021-02-07,Positive energy density leads to no squeezing,"We consider two kinds of superpositions of squeezed states of light. In the
case of superpositions of first kind, the squeezing and all higher order
squeezing vanishes. However, in the case of the second kind, it is possible to
achieve a maximum amount of squeezing by adjusting the parameters in the
superposition. The emergence and vanishing of squeezing for the superposition
states are explained on the basis of expectation values of the energy density.
We show that expectation values of energy density of quantum states which show
no squeezing will be always positive and that of squeezed states will be
negative for some values of spacetime-dependent phase.",2102.03841v1
2013-03-17,"Localization, disorder and boson peak in an amorphous solid","We demonstrate using the classical density functional theory (DFT) model that
an intermediate degree of mass localization in the amorphous state is essential
for producing the boson peak. The localization length $\ell$ is identified from
the width of the gaussian density profile in terms of which the inhomogeneous
density n(x) of the solid is expressed in DFT. At a fixed average density,
there exists a limiting value $\ell_0$ of $\ell$ signifying a minimum mass
localization in the amorphous state. For more delocalized states
($\ell>\ell_0$) occurrence of boson peak is unfeasible.",1303.4049v1
2016-10-25,Biseparability of 3-qubits density matrices using Hilbert-Schmidt decompositions: Sufficient conditions and explicit expressions,"Hilbert-Schmidt (HS) decompositions and Frobenius norms are used to analyze
biseparability of 3-qubit systems, with particular emphasis on density matrices
with maximally disordered subsystems (MDS) and on the W state mixed with white
noise. The biseparable form of a MDS density matrix is obtained by using the
Bell states of a 2-qubit subsystem, multiplied by density matrices of the third
qubit, which include the relevant HS parameters. Using our methods a sufficient
condition and explicit biseparability of the W state mixed with white noise are
given. They are compared with the sufficient condition for explicit full
separability given in a previous work.",1610.07820v1
2021-03-05,Comparison of the Tetrahedron Method to Smearing Methods for the Electronic Density of States,"The electronic density of states (DOS) highlights fundamental properties of
materials that oftentimes dictate their properties, such as the band gap and
Van Hove singularities. In this short note, we discuss how sharp features of
the density of states can be obscured by smearing methods (such as the Gaussian
and Fermi smearing methods) when calculating the DOS. While the common approach
to reach a ""converged"" density of states of a material is to increase the
discrete k-point mesh density, we show that the DOS calculated by smearing
methods can appear to converge but not to the correct DOS. Employing the
tetrahedron method for Brillouin zone integration resolves key features of the
density of states far better than smearing methods.",2103.03469v1
2023-05-01,Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regression,"Functions of the ratio of the densities $p/q$ are widely used in machine
learning to quantify the discrepancy between the two distributions $p$ and $q$.
For high-dimensional distributions, binary classification-based density ratio
estimators have shown great promise. However, when densities are well
separated, estimating the density ratio with a binary classifier is
challenging. In this work, we show that the state-of-the-art density ratio
estimators perform poorly on well-separated cases and demonstrate that this is
due to distribution shifts between training and evaluation time. We present an
alternative method that leverages multi-class classification for density ratio
estimation and does not suffer from distribution shift issues. The method uses
a set of auxiliary densities $\{m_k\}_{k=1}^K$ and trains a multi-class
logistic regression to classify the samples from $p, q$, and $\{m_k\}_{k=1}^K$
into $K+2$ classes. We show that if these auxiliary densities are constructed
such that they overlap with $p$ and $q$, then a multi-class logistic regression
allows for estimating $\log p/q$ on the domain of any of the $K+2$
distributions and resolves the distribution shift problems of the current
state-of-the-art methods. We compare our method to state-of-the-art density
ratio estimators on both synthetic and real datasets and demonstrate its
superior performance on the tasks of density ratio estimation, mutual
information estimation, and representation learning. Code:
https://www.blackswhan.com/mdre/",2305.00869v1
2023-05-28,Cluster model of 12C in density functional theory framework,"We employ the constrained density functional theory to investigate cluster
phenomena for the $^{12}$C nucleus. The proton and neutron densities are
generated from the placement of three $^{4}$He nuclei (alpha particles)
geometrically. These densities are then used in a density constrained
Hartree-Fock calculation that produces an antisymmetrized state with the same
densities through energy minimization. In the calculations no \textit{a priori}
analytic form for the single-particle states is assumed and the full energy
density functional is utilized. The geometrical scan of the energy landscape
provides the ground state of $^{12}$C as an equilateral triangular
configuration of three alphas with molecular bond like structures. The use of
the nucleon localization function provides further insight to these
configurations. One can conclude that these configurations are a hybrid between
a pure mean-field and a pure alpha particle condensate. This development could
facilitate DFT based fusion calculations with a more realistic $^{12}$C ground
state.",2305.17752v1
2004-06-22,The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states,"We study entanglement properties of mixed density matrices obtained from
combinatorial Laplacians. This is done by introducing the notion of the density
matrix of a graph. We characterize the graphs with pure density matrices and
show that the density matrix of a graph can be always written as a uniform
mixture of pure density matrices of graphs. We consider the von Neumann entropy
of these matrices and we characterize the graphs for which the minimum and
maximum values are attained. We then discuss the problem of separability by
pointing out that separability of density matrices of graphs does not always
depend on the labelling of the vertices. We consider graphs with a tensor
product structure and simple cases for which combinatorial properties are
linked to the entanglement of the state. We calculate the concurrence of all
graph on four vertices representing entangled states. It turns out that for
some of these graphs the value of the concurrence is exactly fractional.",0406165v2
2003-07-11,Quantum states with negative energy density in the Dirac field and quantum inequalities,"Energy densities of the quantum states that are superposition of two
multi-electron-positron states are examined. It is shown that the energy
densities can be negative only when two multi-particle states have the same
number of electrons and positrons or when one state has one more
electron-positron pair than the other. In the cases in which negative energy
could arise, we find that the energy is that of a positive constant plus a
propagating part which oscillates between positive and negative, and the energy
can dip to negative at some places at for a certain period of time if the
quantum states are properly manipulated. It is demonstrated that the negative
energy densities satisfy the quantum inequality. Our results also reveal that
for a given particle content, the detection of negative energy is an operation
that depends on the frame where any measurement is to be performed. This
suggests that the sign of energy density for a quantum state may be a
coordinate-dependent quantity in quantum theory.",0307102v3
2015-05-12,Lyapunov-based Stochastic Nonlinear Model Predictive Control: Shaping the State Probability Density Functions,"Stochastic uncertainties in complex dynamical systems lead to variability of
system states, which can in turn degrade the closed-loop performance. This
paper presents a stochastic model predictive control approach for a class of
nonlinear systems with unbounded stochastic uncertainties. The control approach
aims to shape probability density function of the stochastic states, while
satisfying input and joint state chance constraints. Closed-loop stability is
ensured by designing a stability constraint in terms of a stochastic control
Lyapunov function, which explicitly characterizes stability in a probabilistic
sense. The Fokker-Planck equation is used for describing the dynamic evolution
of the states' probability density functions. Complete characterization of
probability density functions using the Fokker-Planck equation allows for
shaping the states' density functions as well as direct computation of joint
state chance constraints. The closed-loop performance of the stochastic control
approach is demonstrated using a continuous stirred-tank reactor.",1505.02871v1
2016-01-21,First-Principles Equation of State and Electronic Properties of Warm Dense Oxygen,"We perform all-electron path integral Monte Carlo (PIMC) and density
functional theory molecular dynamics (DFT-MD) calculations to explore warm
dense matter states of oxygen. Our simulations cover a wide density-temperature
range of $1-100$~g$\,$cm$^{-3}$ and $10^4-10^9$~K. By combining results from
PIMC and DFT-MD, we are able to compute pressures and internal energies from
first-principles at all temperatures and provide a coherent equation of state.
We compare our first-principles calculations with analytic equations of state,
which tend to agree for temperatures above 8$\times$10$^6$~K. Pair-correlation
functions and the electronic density of states reveal an evolving plasma
structure and ionization process that is driven by temperature and density. As
we increase the density at constant temperature, we find that the ionization
fraction of the 1s state decreases while the other electronic states move
towards the continuum. Finally, the computed shock Hugoniot curves show an
increase in compression as the first and second shells are ionized.",1601.05782v1
2021-12-16,On the Normalization and Density of 1D Scattering States,"The normalization of scattering states is more than a rote step necessary to
calculate expectation values. This normalization actually contains important
information regarding the density of the scattering spectrum (along with useful
details on the bound states). For many applications, this information is more
useful than the wavefunctions themselves. In this paper we show that this
correspondence between scattering state normalization and the density of states
is a consequence of the completeness relation, and we present formulas for
calculating the density of states which are applicable to certain potentials.
We then apply these formulas to the delta function potential and the square
well. We then illustrate how the density of states can be used to calculate the
partition function for a system of two particles with a point-like (delta
potential) interaction.",2112.09108v6
2017-11-03,Density-functional theory for internal magnetic fields,"A density-functional theory is developed based on the Maxwell--Schr\""odinger
equation with an internal magnetic field in addition to the external
electromagnetic potentials. The basic variables of this theory are the electron
density and the total magnetic field, which can equivalently be represented as
a physical current density. Hence, the theory can be regarded as a physical
current-density functional theory and an alternative to the paramagnetic
current density-functional theory due to Vignale and Rasolt. The energy
functional has strong enough convexity properties to allow a formulation that
generalizes Lieb's convex analysis-formulation of standard density-functional
theory. Several variational principles as well as a Hohenberg--Kohn-like
mapping between potentials and ground-state densities follow from the
underlying convex structure. Moreover, the energy functional can be regarded as
the result of a standard approximation technique (Moreau--Yosida
regularization) applied to the conventional Schr\""odinger ground state energy,
which imposes limits on the maximum curvature of the energy (w.r.t.\ the
magnetic field) and enables construction of a (Fr\'echet) differentiable
universal density functional.",1711.01216v1
2024-02-19,Geometric States,"We introduce a special family of distributional alpha-densities and give a
transversality criterion stating when their product is defined, closely related
to Hormander's criterion for general distributions. Moreover, we show that for
the subspace of distributional half-densities in this family the distribution
product naturally yields a pairing that extends the usual one on smooth
half-densities.",2402.11854v1
2008-01-21,Density-induced suppression of the alpha-particle condensate in nuclear matter and the structure of alpha cluster states in nuclei,"At low densities, with decreasing temperatures, in symmetric nuclear matter
alpha-particles are formed, which eventually give raise to a quantum condensate
with four-nucleon alpha-like correlations (quartetting). Starting with a model
of alpha-matter, where undistorted alpha particles interact via an effective
interaction such as the Ali-Bodmer potential, the suppression of the condensate
fraction at zero temperature with increasing density is considered. Using a
Jastrow-Feenberg approach, it is found that the condensate fraction vanishes
near saturation density. Additionally, the modification of the internal state
of the alpha particle due to medium effects will further reduce the condensate.
  In finite systems, an enhancement of the S state wave function of the c.o.m.
orbital of alpha particle motion is considered as the correspondence to the
condensate. Wave functions have been constructed for self-conjugate 4n nuclei
which describe the condensate state, but are fully antisymmetrized on the
nucleonic level. These condensate-like cluster wave functions have been
successfully applied to describe properties of low-density states near the n
alpha threshold. Comparison with OCM calculations in 12C and 16O shows strong
enhancement of the occupation of the S-state c.o.m. orbital of the
alpha-particles. This enhancement is decreasing if the baryon density
increases, similar to the density-induced suppression of the condensate
fraction in alpha matter. The ground states of 12C and 16O show no enhancement
at all, thus a quartetting condensate cannot be formed at saturation densities.",0801.3131v1
2009-06-05,Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method,"The ground-state and low-energy excitations of quantum Hall systems are
studied by the density matrix renormalization group (DMRG) method. From the
ground-state pair correlation functions and low-energy excitions, the
ground-state phase diagram is determined, which consists of incompressible
liquid states, Fermi liquid type compressible liquid states, and many kinds of
CDW states called stripe, bubble and Wigner crystal. The spin transition and
the domain formation are studied at v=2/3. The evolution from composite fermion
liquid state to an excitonic state in bilayer systems is investigated at total
filling factor v=1.",0906.1036v1
2022-10-18,Two-dimensional hydrodynamic simulation for synchronization in coupled density oscillators,"A density oscillator is a fluid system in which oscillatory flow occurs
between different density fluids through the pore connecting them. We
investigate the synchronization in coupled density oscillators using
two-dimensional hydrodynamic simulation and analyze the stability of the
synchronous state based on the phase reduction theory. Our results show that
the anti-phase, three-phase, and 2-2 partial-in-phase synchronization modes
spontaneously appear as stable states in two, three, and four coupled
oscillators, respectively. The phase dynamics of coupled density oscillators is
interpreted with their sufficiently large first Fourier components of the phase
coupling function.",2210.09762v2
1999-08-12,Spatial structure of an incompressible Quantum Hall strip,"The incompressible Quantum Hall strip is sensitive to charging of localized
states in the cyclotron gap. We study the effect of localized states by a
density functional approach and find electron density and the strip width as a
function of the density of states in the gap. Another important effect is
electron exchange. By using a model density functional which accounts for
negative compressibility of the QH state, we find electron density around the
strip. At large exchange, the density profile becomes nonmonotonic, indicating
formation of a 1D Wigner crystal at the strip edge. Both effects, localized
states and exchange, lead to a substantial increase of the strip width.",9908187v1
2011-09-26,"First-principles calculations of phonon and thermodynamic properties of AlRE (RE= Y, Gd, Pr, Yb) intermetallic compounds","The phonon and thermodynamic properties of rare-earth-aluminum intermetallics
AlRE (RE=Y, Gd, Pr, Yb) with B2-type structure are investigated by performing
density functional theory and density functional perturbation theory within the
quasiharmonic approximation. The phonon spectra and phonon density of states,
including the phonon partial density of states and total density of states,
have been discussed. Our results demonstrate that the density of states is
mostly composed of Al states at the high frequency. The temperature dependence
of various quantities such as the thermal expansions, the heat capacities at
constant volume and constant pressure, the isothermal bulk modulus, and the
entropy are obtained. The electronic contribution to the specific heat is
discussed, and the presented results show that the thermal electronic
excitation affecting the thermal properties is inessential.",1109.5451v1
2009-05-17,Gaps and tails in graphene and graphane,"We study the density of states in monolayer and bilayer graphene in the
presence of a random potential that breaks sublattice symmetries. While a
uniform symmetry-breaking potential opens a uniform gap, a random
symmetry-breaking potential also creates tails in the density of states. The
latter can close the gap again, preventing the system to become an insulator.
However, for a sufficiently large gap the tails contain localized states with
nonzero density of states. These localized states allow the system to conduct
at nonzero temperature via variable-range hopping. This result is in agreement
with recent experimental observations in graphane by Elias {\it et al.}.",0905.2766v1
2023-04-26,Controlled density transport using Perron Frobenius generators,"We consider the problem of the transport of a density of states from an
initial state distribution to a desired final state distribution through a
dynamical system with actuation. In particular, we consider the case where the
control signal is a function of time, but not space; that is, the same
actuation is applied at every point in the state space. This is motivated by
several problems in fluid mechanics, such as mixing and manipulation of a
collection of particles by a global control input such as a uniform magnetic
field, as well as by more general control problems where a density function
describes an uncertainty distribution or a distribution of agents in a
multi-agent system. We formulate this problem using the generators of the
Perron-Frobenius operator associated with the drift and control vector fields
of the system. By considering finite-dimensional approximations of these
operators, the density transport problem can be expressed as a control problem
for a bilinear system in a high-dimensional, lifted state. With this system, we
frame the density control problem as a problem of driving moments of the
density function to the moments of a desired density function, where the
moments of the density can be expressed as an output which is linear in the
lifted state. This output tracking problem for the lifted bilinear system is
then solved using differential dynamic programming, an iterative trajectory
optimization scheme.",2304.13829v2
2013-04-27,Nuclear state densities of odd-mass heavy nuclei in the shell model Monte Carlo approach,"While the shell model Monte Carlo approach has been successful in the
microscopic calculation of nuclear state densities, it has been difficult to
calculate accurately state densities of odd-even heavy nuclei. This is because
the projection on an odd number of particles in the shell model Monte Carlo
method leads to a sign problem at low temperatures, making it impractical to
extract the ground-state energy in direct Monte Carlo calculations. We show
that the ground-state energy can be extracted to a good precision by using
level counting data at low excitation energies and the neutron resonance data
at the neutron threshold energy. This allows us to extend recent applications
of the shell-model Monte Carlo method in even-even rare-earth nuclei to the
odd-even isotopic chains of $^{149-155}$Sm and $^{143-149}$Nd. We calculate the
state densities of the odd-even samarium and neodymium isotopes and find close
agreement with the state densities extracted from experimental data.",1304.7405v1
2019-08-28,Infinite invariant density in a semi-Markov process with continuous state variables,"We report on a fundamental role of a non-normalized formal steady state,
i.e., an infinite invariant density, in a semi-Markov process where the state
is determined by the inter-event time of successive renewals. The state
describes certain observables found in models of anomalous diffusion, e.g., the
velocity in the generalized L\'evy walk model and the energy of a particle in
the trap model. In our model, the inter-event-time distribution follows a
fat-tailed distribution, which makes the state value more likely to be zero
because long inter-event times imply small state values. We find two scaling
laws describing the density for the state value, which accumulates in the
vicinity of zero in the long-time limit. These laws provide universal behaviors
in the accumulation process and give the exact expression of the infinite
invariant density. Moreover, we provide two distributional limit theorems for
time-averaged observables in these non-stationary processes. We show that the
infinite invariant density plays an important role in determining the
distribution of time averages.",1908.10501v2
2004-07-26,Mapping from current densities to vector potentials in time-dependent current-density functional theory,"We show that the time-dependent particle density $n(\vec r,t)$ and the
current density ${\vec j}(\vec r,t)$ of a many-particle system that evolves
under the action of external scalar and vector potentials $V(\vec r,t)$ and
$\vec A(\vec r,t)$ and is initially in the quantum state $|\psi (0)>$, can
always be reproduced (under mild assumptions) in another many-particle system,
with different two-particle interaction, subjected to external potentials
$V'(\vec r,t)$ and $\vec A'(\vec r,t)$, starting from an initial state $|\psi'
(0)>$, which yields the same density and current as $|\psi (0)>$. Given the
initial state of this other many-particle system, the potentials $V'(\vec r,t)$
and $\vec A'(\vec r,t)$ are uniquely determined up to gauge transformations
that do not alter the initial state. As a special case, we obtain a new and
simpler proof of the Runge-Gross theorem for time-dependent current density
functional theory. This theorem provides a formal basis for the application of
time-dependent current density functional theory to transport problems.",0407682v1
2002-11-06,Low Mass Neutron Stars and the Equation of State of Dense Matter,"Neutron-star radii provide useful information on the equation of state of
neutron rich matter. Particularly interesting is the density dependence of the
equation of state (EOS). For example, the softening of the EOS at high density,
where the pressure rises slower than anticipated, could signal a transition to
an exotic phase. However, extracting the density dependence of the EOS requires
measuring the radii of neutron stars for a broad range of masses. A ``normal''
1.4 solar mass neutron star has a central density of a few times nuclear-matter
saturation density. In contrast, low mass (of the order of 0.5 solar masses)
neutron stars have central densities near nuclear-matter saturation density so
its radius provides information on the EOS at low density. Unfortunately,
low-mass stars are rare because they may be hard to form. Instead, a precision
measurement of nuclear radii on atomic nuclei may contain similar information.
Indeed, we find a strong correlation between the neutron radius of 208Pb and
the radius of a 0.5 solar-mass neutron star. Thus, the radius of such a neutron
star can be inferred from a measurement of the the neutron radius of 208Pb.
Comparing this value to the measured radius of a 1.4 solar-mass neutron star
should provide the strongest constraint to date on the density dependence of
the equation of state.",0211015v1
2013-02-26,Electronic and optical properties of carbon nanodisks and nanocones,"A theoretical study of the electronic properties of nanodisks and nanocones
is presented within the framework of a tight-binding scheme. The electronic
densities of states and absorption coefficients are calculated for such
structures with different sizes and topologies. A discrete position
approximation is used to describe the electronic states taking into account the
effect of the overlap integral to first order. For small finite systems, both
total and local densities of states depend sensitively on the number of atoms
and characteristic geometry of the structures. Results for the local densities
of charge reveal a finite charge distribution around some atoms at the apices
and borders of the cone structures. For structures with more than 5000 atoms,
the contribution to the total density of states near the Fermi level
essentially comes from states localized at the edges. For other energies the
average density of states exhibits similar features to the case of a graphene
lattice. Results for the absorption spectra of nanocones show a peculiar
dependence on the photon polarization in the infrared range for all
investigated structures.",1302.6568v1
2008-03-06,Finite doping of a one-dimensional charge density wave: solitons vs. Luttinger liquid charge density,"The effects of doping on a one-dimensional wire in a charge density wave
state are studied using the density-matrix renormalization group method. We
show that for a finite number of extra electrons the ground state becomes
conducting but the particle density along the wire corresponds to a charge
density wave with an incommensurate wave number determined by the filling. We
find that the absence of the translational invariance can be discerned even in
the thermodynamic limit, as long as the number of doping electrons is finite.
Luttinger liquid behavior is reached only for a finite change in the electron
filling factor, which for an infinite wire corresponds to the addition of an
infinite number of electrons. In addition to the half filled insulating Mott
state and the conducting states, we find evidence for subgap states at fillings
different from half filling by a single electron or hole. Finally, we show that
by coupling our system to a quantum dot, one can have a discontinuous
dependence of its population on the applied gate voltage in the thermodynamic
limit, similarly to the one predicted for a Luttinger liquid without umklapp
processes.",0803.0821v1
2018-01-02,Evaluation of two-photon polarization density matrix of polarization-entangled photon-pairs generated through biexciton resonant hyper-parametric scattering,"We have investigated the excitation-power dependence of
polarization-entangled photon-pairs generated from a CuCl single crystal using
biexciton resonant hyper-parametric scattering. The measured two-photon
polarization density matrix which corresponds to the two-photon polarization
state changes with increasing the excitation power. The evaluation of the
tangle and the linear entropy obtained from the measured density matrix
indicates that the two-photon polarization density matrix can be expressed as
the mixed state of an ideal state and a totally mixed state, and the mixture
ratio of the totally mixed state increases as the excitation density increases.
The variations of the density matrix and the mixture ratio with the excitation
power originate from the generation of the multiple photon pairs.",1801.00596v1
2022-06-29,Configurational density of states and melting of simple solids,"We analyze the behavior of the microcanonical and canonical caloric curves
for a piecewise model of the configurational density of states of simple
solids, in the context of melting from the superheated state, as realized
numerically in the Z-method via atomistic molecular dynamics. A first-order
phase transition with metastable regions is reproduced by the model, being
therefore useful to describe aspects of the melting transition. Within this
model, transcendental equations connecting the superheating limit, the melting
point, and the specific heat of each phase are presented and numerically
solved. Our results suggest that the essential elements of the microcanonical Z
curves can be extracted from simple modeling of the configurational density of
states.",2206.14877v1
2022-01-27,Broadened Yu-Shiba-Rusinov states in dirty superconducting films and heterostructures,"The interplay of a potential and magnetic disorder in superconductors remains
an active field of research for decades. Within the framework of the Usadel
equation, we study the local density of states near a solitary classical
magnetic impurity in a dirty superconducting film. We find that a potential
disorder results in broadening of the delta-function in the local density of
states at the Yu-Shiba-Rusinov (YSR) energy. This broadening is proportional to
the square root of a normal-state spreading resistance of the film. We
demonstrate that mesoscopic fluctuations caused by a potential disorder affect
crucially a profile of the local density of states in the vicinity of the YSR
energy. In addition, we demonstrate that a scanning-tunneling-microscopy tip
can mask an YSR feature in the local density of states. Also, we study the
local density of states near a chain of magnetic impurities situated in the
normal region of a dirty superconductor/normal-metal junction. We find a
resonance in the local density of states near the YSR energy. The energy scale
of the resonant peak is controlled by the square root of the film resistance
per square in the normal state.",2201.11723v2
2005-07-12,Cluster Formation and The Virial Equation of State of Low-Density Nuclear Matter,"We present the virial equation of state of low-density nuclear matter
composed of neutrons, protons and alpha particles. The virial equation of state
is model-independent, and therefore sets a benchmark for all nuclear equations
of state at low densities. We calculate the second virial coefficients for
nucleon-nucleon, nucleon-alpha and alpha-alpha interactions directly from the
relevant binding energies and scattering phase shifts. The virial approach
systematically takes into account contributions from bound nuclei and the
resonant continuum, and consequently provides a framework to include
strong-interaction corrections to nuclear statistical equilibrium models. The
virial coefficients are used to make model-independent predictions for a
variety of properties of nuclear matter over a range of densities, temperatures
and compositions. Our results provide constraints on the physics of the
neutrinosphere in supernovae. The resulting alpha particle concentration
differs from all equations of state currently used in supernova simulations.
Finally, the virial equation of state greatly improves our conceptual
understanding of low-density nuclear matter.",0507033v2
2002-03-25,Separability and correlations in composite states based on entropy methods,"This work is an enquiry into the circumstances under which entropy methods
can give an answer to the questions of both quantum separability and classical
correlations of a composite state. Several entropy functionals are employed to
examine the entanglement and correlation properties guided by the corresponding
calculations of concurrence. It is shown that the entropy difference between
that of the composite and its marginal density matrices may be of arbitrary
sign except under special circumstances when conditional probability can be
defined appropriately. This ambiguity is a consequence of the fact that the
overlap matrix elements of the eigenstates of the composite density matrix with
those of its marginal density matrices also play important roles in the
definitions of probabilities and the associated entropies, along with their
respective eigenvalues. The general results are illustrated using pure and
mixed state density matrices of two-qubit systems. Two classes of density
matrices are found for which the conditional probability can defined: (1)
density matrices with commuting decompositions and (2) those which are
decohered in the representation where the density matrices of the marginals are
diagonal. The first class of states encompass those whose separability is
currently understood as due to particular symmetries of the states. The second
are a new class of states which are expected to be useful for understanding
separability. Examples of entropy functionals of these decohered states
including the crucial isospectral case are discussed.",0203124v1
2021-05-18,"Spatial order in a two-dimensional spin-orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation","We demonstrate the formation of stable spatially-ordered states in a {\it
uniform} and also {\it trapped} quasi-two-dimensional (quasi-2D) Rashba or
Dresselhaus spin-orbit (SO) coupled pseudo spin-1/2 Bose-Einstein condensate
using the mean-field Gross-Pitaevskii equation. For weak SO coupling, one can
have a circularly-symmetric $(0,+1)$- or $(0,-1)$-type multi-ring state with
intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where
the numbers in the parentheses denote the net angular momentum projection in
the two components, in addition to a circularly-asymmetric degenerate state
with zero net angular momentum projection. For intermediate SO couplings, in
addition to the above two types, one can also have states with stripe pattern
in component densities with no periodic modulation in total density. The stripe
state continues to exist for large SO coupling. In addition, a new
spatially-periodic state appears in the uniform system: a superlattice state,
possessing some properties of a supersolid, with a square-lattice pattern in
component densities and also in total density. In a trapped system the
superlattice state is slightly different with multi-ring pattern in component
density and a square-lattice pattern in total density. For an equal mixture of
Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only
stripe states are found for all strengths of SO couplings. In a uniform system
all these states are quasi-2D solitonic states.",2105.08849v3
2006-05-08,A Renormalisation-Group Algorithm for Eigenvalue Density Functions of Interacting Quantum Systems,"We present a certifiable algorithm to calculate the eigenvalue density
function -- the number of eigenvalues within an infinitesimal interval -- for
an arbitrary 1D interacting quantum spin system. Our method provides an
arbitrarily accurate numerical representation for the smeared eigenvalue
density function, which is the convolution of the eigenvalue density function
with a gaussian of prespecified width. In addition, with our algorithm it is
possible to investigate the density of states near the ground state. This can
be used to numerically determine the size of the ground-state energy gap for
the system to within a prespecified confidence interval. Our method exploits a
finitely correlated state/matrix product state representation of the propagator
and applies equally to disordered and critical interacting 1D quantum spin
systems. We illustrate our method by calculating an approximation to the
eigenvalue density function for a random antiferromagnetic Heisenberg model.",0605194v1
2018-10-19,Monopole Charge Density Wave States in Weyl Semimetals,"We study a new class of topological charge density wave states exhibiting
monopole harmonic symmetries. The density-wave ordering is equivalent to
pairing in the particle-hole channel due to Fermi surface nesting under
interactions. When electron and hole Fermi surfaces carry different Chern
numbers, the particle-hole pairing exhibits a non-trivial Berry phase inherited
from band structure topology independent of concrete density-wave ordering
mechanism. The associated density-wave gap functions become nodal, and the net
nodal vorticity is determined by the monopole charge of the pairing Berry
phase. The gap function nodes become zero-energy Weyl nodes of the bulk spectra
of quasi-particle excitations. These states can occur in doped Weyl semimetals
with nested electron and hole Fermi surfaces enclosing Weyl nodes of the same
chirality in the weak coupling regime. Topologically non-trivial low-energy
Fermi arc surface states appear in the density-wave ordering state as a
consequence of the emergent zero-energy Weyl nodes.",1810.08715v2
1998-12-09,On the Disentanglement of States,"Disentanglement is the process which transforms a state $\rho$ of two
subsystems into an unentangled state, while not effecting the reduced density
matrices of each of the two subsystems. Recently Terno showed that an arbitrary
state cannot be disentangled into a tensor product of its reduced density
matrices. In this letter we present various novel results regarding
disentanglement of states. Our main result is that there are sets of states
which cannot be successfuly disentangled (not even into a separable state).
Thus, we prove that a universal disentangling machine cannot exist.",9812020v1
2000-06-19,Anomalous peak in the superconducting condensate density of cuprate high T_{c} superconductors at a unique critical doping state,"The doping dependence of the superconducting condensate density, n_{s}^{o},
has been studied by muon-spin-rotation for
Y_{0.8}Ca_{0.2}Ba_{2}(Cu_{1-z}Zn_{z})_{3}O_{7-\delta} and
Tl_{0.5-y}Pb_{0.5+y}Sr_{2}Ca_{1-x}Y_{x}Cu_{2}O_{7}. We find that n_{s}^{o}
exhibits a pronounced peak at a unique doping state in the slightly overdoped
regime. Its position coincides with the critical doping state where the normal
state pseudogap first appears depleting the electronic density of states. A
surprising correlation between n_{s}^{o} and the condensation energy U_{o} is
observed which suggests unconventional behavior even in the overdoped region.",0006288v1
2009-09-08,Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene,"Recent experiments have demonstrated that neutral graphene sheets have an
insulating ground state in the presence of an external magnetic field. We
report on a $\pi$-band tight-binding-model Hartree-Fock calculation which
examines the competition between distinct candidate insulating ground states.
We conclude that for graphene sheets on substrates the ground state is most
likely a field-induced spin-density-wave, and that a charge density wave state
is possible for suspended samples. Neither of these density-wave states support
gapless edge excitations.",0909.1362v1
1996-01-07,Enhancement of the tunneling density of states in Tomonaga--Luttinger Liquids,"We have calculated the tunneling density of states (DOS) at the location of a
backward scattering defect for quantum wires and for edge state electrons in
quantum Hall systems. A singular enhancement of the DOS arises as a result of
the combined effect of multiple backward scattering together with a repulsive
electron---electron interaction.",9601020v1
2005-12-22,Multiparticle entanglement and ranks of density matrices,"Based on the ranks of reduced density matrices, we derive necessary
conditions for the separability of multiparticle arbitrary-dimensional mixed
states, which are equivalent to sufficient conditions for entanglement. In a
similar way we obtain necessary conditions for the separability of a given
mixed state with respect to partitions of all particles of the system into
subsets. The special case of pure states is discussed separately.",0512199v1
2010-10-11,Detecting entanglement of states by entries of their density matrices,"For any bipartite systems, a universal entanglement witness of rank-4 for
pure states is obtained and a class of finite rank entanglement witnesses is
constructed. In addition, a method of detecting entanglement of a state only by
entries of its density matrix with respect to some product basis is obtained.",1010.2078v2
2019-10-25,Experimental study on the bifurcation of a density oscillator depending on density difference,"Hydrodynamic instabilities often cause spatio-temporal pattern formations and
transitions between them. We investigate a model experimental system, a density
oscillator, where the bifurcation from a resting state to an oscillatory state
is triggered by the increase in the density difference of the two fluids. Our
results show that the oscillation amplitude increases from zero and the period
decreases above a critical density difference. The detailed data close to the
bifurcation point provide a critical exponent consistent with the supercritical
Hopf bifurcation.",1910.11573v2
2006-02-03,Density-to-potential map in time-independent excited-state density-functional theory,"In light of the recent work by Sahni et al., Harbola, and Gaudoin and Burke,
the question of mapping from an excited-state density of a many-electron
interacting system to the potential of the related non-interacting system is
analyzed. To do so, we investigate the Levy-Nagy criterion quantitatively for
several excited-states. Our work indicates that Levy-Nagy criterion may fix the
density to potential map uniquely.",0602065v1
2009-01-08,Combinatorial nuclear level-density model,"A microscopic nuclear level-density model is presented. The model is a
completely combinatorial (micro-canonical) model based on the folded-Yukawa
single-particle potential and includes explicit treatment of pairing,
rotational and vibrational states. The microscopic character of all states
enables extraction of level distribution functions with respect to pairing
gaps, parity and angular momentum. The results of the model are compared to
available experimental data: neutron separation energy level spacings, data on
total level-density functions from the Oslo method, cumulative level densities
from low-lying discrete states, and data on parity ratios.",0901.1087v2
2019-01-11,Bayesian Smoothing for the Extended Object Random Matrix Model,"The random matrix model is popular in extended object tracking, due to its
relative simplicity and versatility. In this model, the extended object state
consists of a kinematic vector for the position and motion parameters
(velocity, etc), and an extent matrix. Two versions of the model can be found
in literature, one where the state density is modelled by a conditional
density, and one where the state density is modelled by a factorized density.
In this paper, we present closed form Bayesian smoothing expression for both
the conditional and the factorised model. In a simulation study, we compare the
performance of different versions of the smoother.",1901.05301v1
1999-12-11,Total energy density as an interpretative tool,"We present an unambiguous formulation for the total energy density within
density-functional theory. We propose that it be used as a tool for the
interpretation of computed energy and electronic structure changes during
structural transformations and chemical reactions, augmenting the present use
of electron density changes and changes in the Kohn-Sham local density of
states and Kohn-Sham energy density.",9912202v1
2009-12-16,Reduced density-matrix functional theory in quantum Hall systems,"We apply reduced density-matrix functional theory to the parabolically
confined quantum Hall droplet in the spin-frozen strong magnetic field regime.
One-body reduced density matrix functional method performs remarkably well in
obtaining ground states, energies, and observables derivable from the one-body
reduced density matrix for a wide range of system sizes. At the strongly
correlated regime, the results go well beyond what can be obtained with the
density functional theory. However, some of the detailed properties of the
system, such as the edge Green's function, are not produced correctly unless we
use the much heavier two-body reduced density matrix method.",0912.3154v2
2000-08-08,Density of states and electron concentration of double heterojunctions subjected to an in-plane magnetic field,"We calculate the electronic states of
Al$_x$Ga$_{1-x}$As/GaAs/Al$_x$Ga$_{1-x}$As double heterojunctions subjected to
a magnetic field parallel to the quasi two-dimensional electron gas. We study
the energy dispersion curves, the density of states, the electron concentration
and the distribution of the electrons in the subbands. The parallel magnetic
field induces severe changes in the density of states, which are of crucial
importance for the explanation of the magnetoconductivity in these structures.
However, to our knowledge, there is no systematic study of the density of
states under these circumstances. We attempt a contribution in this direction.
For symmetric heterostructures, the depopulation of the higher subbands, the
transition from a single to a bilayer electron system and the domination of the
bulk Landau levels in the centre the wide quantum well, as the magnetic field
is continuously increased, are presented in the ``energy dispersion picture''
as well as in the ``electron concentration picture'' and in the ``density of
states picture''.",0008131v1
2015-12-06,Spectral properties of reduced fermionic density operators and parity superselection rule,"We consider pure fermionic states with a varying number of quasiparticles and
analyze two types of reduced density operators: one is obtained via tracing out
modes, the other is obtained via tracing out particles. We demonstrate that
spectra of mode-reduced states are not identical in general and fully
characterize pure states with equispectral mode-reduced states. Such states are
related via local unitary operations with states satisfying the parity
superselection rule. Thus, valid purifications for fermionic density operators
are found. To get particle-reduced operators for a general system, we introduce
the operation $\Phi(\varrho) = \sum_i a_i \varrho a_i^{\dag}$. We conjecture
that spectra of $\Phi^p(\varrho)$ and conventional $p$-particle reduced density
matrix $\varrho_p$ coincide. Nontrivial generalized Pauli constraints are
derived for states satisfying the parity superselection rule.",1512.01828v2
2021-09-21,Ultrafast excitation and topological soliton formation in incommensurate charge density wave states,"Topological soliton is a nonperturbative excitation in commensurate density
wave states and connects degenerate ground states. In incommensurate density
wave states, ground states are continuously degenerate and topological soliton
is reckoned to be smoothly connected to the perturbative phason excitation. We
study the ultrafast nonequilibrium dynamics due to photoexcited electron-hole
pair in a one-dimensional chain with an incommensurate charge density wave
ground state. Time-resolved evolution reveals both perturbative excitation of
collective modes and nonperturbative topological phase transition due to
creating novel topological solitons, where the continuous complex order
parameter with amplitude and phase is essential. We identify the nontrivial
phase-winding solitons in the complex plane unique to this nonequilibrium state
and capture it by a low-energy effective model. The perturbative temporal gap
oscillation and the solitonic in-gap states enter the optical conductivity
absorption edge and the spectral density related to spectroscopic measurement,
providing concrete connections to real experiments.",2109.09895v1
2003-12-05,High magnetic field induced charge density wave states in a quasi-one dimensional organic conductor,"We have measured the high field magnetoresistence and magnetization of
quasi-one- dimensional (Q1D) organic conductor (Per)2Pt(mnt)2 (where Per =
perylene and mnt = maleonitriledithiolate), which has a charge density wave
(CDW) ground state at zero magnetic field below 8 K. We find that the CDW
ground state is suppressed with moderate magnetic fields of order 20 T, as
expected from a mean field theory treatment of Pauli effects[W. Dieterich and
P. Fulde, Z. Physik 265, 239 - 243 (1973)]. At higher magnetic fields, a new,
density wave state with sub-phases is observed in the range 20 to 50 T, which
is reminiscent of the cascade of field induced, quantized, spin density wave
phases (FISDW) observed in the Bechgaard salts. The new density wave state,
which we tenatively identify as a field induced charge density wave state
(FICDW), is re-entrant to a low resistance state at even higher fields, of
order 50 T and above. Unlike the FISDW ground state, the FICDW state is only
weakly orbital, and appears for all directions of magnetic field. Our findings
are substantiated by electrical resistivity, magnetization, thermoelectric, and
Hall measurements. We discuss our results in light of theoretical work
involving magnetic field dependent Q1D CDW ground states in high magnetic
fields [D. Zanchi, A. Bjelis, and G. Montambaux, Phys. Rev. B 53, (1996)1240;
A. Lebed, JETP Lett. 78,138(2003)].",0312172v1
2009-10-08,State price density estimation via nonparametric mixtures,"We consider nonparametric estimation of the state price density encapsulated
in option prices. Unlike usual density estimation problems, we only observe
option prices and their corresponding strike prices rather than samples from
the state price density. We propose to model the state price density directly
with a nonparametric mixture and estimate it using least squares. We show that
although the minimization is taken over an infinitely dimensional function
space, the minimizer always admits a finite dimensional representation and can
be computed efficiently. We also prove that the proposed estimate of the state
price density function converges to the truth at a ``nearly parametric'' rate.",0910.1430v1
2010-09-06,Information geometry of density matrices and state estimation,"Given a pure state vector |x> and a density matrix rho, the function
p(x|rho)=<x|rho|x> defines a probability density on the space of pure states
parameterised by density matrices. The associated Fisher-Rao information
measure is used to define a unitary invariant Riemannian metric on the space of
density matrices. An alternative derivation of the metric, based on square-root
density matrices and trace norms, is provided. This is applied to the problem
of quantum-state estimation. In the simplest case of unitary parameter
estimation, new higher-order corrections to the uncertainty relations,
applicable to general mixed states, are derived.",1009.1115v2
2019-04-05,Probability representation of quantum channels,"Using the known possibility to associate the completely positive maps with
density matrices and recent results on expressing the density matrices with
sets of classical probability distributions of dichotomic random variables we
construct the probability representation of the completely positive maps. In
this representation, any completely positive map of qudit state density matrix
is identified with the set of classical coin probability distributions.
Examples of the maps of qubit states are studied in detail. The evolution
equation of quantum states is written in the form of the classical-like kinetic
equation for probability distributions identified with qudit state.",1904.03036v2
2012-09-22,Density functional approaches to atomic nuclei,"Nuclear mean-field models are briefly reviewed to illustrate its foundation
and necessity of state dependence in effective interactions. This state
dependence is successfully taken into account by the density dependence,
leading to the energy density functional. Recent results for photoabsorption
cross sections in spherical and deformed Nd isotopes are shown.",1209.4966v1
2011-04-05,Determination of electron density and filling factor for soft X-ray flare kernels,"In a standard method of determining electron density for soft X-ray (SXR)
flare kernels it is necessary to assume what is the extension of a kernel along
the line of sight. This is a source of significant uncertainty of the obtained
densities. In our previous paper (Bak-Steslicka and Jakimiec, 2005) we have
worked out another method of deriving electron density, in which it is not
necessary to assume what is the extension of a kernel along the line of sight.
The point is that many flares, during their decay phase, evolve along the
sequence of steady-state models [quasi-steady-state (QSS) evolution] and then
the scaling law, derived for steady-state models, can be used to determine the
electron density. The aim of the present paper is: (1) to improve the two
methods of density determination, (2) to compare the densities obtained with
the two methods. We have selected a number of flares which showed QSS evolution
during the decay phase. For these flares the electron density, N, has been
derived by means of standard method and with our QSS method. Comparison of the
N values obtained with the two different methods allowed us: (1) to test the
obtained densities, (2) to evaluate the volume filling factor of the SXR
emitting plasma. Generally, we have found good agreement (no large systematic
difference) between the values of electron density obtained with the two
methods, but for some cases the values can differ by a factor up to 2. For most
flare kernels estimated filling factor turned out to be about 1, near the flare
maximum.",1104.0845v1
2005-02-16,First-principles study on scanning tunneling microscopy images of hydrogen-terminated Si(110) surfaces,"Scanning tunneling microscopy images of hydrogen-terminated Si(110) surfaces
are studied using first-principles calculations. Our results show that the
calculated filled-state images and local density of states are consistent with
recent experimental results, and the empty-state images appear significantly
different from the filled-state ones. To elucidate the origin of this
difference, we examined in detail the local density of states, which affects
the images, and found that the bonding and antibonding states of surface
silicon atoms largely affect the difference between the filled- and empty-state
images.",0502381v1
1996-10-08,Nuclear Density-Dependent Effective Coupling Constants in the Mean-Field Theory,"It is shown that the equation of state of nuclear matter can be determined
within the mean-field theory of $\sigma \omega$ model provided only that the
nucleon effective mass curve is given. We use a family of the possible nucleon
effective mass curves that reproduce the empirical saturation point in the
calculation of the nuclear binding energy curves in order to obtain
density-dependent effective coupling constants. The resulting density-dependent
coupling constants may be used to study a possible equation of state of nuclear
system at high density or neutron matter. Within the constraints used in this
paper to $M^*$ of nuclear matter at saturation point and zero density, neutron
matter of large incompressibility is strongly bound at high density while soft
neutron matter is weakly bound at low density. The study also exhibits the
importance of surface vibration modes in the study of nuclear equation of
state.",9610010v1
2024-03-04,Spatially dispersing in-gap states induced by Andreev tunneling through single electronic state,"By using low-temperature scanning tunneling microscopy and spectroscopy
(STM/STS), we observe superconducting in-gap states induced by Andreev
tunneling through single impurity state in a low-carrier-density superconductor
(NaAlSi). The energy-symmetric in-gap states appear when the impurity state is
located within the superconducting gap. Superconducting in-gap states can cross
the Fermi level, and show X-shaped spatial dispersion. We interpret the in-gap
states as a consequence of the Andreev tunneling through the impurity state,
which involves the formation or breakup of a Cooper pair. Due to the low
carrier density in NaAlSi, the in-gap state is tunable by controlling the STM
tip-sample distance. Under strong external magnetic fields, the impurity state
shows Zeeman splitting when it is located near the Fermi level. Our findings
not only demonstrate the Andreev tunneling involving single electronic state,
but also provide new insights for understanding the spatially dispersing in-gap
states in low-carrier-density superconductors.",2403.01949v1
2007-02-16,Effective density of states profiles of heterogeneous microcrystalline silicon,"The steady state photoconductivity as a function of temperature and light
intensity was measured on plasma deposited highly crystalline undoped
hydrogenated microcrystalline silicon films possessing different thicknesses
and microstructures. Different phototransport behaviors were observed
experimentally in films having dissimilar microstructural attributes. This has
been explained by numerical modeling to link these behaviors to different
features of the proposed density of states maps of the material.",0702380v1
2013-10-22,Impurity Effect on the Local Density of States around a Vortex in Noncentrosymmetric Superconductors,"We numerically study the effect of non-magnetic impurities on the vortex
bound states in noncentrosymmetric systems. The local density of states (LDOS)
around a vortex is calculated by means of the quasiclassical Green's function
method. We find that the zero energy peak of the LDOS splits off with
increasing the impurity scattering rate.",1310.5851v1
2017-02-02,Universality of density of states in configuration space,"In this study, we confirm the universality of density of microscopic states
in non-interacting system; this means statistical interdependence is vanished
in any lattices. This enable one to obtain information of configuration of
solute atoms, free energy, phase diagram with performing first-principles
calculation on few special microscopic states combined with our established
theory.",1702.00543v1
2009-02-25,Superposition rule and entanglement in diagonal and probability representations of density states,"The quasidistributions corresponding to the diagonal representation of
quantum states are discussed within the framework of operator-symbol
construction. The tomographic-probability distribution describing the quantum
state in the probability representation of quantum mechanics is reviewed. The
connection of the diagonal and probability representations is discussed. The
superposition rule is considered in terms of the density-operator symbols. The
separability and entanglement properties of multipartite quantum systems are
formulated as the properties of the density-operator symbols of the system
states.",0902.4351v1
1997-05-30,Phase separation in the neutral Falicov-Kimball model,"The Falicov-Kimball model consists of spinless electrons and classical
particles (ions) on a lattice. The electrons hop between nearest neighbor sites
while the ions do not. We consider the model with equal numbers of ions and
electrons and with a large on-site attractive force between ions and electrons.
For densities 1/4 and 1/5 the ion configuration in the ground state had been
proved to be periodic. We prove that for density 2/9 it is periodic as well.
However, for densities between 1/4 and 1/5 other than 2/9 we prove that the ion
configuration in the ground state is not periodic. Instead there is phase
separation. For densities in (1/5,2/9) the ground state ion configuration is a
mixture of the density 1/5 and 2/9 ground state ion configurations. For the
interval (2/9,1/4) it is a mixture of the density 2/9 and 1/4 ground states.",9705315v1
2000-06-02,Charge Current Density from the Scattering Matrix,"A method to derive the charge current density and its quantum mechanical
correlation from the scattering matrix is discussed for quantum scattering
systems described by a time-dependent Hamiltonian operator. The current density
and charge density are expressed with the help of functional derivatives with
respect to the vector potential and the electric potential. A condition imposed
by the requirement that these local quantities are gauge invariant is
considered. Our formulas lead to a direct relation between the local density of
states and the total current density at a given energy. To illustrate the
results we consider, as an example, a chiral ladder model.",0006031v1
2009-04-15,Carrier Density and Magnetism in Graphene Zigzag Nanoribbons,"The influence of carrier density on magnetism in a zigzag graphene nanoribbon
is studied in a $\pi$-orbital Hubbard-model mean-field approximation.
Departures from half-filling alter the magnetism, leading to states with charge
density variation across the ribbon and parallel spin-alignment on opposite
edges. Finite carrier densities cause the spin-density near the edges to
decrease steadily, leading eventually to the absence of magnetism. At low
doping densities the system shows a tendency to multiferroic order in which
edge charges and spins are simultaneously polarized.",0904.2396v2
1999-09-16,Effect of Excluded Volume and Anisotropy on Granular Statistics: 'Fermi Statistics' and Condensation,"We explore the consequences of the excluded volume interaction of hard
spheres at high densities and present a theory for excited granular materials.
We first demonstrate that, in the presence of gravity, the granular density
crosses over from Boltzmann to Fermi statistics, when temperature is decreased
in the weak excitation limit. Comparisons of numerical simulations with our
predictions concerning the scaling behavior of temperature with agitation
frequency, gravity and particle-diameter show satisfying agreement. Next,
within the framework of the Enskog theory of hard spheres, we interpret this
crossover as a 'condensation' of hard spheres from the dilute gas-state to a
high density solid-like state. In the high density, low temperature limit
Enskog theory fails because it predicts densities larger than the closed packed
density below a certain temperature. We show how to extend the range of
applicability of the Enskoq theory to arbitrarily low temperatures by
constructing a physical solution: all particles that are situated in regions
with densities larger than a certain maximum density are assumed to be
'condensed.'",9909252v1
2013-12-18,Density of states of the $XY$ model: an energy landscape approach,"Among the stationary configurations of the Hamiltonian of a classical O$(n)$
lattice spin model, a class can be identified which is in one-to-one
correspondence with all the the configurations of an Ising model defined on the
same lattice and with the same interactions. Starting from this observation it
has been recently proposed that the microcanonical density of states of an
O$(n)$ model could be written in terms of the density of states of the
corresponding Ising model. Later, it has been shown that a relation of this
kind holds exactly for two solvable models, the mean-field and the
one-dimensional $XY$ model, respectively. We apply the same strategy to derive
explicit, albeit approximate, expressions for the density of states of the
two-dimensional $XY$ model with nearest-neighbor interactions on a square
lattice. The caloric curve and the specific heat as a function of the energy
density are calculated and compared against simulation data, yielding a very
good agreement over the entire energy density range. The concepts and methods
involved in the approximations presented here are valid in principle for any
O$(n)$ model.",1312.5223v1
2022-03-15,TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation,"Real-time density estimation is ubiquitous in many applications, including
computer vision and signal processing. Kernel density estimation is arguably
one of the most commonly used density estimation techniques, and the use of
""sliding window"" mechanism adapts kernel density estimators to dynamic
processes. In this paper, we derive the asymptotic mean integrated squared
error (AMISE) upper bound for the ""sliding window"" kernel density estimator.
This upper bound provides a principled guide to devise a novel estimator, which
we name the temporal adaptive kernel density estimator (TAKDE). Compared to
heuristic approaches for ""sliding window"" kernel density estimator, TAKDE is
theoretically optimal in terms of the worst-case AMISE. We provide numerical
experiments using synthetic and real-world datasets, showing that TAKDE
outperforms other state-of-the-art dynamic density estimators (including those
outside of kernel family). In particular, TAKDE achieves a superior test
log-likelihood with a smaller runtime.",2203.08317v2
2022-10-07,A convolution formalism for defining spatial densities of hadrons,"We clarify the meaning of spatial densities of hadrons. A physical density is
given by the expectation value of a local operator for a physical state, and
depends on both internal structure and the hadron's wave packet. In some
particular cases, the physical density can be written as a convolution between
a density function that depends on internal structure but not wave packet, and
a smearing function that depends on wave packet but not internal structure. We
show that the light front densities often encountered in the literature have
this property but that instant form densities do not. For hadrons prepared in
broad wave packets, physical instant form densities approximately obey such a
convolution relation, with Breit frame densities as the apparent internal
densities. However, there is an infinite series of relativistic corrections to
this convolution formula.",2210.03807v2
2023-07-04,Semantic Segmentation on 3D Point Clouds with High Density Variations,"LiDAR scanning for surveying applications acquire measurements over wide
areas and long distances, which produces large-scale 3D point clouds with
significant local density variations. While existing 3D semantic segmentation
models conduct downsampling and upsampling to build robustness against varying
point densities, they are less effective under the large local density
variations characteristic of point clouds from surveying applications. To
alleviate this weakness, we propose a novel architecture called HDVNet that
contains a nested set of encoder-decoder pathways, each handling a specific
point density range. Limiting the interconnections between the feature maps
enables HDVNet to gauge the reliability of each feature based on the density of
a point, e.g., downweighting high density features not existing in low density
objects. By effectively handling input density variations, HDVNet outperforms
state-of-the-art models in segmentation accuracy on real point clouds with
inconsistent density, using just over half the weights.",2307.01489v1
2023-08-15,Attraction Domain Analysis for Steady States of Markovian Open Quantum Systems,"This article concerns the attraction domain analysis for steady states in
Markovian open quantum systems. The central question is proposed as: given a
steady state, which part of the state space of density operators does it
attract and which part does it not attract? We answer this question by
presenting necessary and sufficient conditions that determine, for any steady
state and initial state, whether the latter belongs to the attraction domain of
the former. Moreover, we show that steady states without uniqueness in the set
of density operators have attraction domains with measure zero under some
translation invariant and locally finite measures. Finally, an example
regarding an open Heisenberg XXZ spin chain is presented.",2308.07602v1
2010-10-27,Novel Ground-State Crystals with Controlled Vacancy Concentrations: From Kagomé to Honeycomb to Stripes,"We introduce a one-parameter family, $0 \leq H \leq 1$, of pair potential
functions with a single relative energy minimum that stabilize a range of
vacancy-riddled crystals as ground states. The ""quintic potential"" is a
short-ranged, nonnegative pair potential with a single local minimum of height
$H$ at unit distance and vanishes cubically at a distance of $\rt$. We have
developed this potential to produce ground states with the symmetry of the
triangular lattice while favoring the presence of vacancies. After an
exhaustive search using various optimization and simulation methods, we believe
that we have determined the ground states for all pressures, densities, and $0
\leq H \leq 1$. For specific areas below $3\rt/2$, the ground states of the
""quintic potential"" include high-density and low-density triangular lattices,
kagom\'{e} and honeycomb crystals, and stripes. We find that these ground
states are mechanically stable but are difficult to self-assemble in computer
simulations without defects. For specific areas above $3\rt/2$, these systems
have a ground-state phase diagram that corresponds to hard disks with radius
$\rt$. For the special case of H=0, a broad range of ground states is
available. Analysis of this case suggests that among many ground states, a
high-density triangular lattice, low-density triangular lattice, and striped
phases have the highest entropy for certain densities. The simplicity of this
potential makes it an attractive candidate for experimental realization with
application to the development of novel colloidal crystals or photonic
materials.",1010.5708v1
2011-06-20,Density Functional Resonance Theory of Unbound Electronic Systems,"Density Functional Resonance Theory (DFRT) is a complex-scaled version of
ground-state Density Functional Theory (DFT) that allows one to calculate the
resonance energies and lifetimes of metastable anions. In this formalism, the
exact energy and lifetime of the lowest-energy resonance of unbound systems is
encoded into a complex ""density"" that can be obtained via complex-coordinate
scaling. This complex density is used as the primary variable in a DFRT
calculation just as the ground-state density would be used as the primary
variable in DFT. As in DFT, there exists a mapping of the N-electron
interacting system to a Kohn-Sham system of N non-interacting particles in
DFRT. This mapping facilitates self consistent calculations with an initial
guess for the complex density, as illustrated with an exactly-solvable model
system. Whereas DFRT yields in principle the exact resonance energy and
lifetime of the interacting system, we find that neglecting the
complex-correlation contribution leads to errors of similar magnitude to those
of standard scattering close-coupling calculations under the bound-state
approximation.",1106.3911v1
2021-04-28,Auxiliary many-body wavefunctions for TDDFRT electronic excited states: Consequences for the representation of molecular electronic transitions,"This contribution reports the study of a set of molecular
electronic-structure reorganization representations related to light-induced
electronic transitions, modeled in the framework of time-dependent
density-functional response theory. More precisely, the work related in this
paper deals with the consequences, for the electronic transitions
natural-orbital characterization, that are inherent to the use of auxiliary
many-body wavefunctions constructed a posteriori and assigned to excited states
- since time-dependent density-functional response theory does not provide
excited state ans\""atze in its native formulation. Three types of such
auxiliary many-body wavefunctions are studied, and the structure and spectral
properties of the relevant matrices (the one-electron reduced difference and
transition density matrices) is discussed and compared with the native
equation-of-motion time-dependent density functional response theory picture of
an electronic transition - we see for instance that within this framework the
detachment and attachment density matrices can be derived without diagonalizing
the one-body reduced difference density matrix. The common departure/arrival
wavefunction-based representation of the electronic transitions computed with
this method is discussed, and two such common departure/arrival density-based
pictures are also compared.",2104.13616v1
1998-10-09,Vortex Density of States and Absorption in Clean Layered Superconductors,"We study the spectrum of the states localized in the vortex cores in the
mixed state of clean layered superconductors. S-wave coupling is assumed. It is
found that in a large region of parameters adjacent to the superclean case a
new universal (i.e. independent of the density of impurities) class of level
statistics arises. It is the circular unitary random matrix ensemble. The
density of states for such conditions is calculated. The absorption resulting
from the Landau-Zener transitions between these levels is different from the
classical result for an isotropic three-dimensional system.",9810125v2
2020-12-24,Enhancement in tunneling density of states in Luttinger liquid -- role of non-local interaction,"Power law suppression of local electronic tunneling density of states (TDOS)
in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the
interacting 1-D electron system. We present a theoretical model which hosts LL
state with the surprising feature of enhancement rather than suppression in
local TDOS originating from non-local and repulsive density-density
interactions. Importantly, we find enhancement of TDOS in the manifold of
parameter space where the system is stable in the renormalization group (RG)
sense. We argue that enhancement of TDOS along with RG stability is possible
only when the system has broken parity symmetry about the position of local
TDOS enhancement. Such a model could be realized on the edge states of a
bi-layer quantum Hall system where both intra-layer and inter-layer
density-density interactions are present mimicking the role of local and
non-local interactions respectively.",2012.13414v2
2006-08-02,Spin ordered phase transitions in isospin asymmetric nuclear matter,"The possibility of appearance of spin polarized states in nuclear matter is
studied within the framework of a Fermi liquid theory with Skyrme effective
forces in a wide range of isospin asymmetries and densities. There are a few
possible scenarios of spin ordered phase transitions: (a) nuclear matter with
SLy4 interaction undergoes at some critical density a phase transition to a
spin polarized state with the oppositely directed spins of neutrons and
protons; (b) in nuclear matter with SkI5 interaction a spin polarized state
with the like-directed neutron and proton spins is formed; (c) nuclear matter
with SkI3 interaction under increasing density, at first, undergoes a phase
transition to the state with the opposite directions of neutron and proton
spins, which goes over at larger density to the state with the same direction
of nucleon spins. Spin polarized states at strong excess neutrons over protons
are accompanied by the long tails in the density profiles of the neutron spin
polarization parameter near the critical density, if the energy gain of the
transition from the nonpolarized state to the polarized one is the decreasing
function of isospin asymmetry (SLy4 force). In the opposite case, if the energy
gain is increased with isospin asymmetry, there are no long tails in the
density distribution of the neutron spin polarization parameter (SkI3, SkI5
forces).",0608008v2
1995-11-13,Gas of D-Branes and Hagedorn Density of BPS States,"We test the prediction of a hagedorn density of BPS states which carry RR
charge in type II compactifications. We find that in certain cases they
correspond to the supersymmetric ground states for a gas of identical 0-branes.",9511088v2
2009-08-19,Conductance characteristics of current-carrying d-wave weak links,"The local quasiparticle density of states in the current-carrying d-wave
superconducting structures was studied theoretically. The density of states can
be accessed through the conductance of the scanning tunnelling microscope. Two
particular situations were considered: the current state of the homogeneous
film and the weak link between two current-carrying d-wave superconductors.",0908.2743v1
2014-02-02,Free-fall energy density and flux in the Schwarzschild black hole,"In the four-dimensional background of Schwarzschild black hole, we
investigate the energy densities and fluxes in the freely falling frames for
the Boulware, Unruh, and Israel-Hartle-Hawking states. In particular, we study
their behaviors near the horizon and asymptotic spatial infinity by using the
trace anomaly of a conformally invariant scalar field. In the Boulware state,
both the energy density and flux are negative divergent when the observer is
dropped at the horizon, and asymptotically vanish. In the Unruh state, the
energy density is also negative divergent at the horizon while it is positive
finite asymptotically. The flux in the Unruh state is always positive and
divergent at the horizon. In the Israel-Hartle-Hawking state, the energy
density depends on the angular motion of free fall, and fluxes vanish at the
horizon and the spatial infinity. Finally, we discuss the role of the negative
energy density near the horizon in the evaporating black hole.",1402.0202v2
2019-09-30,Effect of Coulomb Interaction and Disorder on Density of States in Conventional Superconductors,"The density of states of the disordered s-wave superconductor is calculated
perturbatively. The effect of Coulomb interaction on diffusively moving
electrons in the normal state has been known before, but in the superconducting
state both diffuson and the screened Coulomb interaction are modified.
Therefore, the correction to the density of states in the superconducting state
exhibits an energy dependence different from that of the normal state. There is
a dip structure in the correction part because the interaction has a peak at
twice the energy of the superconducting gap. The Coulomb interaction and the
superconducting fluctuation cannot be treated separately because the density
fluctuation is coupled to the phase fluctuation in the superconducting state.
This coupling results in the absence of divergence around the gap edge in the
correction part, which suggests the validity of this perturbation calculation.",1909.13478v1
2019-07-29,Learn to Scale: Generating Multipolar Normalized Density Maps for Crowd Counting,"Dense crowd counting aims to predict thousands of human instances from an
image, by calculating integrals of a density map over image pixels. Existing
approaches mainly suffer from the extreme density variances. Such density
pattern shift poses challenges even for multi-scale model ensembling. In this
paper, we propose a simple yet effective approach to tackle this problem.
First, a patch-level density map is extracted by a density estimation model and
further grouped into several density levels which are determined over full
datasets. Second, each patch density map is automatically normalized by an
online center learning strategy with a multipolar center loss. Such a design
can significantly condense the density distribution into several clusters, and
enable that the density variance can be learned by a single model. Extensive
experiments demonstrate the superiority of the proposed method. Our work
outperforms the state-of-the-art by 4.2%, 14.3%, 27.1% and 20.1% in MAE, on
ShanghaiTech Part A, ShanghaiTech Part B, UCF_CC_50 and UCF-QNRF datasets,
respectively.",1907.12428v2
2020-08-03,Effects of density-dependent scenarios of in-medium nucleon-nucleon interactions in heavy-ion collisions,"Using a more reasonable separate density-dependent scenario instead of the
total density-dependent scenario for in-medium $nn$, $pp$ and $np$
interactions, we examine effects of differences of in-medium nucleon-nucleon
interactions in two density-dependent scenarios on isospin-sensitive
observables in central $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon.
Moreover, to more physically detect the differences between the nucleon-nucleon
interactions in two density-dependent scenarios, we also map the
nucleon-nucleon interaction in the separate density-dependent scenario into
that in the total density-dependent scenario through fitting the identical
constraints for symmetric nuclear matter as well as the identical slope
parameter of nuclear symmetry energy at the saturation density. It is shown
that two density-dependent scenarios also lead to essentially different
symmetry potentials especially at high densities although they can lead to the
identical equation of state for the symmetry nuclear matter as well as the
identical symmetry energy for the isospin asymmetric nuclear matter.
Consequently, these isospin-sensitive observables are also appreciably affected
by the different density-dependent scenarios of in-medium nucleon-nucleon
interactions. Therefore, according to these findings, it is suggested that
effects of the separate density-dependent scenario of in-medium nucleon-nucleon
interactions should be taken into account when probing the high-density
symmetry energy using these isospin-sensitive observables in heavy-ion
collisions.",2008.01103v1
2017-03-10,Density of States FFA analysis of SU(3) lattice gauge theory at a finite density of color sources,"We present a Density of States calculation with the Functional Fit Approach
(DoS FFA) in SU(3) lattice gauge theory with a finite density of static color
sources. The DoS FFA uses a parameterized density of states and determines the
parameters of the density by fitting data from restricted Monte Carlo
simulations with an analytically known function. We discuss the implementation
of DoS FFA and the results for a qualitative picture of the phase diagram in a
model which is a further step towards implementing DoS FFA in full QCD. We
determine the curvature $\kappa$ in the $\mu$-$T$ phase diagram and find a
value close to the results published for full QCD.",1703.03614v2
2008-09-04,Impurity states in antiferromagnetic Iron Arsenides,"We explore theoretically impurity states in the antiferromagnetic
spin-density wave state of the iron arsenide. Two types of impurity models are
employed: one has only the intraband scattering while the other has both the
intraband and interband scattering with the equal strength. Interestingly, the
impurity bound state is revealed around the impurity site in the energy gap for
both models. However, the impurity state is doubly degenerate with respect to
spin for the first case; while the single impurity state is observed in either
the spin-up or spin-down channel for the second one. The impurity-induced
variations of the local density of states are also examined.",0809.0795v1
2015-02-26,Excited state geometry optimization with the density matrix renormalization group as applied to polyenes,"We describe and extend the formalism of state-specific analytic density
matrix renormalization group (DMRG) energy gradients, first used by Liu et al
(J. Chem. Theor.Comput. 9, 4462 (2013)). We introduce a DMRG wavefunction
maximum overlap following technique to facilitate state-specific DMRG excited
state optimization. Using DMRG configuration interaction (DMRG-CI) gradients we
relax the low-lying singlet states of a series of trans-polyenes up to C20H22.
Using the relaxed excited state geometries as well as correlation functions, we
elucidate the exciton, soliton, and bimagnon (""single-fission"") character of
the excited states, and find evidence for a planar conical intersection.",1502.07731v2
2024-03-03,Oscillating-charged Andreev Bound States and Their Appearance in UTe$_2$,"In a superconductor with a sublattice degree of freedom, we find
unconventional Andreev bound states whose charge density oscillates in sign
between the two sublattices. The appearance of these oscillating-charged
Andreev bound states is characterized by a Zak phase, rather than a
conventional topological invariant. In contrast to conventional Andreev bound
states, for oscillating-charged Andreev bound states the proportionality
between the electron-like spectral function, the local density of states and
the tunneling conductance is broken. We examine the possible appearance of
these novel Andreev bound states in UTe$_2$ and locally noncentrosymmetric
superconductors.",2403.01502v1
2022-07-12,Local and global ordering dynamics in multi-state voter models,"We investigate the time evolution of the density of active links and of the
entropy of the distribution of agents among opinions in multi-state voter
models with all-to-all interaction and on uncorrelated networks. Individual
realisations undergo a sequence of eliminations of opinions until consensus is
reached. After each elimination the population remains in a meta-stable state.
The density of active links and the entropy in these states varies from
realisation to realisation. Making some simple assumptions we are able to
analytically calculate the average density of active links and the average
entropy in each of these states. We also show that, averaged over realisations,
the density of active links decays exponentially, with a time scale set by the
size and geometry of the graph, but independent of the initial number of
opinion states. The decay of the average entropy is exponential only at long
times when there are at most two opinions left in the population. Finally, we
show how meta-stable states comprised of only a subset of opinions can be
artificially engineered by introducing precisely one zealot in each of the
prevailing opinions.",2207.05465v1
2008-05-05,Crossover in the local density of states of mesoscopic SNS junctions,"Andreev levels deplete energy states above the superconductive gap, which
leads to the peculiar nonmonotonous crossover in the local density of states of
mesoscopic superconductor/normal-metal/superconductor junctions. This effect is
especially pronounced in the case when the normal metal bridge length is small
compared to the superconductive coherence length. Remarkable property of the
crossover function is that it vanishes not only at the proximity induced gap
but also at the superconductive gap. Analytical expressions for the density of
states at the both gap edges, as well as general structure of the crossover are
discussed.",0805.0542v1
2019-03-06,Observing evolution from steady state,"We study cosmology in the time-translation symmetry of the conformal FLRW
frame $\bar{g}=a^{-2}g$, where constant matter density induces constant
curvature $R_{0}^{-2}$ and where evolution on the common light cone is observed
from a steady state. Equipartition of recessional and peculiar components of
kinetic energy of the gravitational field add to a total curvature
$24R_{0}^{-2}$ of twice the scalar curvature of de Sitter universe, predicting
a matter density $\Omega_{\textrm{m}}=\frac{1}{24}$, or $h\approx0.73$.
Projecting the equilibrium state on the present state in $\Lambda\textrm{CDM}$
returns $\hat{h}\approx0.68$ and densities within confidence limits of Planck
2018 results.",1903.04894v5
2022-08-05,QCD in the cores of neutron stars,"I discuss why state-of-the art perturbative QCD calculations of the equation
of state at large chemical potential that are reliable at asymptotically high
densities constrain the same equation of state at neutron-star densities. I
describe how these theoretical calculations affect the EOS at lower density. I
argue that the ab-initio calculations in QCD offer significant information
about the equation of state of the neutron-star matter, which is complementary
to the current astrophysical observations.",2208.03086v1
2007-04-24,Density of bulk trap states in organic semiconductor crystals: discrete levels induced by oxygen in rubrene,"The density of trap states in the bandgap of semiconducting organic single
crystals has been measured quantitatively and with high energy resolution by
means of the experimental method of temperature-dependent
space-charge-limited-current spectroscopy (TD-SCLC). This spectroscopy has been
applied to study bulk rubrene single crystals, which are shown by this
technique to be of high chemical and structural quality. A density of deep trap
states as low as ~ 10^{15} cm^{-3} is measured in the purest crystals, and the
exponentially varying shallow trap density near the band edge could be
identified (1 decade in the density of states per ~25 meV). Furthermore, we
have induced and spectroscopically identified an oxygen related sharp hole bulk
trap state at 0.27 eV above the valence band.",0704.3218v2
2004-03-29,Density of States and Conductivity of Granular Metal or Array of Quantum Dots,"The conductivity of a granular metal or an array of quantum dots usually has
the temperature dependence associated with variable range hopping within the
soft Coulomb gap of density of states. This is difficult to explain because
neutral dots have a hard charging gap at the Fermi level. We show that
uncontrolled or intentional doping of the insulator around dots by donors leads
to random charging of dots and finite bare density of states at the Fermi
level. Then Coulomb interactions between electrons of distant dots results in
the a soft Coulomb gap. We show that in a sparse array of dots the bare density
of states oscillates as a function of concentration of donors and causes
periodic changes in the temperature dependence of conductivity. In a dense
array of dots the bare density of states is totally smeared if there are
several donors per dot in the insulator.",0403703v3
2002-10-06,Quantal Density Functional Theory of Degenerate States,"The treatment of degenerate states within Kohn-Sham density functional theory
(KS-DFT) is a problem of longstanding interest. We propose a solution to this
mapping from the interacting degenerate system to that of the noninteracting
fermion model whereby the equivalent density and energy are obtained via the
unifying physical framework of quantal density functional theory (Q-DFT). We
describe the Q-DFT of \textit{both} ground and excited degenerate states, and
for the cases of \textit{both} pure state and ensemble v-representable
densities. This then further provides a rigorous physical interpretation of the
density and bidensity energy functionals, and of their functional derivatives,
of the corresponding KS-DFT. We conclude with examples of the mappings within
Q-DFT.",0210129v2
2007-05-12,Equation of state of isospin-asymmetric nuclear matter in relativistic mean-field models with chiral limits,"Using in-medium hadron properties according to the Brown-Rho scaling due to
the chiral symmetry restoration at high densities and considering naturalness
of the coupling constants, we have newly constructed several relativistic
mean-field Lagrangians with chiral limits. The model parameters are adjusted
such that the symmetric part of the resulting equation of state at supra-normal
densities is consistent with that required by the collective flow data from
high energy heavy-ion reactions, while the resulting density dependence of the
symmetry energy at sub-saturation densities agrees with that extracted from the
recent isospin diffusion data from intermediate energy heavy-ion reactions. The
resulting equations of state have the special feature of being soft at
intermediate densities but stiff at high densities naturally. With these
constrained equations of state, it is found that the radius of a 1.4$M_\odot$
canonical neutron star is in the range of 11.9 km$\leq$R$\leq$13.1 km, and the
maximum neutron star mass is around 2.0$M_\odot$ close to the recent
observations.",0705.1738v1
2013-02-28,Number and spin densities in the ground state of a trapped mixture of two pseudospin-1/2 Bose gases with interspecies spin-exchange interaction,"We consider the ground state of a mixture of two pseudospin-$\1/2$ Bose gases
with interspecies spin exchange in a trapping potential. In the mean field
approach, the ground state can be described in terms of four wave functions
governed by a set of coupled Gross-Pitaevskii-like (GP-like) equations, which
differ from the usual GP equations in the existence of an interference term due
to spin-exchange coupling between the two species. Using these GP-like
equations, we calculate such ground state properties as chemical potentials,
density profiles and spin density profiles, which are directly observable in
experiments. We compare the cases with and without spin exchange. It is
demonstrated that the spin exchange between the two species lowers the chemical
potentials, tends to equalize the wave functions of the two pseudospin
components of each species, and thus homogenizes the spin density. The novel
features of the density and spin density profiles can serve as experimental
probes of this novel Bose system.",1302.7217v1
2024-03-02,Diffusive Decay of Collective Quantum Excitations in Electron Gas,"In this work the multistream quasiparticle model of collective electron
excitations is used to study the energy-density distribution of collective
quantum excitations in an interacting electron gas with arbitrary degree of
degeneracy. Generalized relations for the probability current and energy
density distributions is obtained which reveals a new interesting quantum
phenomenon of diffusive decay of pure quasiparticle states at microscopic
level. The effects is studied for various cases of free quasiparticles,
quasiparticle in an infinite square-well potential and half-space collective
excitations. It is shown that plasmon excitations have the intrinsic tendency
to decay into equilibrium state with uniform energy density spacial
distribution. It is found that plasmon levels of quasipaticle in a square-well
potential are unstable decaying into equilibrium state due to the fundamental
property of collective excitations. The decay rates of pure plasmon states are
determined analytically. Moreover, for damped quasiparticle excitations the
non-vanishing probability current divergence leads to imaginary energy density
resulting in damping instability of energy density dynamic. The pronounced
energy density valley close to half-space boundary at low level excitations
predicts attractive force close to the surface. Current research can have
implications with applications in plasmonics and related fields. Current
analysis can be readily generalized to include external potential and magnetic
field effects.",2403.01099v1
2020-07-23,Density Wave Mediated Dzyaloshinskii-Moriya Interactions,"We investigate the effect that density wave states have on the localized
spins of a square lattice. We find that topologically nontrivial density wave
states can induce stable Dzyaloshinskii-Moriya (DM) interactions among the
localized spins of the lattice in the presence of an external magnetic field,
and we study the resulting spin models for both antiferromagnetic and
ferromagnetic backgrounds. While the density wave state itself can contribute
to the the thermal Hall effect, as shown by Li & Lee (arXiv:1905.04248v3),
symmetry considerations preclude the resulting spin excitations from inducing a
further thermal Hall effect. We utilize a Holstein-Primakoff (HP) substitution
about the classical mean-field ground state to calculate the magnon dispersion
for LSCO and find that the density wave induces a weak $d_{x^2-y^2}$
anisotropy; upon calculating the non-Abelian Berry curvature for this magnon
branch we show explicitly that the magnon contribution to $\kappa_{xy}$ is
zero. Finally, we calculate corrections to the magnetic ground state energy,
spin canting angles, and the spin-wave dispersion due to the topological
density wave for ferromagnetic backgrounds. We find that terms linear in the HP
bosons can affect the critical behavior, a point previously overlooked in the
literature.",2007.11719v1
2000-03-27,Quarter-filled spin density wave states with long-range Coulomb interaction,"Spin density wave (SDW) states at quarter-filling, which coexist with charge
density wave (CDW) states, have been examined where the critical temperature is
calculated for an extended Hubbard model with long range repulsive
interactions. Within the mean-field theory, it is shown that the first order
transition occurs with decreasing temperature for interactions located around
the boundary between SDW state and CDW state.",0003422v2
2015-08-19,Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations,"Systems of particles interacting with ""stealthy"" pair potentials have been
shown to possess infinitely degenerate disordered hyperuniform classical ground
states with novel physical properties. Previous attempts to sample the
infinitely degenerate ground states used energy minimization techniques,
introducing algorithmic dependence that is artificial in nature. Recently, an
ensemble theory of stealthy hyperuniform ground states was formulated to
predict the structure and thermodynamics that was shown to be in excellent
agreement with corresponding computer simulation results in the canonical
ensemble (in the zero-temperature limit). In this paper, we provide details and
justifications of the simulation procedure, which involves performing molecular
dynamics simulations at sufficiently low temperatures and minimizing the energy
of the snapshots for both the high-density disordered regime, where the theory
applies, as well as lower densities. We also use numerical simulations to
extend our study to the lower-density regime. We report results for the pair
correlation functions, structure factors, and Voronoi cell statistics. In the
high-density regime, we verify the theoretical ansatz that stealthy disordered
ground states behave like ""pseudo"" disordered equilibrium hard-sphere systems
in Fourier space. These results show that as the density decreases from the
high-density limit, the disordered ground states in the canonical ensemble are
characterized by an increasing degree of short-range order and eventually the
system undergoes a phase transition to crystalline ground states. We also
provide numerical evidence suggesting that different forms of stealthy pair
potentials produce the same ground-state ensemble in the zero-temperature
limit. Our techniques may be applied to sample this limit of the canonical
ensemble of other potentials with highly degenerate ground states.",1508.04749v1
2019-04-14,Truncation scheme of time-dependent density-matrix approach III,"The time-dependent density-matrix theory (TDDM) where the
Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices is
truncated by approximating a three-body density matrix with one-body and
two-body density matrices is applied to the Lipkin model. It is shown that in
the large $N$ limit the ground state in TDDM approaches the exact solution.
Various truncation schemes for the three-body density matrix are also tested
for an extended three-level Lipkin model.",1904.06780v1
2021-06-18,Density induced BCS-Bose evolution in gated two-dimensional superconductors: The Berezinskii-Kosterlitz-Thouless transition as a function of carrier density,"We discuss the evolution from BCS to Bose superconductivity versus carrier
density in gated two-dimensional s-wave superconductors. We show that the
transition from the normal to the superconducting state is controlled by the
Berezinskii-Kosterlitz-Thouless vortex-antivortex pairing mechanism, and that
the evolution from high carrier density (BCS pairing) to low carrier density
(Bose pairing) is just a crossover in s-wave systems. We compare our results to
recent experiments on the superconductor LixZrNCl, a lithium intercalated
layered nitride, and obtain very good quantitative agreement at low and
intermediate densities.",2106.10010v1
2012-08-09,Comparison of Density Functional Approximations and the Finite-temperature Hartree-Fock Approximation in Warm Dense Lithium,"We compare the behavior of the finite-temperature Hartree-Fock model with
that of thermal density functional theory using both ground-state and
temperature-dependent approximate exchange functionals. The test system is bcc
Li in the temperature-density regime of warm dense matter (WDM). In this
exchange-only case, there are significant qualitative differences in results
from the three approaches. Those differences may be important for
Born-Oppenheimer molecular dynamics studies of WDM with ground-state
approximate density functionals and thermal occupancies. Such calculations
require reliable regularized potentials over a demanding range of temperatures
and densities. By comparison of pseudopotential and all-electron results at
${\mathrm T} = 0$K for small Li clusters of local bcc symmetry and bond-lengths
equivalent to high density bulk Li, we determine the density ranges for which
standard projector augmented wave (PAW) and norm-conserving pseudopotentials
are reliable. Then we construct and use all-electron PAW data sets with a small
cutoff radius which are valid for lithium densities up to at least 80 g/cm$^3$.",1208.1910v1
2009-05-14,Spatial distribution of local density of states in vicinity of impurity on semiconductor surface,"We present the results of detailed theoretical investigations of changes in
local density of total electronic surface states in 2D anisotropic atomic
semiconductor lattice in vicinity of impurity atom for a wide range of applied
bias voltage. We have found that taking into account changes in density of
continuous spectrum states leads to the formation of a downfall at the
particular value of applied voltage when we are interested in the density of
states above the impurity atom or even to a series of downfalls for the fixed
value of the distance from the impurity. The behaviour of local density of
states with increasing of the distance from impurity along the chain differs
from behaviour in the direction perpendicular to the chain.",0905.2312v1
2000-08-30,Heterogeneities in Supercooled liquids: A Density Functional Study,"A metastable state, characterized by a low degree of mass localization is
identified using Density Functional Theory. This free energy minimum, located
through the proper evaluation of the competing terms in the free energy
functional, is independent of the specific form of the DFT used. Computer
simulation results on particle motion indicate that this heterogeneous state
corresponds to the supercooled state.",0008436v1
2001-10-10,Field induced d_x^2-y^2+id_xy state in d-density-wave metals,"We argue that the d_{xy} component of the order parameter can be generated to
form the d_x^2-y^2+id_xy-density wave state by the external magnetic field. The
driving force for this transition is the coupling of the magnetic field with
the orbital magnetism. The fully gapped particle spectrum and the magnetically
active collective mode of the condensate are discussed as a possible signature
of the d+id' density wave state.",0110214v1
2007-07-20,Existence of a Density Functional for an Intrinsic State,"A generalization of the Hohenberg-Kohn theorem proves the existence of a
density functional for an intrinsic state, symmetry violating, out of which a
physical state with good quantum numbers can be projected.",0707.3099v3
2012-10-08,Engineering arbitrary pure and mixed quantum states,"This work addresses a fundamental problem of controllability of open quantum
systems, meaning the ability to steer arbitrary initial system density matrix
into any final density matrix. We show that under certain general conditions
open quantum systems are completely controllable and propose the first, to the
best of our knowledge, deterministic method for a laboratory realization of
such controllability which allows for a practical engineering of arbitrary pure
and mixed quantum states. The method exploits manipulation by the system with a
laser field and a tailored nonequilibrium and time-dependent state of the
surrounding environment. As a physical example of the environment we consider
incoherent light, where control is its spectral density. The method has two
specifically important properties: it realizes the strongest possible degree of
quantum state control --- complete density matrix controllability which is the
ability to steer arbitrary pure and mixed initial states into any desired pure
or mixed final state, and is ""all-to-one"", i.e. such that each particular
control can transfer simultaneously all initial system states into one target
state.",1210.2281v1
2023-06-06,Local density approximation for excited states,"The ground state of an homogeneous electron gas is a paradigmatic state that
has been used to model and predict the electronic structure of matter at
equilibrium for nearly a century. For half a century, it has been successfully
used to predict ground states of quantum systems via the local density
approximation (LDA) of density functional theory (DFT); and systematic
improvements in the form of generalized gradient approximations and evolution
thereon. Here, we introduce the LDA for \emph{excited} states by considering a
particular class of non-thermal ensemble states of the homogeneous electron
gas. These states find sound foundation and application in ensemble-DFT -- a
generalization of DFT that can deal with ground and excited states on equal
footing. The ensemble-LDA is shown to successfully predict difficult low-lying
excitations in atoms and molecules for which approximations based on local spin
density approximation (LSDA) and time-dependent-LDA fail.",2306.04023v3
2000-03-29,Role of Phase Variables in Quarter-Filled Spin Density Wave States,"Several kinds of spin density wave (SDW) states with both quarter-filled band
and dimerization are reexamined for a one-dimensional system with on-site,
nearest-neighbor and next-nearest-neighbor repulsive interactions, which has
been investigated by Kobayashi et al. (J. Phys. Soc. Jpn. 67 (1998) 1098).
Within the mean-field theory, the ground state and the response to the density
variation are calculated in terms of phase variables, $\theta$ and $\phi$,
where $\theta$ expresses the charge fluctuation of SDW and $\phi$ describes the
relative motion between density wave with up spin and that with down spin
respectively. It is shown that the exotic state of coexistence of 2k_F-SDW and
2k_F-charge density wave (CDW) is followed by 4k_F-SDW but not by 4k_F-CDW
where k_F denotes a Fermi wave vector. The harmonic potential with respect to
the variation of $\theta$ and/or $\phi$ disappears for the interactions, which
lead to the boundary between the pure 2k_F-SDW state and the corresponding
coexistent state.",0003464v1
2023-10-28,Interplay between Chiral Charge Density Wave and Superconductivity in Kagome Superconductors: A Self-consistent Theoretical Analysis,"Inspired by the recent discovery of a successive evolutions of electronically
ordered states, we present a self-consistent theoretical analysis that treats
the interactions responsible for the chiral charge order and superconductivity
on an equal footing. It is revealed that the self-consistent theory captures
the essential features of the successive temperature evolutions of the
electronic states from the high-temperature ``triple-$Q$"" $2\times 2$
charge-density-wave state to the nematic charge-density-wave phase, and finally
to the low-temperature superconducting state coexisting with the nematic charge
density wave. We provide a comprehensive explanation for the temperature
evolutions of the charge ordered states and discuss the consequences of the
intertwining of the superconductivity with the nematic charge density wave. Our
findings not only account for the successive temperature evolutions of the
ordered electronic states discovered in experiments but also provide a natural
explanation for the two-fold rotational symmetry observed in both the
charge-density-wave and superconducting states. Moreover, the intertwining of
the superconductivity with the nematic charge density wave order may also be an
advisable candidate to reconcile the divergent or seemingly contradictory
experimental outcomes regarding the superconducting properties.",2310.18675v1
2022-06-08,Identification of a Nematic Pair Density Wave State in Bi2Sr2CaCu2O8+x,"Electron-pair density wave (PDW) states are now an intense focus of research
in the field of cuprate correlated superconductivity. PDWs exhibit periodically
modulating superconductive electron pairing which can be visualized directly
using scanned Josephson tunneling microscopy (SJTM). Although from theory,
intertwining the d-wave superconducting (DSC) and PDW order parameters allows a
plethora of global electron-pair orders to appear, which one actually occurs in
the various cuprates is unknown. Here we use SJTM to visualize the interplay of
PDW and DSC states in Bi2Sr2CaCu2O8+x at a carrier density where the charge
density wave (CDW) modulations are virtually nonexistent. Simultaneous
visualization of their amplitudes reveals that the intertwined PDW and DSC are
mutually attractive states. Then, by separately imaging the electron-pair
density modulations of the two orthogonal PDWs, we discover a robust nematic
PDW state. Its spatial arrangement entails Ising domains of opposite
nematicity, each consisting primarily of unidirectional and lattice
commensurate electron-pair density modulations. Further, we demonstrate by
direct imaging that the scattering resonances identifying Zn impurity atom
sites occur predominantly within boundaries between these domains. This implies
that the nematic PDW state is pinned by Zn atoms, as was recently proposed
(Lozano et al, PHYSICAL REVIEW B 103, L020502 (2021)). Taken in combination,
these data indicate that the PDW in Bi2Sr2CaCu2O8+x is a vestigial nematic pair
density wave state (J. Wardh and M. Granath arXiv:2203.08250v1).",2206.03910v1
2019-12-16,A new state of dense matter in neutron stars with nucleon structure,"The existence of stars with a large mass of 2 solar masses means that the
equation of state is stiff enough to provide high enough pressure at large
central densities. Previous work shows that such a stiff equation of state is
possible if the ground state has nucleons as its constituents. We find this to
be so in a chiral soliton ( skyrmion ) model for a composite nucleon which has
bound state quarks. The strong binding of the quarks in this composite nucleon
is plausibly the origin of the nucleon-nucleon hard core. In this model we find
a new state of superdense matter at high density which is a 'topological'cubic
crystal of overlapping composite nucleons that are solitons with relativistic
quark bound states. The quarks are frozen in a filled band of a unique state,
which not an eigenstate of spin or isospin but an eigenstate of spin plus
isospin, $ \vec S + \vec I = 0$. In this alternative model we find that all
neutron stars have no regular `free'quark matter. Neutron stars whose central
density crosses a threshold baryon density of approximately, $n_b \sim 1/fm^3
$, will become unstable and go through a decompression (sudden) density
discontinuity to conventional quark matter. Sequentially, this contraction of
the core of the star will soften the equation of state release a large amount
of gravitational potential energy which can give rise to a shock wave and
matter ejection. Since the merger of two neutron stars gives a compact state
whose mass is larger than the allowed maximum mass, this will be followed by a
jet and a short gamma ray burst while transiting into a black hole.",1912.08096v1
2007-02-16,Distribution of local density of states in superstatistical random matrix theory,"We expose an interesting connection between the distribution of local
spectral density of states arising in the theory of disordered systems and the
notion of superstatistics introduced by Beck and Cohen and recently
incorporated in random matrix theory. The latter represents the matrix-element
joint probability density function as an average of the corresponding quantity
in the standard random-matrix theory over a distribution of level densities. We
show that this distribution is in reasonable agreement with the numerical
calculation for a disordered wire, which suggests to use the results of theory
of disordered conductors in estimating the parameter distribution of the
superstatistical random-matrix ensemble.",0702395v1
2019-06-14,Friedel oscillations in 2D electron gas from spin-orbit interaction in a parallel magnetic field,"Effects associated with the interference of electron waves around a magnetic
point defect in two-dimensional electron gas with combined Rashba-Dresselhaus
spin-orbit interaction in the presence of a parallel magnetic field are
theoretically investigated. The effect of a magnetic field on the anisotropic
spatial distribution of the local density of states and the local density of
magnetization is analyzed. The existence of oscillations of the density of
magnetization with scattering by a non-magnetic defect and the contribution of
magnetic scattering (accompanied by spin-flip) in the local density of electron
states are predicted.",1906.06043v1
2006-09-11,Exact coherent states of a noninteracting Fermi gas in a harmonic trap,"Exact and closed-form expressions of the particle density, the kinetic energy
density, the probability current density, and the momentum distribution are
derived for a coherent state of a noninteracting Fermi gas, while such a state
can be obtained from the ground state in a $d$-dimensional isotropic harmonic
trap by modulating the trap frequency and shifting the trap center.
Conservation laws for the relations of the densities are also given. The
profile of the momentum distribution turns out to be identical in shape with
that of the particle density, however, %as an observable manifestation of the
uncertainty principle, the dispersion of the distribution increases (decreases)
when that of the particle density is decreased (increased). The expressions are
also applicable for a sudden and total opening of the trap, and it is shown
that, after the opening, the gas has a stationary momentum distribution whose
dispersion could be arbitrarily large or small.",0609253v1
2003-07-30,Spin polarized states in strongly asymmetric nuclear matter,"In the framework of a Fermi liquid theory it is considered the possibility of
appearance of spin polarized states in strongly asymmetric nuclear matter with
Skyrme effective interaction. The zero temperature dependence of neutron and
proton spin polarization parameters as functions of density is found for SLy4,
SLy5 effective forces. It is shown that at some critical density it will be
formed the state with the oppositely directed spins of neutrons and protons,
while the state with the same direction of spins does not appear. In comparison
with neutron matter, even small admixture of protons strongly decreases the
threshold density of spin instability. It is clarified that protons become
totally polarized within very narrow density domain while in the density
profile of neutron spin polarization parameter their appear long tails near the
transition density.",0307113v2
2002-10-18,Tail states in superconductors with weak magnetic impurities,"We analyse the behavior of the density of states in a singlet s-wave
superconductor with weak magnetic impurities in the clean limit by using the
method of optimal fluctuation. We show that the density of states varies as
$\ln N(E)\propto -|E-\Delta_0|^{(7-d)/4}$ near the mean field gap edge
$\Delta_0$ in a d-dimensional superconductor. The optimal fluctuation in d>1 is
strongly anisotropic. We compare the density of states with that obtained in
other recent approaches.",0210421v2
2017-04-06,Transition of the uniform statistical field anyon state to the nonuniform one ar low particle densities,"Using results of our exact description of the spinless fermion motion in a
nonhomogeneous magnetic field \( {\bf B} = B( 0, 0, 1/cosh^{2}( \frac{x-x_{0}}{
\delta })) \) we study a gas of these particles moving in this field. For lower
densities \( \nu < \nu_{c}(B, \delta ) \) the corresponding total energy is
lower than that of the uniform field state. Thus when the density of anyons
decreases a transition from the uniform statistical field state to the
nonhomogeneous field state is predicted.",1704.01640v1
1996-03-20,"Partial Densities of States, Scattering Matrices, and Green's Functions","The response of an arbitrary scattering problem to quasi-static perturbations
in the scattering potential is naturally expressed in terms of a set of local
partial densities of states and a set of sensitivities each associated with one
element of the scattering matrix. We define the local partial densities of
states and the sensitivities in terms of functional derivatives of the
scattering matrix and discuss their relation to the Green's function. Certain
combinations of the local partial densities of states represent the injectivity
of a scattering channel into the system and the emissivity into a scattering
channel. It is shown that the injectivities and emissivities are simply related
to the absolute square of the scattering wave-function. We discuss also the
connection of the partial densities of states and the sensitivities to
characteristic times. We apply these concepts to a delta-barrier and to the
local Larmor clock.",9603135v1
2020-10-16,Signatures of triplet correlations in density of states of Ising superconductors,"The few-layer transition metal dichalcogenides (TMDs) have been recently
suggested as a platform for controlled unconventional superconductivity. We
study the manifestations of unconventional triplet pairing in the density of
states of a disordered TMD based monolayer. The conventional singlet pairing
attraction is assumed to be the dominant pairing interaction. We map the phase
diagrams of disordered Ising superconductors in the plane of temperature and
the in-plane magnetic field. The latter suppresses singlet and promote triplet
correlations. The triplet order parameters of a trivial (non-trivial) symmetry
compete (cooperate) with the singlet order parameter which gives rise to a rich
phase diagram. We locate the model-dependent phase boundaries and compute the
order parameters in each of the distinct phases. With this information, we
obtain the density of states by solving the Gorkov equation. The triplet
components of the order parameters may change an apparent width of the density
of states by significantly increasing the critical field. The triplet
components of the order parameters lead to the density of states broadening
significantly exceeding the broadening induced by magnetic field and disorder
in the singlet superconductor.",2010.08224v1
2020-01-09,${\bf 2k_F}$ Density Wave Instability of Composite Fermi Liquid,"We investigate the $2k_F$ density-wave instability of non-Fermi liquid states
by combining exact diagonalization with renormalization group analysis. At the
half-filled zeroth Landau level, we study the fate of the composite Fermi
liquid in the presence of the mass anisotropy and mixed Landau level form
factors. These two experimentally accessible knobs trigger a phase transition
towards a unidirectional charge-density-wave state with a wavevector equal to
$2k_F$ of the composite Fermi liquid. Based on exact diagonalization, we
identify such a transition by examining both the energy spectra and the static
structure factor of charge density-density correlations. Moreover, the
renormalization group analysis reveals that gauge fluctuations render the
non-Fermi liquid state unstable against density-wave orders, consistent with
numerical observations. Possible experimental probes of the density-wave
instability are also discussed.",2001.03202v2
2011-01-06,Non-Universality of Density and Disorder in Jammed Sphere Packings,"We show for the first time that collectively jammed disordered packings of
three-dimensional monodisperse frictionless hard spheres can be produced and
tuned using a novel numerical protocol with packing density $\phi$ as low as
0.6. This is well below the value of 0.64 associated with the maximally random
jammed state and entirely unrelated to the ill-defined ``random loose packing''
state density. Specifically, collectively jammed packings are generated with a
very narrow distribution centered at any density $\phi$ over a wide density
range $\phi \in [0.6,~0.74048\ldots]$ with variable disorder. Our results
support the view that there is no universal jamming point that is
distinguishable based on the packing density and frequency of occurence. Our
jammed packings are mapped onto a density-order-metric plane, which provides a
broader characterization of packings than density alone. Other packing
characteristics, such as the pair correlation function, average contact number
and fraction of rattlers are quantified and discussed.",1101.1327v1
2012-04-02,Constraining the nuclear equation of state at subsaturation densities,"Only one third of the nucleons in $^{208}$Pb occupy the saturation density
area. Consequently nuclear observables related to average properties of nuclei,
such as masses or radii, constrain the equation of state (EOS) not at
saturation density but rather around the so-called crossing density, localised
close to the mean value of the density of nuclei: $\rho\simeq$0.11 fm$^{-3}$.
This provides an explanation for the empirical fact that several EOS quantities
calculated with various functionals cross at a density significantly lower than
the saturation one. The third derivative M of the energy at the crossing
density is constrained by the giant monopole resonance (GMR) measurements in an
isotopic chain rather than the incompressibility at saturation density. The GMR
measurements provide M=1110 $\pm$ 70 MeV (6% uncertainty), whose extrapolation
gives K$_\infty$=230 $\pm$ 40 MeV (17% uncertainty).",1204.0399v3
2021-07-26,Active Matter Shepherding and Clustering in Inhomogeneous Environments,"We consider a mixture of active and passive run-and-tumble disks in an
inhomogeneous environment where only half of the sample contains quenched
disorder or pinning. The disks are initialized in a fully mixed state of
uniform density. We identify several distinct dynamical phases as a function of
motor force and pinning density. At high pinning densities and high motor
forces, there is a two step process initiated by a rapid accumulation of both
active and passive disks in the pinned region, which produces a large density
gradient in the system. This is followed by a slower species phase separation
process where the inactive disks are shepherded by the active disks into the
pin-free region, forming a non-clustered fluid and producing a more uniform
density with species phase separation. For higher pinning densities and low
motor forces, the dynamics becomes very slow and the system maintains a strong
density gradient. For weaker pinning and large motor forces, a floating
clustered state appears and the time averaged density of the system is uniform.
We illustrate the appearance of these phases in a dynamic phase diagram.",2107.12508v1
2017-12-18,DecideNet: Counting Varying Density Crowds Through Attention Guided Detection and Density Estimation,"In real-world crowd counting applications, the crowd densities vary greatly
in spatial and temporal domains. A detection based counting method will
estimate crowds accurately in low density scenes, while its reliability in
congested areas is downgraded. A regression based approach, on the other hand,
captures the general density information in crowded regions. Without knowing
the location of each person, it tends to overestimate the count in low density
areas. Thus, exclusively using either one of them is not sufficient to handle
all kinds of scenes with varying densities. To address this issue, a novel
end-to-end crowd counting framework, named DecideNet (DEteCtIon and Density
Estimation Network) is proposed. It can adaptively decide the appropriate
counting mode for different locations on the image based on its real density
conditions. DecideNet starts with estimating the crowd density by generating
detection and regression based density maps separately. To capture inevitable
variation in densities, it incorporates an attention module, meant to
adaptively assess the reliability of the two types of estimations. The final
crowd counts are obtained with the guidance of the attention module to adopt
suitable estimations from the two kinds of density maps. Experimental results
show that our method achieves state-of-the-art performance on three challenging
crowd counting datasets.",1712.06679v2
2014-07-08,"Excited-State Density-Functional Theory Revisited: on the Uniqueness, Existence, and Construction of the Density-to-Potential Mapping","The generalized constrained search formalism is used to address the issues
concerning density-to-potential mapping for excited states in time-independent
density-functional theory. The multiplicity of potentials for any given density
and the uniqueness in density-to-potential mapping are explained within the
framework of unified constrained search formalism for excited-states due to
G\""orling, Levy-Nagy, Samal-Harbola and Ayers-Levy. The extensions of
Samal-Harbola criteria and it's link to the generalized constrained search
formalism are revealed in the context of existence and unique construction of
the density-to-potential mapping. The close connections between the proposed
criteria and the generalized adiabatic connection are further elaborated so as
to keep the desired mapping intact at the strictly correlated regime.
Exemplification of the unified constrained search formalism is done through
model systems in order to demonstrate that the seemingly contradictory results
reported so far are neither the true confirmation of lack of Hohenberg-Kohn
theorem nor valid representation of violation of Gunnarsson-Lundqvist theorem
for excited states. Hence the misleading interpretation of subtle differences
between the ground and excited state density functional formalism are
exemplified.",1407.1959v3
2002-07-31,I-concurrence and tangle for isotropic states,"We discuss properties of entanglement measures called I-concurrence and
tangle. For a bipartite pure state, I-concurrence and tangle are simply related
to the purity of the marginal density operators. The I-concurrence (tangle) of
a bipartite mixed state is the minimum average I-concurrence (tangle) of
ensemble decompositions of pure states of the joint density operator. Terhal
and Vollbrecht [Phys. Rev. Lett. 85, 2625 (2000)] have given an explicit
formula for the entanglement of formation of isotropic states in arbitrary
dimensions. We use their formalism to derive comparable expressions for the
I-concurrence and tangle of isotropic states.",0208002v1
2023-01-19,Stochastic entropy production associated with quantum measurement in a framework of Markovian quantum state diffusion,"The reduced density matrix that characterises the state of an open quantum
system is a projection from the full density matrix of the quantum system and
its environment, and there are many full density matrices consistent with a
given reduced version. Without a specification of relevant details of the
environment, the evolution of a reduced density matrix is therefore typically
unpredictable, even if the dynamics are deterministic. With this in mind, we
investigate a two level open quantum system using a framework of quantum state
diffusion. We consider the pseudorandom evolution of its reduced density matrix
when subjected to an environment-driven process of continuous quantum
measurement of a system observable, using dynamics that asymptotically send the
system to an eigenstate. The unpredictability is characterised by a stochastic
entropy production, the average of which corresponds to an increase in the
subjective uncertainty of the quantum state adopted by the system and
environment, given the underspecified dynamics. This differs from a change in
von Neumann entropy, and can continue indefinitely as the system is guided
towards an eigenstate. As one would expect, the simultaneous measurement of two
non-commuting observables within the same framework does not send the system to
an eigenstate. Instead, the probability density function describing the reduced
density matrix of the system becomes stationary over a continuum of pure
states, a situation characterised by zero further stochastic entropy
production. Transitions between such stationary states, brought about by
changes in the relative strengths of the two measurement processes, give rise
to finite positive mean stochastic entropy production. The framework
investigated can offer useful perspectives on both the dynamics and
irreversible thermodynamics of measurement in quantum systems.",2301.08197v1
2022-07-10,Semimetallic spin-density wave state in iron pnictides,"We examine the existence of semimetallic spin-density wave states in iron
pnictides. In the experimentally observed metallic spin-density wave state, the
symmetry-protected Dirac cones are located away from the Fermi surface giving
rise to tiny pockets and there are also additional Fermi pockets such as one
around $\Gamma$. We find that the location of a pair of Dirac points with
respect to the Fermi surface exhibits significant sensitivity to the orbital
splitting between the $d_{xz}$ and $d_{yz}$ orbitals. Besides, in the presence
of orbital splitting, the Fermi pockets not associated with the Dirac cones,
can be suppressed so that a semimetallic spin-density wave state can be
realized. We explain these finding in terms of difference in the slopes and
orbital contents of the bands which form the Dirac cone, and obtain the
necessary conditions dependent on these two and other parameters for the
coexisting Dirac semimetallic and spin-density wave states. Additionally, the
topologically protected edge states are studied in the ribbon geometry when the
same are oriented either along $x$ or $y$ axes.",2207.04365v1
2014-06-12,Absorbing Phase Transitions and Dynamic Freezing in Running Active Matter Systems,"We examine a two-dimensional system of sterically repulsive interacting disks
where each particle runs in a random direction. This system is equivalent to a
run-and-tumble dynamics system in the limit where the run time is infinite. At
low densities, we find a strongly fluctuating state composed of transient
clusters. Above a critical density that is well below the density at which
non-active particles would crystallize, the system can organize into a drifting
quiescent or frozen state where the fluctuations are lost and large
crystallites form surrounded by a small density of individual particles.
Although all the particles are still moving, their paths form closed orbits.
The average transient time to organize into the quiescent state diverges as a
power law upon approaching the critical density from above. We compare our
results to the random organization observed for periodically sheared systems
that can undergo an absorbing transition from a fluctuating state to a
dynamical non-fluctuating state. In the random organization studies, the system
organizes to a state in which the particles no longer interact; in contrast, we
find that the randomly running active matter organizes to a strongly
interacting dynamically jammed state. We show that the transition to the frozen
state is robust against a certain range of stochastic fluctuations. We also
examine the effects of adding a small number of pinned particles to the system
and find that the transition to the frozen state shifts to significantly lower
densities and arises via the nucleation of faceted crystals centered at the
obstacles.",1406.3383v1
2018-08-22,Suppression of Dielectronic Recombination Due to Finite Density Effects II: Analytical Refinement and Application to Density-dependent Ionization Balances and AGN Broad-line Emission,"We present improved fits to our treatment of suppression of dielectronic
recombination at intermediate densities. At low densities, most recombined
excited states eventually decay to the ground state, and therefore the total
dielectronic recombination rate to all levels is preserved. At intermediate
densities, on the other hand, collisions can lead to ionization of higher-lying
excited states, thereby suppressing the dielectronic recombination rate. The
improved suppression factors presented here, although highly approximate, allow
summed recombination rate coefficients to be used to intermediate densities.
There have been several technical improvements to our previously presented
fits. For H- through B-like ions the activation log densities have been
adjusted to better reproduce existing data. For B-, C-, Al-, and Si-like ions
secondary autoionization is now included. The treatment of density
discontinuity in electron excitations out of ground state H-, He-, and Ne-like
ions has been improved. These refined dielectronic recombination suppression
factors are used in the most recent version of the plasma simulation code
Cloudy. We show how the ionization and emission spectrum change when this
physics is included. Although these suppression factors improve the treatment
of intermediate densities, they are highly approximate and are not a
substitution for a complete collisional-radiative model of the ionization
balance.",1808.07365v1
2023-09-27,Holographic massive plasma state in Friedman Universe: cosmological fine-tuning and coincidence problems,"Massive particle and antiparticle pair production and oscillation on the
horizon form a holographic and massive pair plasma state in the Friedman
Universe. Via this state, the Einstein cosmology $\Lambda$ term (dark energy)
interacts with matter and radiation in Universe evolution. It is determined by
a close set of ordinary differential equations and the initial conditions given
by observations. In inflation and reheating, dark energy density decreases from
the inflation scale, converting to matter and radiation energy densities. In
standard cosmology, matter and radiation energy densities convert to dark
energy density, reaching the present Universe. These results can be the
possible solutions for cosmological fine-tuning and coincidence problems.",2309.15488v1
2009-05-20,Density-functional theory of two-component Bose gases in one-dimensional harmonic traps,"We investigate the ground-state properties of two-component Bose gases
confined in one-dimensional harmonic traps in the scheme of density-functional
theory. The density-functional calculations employ a Bethe-ansatz-based
local-density approximation for the correlation energy, which accounts for the
correlation effect properly in the full physical regime. For the binary Bose
mixture with spin-independent interaction, the homogeneous reference system is
exactly solvable by the Bethe-ansatz method. Within the local-density
approximation, we determine the density distribution of each component and
study its evolution from Bose distributions to Fermi-like distribution with the
increase in interaction. For the binary mixture of Tonks-Girardeau gases with a
tunable inter-species repulsion, with a generalized Bose-Fermi transformation
we show that the Bose mixture can be mapped into a two-component Fermi gas,
which corresponds to exact soluble Yang-Gaudin model for the homogeneous
system. Based on the ground-state energy function of the Yang-Gaudin model, the
ground-state density distributions are calculated for various inter-species
interactions. It is shown that with the increase in inter-species interaction,
the system exhibits composite-fermionization crossover.",0905.3207v1
2021-06-24,Density Constrained Reinforcement Learning,"We study constrained reinforcement learning (CRL) from a novel perspective by
setting constraints directly on state density functions, rather than the value
functions considered by previous works. State density has a clear physical and
mathematical interpretation, and is able to express a wide variety of
constraints such as resource limits and safety requirements. Density
constraints can also avoid the time-consuming process of designing and tuning
cost functions required by value function-based constraints to encode system
specifications. We leverage the duality between density functions and Q
functions to develop an effective algorithm to solve the density constrained RL
problem optimally and the constrains are guaranteed to be satisfied. We prove
that the proposed algorithm converges to a near-optimal solution with a bounded
error even when the policy update is imperfect. We use a set of comprehensive
experiments to demonstrate the advantages of our approach over state-of-the-art
CRL methods, with a wide range of density constrained tasks as well as standard
CRL benchmarks such as Safety-Gym.",2106.12764v1
2012-09-27,Does the derivative of the energy density functional provide a proper quantitative formulation of electronegativity?,"It is pointed out that the derivative of the energy density functional does
not provide a valid local electronegativity measure, in spite of its appealing
property of becoming constant for ground-state equilibrium systems.",1209.6353v1
1998-06-28,Novel Density-Wave States of Two-Band Peierls-Hubbard Chains,"Based on a symmetry argument we systematically reveal Hartree-Fock
broken-symmetry solutions of the one-dimensional two-band extended
Peierls-Hubbard model, which covers various materials of interest such as
halogen-bridged metal complexes and mixed-stack charge-transfer salts. We find
out all the regular-density-wave solutions with an ordering vector $q=0$ or
$q=\pi$. Changing band filling as well as electron-electron and electron-phonon
interactions, we numerically inquire further into the ground-state phase
diagram and the physical property of each state. The possibility of novel
density-wave states appearing is argued.",9806343v1
1999-06-23,Information Content for Quantum States,"A method of representing probabilistic aspects of quantum systems is
introduced by means of a density function on the space of pure quantum states.
In particular, a maximum entropy argument allows us to obtain a natural density
function that only reflects the information provided by the density matrix.
This result is applied to derive the Shannon entropy of a quantum state. The
information theoretic quantum entropy thereby obtained is shown to have the
desired concavity property, and to differ from the the conventional von Neumann
entropy. This is illustrated explicitly for a two-state system.",9906085v1
2009-05-23,A stochastic optimal velocity model and its long-lived metastability,"In this paper, we propose a stochastic cellular automaton model of traffic
flow extending two exactly solvable stochastic models, i.e., the asymmetric
simple exclusion process and the zero range process. Moreover it is regarded as
a stochastic extension of the optimal velocity model. In the fundamental
diagram (flux-density diagram), our model exhibits several regions of density
where more than one stable state coexists at the same density in spite of the
stochastic nature of its dynamical rule. Moreover, we observe that two
long-lived metastable states appear for a transitional period, and that the
dynamical phase transition from a metastable state to another metastable/stable
state occurs sharply and spontaneously.",0905.3795v1
2011-12-13,Spectral properties of one-dimensional spiral spin density wave states,"We provide a full characterization of the spectral properties of spiral spin
density wave (SSDW) states which emerge in one-dimensional electron systems
coupled to localized magnetic moments or quantum wires with spin-orbit
interactions. We derive analytic results for the spectral function, local
density of states and optical conductivity in the low-energy limit by using
field theory techniques. We identify various collective modes and show that the
spectrum strongly depends on the interaction strength between the electrons.
The results provide characteristic signatures for an experimental detection of
SSDW states.",1112.3045v2
2019-07-25,Comparison Between the f-Electron and Conduction-Electron Density of States in the Falicov-Kimball Model at Low Temperature,"The spinless Falicov-Kimball model is one of the simplest models of many-body
physics. While the conduction-electron density of states is temperature
independent in the normal state, the f-electron density of states is strongly
temperature dependent---it has an orthogonality catastrophe singularity in the
metallic phase and is gapped in the insulating phase. The question we address
here is whether the spectral gap is the same for both electron species as T->0.
We find strong evidence to indicate that the answer is affirmative.",1907.11300v1
2019-10-27,A Dixmier trace formula for the density of states,"A version of Connes trace formula allows to associate a measure on the
essential spectrum of a Schr\""odinger operator with bounded potential. In solid
state physics there is another celebrated measure associated with such
operators --- the density of states. In this paper we demonstrate that these
two measures coincide. We show how this equality can be used to give explicit
formulae for the density of states in some circumstances.",1910.12380v3
2004-07-22,The band-edge behavior of the density of surfacic states,"This paper is devoted to the asymptotics of the density of surfacic states
near the spectral edges for a discrete surfacic Anderson model. Two types of
spectral edges have to be considered : fluctuating edges and stable edges. Each
type has its own type of asymptotics. In the case of fluctuating edges, one
obtains Lifshitz tails the parameters of which are given by the initial
operator suitably ""reduced"" to the surface. For stable edges, the surface
density of states behaves like the surface density of states of a constant
(equal to the expectation of the random potential) surface potential. Among the
tools used to establish this are the asymptotics of the surface density of
states for constant surface potentials.",0407051v1
2007-11-23,On the effect of weak disorder on the density of states in graphene,"The effect of weak potential and bond disorder on the density of states of
graphene is studied. By comparing the self-consistent non-crossing
approximation on the honeycomb lattice with perturbation theory on the Dirac
fermions, we conclude, that the linear density of states of pure graphene
changes to a non-universal power-law, whose exponent depends on the strength of
disorder like 1-4g/sqrt{3}t^2\pi, with g the variance of the Gaussian disorder,
t the hopping integral. This can result in a significant suppression of the
exponent of the density of states in the weak-disorder limit. We argue, that
even a non-linear density of states can result in a conductivity being
proportional to the number of charge carriers, in accordance with experimental
findings.",0711.3748v1
2011-05-16,Local density of states of a quarter-filled one-dimensional Mott insulator with a boundary,"We study the low-energy limit of a quarter-filled one-dimensional Mott
insulator. We analytically determine the local density of states in the
presence of a strong impurity potential, which is modeled by a boundary. To
this end we calculate the Green function using field theoretical methods. The
Fourier transform of the local density of states shows signatures of a pinning
of the spin-density wave at the impurity as well as several dispersing features
at frequencies above the charge gap. These features can be interpreted as
propagating spin and charge degrees of freedom. Their relative strength can be
attributed to the ""quasi-fermionic"" behavior of charge excitations with equal
momenta. Furthermore, we discuss the effect of bound states localized at the
impurity. Finally, we give an overview of the local density of states in
various one-dimensional systems and discuss implications for scanning tunneling
microscopy experiments.",1105.3196v3
2023-01-27,Density of photonic states in aperiodic structures,"Periodicity is usually assumed to be the necessary and sufficient condition
for the formation of band gaps, i.e., energy bands with a suppressed density of
states. Here, we check this premise by analyzing the band gap properties of
three structures that differ in the degree of periodicity and ordering. We
consider a photonic crystal, disordered lattice, and ordered but nonperiodic
quasicrystalline structure. A real-space metric allows us to compare the degree
of periodicity of these different structures. Using this metric, we reveal that
the disordered lattice and the ordered quasicrystal can be attributed to the
same group of material structures. We examine the density of their photonic
states both theoretically and experimentally. The analysis reveals that despite
their dramatically different degrees of periodicity, the photonic crystal and
the quasicrystalline structure demonstrate an almost similar suppression of the
density of states. Our results give new insight into the physical mechanisms
resulting in the formation of band gaps.",2302.02796v1
1999-06-22,The origin and formation of cuspy density profiles through violent relaxation of stellar systems,"It is shown that the cuspy density distributions observed in the cores of
elliptical galaxies can be realized by dissipationless gravitational collapse.
The initial models consist of power-law density spheres such as $\rho\propto
r^{-1}$ with anisotropic velocity dispersions. Collapse simulations are carried
out by integrating the collisionless Boltzmann equation directly, on the
assumption of spherical symmetry. From the results obtained, the extent of
constant density cores, formed through violent relaxation, decreases as the
velocity anisotropy increases radially, and practically disappears for
extremely radially anisotropic models. As a result, the relaxed density
distributions become more cuspy with increasing radial velocity anisotropy. It
is thus concluded that the velocity anisotropy could be a key ingredient for
the formation of density cusps in a dissipationless collapse picture. The
velocity dispersions increase with radius in the cores according to the nearly
power-law density distributions. The power-law index, $n$, of the density
profiles, defined as $\rho\propto r^{-n}$, changes from $n\approx 2.1$ at
intermediate radii, to a shallower power than $n\approx 2.1$ toward the centre.
This density bend can be explained from our postulated local phase-space
constraint that the phase-space density accessible to the relaxed state is
determined at each radius by the maximum phase-space density of the initial
state.",9906354v1
2003-10-09,Restoration of Many Electron Wave Functions from One-Electron Density,"General theorem describing a relation between diagonal of one-electron
density matrix and a certain class of many-electron ensembles of determinant
states is proved. As a corollary to this theorem a constructive proof of
sufficiency of Coleman's representability conditions is obtained. It is shown
that there exist rigorous schemes for construction of energy of many-electron
system as functionals of one-electron density.",0310043v1
2005-12-24,Low density fragile states in cohesive powders,"We discuss the difference between cohesive and non-cohesive granular media in
the context of a recent report of ""dry quicksand."" Weak low density states with
properties like dry quicksand are readily formed in common household powders.
In contrast, such states cannot be formed in cohesionless granular media such
as ordinary sand.",0512637v1
2001-01-14,Hamiltonian lattice QCD at finite density: equation of state in the strong coupling limit,"The equation of state of Hamiltonian lattice QCD at finite density is
examined in the strong coupling limit by constructing a solution to the
equation of motion corresponding to an effective Hamiltonian describing the
ground state of the many body system. This solution exactly diagonalizes the
Hamiltonian to second order in field operators for all densities and is used to
evaluate the vacuum energy density from which we obtain the equation of state.
We find that up to and beyond the chiral symmetry restoration density the
pressure of the quark Fermi sea can be negative indicating its mechanical
instability. Our result is in qualitative agreement with continuum models and
should be verifiable by future lattice simulations of strongly coupled QCD at
finite density.",0101144v3
2009-03-17,Measuring Qutrit-Qutrit Entanglement of Orbital Angular Momentum States of an Atomic Ensemble and a Photon,"Three-dimensional entanglement of orbital angular momentum states of an
atomic qutrit and a single photon qutrit has been observed. Their full state
was reconstructed using quantum state tomography. The fidelity to the maximally
entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result
confirms that the density matrix cannot be decomposed into ensemble of pure
states of Schmidt rank 1 or 2. That is, the Schmidt number of the density
matrix must be equal to or greater than 3.",0903.2903v2
2006-03-17,Exotic Low Density Fermion States in the Two Measures Field Theory: Neutrino Dark Energy,"We study a new field theory effect in the cosmological context in the Two
Measures Field Theory (TMT). TMT is an alternative gravity and matter field
theory where the gravitational interaction of fermionic matter is reduced to
that of General Relativity when the energy density of the fermion matter is
much larger than the dark energy density. In this case also the 5-th force
problem is solved automatically. In the opposite limit, where the magnitudes of
fermionic energy density and scalar field dark energy density become
comparable, nonrelativistic fermions can participate in the cosmological
expansion in a very unusual manner. Some of the features of such states in a
toy model of the late time universe filled with homogeneous scalar field and
uniformly distributed nonrelativistic neutrinos: neutrino mass increases as m ~
a^{3/2}; the neutrino gas equation-of-state approaches w=-1, i.e. neutrinos
behave as a sort of dark energy; the total (scalar field + neutrino)
equation-of-state also approaches w=-1; the total energy density of such
universe is less than it would be in the universe filled with the scalar field
alone. An analytic solution is presented. A domain structure of the dark energy
seems to be possible. We speculate that decays of the CLEP state neutrinos may
be both an origin of cosmic rays and responsible for a late super-acceleration
of the universe. In this sense the CLEP states exhibit simultaneously new
physics at very low densities and for very high particle masses.",0603070v1
2021-08-16,Localized Phonon Densities of States at Grain Boundaries in Silicon,"Since it is now possible to record vibrational spectra at nanometer scales in
the electron microscope it is of interest to explore whether defects such as
dislocations or grain boundaries will result in measurable changes of the
spectra. Phonon densities of states were calculated for a set of high angle
grain boundaries in silicon. Since these boundaries are modeled by supercells
with up to 160 atoms, the density of states was calculated by taking the
Fourier transform of the velocity-velocity autocorrelation function from
molecular dynamics simulations based on new supercells doubled in each
direction. In select cases the results were checked on the original supercells
with fewer atoms by comparison with the densities of states obtained by
diagonalizing the dynamical matrix calculated using density functional theory.
Near the core of the grain boundary the height of the optic phonon peak in the
density of states at 60 meV was suppressed relative to features due to acoustic
phonons that are largely unchanged relative to their bulk values. This can be
attributed to the variation in the strength of bonds in grain boundary core
regions where there is a range of bond lengths. It also means that changes in
the density of states intrinsic to grain boundaries are unlikely to affect
thermal conductivity at ambient temperatures, which are most likely dominated
by the scattering of acoustic phonons.",2108.07333v1
2004-01-23,Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities,"We study driven 1d lattice gas models with two types of particles and nearest
neighbor hopping. We find the most general case when there is a shock solution
with a product measure which has a density-profile of a step function for both
densities. The position of the shock performs a biased random walk. We
calculate the microscopic hopping rates of the shock. We also construct the
hydrodynamic limit of the model and solve the resulting hyperbolic system of
conservation laws. In case of open boundaries the selected steady state is
given in terms of the boundary densities.",0401461v1
1995-10-25,Diffusion Monte Carlo study of two-dimensional liquid $^4$He,"The ground-state properties of two-dimensional liquid $^4$He at zero
temperature are studied by means of a quadratic diffusion Monte Carlo method.
As interatomic potential we use a revised version of the HFDHE2 Aziz potential
which is expected to give a better description of the interaction between
helium atoms. The equation of state is determined with great accuracy over a
wide range of densities in the liquid phase from the spinodal point up to the
freezing density. The spinodal decomposition density is estimated and other
properties of the liquid, such as radial distribution function, static form
factor, momentum distribution and density dependence of the condensate fraction
are all presented.",9510143v1
1999-05-19,Oscillation modes of two-dimensional nanostructures within the time-dependent local-spin-density approximation,"We apply the time-dependent local-spin-density approximation as general
theory to describe ground states and spin-density oscillations in the linear
response regime of two-dimensional nanostructures of arbitrary shape. For this
purpose, a frequency analysis of the simulated real-time evolution is
performed. The effect on the response of the recently proposed spin-density
waves in the ground state of certain parabolic quantum dots is considered. They
lead to the prediction of a new class of excitations, soft spin-twist modes,
with energies well below that of the spin dipole oscillation.",9905288v2
2004-11-27,Density waves in quasi-one-dimensional atomic gas mixture of boson and two-component fermion,"We study the density-wave states of quasi-one-dimensional atomic gas mixture
of one- and two-component boson and fermion using the mean-field approximation.
Owing to the Peierls instability in the quasi-one-dimensional fermion system,
the ground state of the system shows the fermion density wave and the periodic
Bose-Einstein condensation induced by the boson-fermion interatomic
interaction. For the two-component fermions, two density waves appear in these
components, and the phase difference between them distinguishes two types of
ground states, the in-phase and the out-phase density-waves. In this paper, a
self-consistent method in the mean-field approximation is presented to treat
the density-wave states in boson-fermion mixture with two-component fermions.
  From the analysis of the effective potential and the interaction energies
calculated by this method, the density-waves are shown to appear in the ground
state, which are in-phase or out-phase depending on the strength of the
inter-fermion interaction. It is also shown that the periodic Bose-Einstein
condensate coexists with the in-phase density-wave of fermions, but, in the
case of the out-phase one, only the uniform condensate appears. The phase
diagram of the system is given for the effective coupling constants.",0411686v3
2019-04-10,The Quantum Cocktail Party Problem,"The cocktail party problem refers to the famous selective attention problem
of how to find out the signal of each individual sources from signals of a
number of detectors. In the classical cocktail party problem, the signal of
each source is a sequence of data such as the voice from a speaker, and each
detector detects signal as a linear combination of all sources. This problem
can be solved by a unsupervised machine learning algorithm known as the
independent component analysis. In this work we propose a quantum analog of the
cocktail party problem. Here each source is a density matrix of a pure state
and each detector detects a density matrix as a linear combination of all pure
state density matrix. The quantum cocktail party problem is to recover the pure
state density matrix from a number observed mixed state density matrices. We
propose the physical realization of this problem, and how to solve this problem
through either classical Newton's optimization method or by mapping the problem
to the ground state of an Ising type of spin Hamiltonian.",1904.06411v2
2020-08-28,Extending solid-state calculations to ultra long-range length scales,"We present a method which enables solid-state density functional theory
calculations to be applied to systems of almost unlimited size. Computations of
physical effects up to the micron length scale but which nevertheless depend on
the microscopic details of the electronic structure, are made possible. Our
approach is based on a generalization of the Bloch state which involves an
additional sum over a finer grid in reciprocal space around each ${\bf
k}$-point. We show that this allows for modulations in the density and
magnetization of arbitrary length on top of a lattice-periodic solution. Based
on this, we derive a set of ultra long-range Kohn-Sham equations. We
demonstrate our method with a sample calculation of bulk LiF subjected to an
arbitrary external potential containing nearly 3500 atoms. We also confirm the
accuracy of the method by comparing the spin density wave state of bcc Cr
against a direct supercell calculation starting from a random magnetization
density. Furthermore, the spin spiral state of $\gamma$-Fe is correctly
reproduced and the screening by the density of a saw-tooth potential over 20
unit cells of silicon is verified.",2008.12573v2
2015-12-12,Quantum energy inequalities in integrable quantum field theories,"In a large class of factorizing scattering models, we construct candidates
for the local energy density on the one-particle level starting from first
principles, namely from the abstract properties of the energy density. We find
that the form of the energy density at one-particle level can be fixed up to a
polynomial function of energy. On the level of one-particle states, we also
prove the existence of lower bounds for local averages of the energy density,
and show that such inequalities can fix the form of the energy density uniquely
in certain models.",1512.03946v1
2014-09-07,Optoelectronically probing the density of nanowire surface trap states to the single state limit,"Due to the large surface-to-volume ratio, surface trap states play a dominant
role in the optoelectronic properties of nanoscale devices(1-6). Understanding
the surface trap states allows us to properly engineer the device surfaces for
better performance. But characterization of surface trap states at nanoscale
has been a formidable challenge using the traditional capacitive techniques
based on metal-insulator-semiconductor (MIS) structures(7) and deep level
transient spectroscopy (DLTS)(8-11). Here, we demonstrate a simple but powerful
optoelectronic method to probe the density of nanowire surface trap states to
the limit of a single trap state. Unlike traditional capacitive techniques
(Fig1a), in this method we choose to tune the quasi-Fermi level across the
bandgap of a silicon nanowire photoconductor, allowing for capture and emission
of photogenerated charge carriers by surface trap states (Fig1b). The
experimental data show that the energy density of nanowire surface trap states
is in a range from 10^9cm^-2/eV at deep levels to 10^12cm^-2/eV in the middle
of the upper half bandgap. This optoelectronic method allows us to conveniently
probe trap states of ultra-scaled nano/quantum devices at extremely high
precision.",1409.2110v1
2012-08-28,First Principle Local Density Approximation Description of the Electronic Properties of Ferroelectric Sodium Nitrite,"The electronic structure of the ferroelectric crystal, NaNO$_2$, is studied
by means of first-principles, local density calculations. Our ab-initio,
non-relativistic calculations employed a local density functional approximation
(LDA) potential and the linear combination of atomic orbitals (LCAO). Following
the Bagayoko, Zhao, Williams, method, as enhanced by Ekuma, and Franklin
(BZW-EF), we solved self-consistently both the Kohn-Sham equation and the
equation giving the ground state charge density in terms of the wave functions
of the occupied states. We found an indirect band gap of 2.83 eV, from W to R.
Our calculated direct gaps are 2.90, 2.98, 3.02, 3.22, and 3.51 eV at R, W, X,
{\Gamma}, and T, respectively. The band structure and density of states show
high localization, typical of a molecular solid. The partial density of states
shows that the valence bands are formed only by complex anionic states. These
results are in excellent agreement with experiment. So are the calculated
densities of states. Our calculated electron effective masses of 1.18, 0.63,
and 0.73 mo in the {\Gamma}-X, {\Gamma}-R, and {\Gamma}-W directions,
respectively, show the highly anisotropic nature of this material.",1208.5710v2
2010-03-01,"Reentrant fractional quantum Hall states in bilayer graphene: Controllable, driven phase transitions","Here we report from our theoretical studies that in biased bilayer graphene,
one can induce phase transitions from an incompressible state to a compressible
state by tuning the bandgap at a given electron density. Likewise, variation of
the density with a fixed bandgap results in a transition from the FQHE states
at lower Landau levels to compressible states at intermediate Landau levels and
finally to FQHE states at higher Landau levels. This intriguing scenario of
tunable phase transitions in the fractional quantum Hall states is unique to
bilayer graphene and never before existed in conventional semiconductor
systems.",1003.0378v1
1998-05-01,Partial level densities for nuclear data calculations,"The main formalisms of partial level densities (PLD) used in preequilibrium
nuclear reaction models, based on the equidistant spacing model (ESM), are
considered. A collection of FORTRAN77 functions for PLD calculation by using 14
formalisms for the related partial-state densities is provided and 28 sample
cases (73 versions) are described. The results are given in graphic form too.
Composite (recommended) formulas, which include the optional use of various
corrections, i.e. the advanced pairing and shell correction in addition to the
Pauli effect, and average energy-dependent single-particle level densities for
the excited particles and holes, are also given. The formalism comprises the
density of particle-hole bound states, and the effects of an exact correction
for the Pauli-exclusion principle are considered. Keywords: Partial nuclear
level density; Nuclear level density; Single-particle level density;
Equidistant-spacing model; Preequilibrium emission; Nuclear reactions",9805002v1
2024-03-21,Current density functional framework for spin-orbit coupling: Extension to periodic systems,"Spin-orbit coupling induces a current density in the ground state, which
consequently requires a generalization for meta-generalized gradient
approximations. That is, the exchange-correlation energy has to be constructed
as an explicit functional of the current density and a generalized kinetic
energy density has to be formed to satisfy theoretical constraints. Herein, we
generalize our previously presented formalism of spin-orbit current density
functional theory [Holzer et al., J. Chem. Phys. 157, 204102 (2022)] to
non-magnetic and magnetic periodic systems of arbitrary dimension. Besides the
ground-state exchange-correlation potential, analytical derivatives such as
geometry gradients and stress tensors are implemented. The importance of the
current density is assessed for band gaps, lattice constants, magnetic
transitions, and Rashba splittings. For the latter, the impact of the current
density may be larger than the deviation between different density functional
approximations.",2403.14420v1
2007-01-29,Local density of states and Friedel oscillations around a non-magnetic impurity in unconventional density wave,"We present a mean-field theoretical study on the effect of a single
non-magnetic impurity in quasi-one dimensional unconventional density wave. The
local scattering potential is treated within the self-consistent $T$-matrix
approximation. The local density of states around the impurity shows the
presence of resonant states in the vicinity of the Fermi level, much the same
way as in $d$-density waves or unconventional superconductors. The assumption
for different forward and backscattering, characteristic to quasi-one
dimensional systems in general, leads to a resonance state that is double
peaked in the pseudogap. The Friedel oscillations around the impurity are also
explored in great detail, both within and beyond the density wave coherence
length $\xi_0$. Beyond $\xi_0$ we find power law behavior as opposed to the
exponential decay of conventional density wave. The entropy and specific heat
contribution of the impurity are also calculated for arbitrary scattering
strengths.",0701732v1
2015-03-28,Synchrotron and Compton Spectra from a Steady-State Electron Distribution,"Energy densities of relativistic electrons and protons in extended galactic
and intracluster regions are commonly determined from spectral radio and
(rarely) $\gamma$-ray measurements. The time-independent particle spectral
density distributions are commonly assumed to have a power-law (PL) form over
the relevant energy range. A theoretical relation between energy densities of
electrons and protons is usually adopted, and energy equipartition is invoked
to determine the mean magnetic field strength in the emitting region. We show
that for typical conditions, in both star-forming and starburst galaxies, these
estimates need to be scaled down substantially due to significant energy losses
that (effectively) flatten the electron spectral density distribution,
resulting in a much lower energy density than deduced when the distribution is
assumed to have a PL form. The steady-state electron distribution in the
nuclear regions of starburst galaxies is calculated by accounting for Coulomb,
bremsstrahlung, Compton, and synchrotron losses; the corresponding emission
spectra of the latter two processes are calculated and compared to the
respective PL spectra. We also determine the proton steady-state distribution
by taking into account Coulomb and pion production losses, and briefly discuss
implications of our steady-state particle spectra for estimates of proton
energy densities and magnetic fields.",1503.08336v1
2018-11-27,Phenomenological level density model with hybrid parameterization of deformed and spherical state densities,"A phenomenological level density model that has different level density
parameter sets for the state densities of the deformed and the spherical
states, and the optimization of the parameters using experimental data of the
average s-wave neutron resonance spacing are presented. The transition to the
spherical state from the deformed one is described using the parameters derived
from a microscopic nuclear structure calculation. The nuclear reaction
calculation has been performed by the statistical model using the present level
density. Resulting cross sections for various reactions with the spherical,
deformed and transitional target nuclei show a fair agreement with the
experimental data, which indicates the effectiveness of the present model. The
role of the rotational collective enhancement in the calculations of those
cross sections is also discussed.",1811.10754v1
2023-02-17,Light front synchronization and rest frame densities of the proton: Electromagnetic densities,"We clarify the physical origin and meaning of the two-dimensional
relativistic densities of the light front formalism. The densities are shown to
originate entirely from the use of light front time instead of instant form
time, which physically corresponds to using an alternative synchronization
convention. This is shown by using tilted light front coordinates, which
consist of light front time and ordinary spatial coordinates, and which are
also used to show that the obtained densities describe a system at rest rather
than at infinite momentum. These coordinates allow all four components of the
electromagnetic current density to be given clear physical meanings. We
explicate the formalism for spin-half targets, obtaining charge and current
densities of the proton and neutron using empirical form factor
parametrizations, as well as up and down quark densities and currents. Angular
modulations in the densities of transversely-polarized states are explained as
originating from redshifts and blueshifts due to quarks moving in different
longitudinal directions.",2302.09171v2
2007-05-24,"The geometry of density states, positive maps and tomograms","The positive and not completely positive maps of density matrices, which are
contractive maps, are discussed as elements of a semigroup. A new kind of
positive map (the purification map), which is nonlinear map, is introduced. The
density matrices are considered as vectors, linear maps among matrices are
represented by superoperators given in the form of higher dimensional matrices.
Probability representation of spin states (spin tomography) is reviewed and
U(N)-tomogram of spin states is presented. Properties of the tomograms as
probability distribution functions are studied. Notion of tomographic purity of
spin states is introduced. Entanglement and separability of density matrices
are expressed in terms of properties of the tomographic joint probability
distributions of random spin projections which depend also on unitary group
parameters. A new positivity criterion for hermitian matrices is formulated. An
entanglement criterion is given in terms of a function depending on unitary
group parameters and semigroup of positive map parameters. The function is
constructed as sum of moduli of U(N)-tomographic symbols of the hermitian
matrix obtained after action on the density matrix of composite system by a
positive but not completely positive map of the subsystem density matrix. Some
two-qubit and two-qutritt states are considered as examples of entangled
states. The connection with the star-product quantisation is discussed. The
structure of the set of density matrices and their relation to unitary group
and Lie algebra of the unitary group are studied. Nonlinear quantum evolution
of state vector obtained by means of applying purification rule of density
matrices evolving via dynamical maps is considered. Some connection of positive
maps and entanglement with random matrices is discussed and used.",0705.3574v1
2003-01-11,Quasiparticle density of states of d-wave superconductors in a disordered vortex lattice,"We calculate the density of states of a disordered inhomogeneous d-wave
superconductor in a magnetic field. The field-induced vortices are assumed to
be pinned at random positions and the effects of the scattering of the
quasi-particles off the vortices are taken into account using the singular
gauge transformation of Franz and Tesanovic. We find two regimes for the
density of states: at very low energies the density of states follows a law
\rho(\epsilon) \sim \rho_0 + |\epsilon|^{\alpha} where the exponent is close to
1. A good fit of the density of states is obtained at higher energies,
excluding a narrow region around the origin, with a similar power law energy
dependence but with \alpha close to 2. Both at low and at higher energies
\rho_0 scales with the inverse of the magnetic length (\sqrt{B}).",0301170v2
2011-08-30,"Generic phases of cross-linked active gels: Relaxation, Oscillation and Contractility","We study analytically and numerically a generic continuum model of an
isotropic active solid with internal stresses generated by non-equilibrium
`active' mechano-chemical reactions. Our analysis shows that the gel can be
tuned through three classes of dynamical states by increasing motor activity: a
constant unstrained state of homogeneous density, a state where the local
density exhibits sustained oscillations, and a steady-state which is
spontaneously contracted, with a uniform mean density.",1108.5999v2
2021-07-09,Majorana fermion arcs and the local density of states of UTe$_2$,"$\text{UTe}_2$ is a leading candidate for chiral p-wave superconductivity,
and for hosting exotic Majorana fermion quasiparticles. Motivated by recent STM
experiments in this system, we study particle-hole symmetry breaking in chiral
p-wave superconductors. We compute the local density of states from Majorana
fermion surface states in the presence of Rashba surface spin-orbit coupling,
which is expected to be sizeable in heavy-fermion materials like UTe$_2$. We
show that time-reversal and surface reflection symmetry breaking lead to a
natural pairing tendency towards a triplet pair density wave state, which
naturally can account for broken particle-hole symmetry.",2107.04621v1
2010-03-10,The entanglement of few-particle systems when using the local-density approximation,"In this chapter we discuss methods to calculate the entanglement of a system
using density-functional theory. We firstly introduce density-functional theory
and the local-density approximation (LDA). We then discuss the concept of the
`interacting LDA system'. This is characterised by an interacting many-body
Hamiltonian which reproduces, uniquely and exactly, the ground state density
obtained from the single-particle Kohn-Sham equations of density-functional
theory when the local-density approximation is used. We motivate why this idea
can be useful for appraising the local-density approximation in many-body
physics particularly with regards to entanglement and related quantum
information applications. Using an iterative scheme, we find the Hamiltonian
characterising the interacting LDA system in relation to the test systems of
Hooke's atom and helium-like atoms. The interacting LDA system ground state
wavefunction is then used to calculate the spatial entanglement and the results
are compared and contrasted with the exact entanglement for the two test
systems. For Hooke's atom we also compare the entanglement to our previous
estimates of an LDA entanglement. These were obtained using a combination of
evolutionary algorithm and gradient descent, and using an LDA-based
perturbative approach. We finally discuss if the position-space information
entropy of the density---which can be obtained directly from the system density
and hence easily from density-functional theory methods---can be considered as
a proxy measure for the spatial entanglement for the test systems.",1003.2094v1
2000-04-04,Charge-density-wave formation by Van Hove nesting in the α-phase of Sn/Ge(111),"We study the role of electron correlations in the formation of the surface
charge-density-wave state in the Sn/Ge(111) interface. The Fermi energy of the
overlayer is treated as a dynamical variable, which undergoes a substantial
renormalization by the interaction. We show that the Fermi level turns out to
be pinned to a Van Hove singularity in the density of states, which explains
the formation of the charge-density-wave, the observation of a very flat band
in photoemission experiments and the reduction of the spectral weight in the
low-temperature phase.",0004044v1
2017-01-20,Effect of nuclear saturation parameters on possible maximum mass of neutron stars,"In order to systematically examine the possible maximum mass of neutron
stars, which is one of the important properties characterizing the physics in
high-density region, I construct neutron star models by adopting
phenomenological equations of state with various values of nuclear saturation
parameters for low-density region, which are connected to the equation of state
for high-density region characterized by the possible maximum sound velocity in
medium. I derive an empirical formula for the possible maximum mass of neutron
star. If massive neutron stars are observed, it could be possible to get a
constraint on the possible maximum sound velocity for high-density region.",1701.05646v1
2019-02-25,Targeting Multiple States in the Density Matrix Renormalization Group with The Singular Value Decomposition,"In the Density Matrix Renormalization Group (DMRG), multiple states must be
included in the density matrix when properties beyond ground state are needed,
including temperature dependence, time evolution, and frequency-resolved
response functions. How to include these states in the density matrix has been
shown in the past. But it is advantageous to replace the density matrix by a
singular value decomposition (SVD) instead, because of improved performance,
and because it enables multiple targeting in the matrix product state
description of the DMRG. This paper shows how to target multiple states using
the SVD; it analyzes the implication of local symmetries, and discusses typical
performance improvements using the example of the Hubbard model's
photo-emission spectra on a ladder geometry.",1902.09621v1
2022-03-07,A Time-Dependent Random State Approach for Large-scale Density Functional Calculations,"We develop a self-consistent first-principle method based on the density
functional theory. Physical quantities, such as the density of states, Fermi
energy and electron density are obtained using a time-dependent random state
method without diagonalization. The numerical error for calculating either
global or local variables always scales as $1/\sqrt{SN_{e}}$, where $N_{e}$ is
the number of electrons and $S$ is the number of random states, leading to a
sublinear computational cost with the system size. In the limit of large
systems, one random state could be enough to achieve reasonable accuracy. The
method's accuracy and scaling properties are derived analytically and verified
numerically in different condensed matter systems. Our time-dependent random
state approach provides a powerful strategy for large-scale density functional
calculations.",2203.03465v2
2018-08-15,Density-driven correlations in many-electron ensembles: theory and application for excited states,"Density functional theory can be extended to excited states by means of a
unified variational approach for passive state ensembles. This extension
overcomes the restriction of the typical density functional approach to ground
states, and offers useful formal and demonstrated practical benefits. The
correlation energy functional in the generalized case acquires higher
complexity than its ground state counterpart, however. Little is known about
its internal structure nor how to effectively approximate it in general. Here
we show that such a functional can be broken down into natural components,
including what we call ""state-"" and ""density-driven"" correlations, with the
former amenable to conventional approximations, and the latter being a unique
feature of ensembles. Such a decomposition, summarised in eq. (6), provides us
with a pathway to general approximations that are able to routinely handle
low-lying excited states. The importance of density-driven correlations is
demonstrated, an approximation for them is introduced and shown to be useful.",1808.04994v2
2010-10-24,Correlation and Entanglement of Multipartite States,"We derive a classification and a measure of classical- and
quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level
systems, in terms of SU$(n)$ representations of density matrices. We compare
the measure for the case of bipartite correlation with concurrence and the
entropy of entanglement. The characterization of correlation is in terms of the
number of nonzero singular values of the correlation matrix, but that of mixed
state entanglement requires additional invariant parameters in the density
matrix. For the bipartite qubit case, the condition for mixed state
entanglement is written explicitly in terms of the invariant paramters in the
density matrix. For identical particle systems we analyze the effects of
exchange symmetry on classical and quantum correlation.",1010.4935v1
2022-02-06,The two-dimensional density of states in normal and superconducting compounds,"The present work represents a review for the numerical calculation of the
density of states (DoS) for two-dimensional tight-binding models with first
neighbors in its normal state and for two superconducting order parameters. One
is a singlet scalar state and the other is a triplet vector state. At the
beginning an emphasis is given to the general expressions commonly used to the
calculation of the density of states as the number of partial and total number
of states, the degrees of freedom and the ab-initio methods most commonly used
to its calculation. Then, the transition happening to the DoS normal states by
varying the Fermi energy and the hopping parameter is investigated. After that,
the numerical calculation of the superconducting density of states using the
zero-temperature scattering cross-section is performed for the two order
parameters. Finally, the residual density of states depending on disorder and
the scattering potential strength using the Larkin equation are calculated for
the two order parameter symmetries different in nature.",2202.02761v4
2000-06-07,Nonuniqueness of the Potentials of Spin-Density-Functional Theory,"It is shown that, contrary to widely held beliefs, the potentials of
spin-density-functional theory (SDFT) are not unique functionals of the spin
densities. Explicit examples of distinct sets of potentials with the same
ground-state densities are constructed, and general arguments that uniqueness
should not occur in SDFT and other generalized density-functional theories are
given. As a consequence, various types of applications of SDFT require
significant corrections or modifications.",0006116v1
2009-06-15,Schrödinger equations for the square root density of an eigenmixture and % the square root of an eigendensity spin matrix,"We generalize a ""one eigenstate"" theorem of Levy, Perdew and Sahni (LPS) to
the case of densities coming from eigenmixture density operators. The
generalization is of a special interest for the radial density functional
theory (RDFT) for nuclei, a consequence of the rotational invariance of the
nuclear Hamiltonian; when nuclear ground states (GSs) have a finite spin, the
RDFT uses eigenmixture density operators to simplify predictions of GS energies
into one-dimensional, radial calculations. We also study Schr\""odinger
equations governing spin eigendensity matrices.",0906.2668v1
2016-11-03,Convex set of quantum states with positive partial transpose analysed by hit and run algorithm,"The convex set of quantum states of a composite $K \times K$ system with
positive partial transpose is analysed. A version of the hit and run algorithm
is used to generate a sequence of random points covering this set uniformly and
an estimation for the convergence speed of the algorithm is derived. For $K\ge
3$ this algorithm works faster than sampling over the entire set of states and
verifying whether the partial transpose is positive. The level density of the
PPT states is shown to differ from the Marchenko-Pastur distribution, supported
in [0,4] and corresponding asymptotically to the entire set of quantum states.
Based on the shifted semi--circle law, describing asymptotic level density of
partially transposed states, and on the level density for the Gaussian unitary
ensemble with constraints for the spectrum we find an explicit form of the
probability distribution supported in [0,3], which describes well the level
density obtained numerically for PPT states.",1611.01194v2
2008-07-11,The cluster glass state in the two-dimensional extended t-J model,"The recent observation of an electronic cluster glass state composed of
random domains with unidirectional modulation of charge density and/or spin
density on Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} reinvigorates the debate of
existence of competing interactions and their importance in high temperature
superconductivity. By using a variational approach, here we show that the
presence of the cluster glass state is actually an inherent nature of the model
based on the antiferromagnetic interaction (J) only, i.e. the well known t-J
model. There is no need yet to introduce a competing interaction to understand
the existence of the cluster glass state. The long-range pairing correlation is
not much influenced by the disorder in the glass state which also has nodes and
linear density of states. In the antinodal region, the spectral weight is
almost completely suppressed. The modulation also produces subgap structures
inside the ""coherent"" peaks of the local density of states.",0807.1875v1
2011-04-20,Alpha-cluster structure and density wave in oblate nuclei,"Pentagon and triangle shapes in Si-28 and C-12 are discussed in relation with
nuclear density wave. In the antisymmetrized molecular dynamics calculations,
the $K^\pi=5^-$ band in Si-28 and the $K^\pi=3^-$ band in C-12 are described by
the pentagon and triangle shapes, respectively. These negative-parity bands can
be interpreted as the parity partners of the $K^\pi=0^+$ ground bands and they
are constructed from the parity-asymmetric-intrinsic states. The pentagon and
the triangle shapes originate in 7alpha and 3alpha cluster structures,
respectively. In a mean-field picture, they are described also by the static
one-dimensional density wave at the edge of the oblate states. In analysis with
ideal alpha cluster models using Brink-Bloch cluster wave functions and that
with a simplified model, we show that the static edge density wave for the
pentagon and triangle shapes can be understood by spontaneous breaking of axial
symmetry, i.e., the instability of the oblate states with respect to the edge
density wave. The density wave is enhanced in the Z=N nuclei due to the
proton-neutron coherent density waves, while it is suppressed in Z\ne N nuclei.",1104.4140v1
2010-12-14,Theorems on ground-state phase transitions in Kohn-Sham models given by the Coulomb density functional,"Some theorems on derivatives of the Coulomb density functional with respect
to the coupling constant $\lambda$ are given. Consider an electron density
$n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the
reduced coupling constant, $\lambda<1$, is defined to reproduce $n_{GS}({\bf
r})$ and the ground state energy. Fixing the charge density, possible phase
transitions as level crossings detected in a value of the reduced density
functional happen only at discrete points along the $\lambda$ axis. If the
density is $v$-representable also for $\lambda<1$, accumulation of phase
transition points is forbidden when $\lambda\rightarrow 1$. Relevance of the
theorems for the multi-reference density functional theory is discussed.",1012.2964v1
2007-02-17,Analytic Density of States in the Abrikosov-Gorkov Theory,"Since the early 1960s, Abrikosov-Gorkov theory has been used to describe
superconductors with paramagnetic impurities. Interestingly, the density of
states resulting from the theoretical framework has to date only been known
approximately, as a numeric solution of a complex polynomial. Here we introduce
an exact analytic solution for the density of states of a superconductor with
paramagnetic impurities. The solution is valid in the whole regime of
Abrikosov-Gorkov theory; both where there is an energy gap and gapless. While
of fundamental interest, we argue that this solution also has computational
benefits in the evaluation of integrals for tunneling conductances and allows
for an analytic description of materials with densities of states that are
modeled from the basic Abrikosov-Gorkov density of states.",0702404v1
2002-09-25,Measuring the elements of the optical density matrix,"Most methods for experimentally reconstructing the quantum state of light
involve determining a quasiprobability distribution such as the Wigner
function. In this paper we present a scheme for measuring individual density
matrix elements in the photon number state representation. Remarkably, the
scheme is simple, involving two beam splitters and a reference field in a
coherent state.",0209132v1
2000-01-04,Doppler shift on local density of states and local impurity scattering in the vortex state,"The vortex state thermal and transport properties of the high T_c copper
oxides can be understood in a d-wave gap model and are dominated by the
extended quasiparticle states that exist along the nodal directions in momentum
space. The Doppler shift on these states due to the circulating supercurrents
around the vortex core, introduces new van Hove ridges into the energy
dependent local density of states (LDOS) as a function of distance in the
region between cores. We emphasize the topology of these ridges and the effect
on them of local impurity scattering in Born and unitary limit. We treat
possible orthorhombicity. Effective local scttering rates are also obtaines.",0001029v1
2010-05-05,Stationary states in single-well potentials under symmetric Levy noises,"We discuss the existence of stationary states for subharmonic potentials
$V(x) \propto |x|^c$, $c<2$, under action of symmetric $\alpha$-stable noises.
We show analytically that the necessary condition for the existence of the
steady state is $c>2-\alpha$. These states are characterized by heavy-tailed
probability density functions which decay as $P(x) \propto x^{-(c+\alpha -1)}$
for $|x| \to \infty$, i.e. stationary states posses a heavier tail than the
corresponding $\alpha$-stable law. Monte Carlo simulations confirm the
existence of such stationary states and the form of the tails of corresponding
probability densities.",1005.0772v1
2004-03-22,A dynamic localization of 2D electrons at mesoscopic length scales,"We have investigated the local magneto-transport in high-quality 2D electron
systems at low carrier densities. The positive magneto-resistance in
perpendicular magnetic field in the strongly insulating regime has been
measured to evaluate the spatial concentration of localized states within a
mesoscopic region of the samples. An independent measurement of the electron
density within the same region shows an unexpected correspondence between the
density of electrons in the metallic regime and that of the localized states in
the insulating phase. We have argued that this correspondence manifests a rigid
distribution of electrons at low densities.",0403560v1
2010-08-11,"Chirality, charge and spin-density wave instabilities of a two-dimensional electron gas in the presence of Rashba spin-orbit coupling","We show that a result equivalent to Overhauser's famous Hartree-Fock
instability theorem can be established for the case of a two-dimensional
electron gas in the presence of Rashba spin-obit coupling. In this case it is
the spatially homogeneous paramagnetic chiral ground state that is shown to be
differentially unstable with respect to a certain class of distortions of the
spin-density-wave and charge-density-wave type. The result holds for all
densities. Basic properties of these inhomogeneous states are analyzed.",1008.1816v1
2013-02-13,Photon gas with hyperbolic dispersion relations,"We investigate the density of states for a photon gas confined in a
nonmagnetic metamaterial medium in which some components of the permittivity
tensor are negative. We study the effect of the resulting hyperbolic dispersion
relations on the black body spectral density. We show that for both of the
possible wavevector space topologies, the spectral density vanishes at a
certain frequency. We obtain the partition function and derive some
thermodynamical quantities of the system. To leading order, the results
resemble those of a one- or two-dimensional photon gas with an enhanced density
of states.",1302.3034v1
1997-05-28,Effects of gap anisotropy upon the electronic structure around a superconducting vortex,"An isolated single vortex is considered within the framework of the
quasiclassical theory. The local density of states around a vortex is
calculated in a clean type II superconductor with an anisotropy. The anisotropy
of a superconducting energy gap is crucial for bound states around a vortex. A
characteristic structure of the local density of states, observed in the
layered hexagonal superconductor 2H-NbSe2 by scanning tunneling microscopy
(STM), is well reproduced if one assumes an anisotropic s-wave gap in the
hexagonal plane. The local density of states (or the bound states) around the
vortex is interpreted in terms of quasiparticle trajectories to facilitate an
understanding of the rich electronic structure observed in STM experiments. It
is pointed out that further fine structures and extra peaks in the local
density of states should be observed by STM.",9705286v1
2015-09-01,"Onsager rule, quantum oscillation frequencies, and the density of states in the mixed-vortex state of cuprates","The Onsager rule determines the frequencies of quantum oscillations in
magnetic fields. We show that this rule remains intact to an excellent
approximation in the mixed-vortex state of the underdoped cuprates even though
the Landau level index $n$ may be fairly low, $n\sim 10$. The models we
consider are fairly general, consisting of a variety of density wave states
combined with $d$-wave superconductivity within a mean field theory. Vortices
are introduced as quenched disorder and averaged over many realizations, which
can be considered as snapshots of a vortex liquid state. We also show that the
oscillations ride on top of a field independent density of states, $\rho(B)$,
for higher fields. This feature appears to be consistent with recent specific
heat measurements [C. Marcenat, et al. Nature Comm. {\bf 6}, 7927 (2015)]. At
lower fields we model the system as an ordered vortex lattice, and show that
its density of states follows a dependence $\rho(B)\propto \sqrt{B}$ in
agreement with the semiclassical results [G. E. Volovik, JETP Lett. {\bf 58},
469 (1993)].",1509.00494v2
2004-01-05,Influence of s-d scattering on the electron density of states in ferromagnet/superconductor bilayer,"We study the dependence of the electronic density of states (DOS) on the
distance from the boundary for a ferromagnet/superconductor bilayer. We
calculate the electron density of states in such structure taking into account
the two-band model of the ferromagnet (FM) with conducting s and localized d
electrons and a simple s-wave superconductor (SC). It is demonstrated that due
to the electron s-d scattering in the ferromagnetic layer in the third order of
s-d scattering parameter the oscillation of the density of states has larger
period and more drastic decrease in comparison with the oscillation period for
the electron density of states in the zero order.",0401037v2
2009-02-11,Accurate calculation of the local density of optical states in inverse-opal photonic crystals,"We have investigated the local density of optical states (LDOS) in titania
and silicon inverse opals -- three-dimensional photonic crystals that have been
realized experimentally. We used the H-field plane-wave expansion method to
calculate the density of states and the projected local optical density of
states, which are directly relevant for spontaneous emission dynamics and
strong coupling. We present the first quantitative analysis of the frequency
resolution and of the accuracy of the calculated local density of states. We
have calculated the projected LDOS for many different emitter positions in
inverse opals in order to supply a theoretical interpretation for recent
emission experiments and as reference results for future experiments and theory
by other workers. The results show that the LDOS in inverse opals strongly
depends on the crystal lattice parameter as well as on the position and
orientation of emitting dipoles.",0902.1850v1
2005-12-16,Density Induced Quantum Phase Transitions in Triplet Superconductors,"We consider the possibility of quantum phase transitions in the ground state
of triplet superconductors where particle density is the tunning parameter. For
definiteness, we focus on the case of one band quasi-one-dimensional triplet
superconductors but many of our conclusions regarding the nature of the
transition are quite general. Within the functional integral formulation, we
calculate the electronic compressibility and superfluid density tensor as a
function of the particle density for various triplet order parameter symmetries
and find that these quantities are non-analytic when a critical value of the
particle density is reached.",0512405v1
2021-10-21,The complete inverse Kohn-Sham problem: from the density to the energy,"A complete solution to the inverse problem of Kohn-Sham (KS) density
functional theory is proposed. Our method consists of two steps. First, the
effective KS potential is determined from the ground state density of a given
system. Then, the knowledge of the potentials along a path in the space of
densities is exploited in a line integration formula to determine numerically
the KS energy of that system. A possible choice for the density path is
proposed. A benchmark in the case of a simplified yet realistic nuclear system
is shown to be successful, so that the method seems promising for future
applications.",2110.11193v1
2000-03-21,Stripe orders in the extended Hubbard model,"We study stripe orders of charge and spin density waves in the extended
Hubbard model with the nearest-neighbor Coulomb repulsion V within the mean
field approximation. We obtain V vs. T(temperature) phase diagram for the
on-site Coulomb interaction U/t=8.0 and the filling n=0.8, here t is a
nearest-neighbor transfer energy. Our result shows that the diagonal stripe
spin density wave state (SDW) is stable for small V, but for large V the most
stable state changes to a charge density wave-antiferromagnetic (CDW-AF) state.
Especially we find at low temperature and for a certain range of value of V, a
vertical stripe CDW-AF state becomes stable.",0003347v1
2001-05-17,Granular Matter and the Marginal Rigidity State,"Model experiments are reported on the build-up of granular piles in two
dimensions. These show that as the initial density of falling grains is
increased, the resulting pile has decreasing final density and its coordination
number approaches the low value predicted for the theoretical marginal rigidity
state. This provides the first direct experimental evidence for this state of
granular matter. We trace the decrease in the coordination number to the
dynamics within an advancing yield front between the consolidated pile and the
falling grains. We show that the front's size increases with initial density,
diverging as the marginal rigidity state is approached.",0105348v1
2005-01-26,Resonant Nernst effect in the metallic and field-induced spin density wave states of (TMTSF)2ClO4,"We examine an unusual phenomenon where, in tilted magnetic fields near magic
angles parallel to crystallographic planes, a ""giant"" resonant Nernst signal
has been observed by Wu et al.[Phys. Rev. Lett. 91 56601(2003)] in the metallic
state of an organic conducting Bechgaard salt. We show that this effect appears
to be a general feature of these materials, and is also present in the field
induced spin density wave phase with even larger amplitude. Our results place
new restrictions on models that treat the metallic state as an unconventional
density wave or as a state with finite Cooper pairing.",0501649v1
2014-02-11,New approach for solving master equations of density operator for the Jaynes Cummings Model with Cavity Damping,"By introducing thermal entangled state representation which can map master
equations of density operator in quantum statistics as state vector evolution
equations and using dissipative interaction picture we solve the master
equation of J-C model with cavity damping. In addition we derive the Wigner
function for density operator when the atom is initially in the up state and
the cavity mode is in coherent state.",1402.2556v1
2023-12-13,Homogenization of 2D materials in the Thomas-Fermi-von Weizsacker theory,"We study the homogenization of the Thomas-Fermi-von Weizsacker (TFW) model
for 2D materials. It consists in considering 2D-periodic nuclear densities with
periods going to zero. We study the behavior of the corresponding ground state
electronic densities and ground state energies. The main result is that these
three dimensional problems converge to a limit model that is one dimensional.
We also illustrate this convergence with numerical simulations and estimate the
converging rate for the ground state electronic densities and the ground state
energies.",2312.08067v1
2018-07-01,Hidden pair-density-wave order in cuprate superconductors,"When the Mott insulating state is suppressed by charge carrier doping, the
pseudogap phenomenon emerges, where at the low-temperature limit,
superconductivity coexists with some ordered electronic states. Within the
framework of the kinetic-energy-driven superconductivity, the nature of the
pair-density-wave order in cuprate superconductors is studied by taking into
account the pseudogap effect. It is shown that the onset of the
pair-density-wave order does not produce an ordered gap, but rather a novel
hidden order as a result of the interplay of the charge-density-wave order with
superconductivity. As a consequence, this novel hidden pair-density-wave order
as a subsidiary order parameter coexists with the charge-density-wave order in
the superconducting-state, and is absent from the normal-state.",1807.00296v2
2019-01-23,The algebraic molecular model in $^{12}$C and its application to the $α$+$^{12}$C scattering: from densities and transition densities to optical potentials and nuclear formfactors,"The algebraic molecular model is used in $^{12}$C to construct densities and
transition densities connecting low-lying states of the rotovibrational
spectrum, first and foremost those belonging to the rotational bands based on
the ground and the Hoyle states. These densities are then used as basic
ingredients to calculate, besides electromagnetic transition probabilities,
nuclear potentials and formfactors to describe elastic and inelastic
$\alpha$+$^{12}$C scattering processes. The calculated densities and transition
densities are also compared with those obtained by directly solving the problem
of three interacting alpha's within a three-body approach where continuum
effects, relevant in particular for the Hoyle state, are properly taken into
account.",1901.07954v1
1999-03-02,Dynamic States of a Continuum Traffic Equation with On-Ramp,"We study the phase diagram of the continuum traffic flow model of a highway
with an on-ramp. Using an open boundary condition, traffic states and
metastabilities are investigated numerically for several representative values
of the upstream boundary flux $f_{up}$ and for the whole range of the on-ramp
flux $f_{rmp}$. An inhomogeneous but time-independent traffic state (standing
localized cluster state) is found and related to a recently measured traffic
state. Due to the density gradient near the on-ramp, a novel traffic jam can
occur even when the downstream density is below the critical density of the
usual traffic jam formation in homogeneous highways, and its structure varies
qualitatively with $f_{rmp}$. The free flow, the recurring hump (RH) state, and
the traffic jam can all coexist in a certain metastable region where the free
flow can undergo phase transitions either to the RH state or to the traffic jam
state. We also find two nontrivial analytic solutions. These solutions
correspond to the standing localized cluster state and the homogeneous
congested traffic state (one form of the novel traffic jam),which are observed
in numerical simulations.",9903036v1
2021-10-28,"Model-based electron density profile estimation and control, applied to ITER","In contemporary magnetic confinement devices, the density distribution is
sensed with interferometers and actuated with feedback controlled gas injection
and open-loop pellet injection. This is at variance with the density control
for ITER and DEMO, that will depend mainly on pellet injection as an actuator
in feed-back control. This paper presents recent developments in state
estimation and control of the electron density profile for ITER using relevant
sensors and actuators. As a first step, Thomson scattering is included in an
existing dynamic state observer. Second, model predictive control is developed
as a strategy to regulate the density profile while avoiding limits associated
with the total density (Greenwald limit) or gradients in the density
distribution (e.g. neo-classical impurity transport). Simulations show that
high quality density profile estimation can be achieved with Thomson Scattering
and that the controller is capable of regulating the distribution as desired.",2110.14975v1
2007-03-28,Non equilibrium steady states: fluctuations and large deviations of the density and of the current,"These lecture notes give a short review of methods such as the matrix ansatz,
the additivity principle or the macroscopic fluctuation theory, developed
recently in the theory of non-equilibrium phenomena. They show how these
methods allow to calculate the fluctuations and large deviations of the density
and of the current in non-equilibrium steady states of systems like exclusion
processes. The properties of these fluctuations and large deviation functions
in non-equilibrium steady states (for example non-Gaussian fluctuations of
density or non-convexity of the large deviation function which generalizes the
notion of free energy) are compared with those of systems at equilibrium.",0703762v1
2007-07-25,The space of density states in geometrical quantum mechanics,"We present a geometrical description of the space of density states of a
quantum system of finite dimension. After presenting a brief summary of the
geometrical formulation of Quantum Mechanics, we proceed to describe the space
of density states $\D(\Hil)$ from a geometrical perspective identifying the
stratification associated to the natural $GL(\Hil)$--action on $\D(\Hil)$ and
some of its properties. We apply this construction to the cases of quantum
systems of two and three levels.",0707.3759v1
2013-05-05,Convergence of the density of states and delocalization of eigenvectors on random regular graphs,"Consider a random regular graph of fixed degree $d$ with $n$ vertices. We
study spectral properties of the adjacency matrix and of random Schr\""odinger
operators on such a graph as $n$ tends to infinity.
  We prove that the integrated density of states on the graph converges to the
integrated density of states on the infinite regular tree and we give uniform
bounds on the rate of convergence. This allows to estimate the number of
eigenvalues in intervals of size comparable to $\log_{d-1}^{-1}(n)$. Based on
related estimates for the Green function we derive results about delocalization
of eigenvectors.",1305.1039v2
2007-01-02,Quasi-One-Dimensional Spin-Density-Wave States with Two Kinds of Periodic Potentials and a Interchain Misfit,"Spin density wave (SDW) states of a quasi-one-dimensional system with an
incommensurate wave vector perpendicular to the chain have been studied in the
presence of two kinds of commensurate potentials, which originate in a
quarter-filled band and dimerization along the chain. In terms of a phase
variable of the SDW order parameter, we treat classically the two-dimensional
Hamiltonian, which includes both acoustic excitations with long wave length and
a vortex excitation with short wave length. A phase diagram on the plane of
temperature and chemical potential (where the latter corresponds to the
deviation of the transverse wave vector from the commensurate one) exhibits a
variety of states given by the commensurate SDW state without charge density,
the commensurate SDW state with charge density, the incommensurate SDW state
and the disordered state.",0701038v1
2002-11-25,Steady-state properties of a totally asymmetric exclusion process with particles of arbitrary size,"The steady-state currents and densities of a one-dimensional totally
asymmetric exclusion process (TASEP) with particles that occlude an integer
number ($d$) of lattice sites are computed using various mean field
approximations and Monte Carlo simulations. TASEP's featuring particles of
arbitrary size are relevant for modeling systems such as mRNA translation,
vesicle locomotion along microtubules, and protein sliding along DNA. We
conjecture that the nonequilibrium steady-state properties separate into low
density, high density, an maximal current phases similar to those of the
standard ($d=1$) TASEP. A simple mean field approximation for steady-state
particle currents and densities is found to be inaccurate. However, we find
{\it local equilibrium} particle distributions derived from a discrete Tonks
gas partition function yield apparently exact currents within the maximal
current phase. For the boundary-limited phases, the equilibrium Tonks gas
distribution cannot be used to predict currents, phase boundaries, or the order
of the phase transitions. However, we employ a refined mean field approach to
find apparently exact expressions for the steady state currents, boundary
densities, and phase diagrams of the $d\geq 1$ TASEP. Extensive Monte Carlo
simulations are performed to support our analytic, mean field results.",0211555v1
2008-11-27,Continuity of the integrated density of states on random length metric graphs,"We establish several properties of the integrated density of states for
random quantum graphs: Under appropriate ergodicity and amenability
assumptions, the integrated density of states can be defined using an
exhaustion procedure by compact subgraphs. A trace per unit volume formula
holds, similarly as in the Euclidean case. Our setting includes periodic
graphs. For a model where the edge length are random and vary independently in
a smooth way we prove a Wegner estimate and related regularity results for the
integrated density of states. These results are illustrated for an example
based on the Kagome lattice. In the periodic case we characterise all compactly
supported eigenfunctions and calculate the position and size of discontinuities
of the integrated density of states.",0811.4513v2
2015-01-16,Topology of density matrices,"We investigate topological properties of density matrices motivated by the
question to what extent phenomena like topological insulators and
superconductors can be generalized to mixed states in the framework of open
quantum systems. The notion of geometric phases has been extended from pure to
mixed states by Uhlmann in [Rep. Math. Phys. 24, 229 (1986)], where an emergent
gauge theory over the density matrices based on their pure-state representation
in a larger Hilbert space has been reported. However, since the uniquely
defined square root $\sqrt{\rho}$ of a density matrix $\rho$ provides a global
gauge, this construction is always topologically trivial. Here, we study a more
restrictive gauge structure which can be topologically non-trivial and is
capable of resolving homotopically distinct mappings of density matrices
subject to various spectral constraints. Remarkably, in this framework,
topological invariants can be directly defined and calculated for mixed states.
In the limit of pure states, the well known system of topological invariants
for gapped band structures at zero temperature is reproduced. We compare our
construction with recent approaches to Chern insulators at finite temperature.",1501.04135v2
2017-04-28,Short note on the density of states in 3D Weyl semimetals,"The average density of states in a disordered three-dimensional Weyl system
is discussed in the case of a continuous distribution of random scattering. Our
result clearly indicate that the average density of states does not vanish,
reflecting the absence of a critical point for a metal-insulator transition.
This calculation supports recent suggestions of an avoided quantum critical
point in the disordered three-dimensional Weyl semimetal. However, the
effective density of states can be very small such that the
saddle-approximation with a vanishing density of states might be valid for
practical cases.",1705.00019v3
2020-06-25,Modifications on parameters of $Z(4430)$ in a dense medium,"The charmonium-like resonance $ Z_c(3900) $ and its excited state $ Z(4430) $
are among the particles that are serious candidates for double heavy
tetraquarks. Calculations of different parameters associated with these states
both in the vacuum and the medium with finite density are of great importance.
Such investigations help us clarify their nature, internal quark-gluon
organization and quantum numbers. In this accordance, we extend our previous
analyses on the ground state $ Z_c(3900) $ to investigate the medium
modifications on different parameters of the excited $ Z(4430) $ state. In
particular, we calculate the mass, vector self-energy and current coupling of $
Z(4430) $ in terms of density, up to a density comparable to the density of the
cores of massive neutron stars. The obtained results may help experimental
groups aiming to study the behavior of exotic states at higher densities.",2006.14399v2
2022-02-28,Detection of $d_{1}\otimes d_{2}$ Dimensional Bipartite Entangled State: A Graph Theoretical Approach,"Braunstein et. al. have started the study of entanglement properties of the
quantum states through graph theoretical approach. Their idea was to start from
a simple unweighted graph $G$ and then they have defined the quantum state from
the Laplacian of the graph $G$. A lot of research had already been done using
the similar idea. We ask here the opposite one i.e can we generate a graph from
the density matrix? To investigate this question, we have constructed a unital
map $\phi$ such that $\phi(\rho)=L_{\rho}+\rho$, where the quantum state is
described by the density operator $\rho$. The entries of $L_{\rho}$ depends on
the entries of the quantum state $\rho$ and the entries are taken in such a way
that $L_{\rho}$ satisfies all the properties of the Laplacian. This make
possible to design a simple connected weighted graph from the Laplacian
$L_{\rho}$. We show that the constructed unital map $\phi$ characterize the
quantum state with respect to its purity by showing that if the determinant of
the matrix $\phi(\rho)-I$ is positive then the quantum state $\rho$ represent a
mixed state. Moreover, we study the positive partial transpose (PPT) criterion
in terms of the spectrum of the density matrix under investigation and the
spectrum of the Laplacian associated with the given density matrix.
Furthermore, we derive the inequality between the minimum eigenvalue of the
density matrix and the weight of the edges of the connected subgraph of a
simple weighted graph to detect the entanglement of $d_{1} \otimes d_{2}$
dimensional bipartite quantum states. Lastly, We have illustrated our results
with few examples.",2202.13963v2
2006-04-17,Implicit Density Functional Theory,"A fermion ground state energy functional is set up in terms of particle
density, relative pair density, and kinetic energy tensor density. It satisfies
a minimum principle if constrained by a complete set of compatibility
conditions. A partial set, which thereby results in a lower bound energy under
minimization, is obtained from the solution of model systems, as well as a
small number of exact sum rules. Prototypical application is made to several
one-dimensional spinless non-interacting models. The effectiveness of ""atomic""
constraints on model ""molecules"" is observed, as well as the structure of
systems with only finitely many bound states.",0604128v1
2009-05-26,High-Precision Thermodynamics and Hagedorn Density of States,"We compute the entropy density of the confined phase of QCD without quarks on
the lattice to very high accuracy. The results are compared to the entropy
density of free glueballs, where we include all the known glueball states below
the two-particle threshold. We find that an excellent, parameter-free
description of the entropy density between 0.7Tc and Tc is obtained by
extending the spectrum with the exponential spectrum of the closed bosonic
string.",0905.4229v1
2013-08-28,Exact solution for Bloch oscillations of a simple charge-density-wave insulator,"Charge-density-wave systems have a static modulation of the electronic charge
at low temperatures when they enter an ordered state. While they have been
studied for decades in equilibrium, it is only recently that they have been
examined in nonequilibrium with time-resolved studies. Here, we present the
exact solution for the nonequilibrium response of electrons (in the simplest
model for a charge density wave) when the system is placed under a strong DC
electric field. This allows us to examine the formation of driven Bloch
oscillations and how the presence of a current modifies the nonequilibrium
density of states.",1308.6060v1
2022-11-28,Density of states techniques for fermion worldlines,"Worldline representations were established as a powerful tool for studying
bosonic lattice field theories at finite density. For fermions, however, the
worldlines still may carry signs that originate from the Dirac algebra and from
the Grassmann nature of the fermion fields. We show that a density of states
approach can be set up to deal with this remaining sign problem, where finite
density is implemented in a canonical approach by working with a fixed winding
number of the fermion worldlines. We discuss the approach in detail and show
first results of a numerical implementation in 2 dimensions.",2211.15016v1
2013-04-04,Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap,"We propose the density-functional theory for one-dimensional harmonically
trapped spin-1 bosons in the ground state with repulsive density-density
interaction and anti-ferromagnetic spin-exchange interaction. The density
distributions of spin singlet paired bosons and polarized bosons with different
total polarization for various interaction parameters are obtained by solving
the Kohn-Sham equations which are derived based on the local density
approximation and the Bethe ansatz exact results for homogeneous system.
Non-monotonicity of the central densities is attributed to the competition
between the density interaction and spin-exchange. The results reveal the phase
separation of the paired and polarized bosons, the density profiles of which
respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar
bosons in the case of strong interaction. We give the R-P phase diagram at
strong interaction and find the critical polarization, which paves the way to
direct observe the exotic singlet pairing in spinor gas experimentally.",1304.1328v1
2020-04-28,Nuclear Symmetry Energy and Neutron Skin Thickness of $^{208}Pb $ using a finite range effective interaction,"We use a finite range simple effective interaction to construct nuclear
equations of state for the study of the density dependence of the nuclear
symmetry energy. The EoSs provide good descriptions of the nuclear symmetry
energy at a subsaturation density $\rho_c=0.11$ fm$^{-3}$ and at a density
around two times the saturation density $\rho_0$. We obtain a correlation
between the neutron skin thickness in $^{208}$Pb and the density slope
parameter at the subsaturation density. A linear relation is obtained between
the neutron skin thickness and the parameter
$\beta^{\prime}=\frac{L(\rho_c)}{3E_s(\rho_0)}$, where $E_s(\rho_0)$ and
$L(\rho_c)$ are respectively the nuclear symmetry energy at saturation density
and the density slope parameter at the subsaturation density.",2004.14205v2
2010-09-25,Wigner function evolution in self-Kerr Medium derived by Entangled state representation,"By introducing the thermo entangled state representation, we convert the
calculation of Wigner function (WF) of density operator to an overlap between
""two pure"" states in a two-mode enlarged Fock space. Furthermore, we derive a
new WF evolution formula of any initial state in self-Kerr Medium with photon
loss and find that the photon number distribution for any initial state is
independent of the coupling factor with Kerr Medium, where the number state is
not affected by the Kerr nonlinearity and evolves into a density operator of
binomial distribution.",1010.0584v1
2020-06-05,Maximizing optical production of metastable xenon,"The wide range of applications using metastable noble gas atoms has led to a
number of different approaches for producing large metastable state densities.
Here we investigate a recently proposed hybrid approach that combines RF
discharge techniques with optical pumping from an auxiliary state in xenon. We
study the effect of xenon pressure on establishing initial population in both
the auxiliary state and metastable state via the RF discharge, and the role of
the optical pumping beam power in transferring population between the states.
We find experimental conditions that maximize the effects, and provide a robust
platform for producing relatively large long-term metastable state densities.",2006.03200v1
2002-01-09,Quantum Computation by Quantum Operations on Mixed States,"Usually models for quantum computations deal with unitary gates on pure
states. In this paper we generalize the usual model. We consider a model of
quantum computations in which the state is an operator of density matrix and
the gates are quantum operations, not necessarily unitary. A mixed state
(operator of density matrix) of n two-level quantum systems is considered as an
element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates
and nonunitary quantum operations for n-qubit system are considered as
generalized quantum gates acting on mixed state. In this paper we study
universality for quantum computations by quantum operations on mixed states.",0201033v1
2005-11-15,Valence-Bond-Solid state entanglement in a 2-D Cayley tree,"The Valence-Bond-Solid (VBS) states are in general ground states for certain
gapped models. We consider the entanglement of VBS states on a two-dimensional
Cayley tree. We show that the entropy of the reduced density operator does not
depend on the whole size of the Cayley tree. We also show that asymptotically,
the entropy is liearly proportional to the number of singlet states cut by the
reduced density operator of the VBS state.",0511150v2
2011-12-06,Evolution of the single-mode squeezed vacuum state in amplitude dissipative channel,"Using the way of deriving infinitive sum representation of density operator
as a solution to the master equation describing the amplitude dissipative
channel by virtue of the entangled state representation, we show manifestly how
the initial density operator of a single-mode squeezed vacuum state evolves
into a definite mixed state which turns out to be a squeezed chaotic state with
decreasing-squeezing. We investigate average photon number, photon statistics
distributions for this state.",1112.1159v1
2016-12-28,Generalized density functional equation of state for astrophysical simulations with 3-body forces and quark gluon plasma,"We present an updated general purpose nuclear equation of state (EoS) for use
in simulations of core-collapse supernovae, neutron star mergers and black hole
collapse. This EoS is formulated in the context of Density Functional Theory
(DFT) and is generalized to include all DFT EoSs consistent with known nuclear
and astrophysical constraints. This EoS also allows for the possibility of the
formation of material with a net proton excess ($Y_p > 0.5$) and has an
improved treatment of the nuclear statistical equilibrium and the transition to
heavy nuclei as the density approaches nuclear matter density. We include the
effects of pions in the regime above nuclear matter density and incorporate all
of the known mesonic and baryonic states at high temperature.
  We analyze how a 3-body nuclear force term in the DFT at high densities
stiffens the EoS to satisfy the maximum neutron star constraint, however the
density dependence of the symmetry anergy and the formation of pions at high
temperatures allows for a softening of the central core in supernova collapse
calculations leading to a robust explosion. We also add the possibility of a
transition to a QCD chiral-symmetry-restoration and deconfinement phase at
densities above nuclear matter density. This paper details the physics, and
constraints on, this new EoS and presents an illustration of its implementation
in both neutron stars and core-collapse supernova simulations. We present the
first results from core-collapse supernova simulations with this EoS.",1612.08992v1
2022-03-28,Embedding short-range correlations in relativistic density functionals through quasi-deuterons,"The formation of clusters at sub-saturation densities constitutes an
essential feature for a reliable modelization of the nuclear matter equation of
state (EoS). Phenomenological models that make use of energy density
functionals (EDFs) offer a convenient approach to account for the presence of
these bound states of nucleons when introduced as additional degrees of
freedom. However, in these models clusters dissolve, by construction, when the
nuclear saturation density is approached from below, revealing inconsistencies
with recent findings that evidence the existence of short-range correlations
(SRCs) even at larger densities.
  In this work, within the EDF framework, a novel approach is proposed to embed
SRCs within a relativistic mean-field model with density dependent couplings.
This is realized through the introduction of suitable in-medium modifications
of the cluster binding energy shifts, which are responsible for describing the
cluster dissolution. As a first exploratory step, the example of a
quasi-deuteron within the generalized relativistic density functional approach
is investigated.
  For the first time, suitable parameterizations of the cluster mass shift at
zero temperature are derived for all baryon densities. They are constrained by
experimental results for the effective deuteron fraction in nuclear matter near
saturation and by microscopic many-body calculations in the low-density limit.
The strength of the deuteron-meson couplings is assessed to be of crucial
importance. The findings of the present study represent a first step to improve
the description of nuclear matter and its EoS at supra-saturation densities in
EDFs by considering correlations in an effective way. Novel effects on some
thermodynamic quantities, such as the matter incompressibility, the symmetry
energy and its slope, are finally discerned and discussed.",2203.14635v1
2003-02-13,Charge Density Distributions in Doped Antiferromagnetic Insulators,"We consider the form of the charge density nano-scale configurations in
underdoped states of planar antiferromagnetic insulators in the framework of a
soft variant of Faddeev-Niemi model. It is shown that there is such a level of
doping and the temperature range, where charge density distributions in the
form of closed quasi-one-dimensional structures are more preferable.",0302253v1
2011-06-03,Superfluid density of an open dissipative condensate,"I calculate the superfluid density of a non-equilibrium steady state
condensate of particles with finite lifetime. Despite the absence of a simple
Landau critical velocity, a superfluid response survives, but dissipation
reduces the superfluid fraction. I also suggest an idea for how the superfluid
density of an example of such a system, i.e. microcavity polaritons, might be
measured.",1106.0682v1
2017-10-26,Entropic Updating of Probability and Density Matrices,"We find that the standard relative entropy and the Umegaki entropy are
designed for the purpose of inferentially updating probability and density
matrices respectively. From the same set of inferentially guided design
criteria, both of the previously stated entropies are derived in parallel. This
formulates a quantum maximum entropy method for the purpose of inferring
density matrices in the absence of complete information in Quantum Mechanics.",1710.09373v1
2015-02-12,Electronic states induced by nonmagnetic defects in two-dimensional topological insulators,"We study in-gap electronic states induced by a nonmagnetic defect with
short-range potential in two-dimensional topological insulators and trace their
evolution as the distance between the defect and the boundary changes. The
defect located far from the boundary is found to produce two bound states
independently of the sign of its potential. The states are classified as
electronlike and holelike. Each of these states can have two types of the
spatial distribution of the electron density. The first-type states have a
maximum of the density in the center and the second-type ones have a minimum.
When the defect is coupled with the boundary, the bound states are transformed
correspondingly into resonances of two types and take up the form of the edge
states flowing around the defect. Under certain conditions, two resonances
interfere giving rise to the formation of a bound state embedded into the
continuum spectrum of the edge states flowing around the defect. We calculate
the spatial distribution of the electron density in the edge states flowing
around the defect and estimate the charge accumulated near the defect. The
current density field of the edge states flowing around the defect contains two
components one of which flows around the defect and the other circulates around
it.",1502.03718v1
2010-07-18,Searching for topological density wave insulators in multi-orbital square lattice systems,"We study topological properties of density wave states with broken
translational symmetry in two-dimensional multi-orbital systems with a
particular focus on t$_{2g}$ orbitals in square lattice. Due to distinct
symmetry properties of d-orbitals, a nodal charge or spin density wave state
with Dirac points protected by lattice symmetries can be achieved. When an
additional order parameter with opposite reflection symmetry is introduced to a
nodal density wave state, the system can be fully gapped leading to a band
insulator. Among those, topological density wave (TDW) insulators can be
realized, when an effective staggered on-site potential generates a gap to a
pair of Dirac points connected by the inversion symmetry which have the same
topological winding numbers. We also present a mean-field phase diagram for
various density wave states, and discuss experimental implications of our
results.",1007.2998v1
2015-01-28,Odd Frequency Density Waves,"A new type of hidden order in many body systems is explored. This order
appears in states which are analogues to charge density waves, or spin density
waves, but involve anomalous particle-hole correlations that are odd in
relative time and frequency. These states are shown to be inherently different
from the usual states of density waves. We discuss two methods to
experimentally observe the new type of pairing where a clear distinction
between odd and even correlations can be detected: (i) by measuring the
density-density correlation, both in time and space and (ii) via the
conductivity which, according to the Kubo formula, is given by the
current-current correlation. An order parameter for these states is defined and
calculated for a simple model, illuminating the physical nature of this order.",1501.07049v1
2018-05-16,Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene,"We study electronic ordering instabilities of twisted bilayer graphene with
$n=2$ electrons per supercell, where correlated insulator state and
superconductivity are recently observed. Motivated by the Fermi surface nesting
and the proximity to Van Hove singularity, we introduce a hot-spot model to
study the effect of various electron interactions systematically. Using
renormalization group method, we find $d$/$p$-wave superconductivity and
charge/spin density wave emerge as the two types of leading instabilities
driven by Coulomb repulsion. The density wave state has a gapped energy
spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to
$n>2$. The intertwinement of density wave and superconductivity and the
quasiparticle spectrum in the density wave state are consistent with
experimental observations.",1805.06449v2
2018-12-30,Entanglement of multiphoton polarization Fock states and their superpositions,"Density matrices of pure multiphoton Fock polarization states and of arising
from them reduced density matrices of mixed states are expressed in similar
ways in terms of matrices of correlators defined as averaged products of equal
numbers of creation and annihilation operators. Degree of entanglement of
considered states is evaluated for various combinations of parameters of states
and character of their reduction.",1812.11462v3
2010-03-01,Density-matrix formalism with three-body ground-state correlations,"A density-matrix formalism which includes the effects of three-body ground-
state correlations is applied to the standard Lipkin model. The reason to
consider the complicated three-body correlations is that the truncation scheme
of reduced density matrices up to the two-body level does not give satisfactory
results to the standard Lipkin model. It is shown that inclusion of the
three-body correlations drastically improves the properties of the ground
states and excited states. It is pointed out that lack of mean-field effects in
the standard Lipkin model enhances the relative importance of the three-body
ground-state correlations. Formal aspects of the density-matrix formalism such
as a relation to the variational principle and the stability condition of the
ground state are also discussed. It is pointed out that the three-body
ground-state correlations are necessary to satisfy the stability condition.",1003.0246v1
2017-12-31,"Simultaneous conduction and valence band quantisation in ultra-shallow, high density doping profiles in semiconductors","We demonstrate simultaneous quantisation of conduction band (CB) and valence
band (VB) states in silicon using ultra-shallow, high density, phosphorus
doping profiles (so-called Si:P $\delta$-layers). We show that, in addition to
the well known quantisation of CB states within the dopant plane, the
confinement of VB-derived states between the sub-surface P dopant layer and the
Si surface gives rise to a simultaneous quantisation of VB states in this
narrow region. We also show that the VB quantisation can be explained using a
simple particle-in-a-box model, and that the number and energy separation of
the quantised VB states depend on the depth of the P dopant layer beneath the
Si surface. Since the quantised CB states do not show a strong dependence on
the dopant depth (but rather on the dopant density), it is straightforward to
exhibit control over the properties of the quantised CB and VB states
independently of each other by choosing the dopant density and depth
accordingly, thus offering new possibilities for engineering quantum matter.",1801.00373v1
2023-10-06,Control of the local photonic density of states above magneto-optical metamaterials,"The local density of states (LDOS) of electromagnetic field drives many basic
processes associated to light-matter interaction such as the thermal emission
of object, the spontaneous emission of quantum systems or the
fluctuation-induced electromagnetic forces on molecules. Here, we study the
LDOS in the close vincinity of magneto-optical metamaterials under the action
of an external magnetic field and demonstrate that it can be efficiently
changed over a broad or narrow spectral range simply by changing the spatial
orientation or the magnitude of this field. This result paves the way for an
active control of the photonic density of states at deep-subwavelength scale.",2310.04219v1
1999-11-29,A Schmidt number for density matrices,"We introduce the notion of a Schmidt number of a bipartite density matrix,
characterizing the minimum Schmidt rank of the pure states that are needed to
construct the density matrix. We prove that Schmidt number is nonincreasing
under local quantum operations and classical communication. We show that
$k$-positive maps witness Schmidt number, in the same way that positive maps
witness entanglement. We show that the family of states which is made from
mixing the completely mixed state and a maximally entangled state have
increasing Schmidt number depending on the amount of maximally entangled state
that is mixed in. We show that Schmidt number {\it does not necessarily
increase} when taking tensor copies of a density matrix $\rho$; we give an
example of a density matrix for which the Schmidt numbers of $\rho$ and $\rho
\otimes \rho$ are both 2.",9911117v4
2008-05-14,Density of states of disordered graphene,"We calculate the average single particle density of states in graphene with
disorder due to impurity potentials. For unscreened short-ranged impurities, we
use the non-self-consistent and self-consistent Born and $T$-matrix
approximations to obtain the self-energy. Among these, only the self-consistent
$T$-matrix approximation gives a non-zero density of states at the Dirac point.
The density of states at the Dirac point is non-analytic in the impurity
potential. For screened short-ranged and charged long-range impurity
potentials, the density of states near the Dirac point typically increases in
the presence of impurities, compared to that of the pure system.",0805.2148v2
2014-07-08,Amplitude modulated phase in a Bose-Einstein condensate: the role of non-local interactions,"We consider a Gross-Pitaevskii model of BEC with non-local interactions of
range of the order of the s-wave scattering length. With this model, we study
the density modulated phase in 1D and 2D, which are solutions of this modified
model along with the usual uniform density state. We find an exact free energy
functional for our model and show that the 1D density modulated state can have
lower energy than the uniform density state. Although, the density modulated
state can be made to be energetically favourable, we show also that, this state
is inherently dynamically unstable due to the coupling of instabilities to the
spatial order.",1407.2039v5
2016-03-21,Engineering chiral density waves and topological band structures by multiple-$Q$ superpositions of collinear up-up-down-down orders,"Magnetic orders characterized by multiple ordering vectors harbor
noncollinear and noncoplanar spin textures and can be a source of unusual
electronic properties through the spin Berry phase mechanism. We theoretically
show that such multiple-$Q$ states are stabilized in itinerant magnets in the
form of superpositions of collinear up-up-down-down (UUDD) spin states, which
accompany the density waves of vector and scalar chirality. The result is drawn
by examining the ground state of the Kondo lattice model with classical
localized moments, especially when the Fermi surface is tuned to be partially
nested by the symmetry-related commensurate vectors. We unveil the instability
toward the multiple-$Q$ UUDD states with chirality density waves, using the
perturbative theory, variational calculations, and large-scale Langevin
dynamics simulations. We also show that the chirality density waves can induce
rich nontrivial topology of electronic structures, such as the massless Dirac
semimetal, Chern insulator with quantized topological Hall response, and
peculiar edge states which depend on the phase of chirality density waves at
the edges.",1603.06646v1
2018-03-23,Clogging and Depinning of Ballistic Active Matter Systems in Disordered Media,"We numerically examine ballistic active disks driven through a random
obstacle array. Formation of a pinned or clogged state occurs at much lower
obstacle densities for the active disks than for passive disks. As a function
of obstacle density we identify several distinct phases including a depinned
fluctuating cluster state, a pinned single cluster or jammed state, a pinned
multicluster state, a pinned gel state, and a pinned disordered state. At lower
active disk densities, a drifting uniform liquid forms in the absence of
obstacles, but when even a small number of obstacles are introduced, the disks
organize into a pinned phase-separated cluster state in which clusters nucleate
around the obstacles, similar to a wetting phenomenon. We examine how the
depinning threshold changes as a function of disk or obstacle density, and find
a crossover from a collectively pinned cluster state to a disordered plastic
depinning transition as a function of increasing obstacle density. We compare
this to the behavior of nonballistic active particles and show that as we vary
the activity from completely passive to completely ballistic, a clogged
phase-separated state appears in both the active and passive limits, while for
intermediate activity, a readily flowing liquid state appears and there is an
optimal activity level that maximizes the flux through the sample.",1803.08992v1
2003-09-17,Strange Stars with a Density-Dependent Bag Parameter,"We have studied strange quark stars in the framework of the MIT bag model,
allowing the bag parameter B to depend on the density of the medium. We have
also studied the effect of Cooper pairing among quarks, on the stellar
structure. Comparison of these two effects shows that the former is generally
more significant. We studied the resulting equation of state of the quark
matter, stellar mass-radius relation, mass-central-density relation,
radius-central-density relation, and the variation of the density as a function
of the distance from the centre of the star. We found that the
density-dependent B allows stars with larger masses and radii, due to
stiffening of the equation of state. Interestingly, certain stellar
configurations are found to be possible only if B depends on the density. We
have also studied the effect of variation of the superconducting gap parameter
on our results.",0309472v2
2019-11-15,Direct Measurement Methods of Density Matrix of an Entangled Quantum State,"In general, the state of a quantum system represented by density operator and
its determination is a fundamental problem in quantum mechanics. A method of
direct measurement of matrix element of density operator of a single two
dimensional quantum system using weak measurement was theoretically
proposed[Phys. Rev. Lett. 134, 070402(2012)] and experimentally
demonstrated[Phys. Rev. Lett. 117, 120401(2016)] by Lundeen et al. Furthermore,
recently the Guo-Guang Can et al.[Phys. Rev. Lett. 123, 150402(2019)]
investigated the method of direct measurement of a nonlocal entangled quantum
state. However, up to now the methods of directly measure the matrix element of
density operator of an entangled quantum state have not been explicitly studied
yet. As an extension of previous works, in this study we introduce two
theoretical methods such as using postselected weak measurement and sequential
measurements of triple products of complementary observables to direct
measurement of matrix elements of density operator of two photon entangled
quantum system, and discuss the similarity and the feasibility of those
methods.",1911.06609v2
1996-09-17,Quantum state estimation,"New algorithm for quantum state estimation based on the maximum likelihood
estimation is proposed. Existing techniques for state reconstruction based on
the inversion of measured data are shown to be overestimated since they do not
guarantee the positive definiteness of the reconstructed density matrix.",9609012v1
2012-06-25,Separable states and the SPA of a positive map,"We introduce a nessecary condition for a state to be separable and apply this
condition to the SPA of an optimal ositive map and give a proof of the fact
that the SPA need not be the density ooperator for a separable state.",1206.5630v1
2014-02-25,Thermal properties of supernova matter: The bulk homogeneous phase,"We investigate the thermal properties of the potential model equation of
state of Akmal, Pandharipande and Ravenhall. This equation of state
approximates the microscopic model calculations of Akmal and Pandharipande,
which feature a neutral pion condensate. We treat the bulk homogeneous phase
for isospin asymmetries ranging from symmetric nuclear matter to pure neutron
matter and for temperatures and densities relevant for simulations of
core-collapse supernovae, proto-neutron stars, and neutron star mergers.
Numerical results of the state variables are compared with those of a typical
Skyrme energy density functional with similar properties at nuclear densities,
but which differs substantially at supra-nuclear densities. Analytical
formulas, which are applicable to non-relativistic potential models such as the
equations of state we are considering, are derived for all state variables and
their thermodynamic derivatives. A highlight of our work is its focus on
thermal response functions in the degenerate and non-degenerate situations,
which allow checks of the numerical calculations for arbitrary degeneracy.
These functions are sensitive to the density dependent effective masses of
neutrons and protons, which determine the thermal properties in all regimes of
degeneracy. We develop the ""thermal asymmetry free energy"" and establish its
relation to the more commonly used nuclear symmetry energy. We also explore the
role of the pion condensate at supra-nuclear densities and temperatures. Tables
of matter properties as functions of baryon density, composition (i.e., proton
fraction) and temperature are being produced which are suitable for use in
astrophysical simulations of supernovae and neutron stars.",1402.6348v1
2019-03-10,The Local Density Approximation in Density Functional Theory,"We give the first mathematically rigorous justification of the Local Density
Approximation in Density Functional Theory. We provide a quantitative estimate
on the difference between the grand-canonical Levy-Lieb energy of a given
density (the lowest possible energy of all quantum states having this density)
and the integral over the Uniform Electron Gas energy of this density. The
error involves gradient terms and justifies the use of the Local Density
Approximation in the situation where the density is very flat on sufficiently
large regions in space.",1903.04046v2
1999-09-02,Long Range Magnetic Order and the Darwin Lagrangian,"We simulate a finite system of $N$ confined electrons with inclusion of the
Darwin magnetic interaction in two- and three-dimensions. The lowest energy
states are located using the steepest descent quenching adapted for velocity
dependent potentials. Below a critical density the ground state is a static
Wigner lattice. For supercritical density the ground state has a non-zero
kinetic energy. The critical density decreases with $N$ for exponential
confinement but not for harmonic confinement. The lowest energy state also
depends on the confinement and dimension: an antiferromagnetic cluster forms
for harmonic confinement in two dimensions.",9909030v1
2003-04-23,Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder,"We investigate the ground state properties of a two-dimensional electron gas
in the lowest Landau level using the Density Matrix Renormalization Group. The
electron gas is confined to a cylinder with a strong magnetic field
perpendicular to the surface. For a thin cylinder, the ground state is for
generic filling factors a charge density wave state, however, at $\nu=1/2$ a
homogeneous and apparently gapless ground state is found and particle and hole
excitations are studied.",0304517v2
2012-08-30,Composite fermion state of spin-orbit coupled bosons,"We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in
2D. We argue that at low density its groundstate is a composite fermion state
with a Chern-Simons gauge field and filling factor one. The chemical potential
of such a state scales with the density as \mu \propto n^{3/2}. This is a lower
energy per particle than \mu \propto n for the earlier suggested groundstate
candidates: a condensate with broken time-reversal symmetry and a spin density
wave state.",1208.6266v1
2008-12-11,Supersolid state in fermionic optical lattice systems,"We study ultracold fermionic atoms trapped in an optical lattice with
harmonic confinement by combining the real-space dynamical mean-field theory
with a two-site impurity solver. By calculating the local particle density and
the pair potential in the systems with different clusters, we discuss the
stability of a supersolid state, where an s-wave superfluid coexists with a
density-wave state of checkerboard pattern. It is clarified that a confining
potential plays an essential role in stabilizing the supersolid state. The
phase diagrams are obtained for several effective particle densities.",0812.2231v1
2003-09-05,Influence of Fermi surface topology on the quasiparticle spectrum in the vortex state,"We study the influence of Fermi surface topology on the quasiparticle density
of states in the vortex state of type II superconductors. We observe that the
field dependence and the shape of the momentum and spatially averaged density
of states is affected significantly by the topology of the Fermi surface. We
show that this behavior can be understood in terms of characteristic Fermi
surface functions and that an important role is played by the number of points
on the Fermi surface at which the Fermi velocity is directed parallel to the
magnetic field. A critical comparison is made with a broadened BCS type density
of states, that has been used frequently in analysis of tunneling data. We
suggest a new formula as a replacement for the broadened BCS model for the
special case of a cylindrical Fermi surface. We apply our results to the two
gap superconductor MgB$_2$ and show that in this particular case the field
dependence of the partial densities of states of the two gaps behaves very
differently due to the different topologies of the corresponding Fermi
surfaces, in qualitative agreement with recent tunneling experiments.",0309142v1
2002-10-22,Conditional Density Matrix: Systems and Subsystems in Quantum Mechanics,"A new quantum mechanical notion -- Conditional Density Matrix -- is discussed
and is applied to describe some physical processes. This notion is a natural
generalization of von Neumann density matrix for such processes as divisions of
quantum systems into subsystems and reunifications of subsystems into new joint
systems. Conditional Density Matrix assigns a quantum state to a subsystem of a
composite system under condition that another part of the composite system is
in some pure state.",0210149v1
2015-10-12,A Gaussian density matrix under decoherence and friction,"The time evolution of a Gaussian density matrix of a one dimensional
particle, generated by a quadratic, ${\cal O}(\partial_t^2)$ effective
Lagrangian, describing a harmonic potential, a friction force and decoherence,
is studied within the Closed Time Path formalism. The density matrix converges
to an asymptotic form, given by a completely decohered thermal state with an
${\cal O}(\hbar)$ temperature in the translation invariant case. The time
evolution of the state of a harmonic oscillator is followed numerically. The
asymptotic density matrix, the fixed point of the master equation, is found
analytically and its dependence on the oscillator frequency, the friction
constant and the decoherence strength is explored.",1510.03212v1
2021-07-15,Probability density evolution filter,"Based on probability density evolution method (PDEM) and Bayes law, a new
filter strategy is proposed, in which the prior probability of system state of
interest is predicted by solving the general density evolution equation (GDEE),
the posterior probability of system state is then updated in terms of Bayes
formula. Furthermore, a Chebyshev polynomial-based collocation method is
employed to obtain numerical solutions of the prior probability. An
illustrative example is finally presented to validate the probability density
evolution filter (PDEF) in comparison to particle filter (PF) and UKF. Overall,
PDEF exhibits accuracy close to PF without any resampling algorithm.",2107.09514v1
2010-04-24,Fluctuations around Periodic BPS-Density Waves in the Calogero Model,"The collective field formulation of the Calogero model supports periodic
density waves. An important set of such density waves is a two-parameter family
of BPS solutions of the equations of motion of the collective field theory. One
of these parameters is essentially the average particle density, which
determines the period, while the other parameter determines the amplitude.
These BPS solutions are sometimes referred to as ""small amplitude waves"" since
they undulate around their mean density, but never vanish. We present complete
analysis of quadratic fluctuations around these BPS solutions. The
corresponding fluctuation hamiltonian (i.e., the stability operator) is
diagonalized in terms of bosonic creation and annihilation operators which
correspond to the complete orthogonal set of Bloch-Floquet eigenstates of a
related periodic Schr\""odinger hamiltonian, which we derive explicitly.
Remarkably, the fluctuation spectrum is independent of the parameter which
determines the density wave's amplitude. As a consequence, the sum over
zero-point energies of the field-theoretic fluctuation hamiltonian, and its
ensuing normal-ordering and regularization, are the same as in the case of
fluctuations around constant density background, namely, the ground state.
Thus, quadratic fluctuations do not shift the energy density tied with the
BPS-density waves studied here, compared to its ground state value. Finally, we
also make some brief remarks concerning fluctuations around non-BPS density
waves",1004.4283v2
2020-11-10,Continuum model of the simple dielectric fluid: Consistency between density based and continuum mechanics methods,"The basic continuum model for polar fluids is deceptively simple. The free
energy integral consists of four terms: The coupling of polarization to an
external field, the electrostatic energy of the induced electric field
interacting with itself and the stored polarization energy quadratic in the
polarization. A local function of density accounts for the mechanical state of
the fluid. Viewed as a non-equilibrium free energy functional of number density
and polarization, minimization in these two densities under constraints of the
Maxwell field equations should lead the correct equilibrium state. The
alternative is a continuum mechanics approach in which the mechanical degree of
freedom is extended to full deformation. We show that the continuum
electromechanics method leads to a force balance equation which is consistent
with the density functional equilibrium equation. The continuum mechanics
procedure is significantly more demanding. The gain is a well defined pressure
tensor derived from deformation of total energy. This resolves the issue of the
uncertainty in the pressure tensor obtained from integration of the force
density, which is the conventional method in density based thermomechanics. Our
derivation is based on the variational electrostatics approach developed by
Ericksen (Arch. Rational Mech. Anal. {\bf 183} 299 (2007)).",2011.05052v1
2020-12-14,Optical nonlinearities in the excited carrier density of atomically thin transition metal dichalcogenides,"In atomically thin semiconductors based on transition metal dichalcogenides,
photoexcitation can be used to generate high densities of electron-hole pairs.
Due to optical nonlinearities, which originate from Pauli blocking and
many-body effects of the excited carriers, the generated carrier density will
deviate from a linear increase in pump fluence. In this paper, we use a
theoretical approach that combines results from ab-initio electronic-state
calculations with a many-body treatment of optical excitation to describe
nonlinear absorption properties and the resulting excited carrier dynamics. We
determine the validity range of a linear approximation for the excited carrier
density vs. pump power and identify the role and magnitude of optical
nonlinearities at elevated excitation carrier densities for MoS2, MoSe2, WS2,
and WSe2 considering various excitation conditions. We find that for
above-band-gap photoexcitation, the use of a linear absorption coefficient of
the unexcited system can strongly underestimate the achievable carrier density
for a wide range of pump fluences due to many-body renormalizations of the
two-particle density-of-states.",2012.07642v1
1996-06-21,Star-shaped Local Density of States around Vortices in a Type II Superconductor,"The electronic structure of vortices in a type II superconductor is analyzed
within the quasi-classical Eilenberger framework. The possible origin of a
sixfold ``star'' shape of the local density of states, observed by scanning
tunneling microscope experiments on NbSe$_2$, is examined in the light of the
three effects; the anisotropic pairing, the vortex lattice, and the anisotropic
density of states at the Fermi surface. Outstanding features of split parallel
rays of this star are well explained in terms of an anisotropic $s$-wave
pairing. This reveals a rich internal electronic structure associated with a
vortex core.",9606002v1
2015-02-10,Evolution of nonclassicality of the quasi-Bell states for a strongly coupled qubit-oscillator system,"Starting with the quasi-Bell states of the qubit-oscillator system, we obtain
time evolution of the density matrix under the adiabatic approximation. The
composite density matrix leads to, via partial tracing of the qubit degree of
freedom, the reduced density matrix of the oscillator that is utilized to
obtain the quasi-probability distributions such as Glauber-Sudarshan P
function, Wigner W function and Husimi Q function. The negativity of the Wigner
function acts as a measure of the nonclassicality of the state. The negativity
becomes particularly relevant in understanding a comparison between the Wigner
entropy with the Wehrl entropy, which are based on the W function and Q
function, respectively.",1502.02884v1
2012-01-09,Difference of energy density of states in the Wang-Landau algorithm,"Paying attention to the difference of density of states, \Delta ln g(E) = ln
g(E+\Delta E) - ln g(E), we study the convergence of the Wang-Landau method. We
show that this quantity is a good estimator to discuss the errors of
convergence, and refer to the $1/t$ algorithm. We also examine the behavior of
the 1st-order transition with this difference of density of states in
connection with Maxwell's equal area rule. A general procedure to judge the
order of transition is given.",1201.1683v1
2017-07-13,Mesoscopic fluctuations of the local density of states in interacting electron systems,"We review our recent theoretical results for mesoscopic fluctuations of the
local density of states in the presence of electron-electron interaction. We
focus on the two specific cases: (i) a vicinity of interacting critical point
corresponding to Anderson-Mott transition, and (ii) a vicinity of
non-interacting critical point in the presence of a weak electron-electron
attraction. In both cases strong mesoscopic fluctuations of the local density
of states exist.",1707.03973v1
2021-01-11,Bose Einstein condensation and ferromagnetism of low density Bose gas of particles with arbitrary spin,"Properties of the ground state and the spectrum of elementary excitations are
investigated for the low density ultracold spinor 3D Bose gas of particles with
arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the
framework of the considering interaction Hamiltonian it is shown that the
ground state spin structure and spin part of the chemical potential is
determined by the renormalized interaction, being defined by the contribution
of the virtual large momenta. The ferromagnetic structure of the ground state,
and the equation of the phase, density, and spin dynamics are obtained from
Gross-Pitaevskii equations.",2101.03744v2
2022-04-08,Configuration interaction projected density functional theory: effects of four-quasiparticle configurations and time-odd interactions,"The effects of four-quasiparticle configurations and time-odd interactions
are investigated in the framework of configuration interaction projected
density functional theory by taking the yrast states of 60Fe as examples. Based
on the universal PC-PK1 density functional, the energies of the yrast states
with spin up to 20\hbar and the available B(E2) transition probabilities are
well reproduced. The yrast states are predicted to be of four-quasiparticle
structure above spin I = 16\hbar. The inclusion of the time-odd interactions
increases the kinetic moments of inertia and delays the appearance of the first
band crossing, and, thus, improves the description of the data.",2204.03866v1
2020-06-09,Tripartite genuinely entangled states from entanglement-breaking subspaces,"The determination of genuine entanglement is a central problem in quantum
information processing. We investigate the tripartite state as the tensor
product of two bipartite entangled states by merging two systems. We show that
the tripartite state is a genuinely entangled state when the range of both
bipartite states are entanglement-breaking subspaces. We further investigate
the tripartite state when one of the two bipartite states has rank two. Our
results provide the latest progress on a conjecture proposed in the paper [Yi
Shen $\textit{et al}$, J. Phys. A 53, 125302 (2020)]. We apply our results to
construct multipartite states whose bipartite reduced density operators have
additive EOF. Further, such states are distillable across every bipartition
under local operations and classical communications.",2006.05128v1
2022-08-12,How good are recent density functionals for ground and excited states of one-electron systems?,"Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density
functional approximations (DFAs) should exhibit large energy errors for excited
states as a necessary consequence of orbital nodality. Motivated by
self-interaction corrected density functional calculations on many-electron
systems, we continue their study with the exactly solvable $1s$, $2p$, and $3d$
states of 36 hydrogenic one-electron ions (H-Kr$^{35+}$) and demonstrate with
self-consistent calculations that state-of-the-art DFAs indeed exhibit large
errors for the $2p$ and $3d$ excited states. We consider 56 functionals at the
local density approximation (LDA), generalized gradient approximation (GGA) as
well as meta-GGA levels, also including several hybrid functionals like the
recently proposed machine-learned DM21 local hybrid functional. The best
non-hybrid functional for the $1s$ ground state is revTPSS. The $2p$ and $3d$
excited states are more difficult for DFAs as Sun et al. predicted, and LDA
functionals turn out to yield the most systematic accuracy for these states
amongst non-hybrid functionals. The best performance for the three states
overall is observed with the BHandH global hybrid GGA functional, which
contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of
DM21 is found to be inconsistent, yielding good accuracy for some states and
systems and poor accuracy for others. Based on these results, we recommend
including a variety of one-electron cations in future training of
machine-learned density functionals.",2208.06482v3
2003-12-19,The Role of hybridization in NaxCoO2 and the Effect of Hydration,"Density functional theory (DFT) within the local density approximation (LDA)
is used to understand the electronic properties of Na1/3CoO2 and
Na1/3CoO2(H2O)4/3, which was recently found to be superconducting1. Comparing
the LDA charge density of CoO2 and the Na doped phases indicates that doping
does not simply add electrons to the t2g states. In fact, the electron added in
the t2g state is dressed by hole density in the eg state and electron density
in the oxygen states via rehybridization. In order to fully understand this
phenomenon, a simple extension of the Hubbard Hamiltonian is proposed and
solved using the dynamical mean-field theory (DMFT). This simple model confirms
that the rehybridization is driven by a competition between the on-site coulomb
interaction and the hybridization. In addition, we find that the presence of
eg-oxygen hybridization effectively screens the low energy excitations. To
address the role that water plays in creating the superconducting state, we
compare the LDA band structure of Na1/3CoO2 and its hydrated counterpart. This
demonstrates that hydration does cause the electronic structure to become more
two-dimensional.",0312514v1
2015-03-18,Immiscibile two-component Bose Einstein condensates beyond mean-field approximation: phase transitions and rotational response,"We consider a two-component immiscible Bose-Einstein condensate with
dominating intra-species repulsive density-density interactions. In the
ground-state phase of such a system only one condensates is present. This can
be viewed as a spontaneous breakdown of $\mathbb{Z}_2$ symmetry. We study the
phase diagram of the system at finite temperature beyond mean-field
approximation. In the absence of rotation, we show that the system undergoes a
first order phase transition from this ground state to a miscible two-component
normal fluid as temperature is increased. In the presence of rotation, the
system features a competition between vortex-vortex interaction and short range
density-density interactions. This leads to a rotation-driven ""mixing"" phase
transition in a spatially inhomogeneous state with additional broken
$\mathrm{U}(1)$ symmetry. Thermal fluctuations in this state lead to nematic
two-component sheets of vortex liquids. At sufficiently strong inter-component
interaction, we find that the superfluid and $\mathbb{Z}_2$ phase transitions
split. This results in the formation of an intermediate state which breaks only
$\mathbb{Z}_2$ symmetry. It represents two phase separated normal fluids with
density imbalance.",1503.05583v1
2016-04-27,Direct measurement of the density matrix of a quantum system,"One drawback of conventional quantum state tomography is that it does not
readily provide access to single density matrix elements, since it requires a
global reconstruction. Here we experimentally demonstrate a scheme that can be
used to directly measure individual density matrix elements of general quantum
states. The scheme relies on measuring a sequence of three observables, each
complementary to the last. The first two measurements are made weak to minimize
the disturbance they cause to the state, while the final measurement is strong.
We perform this joint measurement on polarized photons in pure and mixed states
to directly measure their density matrix. The weak measurements are achieved
using two walk-off crystals, each inducing a polarization-dependent spatial
shift that couples the spatial and polarization degree of freedom of the
photons. This direct measurement method provides an operational meaning to the
density matrix and promises to be especially useful for large dimensional
states.",1604.07917v2
1998-07-09,Loss of Quantum Coherence and Positivity of Energy Density in Semiclassical Quantum Gravity,"In the semiclassical quantum gravity derived from the Wheeler-DeWitt
equation, the energy density of a matter field loses quantum coherence due to
the induced gauge potential from the parametric interaction with gravity in a
non-static spacetime. It is further shown that the energy density takes only
positive values and makes superposition principle hold true. By studying a
minimal massive scalar field in a FRW spacetime background, we illustrate the
positivity of energy density and obtain the classical Hamiltonian of a complex
field from the energy density in coherent states.",9807023v2
2013-06-29,$N$-representability in non-collinear spin-polarized density functional theory,"The $N$-representability problem for non-collinear spin-polarized densities
was left open in the pioneering work of von Barth and Hedin setting up the
Kohn-Sham density functional theory for magnetic compounds. In this letter, we
demonstrate that, contrarily to the non-polarized case, the sets of pure and
mixed state $N$-representable densities are different in general. We provide a
simple characterization of the latter by means of easily checkable necessary
and sufficient conditions on the components $\rho^{\alpha \beta} (\br)$ of the
spin-polarized density.",1307.0139v2
2010-05-05,Density oscillations in trapped dipolar condensates,"We investigated the ground state wave function and free expansion of a
trapped dipolar condensate. We find that dipolar interaction may induce both
biconcave and dumbbell density profiles in, respectively, the pancake- and
cigar-shaped traps. On the parameter plane of the interaction strengths, the
density oscillation occurs only when the interaction parameters fall into
certain isolated areas. The relation between the positions of these areas and
the trap geometry is explored. By studying the free expansion of the condensate
with density oscillation, we show that the density oscillation is detectable
from the time-of-flight image.",1005.0666v1
2023-03-23,Calculating the many-body density of states on a digital quantum computer,"Quantum statistical mechanics allows us to extract thermodynamic information
from a microscopic description of a many-body system. A key step is the
calculation of the density of states, from which the partition function and all
finite-temperature equilibrium thermodynamic quantities can be calculated. In
this work, we devise and implement a quantum algorithm to perform an estimation
of the density of states on a digital quantum computer which is inspired by the
kernel polynomial method. Classically, the kernel polynomial method allows to
sample spectral functions via a Chebyshev polynomial expansion. Our algorithm
computes moments of the expansion on quantum hardware using a combination of
random state preparation for stochastic trace evaluation and a controlled
unitary operator. We use our algorithm to estimate the density of states of a
non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a
controlled register of 18 qubits. This not only represents a state-of-the-art
calculation of thermal properties of a many-body system on quantum hardware,
but also exploits the controlled unitary evolution of a many-qubit register on
an unprecedented scale.",2303.13476v1
2005-04-06,Continuous optimal ensembles II. Reducing the separability condition to numerical equations,"A density operator of a bipartite quantum system is called robustly separable
if it has a neighborhood of separable operators. Given a bipartite density
matrix, its property to be robustly separable is reduced, using the continuous
ensemble method, to a finite number of numerical equations. The solution of
this system exists for any robustly separable density operator and provides its
representation by a continuous mixture of pure product states.",0504034v1
2013-04-17,Towards a better knowledge of the nuclear equation of state from the isoscalar breathing mode,"The measurements of the isoscalar giant monopole resonance (GMR), also called
the breathing mode, are analyzed with respect to their constraints on the
quantity $M_c$, e.g. the density dependence of the nuclear incompressibility
around the so-called crossing density $\rho_c$=0.1 fm$^{-3}$. The correlation
between the centroid of the GMR, $E_\mathrm{GMR}$, and $M_c$ is shown to be
more accurate than the one between $E_\mathrm{GMR}$ and the incompressibility
modulus at saturation density, $K_\infty$, giving rise to an improved
determination on the nuclear equation of state. The relationship between $M_c$
and $K_\infty$ is given as a function of the skewness parameter $Q_\infty$
associated to the density dependence of the equation of state. The large
variation of $Q_\infty$ among different energy density functionnals directly
impacts the knowledge of $K_\infty$: a better knowledge of $Q_\infty$ is
required to deduce more accurately $K_\infty$. Using the Local Density
Approximation, a simple and accurate expression relating $E_\mathrm{GMR}$ and
the quantity $M_c$ is derived and successfully compared to the fully
microscopic predictions.",1304.4721v1
2017-07-26,Composite boson description of a low density gas of excitons,"Ground state properties of a fermionic Coulomb gas are calculated using the
fixed-node diffusion Monte Carlo method. The validity of the composite boson
description is tested for different densities. We extract the exciton-exciton
$s$-wave scattering length by solving the four-body problem in a harmonic trap
and mapping the energy to that of two trapped bosons. The equation of state is
consistent with the Bogoliubov theory for composite bosons interacting with the
obtained $s$-wave scattering length. The perturbative expansion at low density
has contributions physically coming from (a) exciton binding energy, (b)
mean-field Gross-Pitaevskii interaction between excitons, (c) quantum depletion
of the excitonic condensate (Lee-Huang-Yang terms for composite bosons). In
addition, for low densities we find a good agreement with the Bogoliubov
bosonic theory for the condensate fraction of excitons. The equation of state
in the opposite limit of large density is found to be well described by the
perturbative theory including (a) mixture of two ideal Fermi gases (b) exchange
energy. We find that for low densities both energetic and coherent properties
are correctly described by the picture of composite bosons (excitons).",1707.08521v1
2022-12-14,Kinetics and steady state of polar flock with birth and death,"We study a collection of polar self-propelled particles or polar flock on a
two dimensional substrate with birth and death. Most of the previous studies of
polar flock with birth and death have assumed the compressible flock, such that
the local density of flock is completely ignored. Effect of birth and death of
particles on the flock with moderate density is focus of our study. System is
modeled using coarse-grained hydrodynamic equations of motion for local density
and velocity of the flock and solved using numerical integration of the
nonlinear coupled partial differential equations of motion and linearised
hydrodynamics about the broken symmetry state. We studied the ordering kinetics
as well as the steady state properties of the immortal flock and flock with
finite birth and death rate. The ordering kinetics of the velocity field
remains unaffected whereas the density field shows a crossover from asymptotic
growth exponent $5/6$ for the immortal flock to diffusive limit $1/3$ for large
birth and death rates. In the steady state, the presence of birth and death
rate leads to the suppression of speed of sound wave and density fluctuations
in the system.",2212.07191v2
2010-11-22,Finite-Temperature Density-Functional Theory of Bose-Einstein Condensates,"The thermodynamic approach to density functional theory (DFT) is used to
derive a versatile theoretical framework for the treatment of
finite-temperature (and in the limit, zero temperature) Bose-Einstein
condensates (BECs). The simplest application of this framework, using the
overall density of bosons alone, would yield the DFT of Nunes (1999). It is
argued that a significant improvement in accuracy may be obtained by using
additional density fields: the condensate amplitude and the anomalous density.
Thus, two advanced schemes are suggested, one corresponding to a generalized
two-fluid model of condensate systems, and another scheme which explicitly
accounts for anomalous density contributions and anomalous effective
potentials. The latter reduces to the Hartree-Fock-Bogoliubov approach in the
limit of weak interactions. For stronger interactions, a local density
approximation is suggested, but its implementation requires accurate data for
the thermodynamic properties of uniform interacting BEC systems, including
fictitious perturbed states of such systems. Provided that such data becomes
available, e.g., from quantum Monte Carlo computation, DFT can be used to
obtain high-accuracy theoretical results for the equilibrium states of BECs of
various geometries and external potentials.",1011.4907v1
2021-11-26,Giant van Hove Density of States Singularities and Anomalies of Electron and Magnetic Properties in Cubic Lattices,"Densities of states for simple (sc) and base-centered (bcc) cubic lattices
with account of nearest and next-nearest neighbour hopping integrals $t$ and
$t'$ are investigated in detail. It is shown that at values of $\tau \equiv
t'/t = \tau_\ast$, corresponding to the change of isoenergetic surface
topology, the formation of van Hove $\bf k$ lines takes place. At small
deviation from these special values, the weakly dispersive spectrum in the
vicinity of van Hove lines is replaced by a weak $\bf k$-dependence in the
vicinity of few van Hove points which possess huge masses proportional to
$|\tau - \tau_\ast|^{-1}$. The singular contributions to the density of states
originating from van Hove points and lines are considered, as well as the
change in the topology of isoenergetic surfaces in the $\bf k$-space with the
variation of $\tau$. Closed analytical expressions for density of states as a
function of energy and $\tau$ in terms of elliptic integrals, and power-law
asymptotics at $\tau = \tau_\ast$ are obtained. Besides the case of sc lattice
with small $\tau$ (maximum of density of states corresponds to energy level of
X $\bf k$-point), maximal value of the density of states is always achieved at
energies corresponding to \textit{inner} $\bf k$-points of the Brillouin zone
positioned in high-symmetry directions, and not at zone faces.",2111.13497v1
2014-04-12,Non-existence of a Hohenberg-Kohn Variational Principle in Total Current Density Functional Theory,"For a many-electron system, whether the particle density $\rho(\mathbf{r})$
and the total current density $\mathbf{j}(\mathbf{r})$ are sufficient to
determine the one-body potential $V(\mathbf{r})$ and vector potential
$\mathbf{A}(\mathbf{r})$, is still an open question. For the one-electron case,
a Hohenberg-Kohn theorem exists formulated with the total current density. Here
we show that the generalized Hohenberg-Kohn energy functional $\mathord{\cal
E}_{V_0,\mathbf{A}_0}(\rho,\mathbf{j}) = \langle
\psi(\rho,\mathbf{j}),H(V_0,\mathbf{A}_0)\psi(\rho,\mathbf{j})\rangle$ can be
minimal for densities that are not the ground-state densities of the fixed
potentials $V_0$ and $\mathbf{A}_0$. Furthermore, for an arbitrary number of
electrons and under the assumption that a Hohenberg-Kohn theorem exists
formulated with $\rho$ and $\mathbf{j}$, we show that a variational principle
for Total Current Density Functional Theory as that of Hohenberg-Kohn for
Density Functional Theory does not exist. The reason is that the assumed map
from densities to the vector potential, written $(\rho,\mathbf{j})\mapsto
\mathbf{A}(\rho,\mathbf{j};\mathbf{r})$, enters explicitly in $\mathord{\cal
E}_{V_0,\mathbf{A}_0}(\rho,\mathbf{j})$.",1404.3297v1
2018-09-21,Density of states and ground state magnetic ordering of the triangular lattice three-state Potts model,"This study present a Monte Carlo investigations of low-temperature magnetic
ordering and phase transitions in three-state Potts model on triangular lattice
with various exchange interactions between nearest (J1) and next-nearest (J2)
neighbors. The density of states for varying J1 and J2 are calculated. The
magnetic structure of the ground state for various J1 and J2 are obtained. The
critical temperature are calculated and the order of the phase transition
determined. The density of states difference (DOSD) and histogram analysis
method are used to investigate the order of the phase transitions. The
frustrated regions are determined. It is shown, that for negative J1 the high
degeneration of the ground state are in fully frustrated area
-1<=J2/abs(J1)<=-0.2. For positive J1 frustration are occurred in area
-1<=J2/J1<=-0.5, but only in point J2/J1=-1 the system have a high degeneration
and are fully frustrated. The phase diagram of the three-state triangular Potts
model are show.",1809.08129v1
1994-03-08,Fourier Path Integral Monte Carlo Method for the Calculation of the Microcanonical Density of States,"Using a Hubbard-Stratonovich transformation coupled with Fourier path
integral methods, expressions are derived for the numerical evaluation of the
microcanonical density of states for quantum particles obeying Boltzmann
statistics. A numerical algorithmis suggested to evaluate the quantum density
of states and illustrated on a one-dimensional model system.",9403001v1
1997-06-28,Density of states of a type-II superconductor in a high magnetic field: Impurity effects,"We have calculated the density of states $N(\omega)$ of a dirty but
homogeneous superconductor in a high magnetic field. We assume a dilute
concentration of scalar impurities and find how $N(\omega)$ behaves as one
crosses from the weak scattering to the strong scattering limit. At low
energies, $N(\omega)\sim \omega ^2$ for small values of the impurity
concentration and scattering strength. When the disorder becomes stronger than
some critical value, a finite density of states is created at the Fermi
surface. These results are a consequence of the gapless nature of the
quasiparticle excitation spectrum in a high magnetic field.",9706290v1
2004-03-31,Quantum interference in nanofractals and its optical manifestation,"We consider quantum interferences of ballistic electrons propagating inside
fractal structures with nanometric size of their arms. We use a scaling
argument to calculate the density of states of free electrons confined in a
simple model fractal. We show how the fractal dimension governs the density of
states and optical properties of fractal structures in the RF-IR region. We
discuss the effect of disorder on the density of states along with the
possibility of experimental observation.",0403748v1
2005-02-14,Berry phase correction to electron density of states in solids,"Liouville's theorem on the conservation of phase space volume is violated by
Berry phase in the semiclassical dynamics of Bloch electrons. This leads to a
modification of the phase space density of states, whose significance is
discussed in a number of examples: field modification of the Fermi-sea volume,
connection to the anomalous Hall effect, and a general formula for orbital
magnetization. The effective quantum mechanics of Bloch electrons is also
sketched, where the modified density of states plays an essential role.",0502340v2
1995-11-03,General relation between state density and dwell times in mesoscopic systems,"A relevant relation between the dwell time and the density of states for a
three dimensional system of arbitrary shape with an arbitrary number of
incoming channel is derived. This result extends the one obtained by Gasparian
et al. for the special case of a layered one dimensional symmetrical system. We
believe that such a strong relation between the most widely accepted time
related to the dynamics of a particle and the density of states in the barrier
region, one of the most relevant properties of a system in equilibrium, is rich
of physical significance.",9511004v1
2008-08-19,Density of States for a Short Overlapping-Bead Polymer: Clues to a Mechanism for Helix Formation?,"The densities of states are evaluated for very short chain molecules made up
of overlapping monomers, using a model which has previously been shown to
produce helical structure. The results of numerical calculations are presented
for tetramers and pentamers. We show that these models demonstrate behaviors
relevant to the behaviors seen in longer, helix forming chains, particularly,
""magic numbers"" of the overlap parameter where the derivatives of the densities
of states change discontinuously, and a region of bimodal energy probability
distributions, reminiscent of a first order phase transition in a bulk system.",0808.2559v1
2008-12-10,Theory of charged impurity scattering in two dimensional graphene,"We review the physics of charged impurities in the vicinity of graphene. The
long-range nature of Coulomb impurities affects both the nature of the ground
state density profile as well as graphene's transport properties. We discuss
the screening of a single Coulomb impurity and the ensemble averaged density
profile of graphene in the presence of many randomly distributed impurities.
Finally, we discuss graphene's transport properties due to scattering off
charged impurities both at low and high carrier density.",0812.1795v1
2010-03-03,Inhomogeneous Fixed Point Ensembles Revisited,"The density of states of disordered systems in the Wigner-Dyson classes
approaches some finite non-zero value at the mobility edge, whereas the density
of states in systems of the chiral and Bogolubov-de Gennes classes shows a
divergent or vanishing behavior in the band centre. Such types of behavior were
classified as homogeneous and inhomogeneous fixed point ensembles within a
real-space renormalization group approach. For the latter ensembles the scaling
law $\mu=d\nu-1$ was derived for the power laws of the density of states
$\rho\propto|E|^\mu$ and of the localization length $\xi\propto|E|^{-\nu}$.
This prediction from 1976 is checked against explicit results obtained
meanwhile.",1003.0787v1
2010-03-17,On the present state of the Andersen-Lempert theory,"In this survey of the Andersen-Lempert theory we present the state of the art
in the study of the density property (which means that the Lie algebra
generated by completely integrable holomorphic vector fields on a given Stein
manifold is dense in the space of all holomorphic vector fields). There are
also two new results in the paper one of which is the theorem stating that the
product of Stein manifolds with the volume density property possesses such a
property as well. The second one is a meaningful example of an algebraic
surface without the algebraic density property. The proof of the last fact
requires Brunella's technique.",1003.3434v1
2011-04-19,"Magnetization dependent current rectification in (Ga,Mn)As magnetic tunnel junctions","We have found that the current rectification effect in triple layer (double
barrier) (Ga,Mn)As magnetic tunnel junctions strongly depends on the
magnetization alignment. The direction as well as the amplitude of the
rectification changes with the alignment, which can be switched by
bi-directional spin-injection with very small threshold currents. A possible
origin of the rectification is energy dependence of the density of states
around the Fermi level. Tunneling density of states in (Ga,Mn)As shows
characteristic dip around zero-bias indicating formation of correlation gap,
the asymmetry of which would be a potential source of the energy dependent
density of states.",1104.3619v1
2011-10-27,The two dimensional local density of states of a Topological Insulator with an edge dislocation,"We investigate the effect of a crystal edge dislocation on the metallic
surface of a Topological Insulator. The edge dislocation gives rise to torsion
which the electrons experience as a spin connection. As a result the electrons
propagate along confined two dimensional regions and circular contours. Due to
the edge dislocations the parity symmetry is violated resulting in a current
measured by the in-plane component of the spin on the surface.
  The tunneling density of states for Burger vectors in the $y$ direction is
maximal along the $x$ direction. The evidence of the enhanced tunneling density
of states can be verified with the help of the scanning tunneling technique.",1110.6196v1
2014-08-29,"Local behavior of solutions of the stationary Schr\"" odinger equation with singular potentials and bounds on the density of states of Schrödinger operators","We study the local behavior of solutions of the stationary Schr\"" od\-inger
equation with singular potentials, establishing a local decomposition into a
homogeneous harmonic polynomial and a lower order term. Combining a corollary
to this result with a quantitative unique continuation principle for singular
potentials we obtain log-H\""older continuity for the density of states
outer-measure in one, two, and three dimensions for Schr\"" odinger operators
with singular potentials, results that hold for the density of states measure
when it exists.",1408.7111v1
2012-04-15,The density of states in gauge theories,"The density of states is calculated for a SU(2) and a compact U(1) lattice
gauge theory using a modified version of the Wang-Landau algorithm. We find
that the density of states of the SU(2) gauge theory can be reliably calculated
over a range of 120,000 orders of magnitude for lattice sizes as big as 20^4.
We demonstrate the potential of the algorithm by reproducing the SU(2) average
action, its specific heat and the critical couplings of the weak first order
transition in U(1).",1204.3243v1
2016-12-09,A condition for purely absolutely continuous spectrum for CMV operators using the density of states,"We prove an averaging formula for the derivative of the absolutely continuous
part of the density of states measure for an ergodic family of CMV matrices. As
a consequence, we show that the spectral type of such a family is almost surely
purely absolutely continuous if and only if the density of states is absolutely
continuous and the Lyapunov exponent vanishes almost everywhere with respect to
the same. Both of these results are CMV operator analogues of theorems obtained
by Kotani for Schr\""odinger operators.",1612.03208v1
2020-11-18,Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise,"We construct the integrated density of states of the Anderson Hamiltonian
with two-dimensional white noise by proving the convergence of the Dirichlet
eigenvalue counting measures associated with the Anderson Hamiltonians on the
boxes. We also determine the logarithmic asymptotics of the left tail of the
integrated density of states. Furthermore, we apply our result to a moment
explosion of the parabolic Anderson model in the plane.",2011.09180v3
2022-03-28,Correlation of local densities of states on mesoscopic energy scales in random band matrices,"We are interested in the phase transition of the correlation function of
local densities of states at mesoscopic scales of random band matrices of width
$W$ in dimension $2$. As a result, we show that the local densities of states
are alternately positively and negatively correlated in the diffusive regime
$O(\log(L/W))$ times, $L$ being the size of he system.",2203.14847v2
2015-07-24,Analytic models for density of a ground-state spinor condensate,"We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor
ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a
single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the
ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi
approximation (TFA) to this decoupled equation. Similarly, for the ground
states of spin-1 anti-ferromagnetic and spin-2 anti-ferromagnetic and cyclic
BECs, some of the spin component densities are zero which reduces the coupled
GP equation to a simple reduced form. Analytic models for ground state
densities are also obtained for anti-ferromagnetic and cyclic BECs from the TFA
to the respective reduced GP equations. The analytic densities are illustrated
and compared with the full numerical solution of the GP equation with realistic
experimental parameters.",1507.06883v1
2013-08-21,Generalized adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule,"A generalized adiabatic connection for ensembles (GACE) is presented. In
contrast to the traditional adiabatic connection formulation, both ensemble
weights and interaction strength can vary along a GACE path while the ensemble
density is held fixed. The theory is presented for non-degenerate two-state
ensembles but it can in principle be extended to any ensemble of fractionally
occupied excited states. Within such a formalism an exact expression for the
ensemble exchange-correlation density-functional energy, in terms of the
conventional ground-state exchange-correlation energy, is obtained by
integration over the ensemble weight. Stringent constraints on the functional
are thus obtained when expanding the ensemble exchange-correlation energy
through second order in the ensemble weight. For illustration purposes, the
analytical derivation of the GACE is presented for the H2 model system in a
minimal basis, leading thus to a simple density-functional approximation to the
ensemble exchange-correlation energy. Encouraging results were obtained with
this approximation for the description in a large basis of the first
^1\Sigma^+_g excitation in H2 upon bond stretching. Finally, a range-dependent
GACE has been derived, providing thus a pathway to the development of a
rigorous state-average multi-determinant density-functional theory.",1308.4596v2
2023-05-26,Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies,"The basis-set correction method based on density-functional theory consists
in correcting the energy calculated by a wave-function method with a given
basis set by a density functional. This basis-set correction density functional
incorporates the short-range electron correlation effects missing in the basis
set. This results in accelerated basis convergences of ground-state energies to
the complete-basis-set limit. In this work, we extend the basis-set correction
method to a linear-response formalism for calculating excited-state energies.
We give the general linear-response equations, as well as the more specific
equations for configuration-interaction wave functions. As a proof of concept,
we apply this approach to the calculations of excited-state energies in a
one-dimensional two-electron model system with harmonic potential and a
Dirac-delta electron-electron interaction. The results obtained with
full-configuration-interaction wave functions expanded in a basis of Hermite
functions and a local-density-approximation basis-set correction functional
show that the present approach does not help in accelerating the basis
convergence of excitation energies. However, we show that it significantly
accelerates basis convergences of excited-state total energies.",2305.17093v1
2019-03-15,Decoherence of charge density waves in beam splitters for interacting quantum wires,"Simple intersections between one-dimensional channels can act as coherent
beam splitters for non-interacting electrons. Here we examine how coherent
splitting at such intersections is affected by inter-particle interactions, in
the special case of an intersection of topological edge states. We derive an
effective impurity model which represents the edge-state intersection within
Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the
exact time-dependent expectation values of the charge density as well as the
density-density correlation functions. In general a single incoming charge
density wave packet will split into four outgoing wave packets with
transmission and reflection coefficients depending on the strengths of the
tunnelling processes between the wires at the junction. We find that when
multiple charge density wave packets from different directions pass through the
intersection at the same time, reflection and splitting of the packets depend
on the relative phases of the waves. Active use of this phase-dependent
splitting of wave packets may make Luttinger interferometry possible. We also
find that coherent incident packets generally suffer partial decoherence from
the intersection, with some of their initially coherent signal being
transferred into correlated quantum noise. In an extreme case four incident
coherent wave packets can be transformed entirely into density-density
correlations, with the charge density itself having zero expectation value
everywhere in the final state.",1903.06431v1
2002-07-18,Bose-Einstein Condensation and Intermediate State of the Photon Gas,"Possibility of establishment of equilibrium between the photon and the dense
photon bunch is studied. In the case, when the density of plasma does not
change, the condition of production of the Bose-Einstein condensate is
obtained. It is shown that the inhomogeneity of density of photons leads to a
new intermediate state of the photon gas.",0207074v1
2000-11-21,Fractionnally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons,"Elementary excitations of the 4k$_F$ charge density wave state of a
quarter-filled strongly correlated electronic one-dimensional chain are
investigated in the presence of dispersionless quantum optical phonons using
Density Matrix Renormalization Group techniques. Such excitations are shown to
be topological unbound solitons carrying charge $e/2$. Relevance to the 4k$_F$
charge density wave instability in $\rm (DI-DCNQI)_2Ag$ or recently discovered
in (TMTTF)$_2$X (X=PF$_6$, AsF$_6$) is discussed.",0011358v2
2009-10-23,Resonance Lifetimes from Complex Densities,"The ab-initio calculation of resonance lifetimes of metastable anions
challenges modern quantum-chemical methods. The exact lifetime of the
lowest-energy resonance is encoded into a complex ""density"" that can be
obtained via complex-coordinate scaling. We illustrate this with one-electron
examples and show how the lifetime can be extracted from the complex density in
much the same way as the ground-state energy of bound systems is extracted from
its ground-state density.",0910.4599v1
2010-11-12,Lattice density-functional theory on graphene,"A density-functional approach on the hexagonal graphene lattice is developed
using an exact numerical solution to the Hubbard model as the reference system.
Both nearest-neighbour and up to third nearest-neighbour hoppings are
considered and exchange-correlation potentials within the local density
approximation are parameterized for both variants. The method is used to
calculate the ground-state energy and density of graphene flakes and infinite
graphene sheet. The results are found to agree with exact diagonalization for
small systems, also if local impurities are present. In addition, correct
ground-state spin is found in the case of large triangular and bowtie flakes
out of the scope of exact diagonalization methods.",1011.2892v1
2016-06-14,Thermodynamics vs. local density fluctuations in the metal/Mott-insulator crossover,"The crossover between a metal and a Mott insulator leads to a localization of
fermions from delocalized Bloch states to localized states. We experimentally
study this crossover using fermionic atoms in an optical lattice by measuring
thermodynamic and local (on--site) density correlations. In the metallic phase
at incommensurable filling we observe the violation of the local
fluctuation--dissipation theorem indicating that the thermodynamics cannot be
explained by local observables. In contrast, in the Mott-insulator we observe
the convergence of local and thermodynamic fluctuations indicating the absence
of long--range density-density correlations.",1606.04580v1
2021-06-29,Density-Functional Theory on Graphs,"The principles of density-functional theory are studied for finite lattice
systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn
theorem is found void in general, while many insights into the topological
structure of the density-potential mapping can be won. We give precise
conditions for a ground state to be uniquely v-representable and are able to
prove that this property holds for almost all densities. A set of examples
illustrates the theory and demonstrates the non-convexity of the pure-state
constrained-search functional.",2106.15370v2
2013-04-30,Parity doubling structure of nucleon at non-zero density in the holographic mean field theory,"We develope the holographic mean field theory approach in a bottom-up
holographic QCD model including baryons and scalar mesons in addition to vector
mesons and pions. We study the effect of parity doubling structure of baryons
at non-zero density to the equation of state between the chemical potential and
the baryon number density. We first show that we can adjust the amount of
nucleon mass coming from the chiral symmetry breaking by changing the boundary
value of the five-dimensional baryon fields. Then, introducing the mean field
for the baryon fields, we calculate the equation of state between the baryon
number density and its corresponding chemical potential. Then, comparing the
predicted equation of state with the one obtained in a Walecka type model, we
extract the density dependence of the effective nucleon mass. The result shows
that the effective mass decreases with increasing density, and that the rate of
decreasing is more rapid for the larger percentage of the mass coming from the
chiral symmetry breaking.",1304.7866v2
2001-07-26,Separability of Two-Party Gaussian States,"We investigate the separability properties of quantum two-party Gaussian
states in the framework of the operator formalism for the density operator.
Such states arise as natural generalizations of the entangled state originally
introduced by Einstein, Podolsky, and Rosen. We present explicit forms of
separable and nonseparable Gaussian states.",0107131v1
2011-04-06,Nuclear Density Functional Theory and the Equation of State,"A nuclear density functional can be used to find the binding energy and shell
structure of nuclei and the energy gap in superconducting nuclear matter. In
this paper, we study the possible application of a nuclear density functional
theory to nuclear astrophysics. From energy density functional theory, we can
deduce the interaction between nucleons to find a rough estimate of the charge
radius of the specific nuclei. Compared to the Finite-Range Thomas Fermi model,
we include three-body forces, which might be important at densities several
times that of nuclear matter density. We also add the momentum dependent
interaction to take into account the effective mass of the nucleons. We study
matter in the neutron star crust using the Wigner-Seitz cell method. By
constructing the mass-radius relation of neutron stars and investigating
lepton-rich nuclear matter in proto-neutron stars, we find that the density
functional can be used to construct an equation of state of hot dense matter.",1104.1194v1
2017-10-09,Properties of the electrostatically driven helical plasma state,"A novel plasma state has been found [C.~Ak\c{c}ay, J.~Finn, R.~Nebel and
D.~Barnes, Phys.~Plasmas \textbf{24}, 052503 (2017)] in the presence of a
uniform applied axial magnetic field in periodic cylindrical geometry. This
state is driven by external electrostatic fields provided by helical
electrodes, and depends on radius $r<r_w$ and $m\theta-n\zeta$, where $m=n=1$,
$\theta$ is the poloidal angle, and $\zeta=z/R$ is the toroidal angle. In this
reference, the strongly driven form of the state was found to have a strong
axial mean current density, with a mean-field line safety factor $q_0(r)$ just
above the pitch of the electrodes $m/n=1$ in the interior, where the plasma is
nearly force-free. However, at the edge the current density has a component
perpendicular to $\mathbf{B}$. This perpendicular current density drives nearly
Alfv\'enic helical plasma flows, an notable feature of these states. This state
is being studied for its possible application to DC electrical transformers and
possibly tailoring the current profile in tokamaks. We present results on
several issues of importance for these applications: the transient leading to
the steady state; the twist and writhe of the field lines and their relation
with the current density; the properties of the current density streamlines and
length of the current density lines connected to the electrodes; the
sensitivity to changes in the velocity boundary conditions; the effect of
varying the radial resistivity profile; and the effects of a concentrated
electrode potential.",1710.03339v1
2001-10-21,Two-dimensional electron gas: correlation energy versus density and spin polarization,"We propose a simple analytic representation of the correlation energy for the
two-dimensional electron gas, as a function of the density and the spin
polarization. This new parametrization includes most of the known high- and
low- density limits and fits our new fixed-node diffusion Monte Carlo
simulations, performed for a wide range of electron densities and
spin-polarization states. In this way we provide a reliable local-spin-density
energy functional for two-dimensional systems. The corresponding correlation
potential is discussed and compared with previous models.",0110444v2
2002-11-01,Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping,"We use time-dependent spin-density-functional theory to study dynamical
magnetic phenomena. First, we recall that the local-spin-density approximation
(LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic
state of iron and other itinerant ferromagnets. Next, we construct a
gradient-dependent density functional that does not suffer from this problem of
the LSDA. This functional is then used to derive, for the first time, the
phenomenological Gilbert equation of micromagnetics directly from
time-dependent density-functional theory. Limitations and extensions of Gilbert
damping are discussed on this basis, and some comparisons with phenomenological
theories and experiments are made.",0211021v1
2004-02-04,Density functional theory in one-dimension for contact-interacting fermions,"A density functional theory is developed for fermions in one dimension,
interacting via a delta-function. Such systems provide a natural testing ground
for questions of principle, as the local density approximation should work well
for short-ranged interactions. The exact-exchange contribution to the total
energy is a local functional of the density. A local density approximation for
correlation is obtained using perturbation theory and Bethe-Ansatz results for
the one-dimensional contact-interacting uniform Fermi gas. The ground-state
energies are calculated for two finite systems, the analogs of Helium and of
Hooke's atom. The local approximation is shown to be excellent, as expected.",0402108v1
2001-12-12,No First-Order Phase Transition in the Gross-Neveu Model?,"Within a variational calculation we investigate the role of baryons for the
structure of dense matter in the Gross-Neveu model. We construct a trial ground
state at finite baryon density which breaks translational invariance. Its
scalar potential interpolates between widely spaced kinks and antikinks at low
density and the value zero at infinite density. Its energy is lower than the
one of the standard Fermi gas at all densities considered. This suggests that
the discrete gamma_5 symmetry of the Gross-Neveu model does not get restored in
a first order phase transition at finite density, at variance with common
wisdom.",0112105v1
2006-07-12,Low density expansion for Lyapunov exponents,"In some quasi-one-dimensional weakly disordered media, impurities are large
and rare rather than small and dense. For an Anderson model with a low density
of strong impurities, a perturbation theory in the impurity density is
developed for the Lyapunov exponent and the density of states. The Lyapunov
exponent grows linearly with the density. Anomalies of the Kappus-Wegner type
appear for all rational quasi-momenta even in lowest order perturbation theory.",0607027v1
2006-07-18,The High-Density Symmetry Energy and Direct Urca,"The symmetry energy of nucleonic matter is usually assumed to be quadratic in
the isospin density. While this may be justified at sub-saturation densities,
there is no need to enforce this restriction at super-saturation densities. The
presence of a quartic term can strongly modify the critical density for the
direct Urca process which leads to faster cooling of neutron stars. Neutron
star cooling predictions which lie below the observational data can, for some
equations of state, be repaired with a quartic term which effectively turns off
the direct Urca process.",0607040v1
2007-12-10,Internal energy in dissipative relativistic fluids,"Liu procedure is applied to a first order weakly nonlocal special
relativistic fluid. It is shown, that a reasonable relativistic theory is and
extended one, where the basic state space contains the momentum density. This
property follows from the structure of the energy-momentum balance and the
Second Law of thermodynamics. Moreover, the entropy depends on the energy
density and the momentum density on a given specific way, indicating that the
local rest frame energy density cannot be interpreted as the internal energy,
the local rest frame momentum density should be considered, too. The
corresponding constitutive relations for the stress and the energy flux are
derived.",0712.1437v1
2008-05-14,Massless fermions in multi-flavor QED_2,"The ground state of the multi-flavor 2-dimensional quantum electrodynamics
(QED_2) is determined in the presence of finite baryon density, and it is shown
that the model possesses two phases, the low density phase where the external
baryon density is totally screened, and the high density phase, where the
screening is only partial. The renormalization of the bosonized version of the
model is also performed for both the zero and the finite density model giving
massless multi-flavor QED_2 in both cases.",0805.2009v2
2010-09-07,Lattice QCD at finite temperature and density,"We study the phase structure of QCD at finite temperature and density by
numerical simulations on a lattice. The most important point for the numerical
study at finite density is treatment of the sign problem. We propose a method
to avoid the sign problem, which is based on a cumulant expansion of the
complex phase in the density of state method combined with the reweighting
method. Using the method, we study the critical point terminating a first order
phase transition line in lattice QCD at high temperature and density.",1009.1186v1
2018-06-02,Fast Exact Univariate Kernel Density Estimation,"This paper presents new methodology for computationally efficient kernel
density estimation. It is shown that a large class of kernels allows for exact
evaluation of the density estimates using simple recursions. The same
methodology can be used to compute density derivative estimates exactly. Given
an ordered sample the computational complexity is linear in the sample size.
Combining the proposed methodology with existing approximation methods results
in extremely fast density estimation. Extensive experimentation documents the
effectiveness and efficiency of this approach compared with the existing
state-of-the-art.",1806.00690v3
2023-09-08,Glassy phases of the Gaussian Core Model,"We present results from molecular dynamics simulations exploring the
supercooled dynamics of the Gaussian Core Model in the low- and
intermediate-density regimes. In particular, we discuss the transition from the
low-density hard-sphere-like glassy dynamics to the high-density one. The
dynamics at low densities is well described by the caging mechanism, giving
rise to intermittent dynamics. At high densities, the particles undergo a more
continuous motion in which the concept of cage loses its meaning. We elaborate
on the idea that these different supercooled dynamics are in fact the
precursors of two different glass states.",2309.04323v1
2009-01-20,Analytic response theory for the density matrix renormalization group,"We propose an analytic response theory for the density matrix renormalization
group whereby response properties correspond to analytic derivatives of density
matrix renormalization group observables with respect to the applied
perturbations. Both static and frequency-dependent response theories are
formulated and implemented. We evaluate our pilot implementation by calculating
static and frequency dependent polarizabilities of short oligo-di-acetylenes.
The analytic response theory is competitive with dynamical density matrix
renormalization group methods and yields significantly improved accuracies when
using a small number of density matrix renormalization group states. Strengths
and weaknesses of the analytic approach are discussed.",0901.3166v1
2006-08-17,Generalized Quantum Hall Projection Hamiltonians,"Certain well known quantum Hall states -- including the Laughlin states, the
Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined
as the unique lowest degree symmetric analytic function that vanishes as at
least p powers as some number (g+1) of particles approach the same point.
Analogously, these same quantum Hall states can be generated as the exact
highest density zero energy state of simple angular momentum projection
operators. Following this theme we determine the highest density zero energy
state for many other values of p and g.",0608378v1
2004-05-23,New Cosmic Low Energy States of Neutrino,"A field theory is studied where the consistency condition of equations of
motion dictates strong correlation between states of ""primordial"" fermion
fields and local value of the dark energy. In regime of the fermion densities
typical for normal particle physics, the primordial fermions split into three
families identified with regular fermions. When fermion energy density is
comparable with dark energy density, the theory allows transition to new type
of states. The possibility of such Cosmo-Low Energy Physics (CLEP) states is
demonstrated in a model of FRW universe filled with homogeneous scalar field
and uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state
are drawn into cosmological expansion by means of dynamically changing their
own parameters. One of the features of the fermions in CLEP state is that in
the late time universe their masses increase as $a^{3/2}$ ($a=a(t)$ is the
scale factor). The energy density of the cold dark matter consisting of
neutrinos in CLEP state scales as a sort of dark energy; this cold dark matter
possesses negative pressure and for the late time universe its equation of
state approaches that of the cosmological constant. The total energy density of
such universe is less than it would be in the universe free of fermionic matter
at all.",0405199v1
2008-01-10,Determination of the Equation of State of a Two-Component Fermi Gas at Unitarity,"We report on the measurement of the equation of state of a two-component
Fermi gas of $^6$Li atoms with resonant interactions. By analyzing the
\textit{in situ} density distributions of a population-imbalanced Fermi mixture
reported in the recent experiment [Y. Shin \textit{et al.}, Nature
\textbf{451}, 689 (2008)], we determine the energy density of a resonantly
interacting Fermi gas as a function of the densities of the two components. We
present a method to determine the equation of state directly from the shape of
the trapped cloud, where the fully-polarized, non-interacting ideal Fermi gas
in the outer region provides the absolute calibration of particle density. From
the density profiles obtained at the lowest temperature, we estimate the
zero-temperature equation of state.",0801.1523v2
1996-03-25,Slow relaxation in granular compaction,"Experimental studies show that the density of a vibrated granular material
evolves from a low density initial state into a higher density final steady
state. The relaxation towards the final density value follows an inverse
logarithmic law. We propose a simple stochastic adsorption-desorption process
which captures the essential mechanism underlying this remarkably slow
relaxation. As the system approaches its final state, a growing number of beads
have to be rearranged to enable a local density increase. In one dimension,
this number grows as $N=\rho/(1-\rho)$, and the density increase rate is
drastically reduced by a factor $e^{-N}$. Consequently, a logarithmically slow
approach to the final state is found $\rho_{\infty}-\rho(t)\cong 1/\ln t$.",9603150v1
2013-07-11,Hartree-Fock Ground State Phase Diagram of Jellium,"We calculate the ground state phase diagram of the homogeneous electron gas
in three dimensions within the Hartree-Fock approximation and show that broken
symmetry states are energetically favored at any density against the
homogeneous Fermi gas state with isotropic Fermi surface. At high density, we
find metallic spin-unpolarized solutions where electronic charge and spin
density form an incommensurate crystal having more crystal sites than
electrons. For $r_s \to 0$, our solutions approach pure spin-density waves,
whereas the commensurate Wigner crystal is favored at lower densities, $r_s >
3.4$. Decreasing the density, the system undergoes several structural phase
transitions with different lattice symmetries. The polarization transition
occurs around $r_s \approx 8.5$.",1307.3081v2
2011-01-21,Multiple spin state analysis of magnetic nano graphene,"Recent experiments indicate room-temperature ferromagnetism in graphite-like
materials. This paper offers multiple spin state analysis applied to asymmetric
graphene molecule to find out mechanism of ferromagnetic nature. First
principle density functional theory is applied to calculate spin density,
energy and atom position depending on each spin state. Molecules with
dihydrogenated zigzag edges like C64H27, C56H24, C64H25, C56H22 and C64H23 show
that in every molecule the highest spin state is the most stable one with over
3000 K energy difference with next spin state. This result suggests a stability
of room temperature ferromagnetism in these molecules. In contrast, nitrogen
substituted molecules like C59N5H22, C52N4H20, C61N3H22, C54N2H20 and C63N1H22
show opposite result that the lowest spin state is the most stable. Magnetic
stability of graphene molecule can be explained by three key issues, that is,
edge specified localized spin density, parallel spins exchange interaction
inside of a molecule and atom position optimization depending on spin state.
Those results will be applied to design a carbon-base ferro-magnet, an ultra
high density 100 tera bit /inch2 class information storage and spintronic
devices.",1101.4080v1
1996-08-15,Exact shape of the lowest Landau level in a double--layer system and a superlattice with uncorrelated disorder,"We extend Wegner's exact solution for the 2D density of states at the lowest
Landau level with a short--range disorder to the cases of a double--layer
system and a superlattice. For the double--layer system, an analytical
expression for the density of states, illustrating the interplay between the
tunnel splitting of Landau levels and the disorder--induced broadening, is
obtained. For the superlattice, we derive an integral equation, the eigenvalue
of which determines the exact density of states. By solving this equation
numerically, we trace the disappearance of the miniband with increasing
disorder.",9608066v1
2000-04-11,Spin Effects in the Local Density of States of GaAs,"We present spin-resolved measurements of the local density of states in Si
doped GaAs. Both spin components exhibit strong mesoscopic fluctuations. In the
magnetic quantum limit, the main features of the spin-up and spin-down
components of the local density of states are found to be identical apart from
Zeeman splitting. Based on this observation, we introduce a mesoscopic method
to measure the $g$-factor in a material where macroscopic methods are severely
restricted by disorder. Differences between the spin-up and spin-down
components are discussed in terms of spin relaxation due to spin-orbit
coupling.",0004165v1
2004-12-19,Tails of the Density of States in a Random Magnetic Field,"We study the tails of the density of states of fermions subject to a random
magnetic field with non-zero mean with the Optimum Fluctuation Method (OFM).
Closer to the centres of the Landau levels, the density of states is found to
be Gaussian, whereas the energy dependence is non-analytic near the lower bound
of the spectrum.",0412517v1
2006-09-14,Continuity of integrated density of states -- independent randomness,"In this paper we discuss the continuity properties of the integrated density
of states for random models based on that of the single site distribution. Our
results are valid for models with independent randomness with arbitrary free
parts. In particular in the case of the Anderson type models (with stationary,
growing, decaying randomness) on the $\nu$ dimensional lattice, with or without
periodic and almost periodic backgrounds, we show that if the single site
distribution is uniformly $\alpha$-H\""older continuous, $ 0 < \alpha \leq 1$,
then the density of states is also uniformly $\alpha$-H\""older continuous.",0609040v2
1994-09-02,The Determination of Nuclear Level Densities from Experimental Information -,"A novel Information Theory based method for determining the density of states
from prior information is presented. The energy dependence of the density of
states is determined from the observed number of states per energy interval and
model calculations suggest that the method is sufficiently reliable to
calculate the thermal properties of nuclei over a reasonable temperature range.",9409001v1
2002-11-24,Robustness of entanglement for two qubit density matrix,"By considering the decomposition of a generic two qubit density matrix
presented by Wootters [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)],
the robustness of entanglement for any mixed state of two qubit systems is
obtained algebraically. It is shown that the robustness of entanglement is
proportional to concurrence and in Bell decomposable density matrices it is
equal to the concurrence. We also give an analytic expression for two separable
states which wipe out all entanglement of these states. Since thus obtained
robustness is function of the norm of the vectors in the decomposition we give
an explicit parameterization for the decomposition.",0211156v1
2013-06-13,Generalized qubit portrait of the qutrit state density matrix,"New inequalities for tomographic probability distributions and density
matrices of qutrit states are obtained by means of generalization of qubit
portrait method. The approach based on the qudit portrait method to get new
entropic inequalities is proposed. It can be applied to the case of arbutrary
nonnegative hermitian matrices including the density matrices of multipartite
qudit states.",1306.3182v1
2020-07-07,Density of States of a Coupled-Channel System,"We demonstrate how an effective density of states can be derived from the
S-matrix describing a coupled-channel system. Besides the locations of poles,
the phase of the determinant of the S-matrix encodes essential details in
characterizing the dynamics of resonant and non-resonant interactions. The
density of states is computed for the two channel scattering problem ($\pi\pi,
K \bar{K}$, S-wave), and the influences from the various dynamical structures:
poles, roots, branch cuts, and Riemann sheets, are examined.",2007.03392v1
2023-10-16,"Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasiperiodic $M(2, \mathbb{C})$ cocycles","It is known that the Lyapunov exponent for multifrequency analytic cocycles
is weak-H\""older continuous in cocycle for certain Diophantine frequencies, and
that this implies certain regularity of the integrated density of states in
energy for Jacobi operators. In this paper, we establish the pointwise modulus
of continuity in both cocycle and frequency and obtain analogous regularity of
the integrated density of states in energy, potential, and frequency.",2310.10472v1
2000-11-18,The Density of States and the Spectral Shift Density of Random Schroedinger Operators,"In this article we continue our analysis of Schroedinger operators with a
random potential using scattering theory. In particular the theory of Krein's
spectral shift function leads to an alternative construction of the density of
states in arbitrary dimensions. For arbitrary dimension we show existence of
the spectral shift density, which is defined as the bulk limit of the spectral
shift function per unit interaction volume. This density equals the difference
of the density of states for the free and the interaction theory. This extends
the results previously obtained by the authors in one dimension. Also we
consider the case where the interaction is concentrated near a hyperplane.",0011033v1
2014-02-12,A High-Performance Triple Patterning Layout Decomposer with Balanced Density,"Triple patterning lithography (TPL) has received more and more attentions
from industry as one of the leading candidate for 14nm/11nm nodes. In this
paper, we propose a high performance layout decomposer for TPL. Density
balancing is seamlessly integrated into all key steps in our TPL layout
decomposition, including density-balanced semi-definite programming (SDP),
density-based mapping, and density-balanced graph simplification. Our new TPL
decomposer can obtain high performance even compared to previous
state-of-the-art layout decomposers which are not balanced-density aware, e.g.,
by Yu et al. (ICCAD'11), Fang et al. (DAC'12), and Kuang et al. (DAC'13).
Furthermore, the balanced-density version of our decomposer can provide more
balanced density which leads to less edge placement error (EPE), while the
conflict and stitch numbers are still very comparable to our
non-balanced-density baseline.",1402.2890v1
2017-07-07,"Matter Density versus Distance for the Neutrino Beam from Fermilab to Lead, South Dakota, and Comparison of Oscillations with a Variable and a Constant Density","This paper is divided into two parts. In the first part, the material
densities passed through for neutrinos going from FNAL to Sanford Laboratory
are calculated using two recent density tables, Crustal [G. Laske, G. Masters.
Z. Ma, and M. Pasyanos, Update on CRUST1.0 -- A 1-degree global model of
Earth's crust, Geophys. Res. Abstracts 15, EGU2013-2658 (2013)] and
Shen-Ritzwoller [W. Shen and M. H. Ritzwoller. Crustal and uppermost mantle
structure beneath the United States, J. Geophys. Res.: Solid Earth 121, 4306
(2016)], as well as the values from an older table PEMC [A. M. Dziewonski, A.
L. Hales and E. R. Lapwood, Parametrically simple earth models consistent with
geophysical data, Phys. Earth Plan. Int. 10 12 (1975)]. In the second part,
neutrino oscillations at Sanford Laboratory are examined for the variable
density table of Shen-Ritzwoller. These results are then compared with
oscillation results using the mean density from the Shen-Ritzwoller tables and
one other fixed density. For the tests made here, the mean density results are
quite similar to those found using the variable density vs distance.",1707.02322v1
2022-08-01,Quantum Adaptive Fourier Features for Neural Density Estimation,"Density estimation is a fundamental task in statistics and machine learning
applications. Kernel density estimation is a powerful tool for non-parametric
density estimation in low dimensions; however, its performance is poor in
higher dimensions. Moreover, its prediction complexity scale linearly with more
training data points. This paper presents a method for neural density
estimation that can be seen as a type of kernel density estimation, but without
the high prediction computational complexity. The method is based on density
matrices, a formalism used in quantum mechanics, and adaptive Fourier features.
The method can be trained without optimization, but it could be also integrated
with deep learning architectures and trained using gradient descent. Thus, it
could be seen as a form of neural density estimation method. The method was
evaluated in different synthetic and real datasets, and its performance
compared against state-of-the-art neural density estimation methods, obtaining
competitive results.",2208.00564v2
2006-03-19,Ground state energy density of a dilute Bose gas in the canonical transformation,"A ground state energy density of an interacting dilute Bose gas system is
studied in the canonical transformation scheme. It is shown that the
transformation scheme enables us to calculate a higher order correction of
order $n a^3$ in the particle depletion and ground state energy density of a
dilute Bose gas system, which corresponds to the density fluctuation
contribution from the excited states. The coefficient of $n a^3$ term is shown
to be $2(\pi - 8/3)$ for the particle depletion, and $16(\pi - 8/3)$ for the
ground state energy density.",0603479v4
2007-09-20,Spin polarization phenomena in dense nuclear matter,"Spin polarized states in nuclear matter with an effective nucleon-nucleon
interaction are studied for a wide range of isospin asymmetries and densities.
Based on a Fermi liquid theory, it is shown that there are a few possible
scenarios of spin ordered phase transitions: (a) nuclear matter undergoes at
some critical density a phase transition to a spin polarized state with the
oppositely directed spins of neutrons and protons (Skyrme SLy4 and Gogny D1S
interactions); (b) at some critical density, a spin polarized state with the
like-directed neutron and proton spins appears (Skyrme SkI5 interaction); (c)
nuclear matter under increasing density, at first, undergoes a phase transition
to the state with the opposite directions of neutron and proton spins, which
goes over at larger density to the state with the same direction of nucleon
spins (Skyrme SkI3 interaction).",0709.3188v1
2021-10-31,Spontaneous emission rate and the density of states inside a one dimensional photonic crystal,"Different densities of electromagnetic states inside a one dimensional
photonic crystal (1D PC) are studied. Hertz vector formalism is used to
calculate Green tensor inside a layered structure, semi-analytically. Based on
the obtained Green tensor, the local density of electromagnetic states (LDOS)
and the density of states (DOS) inside a 1D PC are calculated and discussed.
The Green tensor is also used to approximate the density of Bloch states inside
the 1D PC and is compared with its exact calculation based on the 1D PC
dispersion relations. Using a practical 1D PC parameters in the visible range,
the aforementioned quantities are calculated and verified with a full-wave
solver based on finite element method (FEM). The formulations and the results
are aimed to be helpful in thermal and spontaneous radiation studies.",2111.00571v1
2006-03-08,Electronic Structure of Nearly Ferromagnetic compound HfZn$_{2}$,"The electronic structure of HfZn$_{2}$ has been studied based on the density
functional theory within the local-density approximation. The calculation
indicates that HfZn$_{2}$ shows ferromagnetic instability. Large enhancement of
the static susceptibility over its non-interacting value is found due to a peak
in the density of states at the Fermi level.",0603203v1
2006-03-11,Electronic Structure and Magnetic Properties of $β$-Ti$_{6}$Sn$_{5}$,"The electronic structure of $\beta$-Ti$_{6}$Sn$_{5}$ has been studied based
on the density functional theory within the local-density approximation. The
calculation indicates that $\beta$-Ti$_{6}$Sn$_{5}$ is very close to
ferromagnetic instability and shows ferromagnetic ordering after rare earth
element doping. Large enhancement of the static susceptibility over its
non-interacting value is found due to a peak in the density of states at the
Fermi level.",0603313v1
2000-11-23,Random Lattices and Random Sphere Packings: Typical Properties,"We review results about the density of typical lattices in $R^n.$ They state
that such density is of the order of $2^{-n}.$ We then obtain similar results
for random packings in $R^n$: after taking suitably a fraction $\nu$ of a
typical random packing $\sigma$, the resulting packing $\tau$ has density
$C(\nu) 2^{-n},$ with a reasonable $C(\nu).$ We obtain estimates on $C(\nu).$",0011040v1
2010-09-29,Density quantization method in the optimal portfolio choice with partial observation of stochastic volatility,"Computational aspects of the optimal consumption and investment with the
partially observed stochastic volatility of the asset prices are considered.
The new quantization approach to filtering - density quantization - is
introduced which reduces the original infinite dimensional state space of the
problem to the finite quantization set. The density quantization is embedded
into the numerical algorithm to solve the dynamic programming equation related
to the portfolio optimization.",1009.5806v1
2011-10-31,Three dimensional structure of low-density nuclear matter,"We numerically explore the pasta structures and properties of low-density
nuclear matter without any assumption on the geometry. We observe conventional
pasta structures, while a mixture of the pasta structures appears as a
metastable state at some transient densities. We also discuss the lattice
structure of droplets.",1110.6672v2
2014-05-20,Minkovskii-type inequality for arbitrary density matrix of composite and noncomposite systems,"New kind of matrix inequality known for bipartite system density matrix is
obtained for arbitrary density matrix of composite or noncomposite qudit
systems including the single qudit state. The examples of two qubit system and
qudit with j=3/2 are discussed.",1405.4956v1
2020-08-19,Beyond Density Matrices: Geometric Quantum States,"A quantum system's state is identified with a density matrix. Though their
probabilistic interpretation is rooted in ensemble theory, density matrices
embody a known shortcoming. They do not completely express an ensemble's
physical realization. Conveniently, when working only with the statistical
outcomes of projective and positive operator-valued measurements this is not a
hindrance. To track ensemble realizations and so remove the shortcoming, we
explore geometric quantum states and explain their physical significance. We
emphasize two main consequences: one in quantum state manipulation and one in
quantum thermodynamics.",2008.08682v1
2020-07-06,The Possible Equation Of State Of Dark Matter in Low Surface Brightness Galaxies,"The observed rotation curves of low surface brightness (LSB) galaxies play an
essential role in studying dark matter, and indicate that there exists a
central constant density dark matter core. However, the cosmological N-body
simulations of cold dark matter predict an inner cusped halo with a power-law
mass density distribution, and can't reproduce a central constant-density core.
This phenomenon is called cusp-core problem. When dark matter is quiescent and
satisfies the condition for hydrostatic equilibrium, using the equation of
state can get the density profile in the static and spherically symmetric
space-time. To solve the cusp-core problem, we assume that the equation of
state is independent of the scaling transformation. Its lower order
approximation for this type of equation of state can naturally lead to a
special case, i.e. $p=\zeta\rho+2\epsilon V_{rot}^{2}\rho$, where $p$ and
$\rho$ are the pressure and density, $V_{rot}$ is the rotation velocity of
galaxy, $\zeta$ and $ \epsilon$ are positive constants. It can obtain a density
profile that is similar to the pseudo-isothermal halo model when $\epsilon$ is
around $0.15$. To get a more widely used model, let the equation of state
include the polytropic model, i.e. $p= \frac{\zeta}{\rho_{0}^{s}}\rho^{1+s}+
2\epsilon V_{rot}^{2}\rho$, we can get other kinds of density profiles, such as
the profile that is nearly same with the Burkert profile, where $s$ and
$\rho_{0}$ are positive constants.",2007.02583v3
2019-10-14,Ultrabroadband Density of States of Amorphous In-Ga-Zn-O,"The sub-gap density of states of amorphous indium gallium zinc oxide
($a$-IGZO) is obtained using the ultrabroadband photoconduction (UBPC) response
of thin-film transistors (TFTs). Density functional theory simulations classify
the origin of the measured sub-gap density of states peaks as a series of
donor-like oxygen vacancy states and acceptor-like Zn vacancy states. Donor
peaks are found both near the conduction band and deep in the sub-gap, with
peak densities of $10^{17}-10^{18}$ cm$^{-3}$eV$^{-1}$. Two deep acceptor-like
metal vacancy peaks with peak densities in the range of $10^{18}$
cm$^{-3}$eV$^{-1}$ and lie adjacent to the valance band Urbach tail region at
2.0 to 2.5 eV below the conduction band edge. By applying detailed charge
balance, we show increasing the density of metal vacancy deep-acceptors
strongly shifts the $a$-IGZO TFT threshold voltage to more positive values.
Photoionization (h$\nu$ > 2.0 eV) of metal vacancy acceptors is one cause of
transfer curve hysteresis in $a$-IGZO TFTs owing to longer recombination
lifetimes as they get captured into acceptor-like vacancies.",1910.06264v2
2020-02-21,Configuration Entropy for Quarkonium in a Finite Density Plasma,"In the recent years many examples appeared in the literature where the
configuration entropy (CE), introduced by Gleiser and Stamatopoulos, plays the
role of an indicator of stability of physical systems. It was observed that,
comparing states of the same system, the lower is the value of the CE, the more
stable is the state. In this work we investigate the behaviour of the
differential configuration entropy (DCE) , that is appropriate for systems with
continuous degrees of freedom, in a new context. We consider quasi-states of
quarkonium (a vector meson made of a heavy quark anti-quark pair) inside a
plasma at finite density. It is known that the density increases the
dissociation effect for quasi-particles inside a plasma. So, increasing the
density of a thermal medium corresponds to reducing the stability of the
quasi-particles. In order to investigate how this situation is translated in
the Configutation Entropy context, we use a recently developed holographic
AdS/QCD model for heavy vector mesons. The quasi-normal modes describing the
quasi-states are obtained and the corresponding DCE is calculated. We find, for
bottomonium and charmonium $1 S$ quasi-states, that the DCE increases with the
quark density, or quark chemical potential, of the medium. This result shows
that the DCE works again as an indicator of stability, represented in this case
by the dissociation effect associated with the density.",2002.09413v2
2013-12-10,Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions,"We study the non-integrable Dicke model, and its integrable approximation,
the Tavis-Cummings model, as functions of both the coupling constant and the
excitation energy. Excited-state quantum phase transitions (ESQPT) are found
analyzing the density of states in the semi-classical limit and comparing it
with numerical results for the quantum case in large Hilbert spaces, taking
advantage of efficient methods recently developed. Two different ESQPTs are
identified in both models, which are signaled as singularities in the
semi-classical density of states, one {\em static} ESQPT occurs for any
coupling, whereas a dynamic ESQPT is observed only in the superradiant phase.
The role of the unstable fixed points of the Hamiltonian semi-classical flux in
the occurrence of the ESQPTs is discussed and determined. Numerical evidence is
provided that shows that the semi-classical result describes very well the
tendency of the quantum energy spectrum for any coupling in both models.
Therefore the semi-classical density of states can be used to study the
statistical properties of the fluctuation in the spectra, a study that is
presented in a companion paper.",1312.2665v2
2004-07-15,Multi-dimensional Density of States by Multicanonical Monte Carlo,"Multi-dimensional density of states provides a useful description of complex
frustrated systems. Recent advances in Monte Carlo methods enable efficient
calculation of the density of states and related quantities, which renew the
interest in them. Here we calculate density of states on the plane (energy,
magnetization) for an Ising Model with three-spin interactions on a random
sparse network, which is a system of current interest both in physics of glassy
systems and in the theory of error-correcting codes. Multicanonical Monte Carlo
algorithm is successfully applied, and the shape of densities and its
dependence on the degree of frustration is revealed. Efficiency of
multicanonical Monte Carlo is also discussed with the shape of a projection of
the distribution simulated by the algorithm.",0407396v1
2002-01-16,Calculations of the Local Density of States for some Simple Systems,"A recently proposed convolution technique for the calculation of local
density of states is described more thouroughly and new results of its
application are presented. For separable systems the exposed method allows to
construct the ldos for a higher dimensionality out of lower dimensional parts.
Some practical and theoretical aspects of this approach are also discussed.",0201277v1
2017-10-08,Chemical Bonding Analysis on Amphoteric Hydrogen - Alkaline Earth Ammine Borohydrides,"Usually the ions in solid are in the positive oxidation states or in the
negative oxidation state depending upon the chemical environment. It is highly
unusual for an ion having both positive as well as negative oxidation state in
a particular compound. Structural analysis suggest that the alkaline earth
ammine borohydrides (AABH) with the chemical formula M (BH4)2(NH3)2 (M = Mg,
Ca, or Sr) where hydrogen is present in +1 and -1 oxidation states. In order to
understand the oxidation states of hydrogen and also the character of chemical
bond present in AABH we have made charge density, electron localization
function, Born effective charge, Bader effective charge, and density of states
analyses using result from the density functional calculations. Our detailed
analyses show that hydrogen is in amphoteric behavior with hydrogen closer to
boron is in negative oxidation state and that closer to nitrogen is in the
positive oxidation state. Due to the presence of finite covalent bonding
between the consitutents in AABH the oxidation state of hydrogen is
non-interger value. The confirmation of the presence of amphtoric behavior of
hydrogen in AABH has implication in hydrogen storage applications.",1710.04272v1
2021-09-23,"Correlated insulators, density wave states, and their nonlinear optical response in magic-angle twisted bilayer graphene","The correlated insulator (CI) states and the recently discovered density wave
(DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated
intense research interest. However, up to date, the nature of these
""featureless"" correlated states with zero Chern numbers are still elusive, and
are lack of characteristic experimental signature. Thus, an experimental probe
to identify the characters of these featureless CI and DW states are urgently
needed. In this work, we theoretically study the correlated insulators and
density-wave states at different integer and fractional fillings of the flat
bands in magic-angle TBG based on extended unrestricted Hartree-Fock
calculations including the Coulomb screening effects from the remote bands. We
further investigate the nonlinear optical response of the various correlated
states, and find that the nonlinear optical conductivities can be used to
identify the nature of these CI and DW states at most of the fillings.
Therefore, we propose that nonlinear optical response can serve as a promising
experimental probe to unveil the nature of the CI and DW states observed in
magic-angle TBG.",2109.11441v2
2013-03-21,Density of one-particle states for 2D electron gas in magnetic field,"The density of states of a particle in a 2D area is independent both of the
energy and form of the area only at the region of large values of energy. If
energy is small, the density of states in the rectangular potential well
essentially depends on the form of the area. If the bottom of the potential
well has a potential relief, it can define the small eigenvalues as the
discrete levels. In this case, dimensions and form of the area would not have
any importance. If the conservation of zero value of the angular momentum is
taken into account, the effective one-particle Hamiltonian for the 2D electron
gas in the magnetic field in the circle is the Hamiltonian with the parabolic
potential and the reflecting bounds. It is supposed that in the square, the
Hamiltonian has the same view. The 2D density of states in the square can be
computed as the convolution of 1D densities. The density of one-particle states
for 2D electron gas in the magnetic field is obtained. It consists of three
regions. There is a discrete spectrum at the smallest energy. In the
intervening region the density of states is the sum of the piecewise continuous
function and the density of the discrete spectrum. At great energies, the
density of states is a continuous function. The Fermi energy dependence on the
magnetic field is obtained when the field is small and the Fermi energy is
located in the region of continuous spectrum. The Fermi energy has the
oscillating correction and in the average it increases proportionally to the
square of the magnetic induction. Total energy of electron gas in magnetic
field also oscillates and increases when the magnetic field increases
monotonously.",1303.5206v1
2010-04-01,Equation of State of Dense Matter from a density dependent relativistic mean field model,"We calculate the equation of state (EoS) of dense matter, using a
relativistic mean field (RMF) model with a density dependent coupling that is a
slightly modified form of the original NL3 interaction. For nonuniform nuclear
matter we approximate the unit lattice as a spherical Wigner-Seitz cell,
wherein the meson mean fields and nucleon Dirac wave functions are solved fully
self-consistently. We also calculate uniform nuclear matter for a wide range of
temperatures, densities, and proton fractions, and match them to non-uniform
matter as the density decreases. The calculations took over 6,000 CPU days in
Indiana University's supercomputer clusters. We tabulate the resulting EoS at
over 107,000 grid points in the proton fraction range $Y_P$ = 0 to 0.56. For
the temperature range $T$ = 0.16 to 15.8 MeV we cover the density range $n_B$ =
10$^{-4}$ to 1.6 fm$^{-3}$; and for the higher temperature range $T$ = 15.8 to
80 MeV we cover the larger density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$. In
the future we plan to study low density, low temperature (T$<$15.8 MeV),
nuclear matter using a Virial expansion, and we will match the low density and
high density results to generate a complete EoS table for use in astrophysical
simulations of supernova and neutron star mergers.",1004.0228v2
2016-07-15,Electric and magnetic multipoles and bond orders in excitonic insulators,"We study the charge and spin density distributions of excitonic insulator
(EI) states in the tight-binding approximation. We first discuss the charge and
spin densities of the EI states when the valence and conduction bands are
composed of orthogonal orbitals in a single atom. We show that the anisotropic
charge or spin density distribution occurs in a unit cell (or atom) and a
higher rank electric or magnetic multipole moment becomes finite, indicating
that the EI state corresponds to the multipole order. A full description of the
multipole moments for the $s$, $p$, and $d$ orbitals is then given in general.
We find that, in contrast to the conventional density-wave states, the
modulation of the total charge or net magnetization does not appear in this
case. However, when the conduction and valence bands include the component of
the same orbital, the modulation of the total charge or net magnetization
appears, as in the conventional density-wave state. We also discuss the
electron density distribution in the EI state when the valence and conduction
bands are composed of orbitals located in different atoms. We show that the
excitonic ordering in this case corresponds to the bond order formation. Based
on the results thus obtained we discuss the EI states of real materials
recently reported.",1607.04365v2
2010-04-26,Effects of Quantized Scalar Fields in Cosmological Spacetimes with Big Rip Singularities,"Effects of quantized free scalar fields in cosmological spacetimes with Big
Rip singularities are investigated. The energy densities for these fields are
computed at late times when the expansion is very rapid. For the massless
minimally coupled field it is shown that an attractor state exists in the sense
that, for a large class of states, the energy density of the field
asymptotically approaches the energy density it would have if it was in the
attractor state. Results of numerical computations of the energy density for
the massless minimally coupled field and for massive fields with minimal and
conformal coupling to the scalar curvature are presented. For the massive
fields the energy density is seen to always asymptotically approach that of the
corresponding massless field. The question of whether the energy densities of
quantized fields can be large enough for backreaction effects to remove the Big
Rip singularity is addressed.",1004.4620v3
1998-07-24,Bound Entanglement and Teleportation,"Recently M. Horodecki, P. Horodecki and R. Horodecki have introduced a set of
density matrices of two spin-1 particles from which it is not possible to
distill any maximally entangled states, even though the density matrices are
entangled. Thus these density matrices do not allow reliable teleportation.
However it might nevertheless be the case that these states can be used for
teleportation, not reliably, but still with fidelity greater than that which
may be achieved with a classical scheme. We show that, at least for some of
these density matrices, teleportation cannot be achieved with better than
classical fidelity.",9807069v1
2002-06-24,How to mix a density matrix,"A given density matrix may be represented in many ways as a mixture of pure
states. We show how any density matrix may be realized as a uniform ensemble.
It has been conjectured that one may realize all probability distributions that
are majorized by the vector of eigenvalues of the density matrix. We show that
if the states in the ensemble are assumed to be distinct then it is not true,
but a marginally weaker statement may still be true.",0206169v2
2007-05-09,Ground state of a confined Yukawa plasma including correlation effects,"The ground state of an externally confined one-component Yukawa plasma is
derived analytically using the local density approximation (LDA). In
particular, the radial density profile is computed. The results are compared
with the recently obtained mean-field (MF) density profile
\cite{henning.pre06}. While the MF results are more accurate for weak
screening, LDA with correlations included yields the proper description for
large screening. By comparison with first-principle simulations for
three-dimensional spherical Yukawa crystals we demonstrate that both
approximations complement each other. Together they accurately describe the
density profile in the full range of screening parameters.",0705.1221v1
2017-11-19,Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory,"[Background:] It is well known that effective nuclear interactions are in
general nonlocal. Thus if nuclear densities obtained from {\it ab initio}
no-core-shell-model (NCSM) calculations are to be used in reaction
calculations, translationally invariant nonlocal densities must be available.
[Purpose:] Though it is standard to extract translationally invariant one-body
local densities from NCSM calculations to calculate local nuclear observables
like radii and transition amplitudes, the corresponding nonlocal one-body
densities have not been considered so far. A major reason for this is that the
procedure for removing the center-of-mass component from NCSM wavefunctions up
to now has only been developed for local densities. [Results:] A formulation
for removing center-of-mass contributions from nonlocal one-body densities
obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived,
and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and
$^{16}$O. The nonlocality is studied as a function of angular momentum
components in momentum as well as coordinate space [Conclusions:] We find that
the nonlocality for the ground state densities of the nuclei under
consideration increases as a function of the angular momentum. The relative
magnitude of those contributions decreases with increasing angular momentum. In
general, the nonlocal structure of the one-body density matrices we studied is
given by the shell structure of the nucleus, and can not be described with
simple functional forms.",1711.07080v1
2007-02-13,Coarse-grained V-representability,"The unsolved problem of determining which densities are ground state
densities of an interacting electron system in some external potential is
important to the foundations of density functional theory. A coarse-grained
version of this ensemble V-representability problem is shown to be thoroughly
tractable. Averaging the density of an interacting electron system over the
cells of a regular partition of space produces a coarse-grained density. It is
proved that every strictly positive coarse-grained density is coarse-grained
ensemble V-representable: there is a unique potential, constant over each cell
of the partition, which has a ground state with the prescribed coarse-grained
density. For a system confined to a box, the (coarse-grained) Lieb [Intl. J.
Quantum Chem. 24, 243 (1983)] functional is also shown to be Gateaux
differentiable. All results extend to open systems.",0702291v1
2020-02-26,"Thermal and Pressure Ionization in Warm, Dense MgSiO$_3$ Studied with First-Principles Computer Simulations","Using path integral Monte Carlo and density functional molecular dynamics
(DFT-MD) simulations, we study the properties of MgSiO$_3$ enstatite in the
regime of warm dense matter. We generate a consistent equation of state (EOS)
that spans across a wide range of temperatures and densities (10$^4$--10$^7$ K
and 6.42--64.16 g cm$^{-3}$). We derive the shock Hugoniot curve, that is in
good agreement with the experiments. We identify the boundary between the
regimes of thermal ionization and pressure ionization by locating where the
internal energy at constant temperature attains a minimum as a function of
density or pressure. At low density, the internal energy decreases with
increasing density as the weight of free states changes. Thermal ionization
dominates. Conversely, at high density, in the regime of pressure ionization,
the internal energy increases with density. We determine the boundary between
the two regimes and show that the compression maximum along the shock Hugoniot
curve occurs because K shell electrons become thermally ionized rather than
pressure ionized.",2002.12163v2
2007-08-03,Treatments of the exchange energy in density-functional theory,"Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple
derivation of the density-functional correction of the Hartree-Fock equations,
the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated
view of quantum mechanical theories, in which the Kohn-Sham equations, the
Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation
formally stem from a common ground: density-functional theory, through its
Euler equation for the ground-state density. Along similar lines, the Kohn-Sham
formulation of the Hartree-Fock approach is also considered. Further, it is
pointed out that the exchange energy of density-functional theory built from
the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle
density functionals (N=1,2,...), forming a sequence of degree-two homogeneous
exchange-energy density functionals, the first element of which is minus the
classical Coulomb-repulsion energy functional.",0708.0576v2
2006-03-21,Influence of interface structure on electronic properties and Schottky barriers in Fe/GaAs magnetic junctions,"The electronic and magnetic properties of Fe/GaAs(001) magnetic junctions are
investigated using first-principles density-functional calculations. Abrupt and
intermixed interfaces are considered, and the dependence of charge transfer,
magnetization profiles, Schottky barrier heights, and spin polarization of
densities of states on interface structure is studied. With As-termination, an
abrupt interface with Fe is favored, while Ga-terminated GaAs favors the
formation of an intermixed layer with Fe. The Schottky barrier heights are
particularly sensitive to the abruptness of the interface. A significant
density of states in the semiconducting gap arises from metal interface states.
These spin-dependent interface states lead to a significant minority spin
polarization of the density of states at the Fermi level that persists well
into the semiconductor, providing a channel for the tunneling of minority spins
through the Schottky barrier. These interface-induced gap states and their
dependence on atomic structure at the interface are discussed in connection
with potential spin-injection applications.",0603564v1
2015-01-30,Constraining and applying a generic high-density equation of state,"We discuss the ""constant speed of sound"" (CSS) parametrization of the
equation of state of high-density matter and its application to the field
correlator method (FCM) model of quark matter. We show how observational
constraints on the maximum mass and typical radius of neutron stars are
expressed as constraints on the CSS parameters. We find that the observation of
a $2\,M_{\odot}$ star already severely constrains the CSS parameters, and is
particularly difficult to accommodate if the squared speed of sound in the
high-density phase is assumed to be around $1/3$ or less.
  We show that the FCM equation of state can be accurately represented by the
CSS parametrization, which assumes a sharp transition to a high-density phase
with density-independent speed of sound. We display the mapping between the FCM
and CSS parameters, and see that FCM only allows equations of state in a
restricted subspace of the CSS parameters.",1501.07902v3
1998-05-17,Density of states of a two-dimensional electron gas in a non-quantizing magnetic field,"We study local density of electron states of a two-dimentional conductor with
a smooth disorder potential in a non-quantizing magnetic field, which does not
cause the standart de Haas-van Alphen oscillations. It is found, that despite
the influence of such ``classical'' magnetic field on the average electron
density of states (DOS) is negligibly small, it does produce a significant
effect on the DOS correlations. The corresponding correlation function exhibits
oscillations with the characteristic period of cyclotron quantum
$\hbar\omega_c$.",9805199v1
1999-12-13,Effect of Time Reversal Symmetry Breaking on the Density of States in Small Superconducting Grains,"We show that in ultra-small superconducting grains any concentration of
magnetic impurities or infinitely small orbital effect of magnetic field leads
to destruction of the hard gap in the tunneling density of states. Instead,
though exponentially suppressed at low energies, the tunneling density of
states exhibits the ``soft gap'' behavior, vanishing linearly with excitation
energy, as the energy approaches zero.",9912216v1
2003-03-27,Electronic structure calculations for PrFe4P12 filled skutterudite using Extended Huckel tight-binding method,"To get insight into the electronic properties of PrFe4P12 skutterudite, band
electronic structure calculations, Total and Projected Density of States,
Crystal Orbital Overlap Population and Mulliken Population Analysis were
performed. The energy bands yield a semi metallic behavior with a direct gap
(at gamma) of 0.02 eV. Total and Projected Density of States provided
information of the contribution from each orbital of each atom to the total
Density of States. Moreover, the bonding strength between some atoms within the
unit cell was obtained. Mulliken Population analysis suggests ionic behavior
for this compound.",0303115v1
2006-05-03,On the degeneracy of atomic states within exact-exchange (spin-) density functional theory,"The problem of degenerate ground states of open-shell atoms is investigated
in spin-restricted and unrestricted density functional theory using the exact
exchange energy functional. For the spin-unrestricted case, spurious energy
splittings of the order of 2 to 3 kcal/mol are found for atoms of the second
and third period which is larger than the splittings obtained from recently
proposed approximate exchange functionals depending explicitly on the current
density. In remarkable contrast, for spin-restricted calculations the
degeneracy of different atomic ground states is recovered to within less than
0.6 kcal/mol.",0605032v1
2008-04-11,Bose-Einstein Quantum Statistics and the Ground State of Solid 4He,"The ground state of solid $^4$He is studied using the diffusion Monte Carlo
method and a new trial wave function able to describe the supersolid. The new
wave function is symmetric under the exchange of particles and reproduces the
experimental equation of state. Results for the one-body density matrix show
the existence of off-diagonal long-range order with a very small condensate
fraction $\sim 10^{-4}$. The superfluid density of the commensurate system is
below our resolution threshold, $\rho_s/\rho < 10^{-5}$. With a 1%
concentration of vacancies the superfluid density is manifestly larger,
$\rho_s/\rho=3.2(1) \cdot 10^{-3}$.",0804.1851v1
2008-12-19,Evidence for a hard equation of state in the cores of neutron stars,"The equation of state for matter with energy density above 2 x10^14 g/cm^3 is
parametrized by P = kN^Gamma, where N is the number density, Gamma is the
adiabatic index, and k a constant. Using this scheme to generate thousands of
models, together with data on neutron star masses, it is found, for a core
region with a constant adiabatic index, that the central density must satisfy
10^15 gm/cm^3 < rho_c < 10^16 gm/cm^3, with Gamma > 2.2. Further preliminary
results indicate, based on the observed neutrino flux from supernova 1987a,
that this number must be considerably higher, on the order of 3.5. These
results provide evidence for a hard equation of state in the cores of neutron
stars.",0812.3828v1
2009-02-16,"All electrical measurement of the density of states in (Ga,Mn)As","We report on electrical measurements of the effective density of states in
the ferromagnetic semiconductor material (Ga,Mn)As. By analyzing the
conductivity correction due to enhanced electron-electron interaction the
electrical diffusion constant was extracted for (Ga,Mn)As samples of different
dimensionality. Using the Einstein relation allows to deduce the effective
density of states of (Ga,Mn)As at the Fermi energy.",0902.2675v1
2009-06-22,Model for the boron-doping dependence of the critical temperature of superconducting boron-doped diamond,"We study the concentration dependence of the superconducting critical
temperature Tc in a boron-doped diamond. We evaluate the density of states at
Fermi level within the dynamical cluster approximation obtaining higher values
than from the coherent potential approximation. We discuss the Tc as a function
of density of states within the BCS, the McMillan, and the Belitz theory. The
simplified Belitz theory gives the best agreement with experimental data. Since
the density of states follows a simple power-law for accessible doping
concetrations, the present theory offers an analytical formula for Tc(x).",0906.3948v1
2009-08-21,"Comment on ""Density of States and Critical Behavior of the Coulomb Glass""","In a recent numerical investigation of the Coulomb glass, Surer et al. [Phys.
Rev. Lett. 102, 067205 (2009)] concluded that their simulation results are
consistent with the Efros Shklovskii prediction for the density of states in
the three-dimensional case. Here, we show that this statement has no relevance
concerning the problem of the asymptotic behavior in the Coulomb gap since it
is based on unjustified assumptions. Moreover, for the random-displacement
Coulomb glass model, we demonstrate that a part of the density of states data
by Surer et al. erroneously exhibit a broad gap. This is related to the
staggered occupation being instable contrary to their findings.",0908.3092v1
2010-02-09,"Pure, $Si$ and $sp^3$-doped Graphene nanoflakes: a numerical study of density of states","We built graphene nanoflakes doped or not with $C$ atoms in the $sp^3$
hybridization or with $Si$ atoms. These nanoflakes are isolated, i.e. are not
connected to any object (substrate or junction). We used a modified tight
binding method to compute the $\pi$ and $\sigma$ density of states. The
nanoflakes are semiconducting (due to the armchair geometry of their
boundaries) when their are pure but the become conducting when doped because
doping removes the degeneracy of the density of states levels. Moreover, we
showed that the $\pi$ Fermi level and the Fermi level of both $\pi$ and
$\sigma$ electrons are not superimposed for small isolated nanoflakes.",1002.1888v1
2011-06-29,Mapping the local density of optical states of a photonic crystal with single quantum dots,"We use single self-assembled InGaAs quantum dots as internal probes to map
the local density of optical states of photonic crystal membranes. The employed
technique separates contributions from non-radiative recombination and
spin-flip processes by properly accounting for the role of the exciton fine
structure. We observe inhibition factors as high as 55 and compare our results
to local density of optical states calculations available from the literature,
thereby establishing a quantitative understanding of photon emission in
photonic crystal membranes.",1106.5963v1
2014-11-03,The density of states from first principles,"We present a novel algorithm to compute the density of states, which is
proven to converge to the correct result. The algorithm is very general and can
be applied to a wide range of models, in the frameworks of Statistical
Mechanics and Lattice Gauge Theory. All the thermal or quantum expectation
values can then be obtained by a simple integration of the density of states.
As an application, a numerical study of 4d U(1) compact lattice gauge theory is
presented.",1411.0655v1
2017-01-24,Density of states of Dirac-Landau levels in a gapped graphene monolayer under strain gradient,"We study a gapped graphene monolayer in a combination of uniform magnetic
field and strain-induced uniform pseudomagnetic field. The presence of two
fields completely removes the valley degeneracy. The resulting density of
states shows a complicated behaviour that can be tuned by adjusting the
strength of the fields. We analyze how these features can be observed in the
sublattice, valley and full density of states. The analytical expression for
the valley DOS is derived.",1701.06769v2
2021-08-29,Spin-Symmetry Broken Ground-State of UO$_2$ in DFT+U Approach: The SMC Method,"It turns out that the ground states of some systems are symmetry-broken
states in which some property is not symmetrically distributed. In the case of
strongly correlated electron systems, that were studied by the DFT+U method,
researchers had shown that the total energy of the system is a multi-minima
function of input parameters and one has to single out the ground state out of
the couples of minimum-energy states. However, the methods already introduced
to determine these local minimum states were not able to predict all such
states which may include the ""true"" ground state. In this work, we introduce a
new simple and straight-forward method of SMC to find the GS as well as the
meta-stable states of 1k-order anti-ferromagnetic configuration for UO$_2$.
Using this method, it is shown that the ground state of UO$_2$ system is a
spin-symmetry broken state of the electron spin magnetizations of oxygen atoms.
Depending on the way we apply the SMC method, we obtain different numbers of
meta-stable states, but the same ground states. The energetic properties,
geometric properties, the electronic density distributions, and the electronic
polarization density distributions of the ground state and the meta-stable
states are shown to be different from each other. These properties also are
shown to be sensitive to the magnitude of the initial opposite magnetizations
of U1 and U2 atoms in the 1k-order anti-ferromagnetic configuration, but the
number of meta-stable states as well as the ground-state properties are
insensitive to this magnitude. Using the PBEsol-GGA approximation for the
exchange-correlation we obtain the ground-state properties in excellent
agreement with experiments.",2108.12758v2
2020-01-26,Density driven correlations in ensemble density functional theory: insights from simple excitations in atoms,"Ensemble density functional theory extends the usual Kohn-Sham machinery to
quantum state ensembles involving ground- and excited states. Recent work by
the authors [Phys. Rev. Lett. 119, 243001 (2017); 123, 016401 (2019)] has shown
that both the Hartree-exchange and correlation energies can attain unusual
features in ensembles. Density-driven(DD) correlations -- which account for the
fact that pure-state densities in Kohn-Sham ensembles do not necessarily
reproduce those of interacting pure states -- are one such feature. Here we
study atoms (specifically $S$--$P$ and $S$--$S$ transitions) and show that the
magnitude and behaviour of DD correlations can vary greatly with the variation
of the orbital angular momentum of the involved states. Such estimations are
obtained through an approximation for DD correlations built from relevant exact
conditions Kohn-Sham inversion, and plausible assumptions for weakly correlated
systems.",2001.09429v1
2020-11-15,Creation of a novel inverted charge density wave state,"Charge density wave (CDW) order is an emergent quantum phase that is
characterized by a periodic lattice distortion and charge density modulation,
often present near superconducting transitions. Here we uncover a novel
inverted CDW state by using a femtosecond laser to coherently over-drive the
unique star-of-David lattice distortion in 1T-TaSe$_2$. We track the signature
of this novel CDW state using time- and angle-resolved photoemission
spectroscopy and time-dependent density functional theory, and validate that it
is associated with a unique lattice and charge arrangement never before
realized. The dynamic electronic structure further reveals its novel
properties, that are characterized by an increased density of states near the
Fermi level, high metallicity, and altered electron-phonon couplings. Our
results demonstrate how ultrafast lasers can be used to create unique states in
materials, by manipulating charge-lattice orders and couplings.",2011.07623v2
1999-10-06,Color Superconductivity in Asymmetric Matter,"The influence of different chemical potential for different flavors on color
superconductivity is analyzed.
  It is found that there is a first order transition as the asymmetry grows.
This transition proceeds through the formation of bubbles of low density,
flavor asymmetric normal phase inside a high density, superconducting phase
with a gap {\it larger} than the one found in the symmetric case. For small
fixed asymmetries the system is normal at low densities and superconducting
only above some critical density. For larger asymmetries the two massless
quarks system stays in the mixed state for arbitrarily high densities.",9910247v1
2005-07-24,Density distributions of superheavy nuclei,"We employed the Skyrme-Hartree-Fock model to investigate the density
distributions and their dependence on nuclear shapes and isospins in the
superheavy mass region. Different Skyrme forces were used for the calculations
with a special comparison to the experimental data in $^{208}$Pb. The
ground-state deformations, nuclear radii, neutron skin thicknesses and
$\alpha$-decay energies were also calculated. Density distributions were
discussed with the calculations of single-particle wavefunctions and shell
fillings. Calculations show that deformations have considerable effects on the
density distributions, with a detailed discussion on the $^{292}$120 nucleus.
Earlier predictions of remarkably low central density are not supported when
deformation is allowed for.",0507052v1
2010-03-31,Displacement field and elastic constants in non-ideal crystals,"In this work a periodic crystal with point defects is described in the
framework of linear response theory for broken symmetry states using
correlation functions and Zwanzig-Mori equations. The main results are
microscopic expressions for the elastic constants and for the coarse-grained
density, point-defect density, and displacement field, which are valid in real
crystals, where vacancies and interstitials are present. The coarse-grained
density field differs from the small wave vector limit of the microscopic
density. In the long wavelength limit, we recover the phenomenological
description of elasticity theory including the defect density.",1003.6081v1
2013-07-16,Asymmetric Exclusion Process with Global Hopping,"We study a one-dimensional totally asymmetric simple exclusion process with
one special site from which particles fly to any empty site (not just to the
neighboring site). The system attains a non-trivial stationary state with
density profile varying over the spatial extent of the system. The density
profile undergoes a non-equilibrium phase transition when the average density
passes through the critical value 1-1/[4(1-ln 2)]=0.185277..., viz. in addition
to the discontinuity in the vicinity of the special site, a shock wave is
formed in the bulk of the system when the density exceeds the critical density.",1307.4367v2
2014-01-26,Self Interaction Corrected Density Functional Theory with Unitary Invariance: Applications to Molecules,"Standard spin-density functionals for the exchange-correlation energy of a
many-electron ground state make serious self-interaction errors which can be
corrected by the Perdew-Zunger self-interaction correction (SIC). We propose a
size-extensive construction of SIC orbitals which, unlike earlier
constructions, makes SIC computationally efficient, and a true spin-density
functional. The SIC orbitals are constructed from a unitary transformation that
is explicitly dependent on the non-interacting one-particle density matrix.
When this SIC is applied to the local spin-density approximation, improvements
are found for the atomization energies of molecules.",1401.6650v1
2004-07-14,On validity of the original Bell inequality for the Werner nonseparable state,"In quant-ph/0406139, we have introduced in a very general setting the new
class of quantum states, density source-operator states, satisfying any
classical CHSH-form inequality, and shown that any separable state belongs to
this class. In the present paper, we prove that the Werner nonseparable state
also belongs to the class of density source-operator states. Moreover, for any
dimension d>2, the Werner state is in such a subclass of this class where each
density source-operator state satisfies also the perfect correlation form of
the original Bell inequality regardless of whether or not the Bell perfect
correlation restriction is fulfilled. The latter earlier unknown property of
the Werner state can be verified experimentally.",0407097v1
2003-09-12,Quantal Density Functional Theory of the Hydrogen Molecule,"In this paper we perform a Quantal Density Functional Theory (Q-DFT) study of
the Hydrogen molecule in its ground state.",0309317v2
2000-01-09,On the Non-perturbative Properties of the Yang-Mills Vacuum and the Vacuum Energy Density,"The non-perturbative part of the vacuum energy density for static
configuration in pure SU(2) Y-M theory is described. The vacuum state is
constructed.",0001038v1
1993-11-03,Spectral asymmetries in nucleon sum rules at finite density,"Apparent inconsistencies between different formulations of nucleon sum rules
at finite density are resolved through a proper accounting of asymmetries in
the spectral functions between positive- and negative-energy states.",9311002v1
2010-07-08,Time Evolution of Horizons,"A density matrix is defined using coherent states for space-times with
apparent horizons. Evolving the density matrix in time gives the origin of
Hawking radiation.",1007.1437v1
2014-09-10,Some surprising results of the Kohn-Sham Density Functional,"For some insulators we present a procedure to determine an electronic density
leading to a lower energy than that of the Kohn-Sham ground state.",1409.3075v1
2021-05-20,Density perturbations in axion-like particles: classical vs quantum field treatment,"Axions and axion-like particles are bosonic quantum fields. They are often
assumed to follow classical field equations due to their high degeneracy in the
phase space. In this work, we explore the disparity between classical and
quantum field treatments in the context of density and velocity fields of
axions. Once the initial density and velocity field are specified, the
evolution of the axion fluid is unique in the classical field treatment.
However, in the quantum field treatment, there are many quantum states
consistent with the given initial density and velocity field. We show that
evolutions of the density perturbations for these quantum states are not
necessarily identical and, in general, differ from the unique classical
evolution. To illustrate the underlying physics, we consider a system of large
number of bosons in a one-dimensional box, moving under the gravitational
potential of a heavy static point-mass. We ignore the self-interactions between
the bosons here. Starting with homogeneous number density and zero velocity
field, we determine the density perturbations in the linear regime in both
quantum and classical field theories. We find that classical and quantum
evolutions are identical in the linear regime if only one single-particle state
is occupied by all the bosons and the self-interaction is absent. If more than
one single-particle states are occupied, the density perturbations in quantum
evolutions differ from the classical prediction after a certain time which
depends upon the parameters of the system.",2105.09749v1
2018-03-01,Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer,"Gross-Oliveira-Kohn density-functional theory (GOK-DFT) is an extension of
DFT to excited states where the basic variable is the ensemble density, i.e.
the weighted sum of ground- and excited-state densities. The ensemble energy
(i.e. the weighted sum of ground- and excited-state energies) can be obtained
variationally as a functional of the ensemble density. Like in DFT, the key
ingredient to model in GOK-DFT is the exchange-correlation functional.
Developing density-functional approximations (DFAs) for ensembles is a
complicated task as both density and weight dependencies should in principle be
reproduced. In a recent paper [Phys. Rev. B 95, 035120 (2017)], the authors
applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to
investigate (numerically) the importance of weight dependence in the
calculation of excitation energies. In this work, we derive analytical DFAs for
various density and correlation regimes by means of a Legendre-Fenchel
transform formalism. Both functional and density driven errors are evaluated
for each DFA. Interestingly, when the ensemble exact-exchange-only functional
is used, these errors can be large, in particular if the dimer is symmetric,
but they cancel each other so that the excitation energies obtained by linear
interpolation are always accurate, even in the strongly correlated regime.",1803.00291v2
2022-05-09,Isomorphs in sheared binary Lennard-Jones glass: Transient response,"We have studied shear deformation of binary Lennard-Jones glasses to
investigate the extent to which the transient part of the stress strain curves
is invariant when the thermodynamic state point is varied along an isomorph.
Shear deformations were carried out on glass samples of varying stability,
determined by cooling rate, and at varying strain rates, at a state point deep
in the glass. Density changes up to and exceeding a factor of two were made. We
investigated several different methods for generating isomorphs but none of the
previously developed methods could generate sufficiently precise isomorphs
given the large density changes and non-equilibrium situation. Instead, the
temperatures for these higher densities were chosen to give state points
isomorphic to the starting state point by requiring the steady state flow
stress for isomorphic state points to be invariant in reduced units. In
contrast to the steady state flow stress, we find that the peak stress on the
stress strain curve is not invariant. The peak stress decreases by a few
percent for each ten percent increase in density, although the differences
decrease with increasing density. Analysis of strain profiles and non-affine
motion during the transient phase suggests that the root of the changes in peak
stress is a varying tendency to form shear bands, with the largest tendency
occurring at the lowest densities. We argue that this reflects the effective
steepness of the potential; a higher effective steepness gives a greater
tendency to form shear bands.",2205.04340v2
2008-03-20,Mode-locking and mode-competition in a non-equilibrium solid-state condensate,"A trapped polariton condensate with continuous pumping and decay is analyzed
using a generalized Gross-Pitaevskii model. Whereas an equilibrium condensate
is characterized by a macroscopic occupation of a ground state, here the
steady-states take more general forms. Some are characterized by a large
population in an excited state, and others by large populations in several
states. In the latter case, the highly-populated states synchronize to a common
frequency above a critical density. Estimates for the critical density of this
synchronization transition are consistent with experiments.",0803.2997v1
2002-05-02,Relativistic Hartree-Bogoliubov model with density-dependent meson-nucleon couplings,"The relativistic Hartree-Bogoliubov (RHB) model is extended to include
density dependent meson-nucleon couplings. The effective Lagrangian is
characterized by a phenomenological density dependence for the $\sigma$,
$\omega$ and $\rho$ meson-nucleon vertex functions, adjusted to properties of
nuclear matter and finite nuclei. Pairing correlations are described by the
pairing part of the finite range Gogny interaction. The new density-dependent
effective interaction DD-ME1 is tested in the analysis of the equations of
state for symmetric and asymmetric nuclear matter, and of ground-state
properties of the Sn and Pb isotopic chains. Results of self-consistent RHB
calculations are compared with experimental data, and with results previously
obtained in the RHB model with non-linear self-interactions, as well as in the
density dependent relativistic hadron field (DDRH) model. Parity-violating
elastic electron scattering on Pb and Sn nuclei is calculated using a
relativistic optical model with inclusion of Coulomb distortion effects, and
the resulting asymmetry parameters are related to the neutron ground-state
density distributions.",0205009v1
2010-10-05,Charge density wave in hidden order state of URu$_2$Si$_2$,"We argue that the hidden order state in URu$_2$Si$_2$ will induce a charge
density wave. The modulation vector of the charge density wave will be twice
that of the hidden order state, $Q_{CDW} = 2Q_{HO}$. To illustrate how the
charge density wave arises we use a Ginzburg-Landau theory that contains a
coupling of the charge density wave amplitude to the square of the HO order
parameter $\Delta_{HO}$. This simple analysis allows us to predict the
intensity and temperature dependence of the charge density wave order parameter
in terms of the susceptibilities and coupling constants used in the
Ginzburg-Landau analysis.",1010.0767v1
2016-03-22,"Consequences of minimizing pair correlations in fluids for dynamics, thermodynamics, and structure","Liquid-state theory, computer simulation, and numerical optimization are used
to investigate the extent to which positional correlations of a hard-sphere
fluid--as characterized by the radial distribution function and the
two-particle excess entropy--can be suppressed via the introduction of
auxiliary pair interactions. The corresponding effects of such interactions on
total excess entropy, density fluctuations, and single-particle dynamics are
explored. Iso-g processes, whereby hard-sphere-fluid pair structure at a given
density is preserved at higher densities via the introduction of a
density-dependent, soft repulsive contribution to the pair potential, are
considered. Such processes eventually terminate at a singular density,
resulting in a state that--while incompressible and hyperuniform--remains
unjammed and exhibits fluid-like dynamic properties. The extent to which static
pair correlations can be suppressed to maximize pair disorder in a fluid with
hard cores, determined via direct functional maximization of two-body excess
entropy, is also considered. Systems approaching a state of maximized two-body
entropy display a progressively growing bandwidth of suppressed density
fluctuations, pointing to a relation between ""stealthiness"" and maximal pair
disorder in materials.",1603.06933v1
2013-08-30,The density in the density of states method,"It has been suggested that for QCD at finite baryon density the distribution
of the phase angle, i.e. the angle defined as the imaginary part of the
logarithm of the fermion determinant, has a simple Gaussian form. This
distribution provides the density in the density of states approach to the sign
problem. We calculate this phase angle distribution using i) the hadron
resonance gas model; and ii) a combined strong coupling and hopping parameter
expansion in lattice gauge theory. While the former model leads only to a
Gaussian distribution, in the latter expansion we discover terms which cause
the phase angle distribution to deviate, by relative amounts proportional to
powers of the inverse lattice volume, from a simple Gaussian form. We show that
despite the tiny inverse-volume deviation of the phase angle distribution from
a simple Gaussian form, such non-Gaussian terms can have a substantial impact
on observables computed in the density of states/reweighting approach to the
sign problem.",1308.6712v1
2012-01-16,Ground state energy in the external field and the problem of density functional approximations,"Based on the Schrodinger equation, exact expressions for the non-relativistic
particle energy in the local external field and the external field potential
are derived as inhomogeneous density functionals. On this basis, it is shown
that, when considering more than two noninteracting electrons, the energy of
such a system cannot be an inhomogeneous density functional. The result is
extended for the system of interacting electrons. This means that the
Hohenberg-Kohn lemma which assert that in the ground state to each
inhomogeneous density corresponds only one potential of the external field
cannot be a justification of the existence of the universal density functional
in the general case. At the same time, statements of the density functional
theory remain valid when considering any number of noninteracting ground-state
bosons due to the Bose condensation effect.",1201.3222v1
2021-02-10,Doublon-like excitations and their phononic coupling in a Mott charge-density-wave system,"Electron-phonon-driven charge density waves can in some circumstances allow
electronic correlations to become predominant, driving a system into a Mott
insulating state. New insights into both the Mott state and preceding charge
density wave may result from observations of the coupled dynamics of their
underlying degrees of freedom. Here, tunneling injection of single electrons
into the upper Hubbard band of the Mott charge-density-wave material 1T-TaS2
reveals extraordinarily narrow electronic excitations which couple to amplitude
mode phonons associated with the charge density wave's periodic lattice
distortion. This gives a vivid microscopic view of the interplay between
excitations of the Mott state and the lattice dynamics of its charge density
wave precursor.",2102.05278v1
1998-02-13,Formation of a Heavy-Fermion State in the 2D Periodic Anderson Model,"We study the formation of a heavy-fermion state in the 2D periodic Anerson
model. For U=2, the density of states, imaginary part of the self-energy and
effective magnetic moment all indicate the Kondo screening of local f
electrons, leading to a coherent heavy-fermion state. For U=3 and 4, the
dominance of RKKY interaction over Kondo screening at low temperatures
indicates a magnetic instability at zero temperature. A partial screening of
magnetic moments, however, still gives rise to a relatively sharp peak at the
Fermi energy in the density of states.",9802142v1
2011-06-30,Equation of state at finite baryon density based on lattice QCD,"We employ the lattice QCD data on Taylor expansion coefficients to extend our
previous parametrization of the equation of state to finite baryon density.
When we take into account lattice spacing and quark mass dependence of the
hadron masses, the Taylor coefficients at low temperature are equal to those of
hadron resonance gas. Thus the equation of state is smoothly connected to the
hadron resonance gas equation of state at low temperatures. We also show how
the elliptic flow is affected by this equation of state at the maximum SPS
energy.",1106.6227v1
2022-03-07,High Fidelity Quantum State Transfer by Pontryagin Maximum Principle,"High fidelity quantum state transfer is an essential part of quantum
information processing. In this regard, we address the problem of maximizing
the fidelity in a quantum state transformation process satisfying the
Liouville-von Neumann equation. By introducing fidelity as the performance
index, we aim at maximizing the similarity of the final state density operator
with the one of the desired target state. Optimality conditions in the form of
a Maximum Principle of Pontryagin are given for the matrix-valued dynamic
control systems propagating the probability density function. These provide a
complete set of relations enabling the computation of the optimal control
strategy.",2203.04361v2
2015-09-21,Hyperon puzzle and the RMF model with scaled hadron masses and coupling constants,"The equation of state of cold baryonic matter is studied within a
relativistic mean-field model with hadron masses and coupling constants
depending on a scalar field. We demonstrate that if the effective nucleon mass
stops to decrease with a density increase at densities $n>n_*>n_0$, where $n_0$
is the nuclear saturation density, the equation of state stiffens for these
densities and the limiting neutron star mass increases. The stabilization of
the nucleon mass can be realised if in the equation of motion for the scalar
mean-field there appear a term sharply varying in a narrow vicinity of the
field value corresponding to the density $n_*$. We show several possible
realizations of this mechanism getting sufficiently stiff equations of state.
The appearance of hyperons in dense neutron star interiors is accounted for.
The obtained equations of state remain sufficiently stiff if the reduction of
the $\phi$ meson mass is incorporated. Thereby, the hyperon puzzle can be
resolved.",1509.06312v1
2022-08-25,The high-density equation of state in heavy-ion collisions: Constraints from proton flow,"A set of different equations of state is implemented in the molecular
dynamics part of a non-equilibrium transport simulation (UrQMD) of heavy-ion
collisions. It is shown how different flow observables are affected by the
density dependence of the equation of state. In particular, the effects of a
phase transition at high density are explored, including an expected reduction
in mean $m_T$. We also show that an increase in $v_2$ is characteristic for a
strong softening of the equation of state. The phase transitions with a low
coexistence density, $n_{\mathrm{CE}}<4 n_0$, show a distinct minimum in the
slope of the directed flow as a function of the beam energy, which would be a
clear experimental signal. By comparing our results with experimental data, we
can exclude any strong phase transition at densities below $4n_0$.",2208.12091v2
2004-11-18,Density of states in spin-valve structure with superconducting electrodes,"Energy variation of the density of states (DOS) has been calculated in the
superconductor/ferromagnet/ferromagnet/superconductor structure (SFFS) in the
frame of Gorkov equations taking into account the s-d electron scattering in
the ferromagnetic layers. DOS behavior is presented for the antiparallel and
parallel magnetic moments alignment of two adjacent F layers. The cases of
small and large values of exchange ferromagnetic field are discussed.",0411470v1
2010-11-18,Uniform approximation of the integrated density of states for long-range percolation Hamiltonians,"In this paper we study the spectrum of long-range percolation graphs. The
underlying geometry is given in terms of a finitely generated amenable group.
We prove that the integrated density of states (IDS) or spectral distribution
function can be approximated uniformly in the energy variable. Using this, we
are able to characterise the set of discontinuities of the IDS.",1011.4192v1
2019-03-06,Photon-number tomography of multimode states and positivity of the density matrix,"For one-mode and multimode light, the photon-number tomograms of Gaussian
quantum states are explicitly calculated in terms of multivariable Hermite
polynomials. Positivity of the tomograms is shown to be necessary condition for
positivity of the density matrix.",1903.02310v1
2016-02-24,Black holes as collapsed polymers,"We propose that a large Schwarzschild black hole (BH) is a bound state of
highly excited, long, closed strings at the Hagedorn temperature. The size of
the bound state is smaller than the string random-walk scale and determined
dynamically by the string attractive interactions. It is further proposed that
the effective free-energy density of the bound state should be expressed as a
function of its entropy density. For a macroscopic BH, the free-energy density
contains only linear and quadratic terms, in analogy with that of a collapsed
polymer when expressed as a function of the polymer concentration. Using the
effective free energy, we derive scaling relations for the entropy, energy and
size of the bound state and show that these agree with the scaling relations of
the BH; in particular, with the area law for the BH entropy. The area law
originates from the inverse scaling of the effective temperature with the
bound-state radius. We also find that the energy density of the bound state is
equal to its pressure.",1602.07706v1
2010-06-02,Equation of State of nuclear matter in a Virial expansion of nucleons and nuclei,"We study the equation of state (EOS) of nuclear matter at subnuclear density
in a Virial expansion for a nonideal gas. The gas consists of neutrons,
protons, alpha particles, and 8980 species of nuclei with $A \ge 12$ and masses
from the finite-range droplet model (FRDM). At very low density, the Virial
expansion reduces to nuclear statistical equilibrium. At higher density, the
Virial results match smoothly to the relativistic mean field results discussed
in our previous paper. We tabulate the resulting EOS at over 73,000 grid points
in the temperature range $T$ = 0.158 to 15.8 MeV, the density range $n_B$ =
10$^{-8}$ to 0.1 fm$^{-3}$, and the proton fraction range $Y_P$ = 0.05 to 0.56.
In the future we plan to match these low density results to our earlier high
density mean field results, and generate a full EOS table for use in supernova
and neutron star merger simulations. This Virial EOS is exact in the low
density limit.",1006.0489v2
2014-01-13,The Progressive Proposal Particle Filter: Better Approximations to the Optimal Importance Density,"The crucial step in designing a particle filter for a particular application
is the choice of importance density. The optimal scheme is to use the
conditional posterior density of the state, but this cannot be sampled or
calculated analytically in most case. In practice, approximations of this
density are used, particularly Gaussian densities based on linearisation or the
unscented transform. For many highly nonlinear or non-Gaussian models, these
approximations can be poor, leading to degeneracy of the particle approximation
or even the filter ""losing track"" completely. In this paper, we develop a new
mechanism for approximating the optimal importance density, which we call the
progressive proposal method. This works by introducing the observation
progressively and performing a series of state updates, each using a local
Gaussian approximation to the optimal importance density. A number of
refinements and extensions to the basic algorithm are also introduced.
Simulations are used to demonstrate an improvement in performance over simpler
particle filters on a number of applications.",1401.2791v2
2017-08-08,Spectral density of mixtures of random density matrices for qubits,"We derive the spectral density of the equiprobable mixture of two random
density matrices of a two-level quantum system. We also work out the spectral
density of mixture under the so-called quantum addition rule. We use the
spectral densities to calculate the average entropy of mixtures of random
density matrices, and show that the average entropy of the
arithmetic-mean-state of $n$ qubit density matrices randomly chosen from the
Hilbert-Schmidt ensemble is never decreasing with the number $n$. We also get
the exact value of the average squared fidelity. Some conjectures and open
problems related to von Neumann entropy are also proposed.",1708.02487v2
2001-06-04,Angular quantization and the density matrix renormalization group,"Path integral techniques for the density matrix of a one-dimensional
statistical system near a boundary previously employed in black-hole physics
are applied to providing a new interpretation of the density matrix
renormalization group: its efficacy is due to the concentration of quantum
states near the boundary.",0106049v1
2012-10-25,Variational Formulation of Time-Dependent Density Functional Theory,"We present a variational formulation of Time-Dependent Density Functional
Theory similar to the constrained-search variational formulation of
ground-state density-function theory. The formulation is applied to justify the
time-dependent Kohn-Sham method. Other promising applications to advance TDDFT
are suggested.",1210.6938v1
2023-09-29,Kinematically constrained vortex dynamics in charge density waves,"We build a minimal model of dissipative vortex dynamics in two spatial
dimensions, subject to a kinematic constraint: dipole conservation. The
additional conservation law implies anomalously slow decay rates for vortices.
We argue that this model of vortex dynamics is relevant for a broad range of
time scales during a quench into a uniaxial charge density wave state. Our
predictions are consistent with recent experiments on uniaxial charge density
wave formation in $\mathrm{LaTe}_3$.",2310.00051v1
2023-09-07,A Note on the Estimation of Von Neumann and Relative Entropy via Quantum State Observers,"An essential quantity in quantum information theory is the von Neumann
entropy which depends entirely on the quantum density operator. Once known, the
density operator reveals the statistics of observables in a quantum process,
and the corresponding von Neumann Entropy yields the full information content.
However, the state, or density operator, of a given system may be unknown.
Quantum state observers have been proposed to infer the unknown state of a
quantum system. In this note, we show (i) that the von Neumann entropy of the
state estimate produced by our quantum state observer is exponentially
convergent to that of the system's true state, and (ii) the relative entropy
between the system and observer's state converges exponentially to zero as long
as the system starts in a full-rank state.",2309.03653v1
1994-11-17,Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics,"We use the Thomas-Fermi method to examine the thermodynamics of particles
obeying Haldane exclusion statistics. Specifically, we study
Calogero-Sutherland particles placed in a given external potential in one
dimension. For the case of a simple harmonic potential (constant density of
states), we obtain the exact one-particle spatial density and a {\it closed}
form for the equation of state at finite temperature, which are both new
results. We then solve the problem of particles in a $x^{2/3} ~$ potential
(linear density of states) and show that Bose-Einstein condensation does not
occur for any statistics other than bosons.",9411073v1
1995-07-17,Charge Density Wave Behaviour of the Integer Quantum Hall Effect Edge States,"We analyze the effect that the Coulomb interaction has on the edge
excitations of an electron gas confined in a bar of thickness $W$, and in
presence of a magnetic field corresponding to filling factor 1 Quantum Hall
effect. We find that the long-range interaction between the edges leads the
system to a ground state with a quasi-long range order, similar to a Charge
Density Wave. The spectral density of states vanishes at zero frequency, and
increases with frequency faster than any power law, being the conductance of a
infinite long system zero.",9507063v1
1996-08-29,Frequency dependent admittance of a two-dimensional quantum wire,"The frequency dependent conductance of a two-dimensional quantum wire is
computed using a current conserving formalism. The correction to the
dc-conductance due to a time-dependent potential is related to the local
partial density of states which we compute numerically. The current
conservation is explicitly confirmed by computing the global density of states
and comparing it with a quantity which is related to the electron dwell time.
Our calculation clearly reveals the physical meaning of the various partial
density of states.",9608158v1
1997-03-15,A local approach for global partial density of states,"To apply the scattering approach for the problem of AC transport through
coherent quantum conductors, various partial density of states must be
evaluated. If the global partial density of states (GPDOS) is calculated
externally using the energy derivatives of the scattering matrix, the results
are not precise unless the conductor has a large scattering volume. We propose
a local formula for GPDOS which is suitable for any finite scattering volume.
We apply this formula to compute the emittance of a two-dimensional quantum
wire under the multi-mode and finite temperature condition.",9703156v1
1998-05-04,Density of States Approach to Electric Field Fluctuations in Composite Media,"Spatial fluctuations of the local electric field induced by a constant
applied electric field in composite media are studied analytically and
numerically. It is found that the density of states for the fields exhibit
sharp peaks and abrupt changes in the slope at certain critical points which
are analogous to van Hove singularities in the density of states for phonons
and electrons in solids. As in solids, these singularities are generally
related to saddle and inflection points in the field spectra and are of
considerable value in the characterization of the field fluctuations. The
critical points are very prominent in dispersions with a regular,
``crystal-like'', structure. However, they broaden and eventually disappear as
the disorder increases.",9805030v1
1998-05-07,Instanton calculation of the density of states of disordered Peierls chains,"We use the optimal fluctuation method to find the density of electron states
inside the pseudogap in disordered Peierls chains. The electrons are described
by the one-dimensional Dirac Hamiltonian with randomly varying mass (the
Fluctuating Gap Model). We establish a relation between the disorder average in
this model and the quantum-mechanical average for a certain double-well
problem. We show that the optimal disorder fluctuation, which has the form of a
soliton-antisoliton pair, corresponds to the instanton trajectory in the
double-well problem. We use the instanton method developed for the double-well
problem to find the contribution to the density of states from disorder
realizations close to the optimal fluctuation.",9805085v1
2000-02-15,Density of States of a d-wave Superconductor in the Presence of Strong Impurity Scatterers: a Non Perturbative Result,"We present a method to compute the density of states induced by N non
magnetic impurities in a d-wave superconductor, in the unitary limit of very
strong scatering centers. For frequencies very small as compared to the
superconducting gap ($\omega \ll \Delta_0$) the additional density of states
has the leading divergence ${\displaystyle \delta \rho (\omega) \simeq n_i / [
| 2 \omega | (\ln^2 |\omega/\Delta_0| + (\pi/2)^2)]}$. This result is non
perturbative.",0002227v2
2000-11-08,Fokker-Planck equations and density of states in disordered quantum wires,"We propose a general scheme to construct scaling equations for the density of
states in disordered quantum wires for all ten pure Cartan symmetry classes.
The anomalous behavior of the density of states near the Fermi level for the
three chiral and four Bogoliubov-de Gennes universality classes is analysed in
detail by means of a mapping to a scaling equation for the reflection from a
quantum wire in the presence of an imaginary potential.",0011146v2
2002-05-07,Charge Density Bounds in Superconducting States of Strongly Correlated Systems,"Charge density bounds of knotted and linked vortex states in two-component
Ginzburg-Landau model are considered. When the mutual linking number of vector
order parameter vortex lines is less than the Hopf invariant, these states have
the lower-lying energies. It is shown that a set of local minima of free energy
contains new classes of universality which exist in a hole density range
limited at both finite ends.",0205133v2
2007-12-17,Ground state energy of the low density Hubbard model,"We derive a lower bound on the ground state energy of the Hubbard model for
given value of the total spin. In combination with the upper bound derived
previously by Giuliani, our result proves that in the low density limit, the
leading order correction compared to the ground state energy of a
non-interacting lattice Fermi gas is given by $8\pi a \rho_u \rho_d$, where
$\rho_{u(d)}$ denotes the density of the spin-up (down) particles, and $a$ is
the scattering length of the contact interaction potential. This result extends
previous work on the corresponding continuum model to the lattice case.",0712.2810v1
2009-01-15,"H""older index at a given point for density states of super-alpha-stable motion of index 1+beta","A H""older regularity index at given points for density states of
(alpha,1,beta)-superprocesses with alpha>1+beta is determined. It is shown that
this index is strictly greater than the optimal index of local H""older
continuity for those density states.",0901.2315v3
2009-01-19,Field angle dependence of the zero-energy density of states in unconventional superconductors: analysis of the borocarbide superconductor YNi2B2C,"We investigate the field-angle-dependent zero-energy density of states for
YNi2B2C with using realistic Fermi surfaces obtained by band calculations. Both
the 17th and 18th bands are taken into account. For calculating the oscillating
density of states, we adopt the Kramer-Pesch approximation, which is found to
improve accuracy in the oscillation amplitude. We show that superconducting gap
structure determined by analyzing STM experiments is consistent with thermal
transport and heat capacity measurements.",0901.2758v1
2013-04-05,Fermi level density of states modulation without charge transfer in nickelate superlattices,"By using first-principles density functional theory calculations for
(LaNiO3)m/(SrTiO3)n superlattices, we report a systematic way of electronic
response to the interface geometry. It is found that Fermi level density of
states of metallic nickelate layers is significantly reduced without charge
transfer in the vicinity of interface to the insulating SrTiO3. This type of
electronic state redistribution is clearly distinctive from other interface
phenomena such as charge and orbital reconstruction. Our result sheds new light
towards understanding the nickelates and other transitionmetal oxide
heterostructures.",1304.1615v2
2014-04-30,Properties of Hartree-Fock solutions of the three-dimensional electron gas,"In a previous letter, L. Baguet et al., (Phys. Rev. Lett. {\bf 111}, 166402
(2013)), we presented the ground state phase diagram of the homogeneous
electron gas in three dimensions within the Hartree-Fock approximation yielding
incommensurate crystal states at high density. Here, we analyze the properties
of these solutions. In particular, at high density we find universal behavior
of the incommensurate crystal strongly supporting the existence of a spin
density wave ground state.",1404.7652v3
2014-10-20,Disorder-induced gap in the normal density of states of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br,"The density of states of the organic superconductor
$\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, measured by scanning tunneling
spectroscopy on \textit{in-situ} cleaved surfaces, reveals a logarithmic
suppression near the Fermi edge persisting above the critical temperature
$T_\mathrm{c}$. A soft Hubbard gap as predicted by the Anderson-Hubbard model
for systems with disorder exactly describes the experimentally observed
suppression. The electronic disorder also explains the diminished coherence
peaks of the quasiparticle density of states below $T_\mathrm{c}$.",1410.5245v1
2015-02-20,Renormalized Multicanonical Sampling,"For a homogeneous system divisible into identical, weakly interacting
subsystems, the muticanonical procedure can be accelerated if it is first
applied to determine of the density of states for a single subsystem. This
result is then employed to approximate the state density of a subsystem with
twice the size that forms the starting point of a new multicanonical iteration.
Since this compound subsystem interacts less on average with its environment,
iterating this sequence of steps rapidly generates the state density of the
full system.",1502.05846v1
2015-08-19,Thermodynamics of an attractive 2D Fermi gas,"Thermodynamic properties of matter are conveniently expressed as functional
relations between variables known as equations of state. Here we experimentally
determine the compressibility, density and pressure equations of state for an
attractive 2D Fermi gas in the normal phase as a function of temperature and
interaction strength. In 2D, interacting gases exhibit qualitatively different
features to those found in 3D. This is evident in the normalized density
equation of state, which peaks at intermediate densities corresponding to the
crossover from classical to quantum behaviour.",1508.04502v3
2016-06-07,Semiclassical spectral function and density of states in speckle potentials,"We present a novel analytical method for calculating the spectral function
and the density of states in speckle potentials, valid in the semiclassical
regime. Our approach relies on stationary phase approximations, allowing us to
describe the singular quantum corrections at low energies. We apply it to the
calculation of the spectral function and the density of states in one and
two-dimensional speckle potentials. By connecting our results with those of
previous work valid in the high energy sector, we end up with a consistent
description of the whole energy spectrum, in good agreement with numerical
simulations.",1606.02156v2
2016-12-15,Is it possible to obtain cosmic accelerated expansion through energy transfer between different energy densities?,"The equation of state of an energy density may be significantly modified by
coupling it to another energy density. In the light of this observation we
check the possibility of producing cosmic accelerated expansion in this way. In
particular we consider the case where matter is converted to radiation (or vice
versa by particle physics processes). We find that cosmic accelerated expansion
can be obtained in this way only if an intermediate state with negative
equation of state forms during the conversion.",1612.04864v1
2017-09-29,Use of a sigmoid function to describe second peak in magnetization loops,"Order-disorder transitions of a vortex lattice transfer type-II
superconductors from a low critical current state to a high one. The similar
transition between different current states can be caused by electromagnetic
granularity. A sigmoid curve is proposed to describe the corresponding peak in
a field dependence of the macroscopic critical density. Using the extended
critical state model, analytic expressions are obtained for the field
dependencies of the local critical current density, the depth of equilibrium
surface region, and the macroscopic critical current density. The expressions
are well fit to published data.",1709.10291v1
2023-04-05,"Winding number, density of states and acceleration","Winding number and density of states are two fundamental physical quantities
for non-self-adjoint quasi-periodic Schr\""odinger operators, which reflect the
asymptotic distribution of zeros of the characteristic determinants of the
truncated operators under Dirichlet boundary condition, with respect to
complexified phase and the energy respectively. We will prove that the winding
number is in fact Avila's acceleration and it is also closely related to the
density of states by a generalized Thouless formula for non-self-adjoint
Schr\""odinger operators and Avila's global theory.",2304.02486v1
2023-04-26,A General Dixmier Trace Formula for the Density of States on Open Manifolds,"We give an abstract formulation of the Dixmier trace formula for the density
of states. This recovers prior versions and allows us to provide a Dixmier
trace formula for the density of states of second order elliptic differential
operators on manifolds of bounded geometry satisfying a certain geometric
condition. This formula gives a new perspective on Roe's index on open
manifolds.",2304.13272v2
2020-07-30,Discovery of a Cooper-Pair Density Wave State in a Transition-Metal Dichalcogenide,"Pair density wave (PDW) states are defined by a spatially modulating
superconductive order-parameter. To search for such states in transition metal
dichalcogenides (TMD) we use high-speed atomic-resolution scanned
Josephson-tunneling microscopy (SJTM). We detect a PDW state whose
electron-pair density and energy-gap modulate spatially at the wavevectors of
the preexisting charge density wave (CDW) state. The PDW couples linearly to
both the s-wave superconductor and to the CDW, and exhibits commensurate
domains with discommensuration phase-slips at the boundaries, conforming to
those of the lattice-locked commensurate CDW. Nevertheless, we find a global
$\delta\Phi \sim \pm2\pi/3$ phase difference between the PDW and CDW states,
possibly owing to the Cooper-pair wavefunction orbital content. Our findings
presage pervasive PDW physics in the many other TMDs that sustain both CDW and
superconducting states.",2007.15228v2
2014-05-05,On the Reversal of SFR-Density Relation at z=1: Insights from Simulations,"Recent large surveys have found a reversal of the star formation rate
(SFR)-density relation at z=1 from that at z=0 (e.g. Elbaz et al.; Cooper et
al.), while the sign of the slope of the color-density relation remains
unchanged (e.g. Cucciati et al.; Quadri et al.). We use state-of-the-art
adaptive mesh refinement cosmological hydrodynamic simulations of a 21x24x20
(Mpc/h)$^3$ region centered on a cluster to examine the SFR-density and
color-density relations of galaxies at z=0 and z=1. The local environmental
density is defined by the dark matter mass in spheres of radius 1 Mpc/h, and we
probe two decades of environmental densities. Our simulations produce a large
increase of SFR with density at z=1, as in the observations of Elbaz et al. We
also find a significant evolution to z=0, where the SFR-density relation is
much flatter. The color-density relation in our simulations is consistent from
z=1 to z=0, in agreement with observations. We find that the increase in the
median SFR with local density at z=1 is due to a growing population of
star-forming galaxies in higher-density environments. At z=0 and z=1 both the
SFR and cold gas mass are tightly correlated with the galaxy halo mass, and
therefore the correlation between median halo mass and local density is an
important cause of the SFR-density relation at both redshifts. We also show
that the local density on 1 Mpc/h scales affects galaxy SFRs as much as halo
mass at z=0. Finally, we find indications that the role of the 1 Mpc/h scale
environment reverses from z=0 to z=1: at z=0 high-density environments depress
galaxy SFRs, while at z=1 high-density environments tend to increase SFRs.",1405.1049v1
2010-02-16,Honeycomb optical lattices with harmonic confinement,"We consider the fate of the Dirac points in the spectrum of a honeycomb
optical lattice in the presence of a harmonic confining potential. By
numerically solving the tight binding model we calculate the density of states,
and find that the energy dependence can be understood from analytical
arguments. In addition, we show that the density of states of the harmonically
trapped lattice system can be understood by application of a local density
approximation based on the density of states of the homogeneous lattice. The
Dirac points are found to survive locally in the trap as evidenced by the local
density of states. They furthermore give rise to a distinct spatial profile of
a noninteracting Fermi gas.",1002.3044v2
2011-01-19,Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states,"We consider the problem of a single level quantum dot coupled to the edge of
a one-dimensional Luttinger liquid wire by both a hopping term and
electron-electron interactions. Using bosonization and Coulomb gas mapping of
the Anderson-Yuval type we show that thermodynamic properties of the level, in
particular, its occupation, depend on the various interactions in the system
only through a single quantity --- the corresponding Fermi edge singularity
exponent. However, dynamical properties, such as the level density of states,
depend in a different way on each type of interaction. Hence, we can construct
different models, with and without interactions in the wire, with equal Fermi
edge singularity exponents, which have identical population curves, although
they originate from very different level densities of states. The latter may
either be regular or show a power-law suppression or enhancement at the Fermi
energy. These predictions are verified to a high degree of accuracy using the
density matrix renormalization group algorithm to calculate the dot occupation,
and classical Monte Carlo simulations on the corresponding Coulomb gas model to
extract the level density of states.",1101.3717v1
2022-10-31,Advanced ensemble modeling method for space object state prediction accounting for uncertainty in atmospheric density,"For objects in the low Earth orbit region, uncertainty in atmospheric density
estimation is an important source of orbit prediction error, which is critical
for space situational awareness activities such as the satellite conjunction
analysis. This paper investigates the evolution of orbit error distribution in
the presence of atmospheric density uncertainties, which are modeled using
probabilistic machine learning techniques. The recently proposed HASDM-ML,
CHAMP-ML, and MSIS-UQ machine learning models for density estimation are used
in this work. The investigation is convoluted because of the spatial and
temporal correlation of the atmospheric density values. We develop several
Monte Carlo methods, each capturing a different spatiotemporal density
correlation, to study the effects of density uncertainty on orbit uncertainty
propagation. However, Monte Carlo analysis is computationally expensive, so a
faster method based on the Kalman filtering technique for orbit uncertainty
propagation is also explored. It is difficult to translate the uncertainty in
atmospheric density to the uncertainty in orbital states under a standard
extended Kalman filter or unscented Kalman filter framework. This work uses the
so-called consider covariance sigma point (CCSP) filter that can account for
the density uncertainties during orbit propagation. As a test-bed for
validation purposes, a comparison between CCSP and Monte Carlo methods of orbit
uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML,
and MSIS-UQ density models, we propose an ensemble approach for orbit
uncertainty quantification for four different space weather conditions.",2210.16992v1
2015-03-03,Skyrmions in a density wave state: a mechanism for chiral superconductivity,"Broken symmetry states characterizing density waves of higher angular
momentum in correlated electronic systems are intriguing objects. In the scheme
of characterization by angular momentum, conventional charge and spin density
waves correspond to zero angular momentum. Here we explore a class of exotic
density wave states that have topological properties observed in recently
discovered topological insulators. These rich topological density wave states
deserve closer attention in not only high temperature superconductors but in
other correlated electron states, as in heavy fermions, of which an explicit
example will be discussed.The state discussed has non-trivial charge $2e$
skyrmionic spin texture. These skyrmions can condense into a charged
superfluid. Alternately, they can fractionalize into merons and anti-merons.
The fractionalized particles that are confined in skyrmions in the insulating
phase, can emerge at a deconfined quantum critical point, which separates the
insulating and the superconducting phases. These fractional particles form a
two-component spin-singlet chiral $(d_{x^2-y^2}\pm id_{xy})$ wave
superconducting state that breaks time reversal symmetry. Possible connections
of this exotic order to the superconducting state in the heavy-fermion material
URu$_2$Si$_2$ are suggested. The direct evidence of such a chiral
superconducting state is polar Kerr effect that was observed recently.",1503.01126v1
2006-05-10,"Density dependent equations of state for metal, nonmetal, and transition states for compressed mercury fluid","Analytical equations of state are presented for fluid mercury in metal,
nonmetal, and in metal-nonmetal transition states. Equations of state for metal
and nonmetal states are simple in form but the complexities of transition state
leads to a complex fourth-order equation. The interatomic potential function
used to describe the metal state have a hard repulsive wall, and that of
nonmetal state is the same as potential function of non-polar fluid with
induced dipole intermolecular interaction. Metal-nonmetal transition occurs in
the liquid density range 11-8 g/cm3, and a density dependent interaction
potential which gradually changes from a pure metal interaction to a nonmetal
interaction, on going from metal state to nonmetal state in the transition
region, is used. Well-depth and the position of potential minimum are presented
as temperature dependent quantities; their calculated values for the metal
state are typically within 5.0% and 0.33% of the experimental value,
respectively. The calculated well-depth for nonmetal state is smaller than the
experimental value indicating the effect of high pressure PVT data used, which
pushes a pair of mercury atom further together into the repulsive side. In the
transition region, calculated well-depths are 2-3 order of magnitudes larger
than for the metal state, and contain a sharp rising edge and a steep falling
having a singularity characteristic of phase transition.",0605270v1
1999-09-08,"Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory","The density of an atom in a state of well-defined angular momentum has a
specific finite spherical harmonic content, without and with interactions.
Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and
Local Density Approximations, generally violate this feature. We analyze, by
means of perturbation theory, the degree of this violation and show that it is
small. The correct symmetry of the density can be assured by a
constrained-search formulation without significantly altering the calculated
energies. We compare our procedure to the (different) common practice of
spherically averaging the self-consistent potential. Kohn-Sham density
functional theory with the exact exchange-correlation potential has the correct
finite spherical harmonic content in its density; but the corresponding exact
single particle potential and wavefunctions contain an infinite number of
spherical harmonics.",9909127v2
2024-01-12,Predicting The One-Particle Density Matrix With Machine Learning,"Two of the most widely used electronic structure theory methods, namely
Hartree-Fock and Kohn-Sham density functional theory, both requires the
iterative solution of a set of Schr\""odinger-like equations. The speed of
convergence of such self-consistent field process depends on the complexity of
the system under investigation and on the initial guess for the density matrix.
An initial density matrix close to the ground-state one will effectively allow
one to cut out many of the self-consistent steps necessary to achieve
convergence. Here, we predict the density matrix of Kohn-Sham density
functional theory by constructing a neural network, which uses the atomic
positions as only information. Such neural network provides an initial guess
for the density matrix far superior to any other recipes available, in
particular for molecules with metallic bonds. Furthermore, the quality of such
neural-network density matrix is good enough for the evaluation of interatomic
forces. This allows us to run accelerated {\it ab-initio} molecular dynamics
with little to no self-consistent steps.",2401.06533v1
1995-01-30,On the spin density wave transition in a two dimensional spin liquid,"Strongly correlated two dimensional electrons are believed to form a spin
liquid in some regimes of density and temperature. As the density is varied,
one expects a transition from this spin liquid state to a spin density wave
antiferromagnetic state. In this paper we show that it is self-consistent to
assume that this transition is second order and, on this assumption, determine
the critical behavior of the $2p_F$ susceptibility, the NMR rates $T_1$ and
$T_2$ and the uniform susceptibility. We compare our results to data on high
$T_c$ materials.",9501133v1
1999-05-23,Limiting temperature of hadrons using states predicted from kappa-deformed Poincaré algebra,"The experimental hadronic density of states dN/dm, assumed to be a sum of
normalized Breit- Wigner distributions and plotted as a function of the hadron
mass m, fails to show a Hagedorn like growth beyond 2 GeV, probably due to a
lack of data. Experimental hadronic states are fitted using $\ka$ -deformed
Poincar\'e algebra and the fit is used to extrapolate for including states not
detected. For the theoretical density of states the plot is a straight line in
the log scale even beyond 2 GeV with a limiting temperature of 400 MeV.",9905457v1
2003-01-30,Arbitrary Choice of Basic Variables in Density Functional Theory. I. Formalism,"The Hohenberg-Kohn theorem of the density functional theory is extended by
modifying the Levy constrained-search formulation. The new theorem allows us to
choose arbitrary physical quantities as the basic variables which determine the
ground-state properties of the system. Moreover, the theorem establishes a
minimum principle with respect to variations in the chosen basic variables as
well as with respect to variations in the density. By using this theorem, the
self-consistent single-particle equations are derived. N single-particle
orbitals introduced reproduce the basic variables. The validity of the theory
is confirmed by the examples where the spin-density or paramagnetic
current-density is chosen as one of the basic variables. The resulting
single-particle equations coincide with the Kohn-Sham equations of the
spin-density functional theory (SDFT) or current-density functional theory
(CDFT), respectively. By choosing basic variables appropriate to the system,
the present theory can describe the ground-state properties more efficiently
than the conventional DFT.",0301578v2
2008-03-24,Density-density functionals and effective potentials in many-body electronic structure calculations,"We demonstrate the existence of different density-density functionals
designed to retain selected properties of the many-body ground state in a
non-interacting solution starting from the standard density functional theory
ground state. We focus on diffusion quantum Monte Carlo applications that
require trial wave functions with optimal Fermion nodes. The theory is
extensible and can be used to understand current practices in several
electronic structure methods within a generalized density functional framework.
The theory justifies and stimulates the search of optimal empirical density
functionals and effective potentials for accurate calculations of the
properties of real materials, but also cautions on the limits of their
applicability. The concepts are tested and validated with a near-analytic
model.",0803.3460v1
2019-11-18,Finite temperature density matrix embedding theory,"We describe a formulation of the density matrix embedding theory at finite
temperature. We present a generalization of the ground-state bath orbital
construction that embeds a mean-field finite-temperature density matrix up to a
given order in the Hamiltonian, or the Hamiltonian up to a given order in the
density matrix. We assess the performance of the finite-temperature density
matrix embedding on the 1D Hubbard model both at half-filling and away from it,
and the 2D Hubbard model at half-filling, comparing to exact data where
available, as well as results from finite-temperature density matrix
renormalization group, dynamical mean-field theory, and dynamical cluster
approximations. The accuracy of finite-temperature density matrix embedding
appears comparable to that of the ground-state theory, with at most a modest
increase in bath size, and competitive with that of cluster dynamical
mean-field theory.",1911.07439v1
2021-10-18,On the pure state $v$-representability of density matrix embedding theory,"Density matrix embedding theory (DMET) formally requires the matching of
density matrix blocks obtained from high-level and low-level theories, but this
is sometimes not achievable in practical calculations. In such a case, the
global band gap of the low-level theory vanishes, and this can require
additional numerical considerations. We find that both the violation of the
exact matching condition and the vanishing low-level gap are related to the
assumption that the high-level density matrix blocks are non-interacting
pure-state $v$-representable (NI-PS-V), which assumes that the low-level
density matrix is constructed following the Aufbau principle. In order to relax
the NI-PS-V condition, we develop an augmented Lagrangian method to match the
density matrix blocks without referring to the Aufbau principle. Numerical
results for 2D Hubbard and hydrogen model systems indicate that in some
challenging scenarios, the relaxation of the Aufbau principle directly leads to
exact matching of the density matrix blocks, which also yields improved
accuracy.",2110.09558v2
2021-10-25,Spatially heterogeneous dynamics and locally arrested density fluctuations from first-principles,"We present a first-principles formalism for studying dynamical
heterogeneities in glass forming liquids. Based on the Non-Equilibrium
Self-Consistent Generalized Langevin Equation theory, we were able to describe
the time-dependent local density profile during the particle interchange among
small regions of the fluid. The final form of the diffusion equation contains
both, the contribution of the chemical potential gradient written in terms of a
coarse-grained density and a collective diffusion coefficient as well as the
effect of a history-dependent mobility factor. With this diffusion equation we
captured interesting phenomena in glass forming liquids such as the cases when
a strong density gradient is accompanied with a very low mobility factor
attributable to the denser part: in such circumstances the density profile
falls into an arrested state even in the presence of a density gradient. On the
other hand, we also show that above a certain critical temperature,which
depends on the volume fraction, any density heterogeneity relaxes to a uniform
state in a finite time, known as equilibration time. We further show that such
equilibration time varies little with the temperature in diluted systems but
can change drastically with temperature in concentrated systems.",2110.13243v1
2008-09-02,Contractions of product density operators of systems of identical fermions and bosons,"Recurrence and explicit formulae for contractions (partial traces) of
antisymmetric and symmetric products of identical trace class operators are
derived. Contractions of product density operators of systems of identical
fermions and bosons are proved to be asymptotically equivalent to,
respectively, antisymmetric and symmetric products of density operators of a
single particle, multiplied by a normalization integer. The asymptotic
equivalence relation is defined in terms of the thermodynamic limit of
expectation values of observables in the states represented by given density
operators. For some weaker relation of asymptotic equivalence, concerning the
thermodynamic limit of expectation values of product observables, normalized
antisymmetric and symmetric products of density operators of a single particle
are shown to be equivalent to tensor products of density operators of a single
particle.
  This paper presents the results of a part of the author's thesis [W. Radzki,
""Kummer contractions of product density matrices of systems of $n$ fermions and
$n$ bosons"" (Polish), MS thesis, Institute of Physics, Nicolaus Copernicus
University, Toru\'{n}, 1999].",0809.0474v2
2016-06-05,All states are nonclassical: entanglement of joint statistics,"Joint measurements of two observables reveal that every state is
nonclassical, with the only trivial exception of the state with density matrix
proportional to the identity. This naturally includes states considered
universally as classical-like, such as SU(2) and Glauber coherent states. We
show that this holds because we can always find a joint measurement whose
statistics is not separable.",1606.01478v2
2003-11-11,Color Ferromagnetism and Quantum Hall states in Quark Matter,"We discuss a possibility of the presence of a stable color ferromagnetic
state in SU(2) gauge theory of quark matter; a color magnetic field is
spontaneously generated due tothe gluon's dynamics. The state arises between
the hadronic state and the color superconducting state when the density of
quarks is varied. Although the state has been known to have unstable modes, we
show that unstable modes form quantum Hall states, in which the instability
disappears. Namely, the quark matter possesses a stable phase with the
ferromagnetic state and the quantum Hall state of gluons.",0311136v1
2003-10-21,Lattice QCD at finite T and μ,"Recent results of lattice QCD at finite temperature and density are reviewed.
At vanishing density the transition temperature, the equation of state and
hadron properties are discussed both for the pure gauge theory and for
dynamical staggered, Wilson and overlap fermions. The second part deals with
finite density. There are recent results for full QCD at finite temperature and
moderate density, while at larger densities QCD-like models are studied.",0310051v2
2020-11-03,Fokker-Planck equations and one-dimensional functional inequalities for heavy tailed densities,"We study one-dimensional functional inequalities of the type of Poincar\'e,
logarithmic Sobolev and Wirtinger, with weight, for probability densities with
polynomial tails. As main examples, we obtain sharp inequalities satisfied by
inverse Gamma densities, taking values on $R_+$, and Cauchy-type densities,
taking values on $R$. In this last case, we improve the result obtained by
Bobkov and Ledoux in 2009 by introducing a better weight function in the
logarithmic Sobolev inequality. The results are obtained by resorting to
Fokker-Planck type equations which possess these densities as steady states.",2011.01610v2
2016-04-17,Unphysical features in the application of the Boltzmann collision operator in the time dependent modelling of quantum transport,"In this work, the use of the Boltzmann collision operator for dissipative
quantum transport is analyzed. Its mathematical role on the description of the
time-evolution of the density matrix during a collision can be understood as
processes of adding and subtracting states. We show that unphysical results can
be present in quantum simulations when the old states (that built the density
matrix associated to an open system before the collision) are different from
the additional states generated by the Boltzmann collision operator. As a
consequence of the Fermi Golden rule, the new generated sates are usually
eigenstates of the momentum or kinetic energy. Then, the different
time-evolutions of old and new states involved in a collision process can
originate negative values of the charge density, even longer after the
collision. This unphysical feature disappears when the Boltzmann collision
operator generates states that were already present in the density matrix of
the quantum system before the collision. Following these ideas, in this paper,
we introduce an algorithm that models phonon-electron interactions through the
Boltzmann collision operator without negative values of the charge density. The
model only requires the exact knowledge, at all times, of the states that build
the density matrix of the open system.",1604.04925v2
2019-09-12,"Classical antennae, quantum emitters, and densities of optical states","We provide a pedagogical introduction to the concept of the local density of
optical states (LDOS), illustrating its application to both the classical and
quantum theory of radiation. We show that the LDOS governs the efficiency of a
macroscopic classical antenna, determining how the antenna's emission depends
on its environment. The LDOS is shown to similarly modify the spontaneous
emission rate of a quantum emitter, such as an excited atom, molecule, ion, or
quantum dot that is embedded in a nanostructured optical environment. The
difference between the number density of optical states, the local density of
optical states, and the partial local density of optical states is elaborated
and examples are provided for each density of states to illustrate where these
are required. We illustrate the universal effect of the LDOS on emission by
comparing systems with emission wavelengths that differ by more than 5 orders
of magnitude, and systems whose decay rates differ by more than 5 orders of
magnitude. To conclude we discuss and resolve an apparent difference between
the classical and quantum expressions for the spontaneous emission rate that
often seems to be overlooked, and discuss the experimental determination of the
LDOS.",1909.05619v1
2003-10-10,An ergodic theorem for Delone dynamical systems and existence of the integrated density of states,"We study strictly ergodic Delone dynamical systems and prove an ergodic
theorem for Banach space valued functions on the associated set of pattern
classes. As an application, we prove existence of the integrated density of
states in the sense of uniform convergence in distribution for the associated
random operators.",0310017v1
2005-04-15,On a Density-of-States Approach to Bohmian Mechanics,"We propose the idea that in Bohmian mechanics the wavefunction is related to
a density of states and explore some of its consequences. Specifically, it
allows a maximum-entropy interpretation of quantum probabilities, which creates
a stronger link between it and statistical mechanics. The proposed approach
also allows a range of extensions of the guidance condition in Bohmian
mechanics.",0504110v2
2008-04-22,Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrodinger operator,"We prove the complete asymptotic expansion of the integrated density of
states of a two-dimensional Schrodinger operator with a smooth periodic
potential",0804.3561v2
2013-10-31,Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operators,"We prove estimates on the H\""older exponent of the density of states measure
for discrete Schr\""odinger operators with potential of the form $V(n) =
\lambda(\lfloor(n+1)\beta\rfloor - \lfloor n\beta\rfloor)$, with $\lambda$
large enough, and conclude that for almost all values of $\beta$, the density
of states measure is not H\""older continuous.",1310.8553v2
2017-08-08,Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency,"In this paper, we study the non-self-dual extended Harper's model with a
Liouville frequency. Based on the work of \cite{SY}, we show that the
integrated density of states (IDS for short) of the model is
$\frac{1}{2}$-H$\ddot{\text{o}}$lder continuous. As an application, we also
obtain the Carleson homogeneity of the spectrum.",1708.02670v2
2018-08-05,Note: Effect of localization on mean-field density of state near jamming,"We discuss the effects of the localized modes on the density of state
$D(\omega)$ by introducing the probability distribution function of the
proximity to the marginal stability. Our theoretical treatment reproduces the
numerical results in finite dimensions near the jamming point., in particular,
successfully captures the novel $D(\omega)\sim \omega^4$ scaling including its
pressure dependence of the pre-factor.",1808.01635v1
2022-04-23,Stability of the non-critical spectral properties I: arithmetic absolute continuity of the integrated density of states,"We prove absolute continuity of the integrated density of states for
frequency-independent analytic perturbations of the non-critical almost Mathieu
operator under arithmetic conditions on frequency.",2204.11000v1
2002-07-05,Interference and entanglement: an intrinsic approach,"An addition rule of impure density operators, which provides a pure state
density operator, is formulated. Quantum interference including visibility
property is discussed in the context of the density operator formalism. A
measure of entanglement is then introduced as the norm of the matrix equal to
the difference between a bipartite density matrix and the tensor product of
partial traces. Entanglement for arbitrary quantum observables for multipartite
systems is discussed. Star-product kernels are used to map the formulation of
the addition rule of density operators onto the addition rule of symbols of the
operators. Entanglement and nonlocalization of the pure state projector and
allied operators are discussed. Tomographic and Weyl symbols (tomograms and
Wigner functions) are considered as examples. The squeezed-states and some
spin-states (two qubits) are studied to illustrate the formalism.",0207033v1
2004-03-22,Compatibility Relations between the Reduced and Global Density Matrixes,"It is a hard and important problem to find the criterion of the set of
positive-definite matrixes which can be written as reduced density operators of
a multi-partite quantum state. This problem is closely related to the study of
many-body quantum entanglement which is one of the focuses of current quantum
information theory. We give several results on the necessary compatibility
relations between a set of reduced density matrixes, including: (i)
compatibility conditions for the one-party reduced density matrixes of any
$N_A\times N_B$ dimensional bi-partite mixed quantum state, (ii) compatibility
conditions for the one-party and two-party reduced density matrixes of any
$N_A\times N_B\times N_C$ dimensional tri-partite mixed quantum state, and
(iii) compatibility conditions for the one-party reduced matrixes of any
$M$-partite pure quantum state with the dimension $N^{\otimes M}$.",0403151v1
2012-02-20,Adsorption of hard spheres: structure and effective density according to the potential distribution theorem,"We propose a new type of effective densities via the potential distribution
theorem. These densities are for the sake of enabling the mapping of the free
energy of a uniform fluid onto that of a nonuniform fluid. The potential
distribution theorem gives the work required to insert a test particle into the
bath molecules under the action of the external (wall) potential. This
insertion work W_ins can be obtained from Monte Carlo (MC) simulation (e.g.
from Widom's test particle technique) or from an analytical theory. The
pseudo-densities are constructed thusly so that when their values are
substituted into a uniform-fluid equation of state (e.g. the Carnahan-Starling
equation for the hard-sphere chemical potentials), the MC nonuniform insertion
work is reproduced. We characterize the pseudo-density behavior for the hard
spheres/hard wall system at moderate to high densities (from \rho^*= 0.5745 to
0.9135). We adopt the MC data of Groot et al. for this purpose. The
pseudo-densities show oscillatory behavior out of phase (opposite) to that of
the singlet densities. We also construct a new closure-based density functional
theory (the star-function based density functional theory) that can give
accurate description of the MC density profiles and insertion works. A viable
theory is established for several cases in hard sphere adsorption.",1202.4276v1
2015-05-23,The full weak charge density distribution of 48Ca from parity violating electron scattering,"Background: The ground state neutron density of a medium mass nucleus
contains fundamental nuclear structure information and is at present relatively
poorly known.
  Purpose: We explore if parity violating elastic electron scattering can
provide a feasible and model independent way to determine not just the neutron
radius but the full radial shape of the neutron density $\rho_n(r)$ and the
weak charge density $\rho_W(r)$ of a nucleus.
  Methods: We expand the weak charge density of $^{48}$Ca in a model
independent Fourier Bessel series and calculate the statistical errors in the
individual coefficients that might be obtainable in a model parity violating
electron scattering experiment.
  Results: We find that it is feasible to determine roughly six Fourier Bessel
coefficients of the weak charge density of 48Ca within a reasonable amount of
beam time. However, it would likely be much harder to determine the full weak
density of a significantly heavier nucleus such as 208Pb.
  Conclusions: Parity violating elastic electron scattering can determine the
full weak charge density of a medium mass nucleus in a model independent way.
This weak density contains fundamental information on the size, surface
thickness, shell oscillations, and saturation density of the neutron
distribution in a nucleus. The measured $\rho_W(r)$, combined with the
previously known charge density $\rho_{ch}(r)$, will literally provide a
detailed textbook picture of where the neutrons and protons are located in an
atomic nucleus.",1505.06358v1
2018-01-26,Nuclear fourth-order symmetry energy and its effects on neutron star properties in the relativistic Hartree-Fock theory,"Adopting the density dependent relativistic mean-field (RMF) and relativistic
Hartree-Fock (RHF) approaches, the properties of the nuclear fourth-order
symmetry energy $S_4$ are studied within the covariant density functional (CDF)
theory. It is found that the fourth-order symmetry energies are suppressed in
RHF at both saturation and supranuclear densities, where the extra contribution
from the Fock terms is demonstrated, specifically via the isoscalar
meson-nucleon coupling channels. The reservation of $S_4$ and higher-order
symmetry energies in the nuclear equation of state then affects essentially the
prediction of neutron star properties, which is illustrated in the quantities
such as the proton fraction, the core-crust transition density as well as the
fraction of crustal moment of inertia. Since the Fock terms enhance the density
dependence of the thermodynamical potential, the RHF calculations predict
systematically smaller values of density, proton fraction and pressure at the
core-crust transition boundary of neutron stars than density dependent RMF
ones. In addition, a linear anti-correlation between the core-crust transition
density $\rho_t$ and the density slope of symmetry energy $L$ is found which is
then utilized to constrain the core-crust transition density as
$\rho_t\thicksim[0.069, 0.098]~\rm{fm}^{-3}$ with the recent empirical
information on $L$. The study clarifies the important role of the fourth-order
symmetry energy in determining the properties of nuclear matter at extreme
isospin or density conditions.",1801.08672v1
2003-10-03,Least paradoxical states of the Schrödinger cat,"Modeling the Schr\""{o}dinger cat by a two state system and assuming that the
cat is coupled to the environment we look for the least paradoxical states of
the Schr\""{o}dinger cat in the following way. We require the reduced density
matrix of the cat for one of the two states in the superposition to be the same
as the one for the total state while distinct from the reduced density matrix
of the cat for the other state in the superposition. We then look for the
reduced density matrices for which the cat is as alive as possible for the
first state (and as dead as possible for the second state). The resulting
states are those in which the probability for the cat to be alive (or dead) is
$1/2+\sqrt 2/4\approx 0.854$",0310025v1
2017-03-13,One-particle-density-matrix occupation spectrum of many-body localized states after a global quench,"The emergent integrability of the many-body localized phase is naturally
understood in terms of localized quasiparticles. As a result, the occupations
of the one-particle density matrix in eigenstates show a Fermi-liquid-like
discontinuity. Here we show that in the steady state reached at long times
after a global quench from a perfect density-wave state, this occupation
discontinuity is absent, reminiscent of a Fermi liquid at a finite temperature,
while the full occupation function remains strongly nonthermal. We discuss how
one can understand this as a consequence of the local structure of the
density-wave state and the resulting partial occupation of quasiparticles. This
partial occupation can be controlled by tuning the initial state and can be
described by an effective temperature.",1703.04398v2
2023-08-07,"Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized","Description of many-electron systems with a fractional electron number
$N_\textrm{tot}$ and fractional spin $M_\textrm{tot}$ is of great importance in
physical chemistry, solid state physics and materials science. In this Letter,
we provide an exact description of the zero-temperature ensemble ground state
of a general, finite, many-electron system, and characterize the dependence of
the energy and the spin-densities on both $N_\textrm{tot}$ and
$M_\textrm{tot}$, when the total spin is at its equilibrium value. We
generalize the piecewise-linearity principle and the flat-plane condition and
determine which pure states contribute to the ground-state ensemble. We find a
new derivative discontinuity, which manifests for spin variation at constant
$N_\textrm{tot}$, as a jump in the Kohn-Sham potential. We identify a
previously unknown degeneracy of the ground state, such that the total energy
and density are unique, but the spin-densities are not. Our findings serve as a
basis for development of advanced approximations in density functional theory
and other many-electron methods.",2308.03465v3
2021-02-05,Relation between local density and density relaxation near glass transition in a glass forming binary mixture,"Many investigations shed light on various correlations between structure and
dynamics in supercooled liquids; however, a general relation between structure
and dynamics remains elusive. This molecular dynamics simulation study
identifies the interrelationship between the growth of the highest peak of the
radial distribution function, variation in the radial force from this peak, and
the slowdown of the density relaxation in the supercooled states of a model
binary glass former. From the microscopic string-like motion in supercooled
liquids, we argue that the surface density on a spherical shell around a
reference particle at the highest peak of the radial distribution function can
represent the free volume available for motion. We further show from these
arguments and simulations that density relaxtion time and local density are
connected; in this expression, the dynamics diverge at a higher critical value
of local density. This relation is similar to the Vogel Fulcher Tammann
relation in supercooled liquids, thus giving insight into the structural origin
of the VFT as the jamming of particles in a channel of density relaxation.",2102.03070v2
2021-07-22,"Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model","To study quantum properties of the hadron wavefunction at small x, we derived
the reduced density matrix for soft gluons in the CGC framework. We explicitly
showed that the reduced density matrix is not diagonal in the particle number
basis. The off-diagonal components are usually ignored in the conventional
parton model. We thus defined the density matrix of ignorance by keeping only
the part of the reduced density matrix which can be probed in a limited set of
experimental measurements. We calculated Von Neumann entropy for both the
reduced and ignorance density matrices. The entropy of ignorance is always
greater than the entanglement entropy (computed drom the reduced density
matrix) of gluons. Finally, we showed that the CGC reduced density matrix for
soft gluons can be diagonalized in a thermal basis with Boltzmann weights
suggesting thermalization of new quasi-particle states which we dubbed
entangolons.",2107.10812v2
2022-01-11,Density matrix and space-time distributions of the electronic density and current at fast pulsed photoemission through a double quantum well,"Within the framework of the density matrix method, general formulas obtained
that are convenient for describing fast pulsed photoemission that occurs in a
time less than or on the order of the times of relaxation processes inside the
photocathode. Expressions for the elements of the density matrix are found by
solving the kinetic equation that takes into account the alternating
electromagnetic field of light pumping and inelastic scattering of electrons.
The derived formulas are applied for the numerical-analytical study of a
one-dimensional model of wave-like spatiotemporal modulation of a photoelectron
pulse of suitable duration during its passage through a double-well
quantum-well heterostructure deposited on a volumetric planar photocathode.
This modulation is a quantum beat that occurs as a result of excitation and
subsequent slow oscillatory decay of the superposition of the doublet of
quasi-stationary states of the heterostructure. It is possible to provide
prolongation of generation and even amplification of waves of charge density
and current density of photoelectrons when the photocathode is exposed to a
periodic sequence of light pulses.",2201.03763v1
2022-11-03,Controlling charge density order in 2H-TaSe$_{2}$ using a van Hove singularity,"We report on the interplay between a van Hove singularity and a charge
density wave state in 2H-TaSe$_{2}$. We use angle-resolved photoemission
spectroscopy to investigate changes in the Fermi surface of this material under
surface doping with potassium. At high doping, we observe modifications which
imply the disappearance of the $(3\times 3)$ charge density wave and formation
of a different correlated state. Using a tight-binding-based approach as well
as an effective model, we explain our observations as a consequence of coupling
between the single-particle Lifshitz transition during which the Fermi level
passes a van Hove singularity and the charge density order. In this scenario,
the high electronic density of states associated with the van Hove singularity
induces a change in the periodicity of the charge density wave from the known
$(3\times 3)$ to a new $(2\times 2)$ superlattice.",2211.01780v2
2020-01-31,Complete Solution of the Tight Binding Model on a Cayley Tree: Strongly Localised versus Extended States,"The complete set of Eigenstates and Eigenvalues of the nearest neighbour
tight binding model on a Cayley tree with branching number $b=2$ and $M$
branching generations with open boundary conditions is derived. We find that of
the $N= 1 +3 (2^M-1)$ total states only $3 M +1$ states are extended throughout
the Cayley tree. The remaining $N-(3 M+1)$ states are found to be strongly
localised states with finite amplitudes on only a subset of sites. In
particular, there are, for $M>1$, $3 \times 2^{M-2}$ surface states which are
each antisymmetric combinations of only two sites on the surface of the Cayley
tree and have energy eactly at $E=0$, the middle of the band. The ground state
and the first two excited states of the Cayley tree are found to be extended
states with amplitudes on all sites of the Cayley tree, for all $M$. We use the
results on the complete set of Eigenstates and Eigenvalues to derive the total
density of states and a local density of states.",2001.11814v2
1994-04-04,Ferromagnetism in the Infinite-U Hubbard Model,"We have studied the stability of the ferromagnetic state in the infinite-U
Hubbard model on a square lattice by approximate diagonalization of finite
lattices using the density matrix renormalization group technique. By studying
lattices with up to 5X20 sites, we have found the ferromagnetic state to be
stable below the hole density of 22 percent. Beyond 22 percent of hole doping,
the total spin of the ground state decreased gradually to zero with increasing
hole density.",9404003v2
2000-04-27,Spatial Inhomogeneities in Disordered d-Wave Superconductors: Effect on Density of States and Superfluid Stiffness,"We study a short coherence length d-wave superconductor with finite density
of unitary scatterers using the Bogoliubov-deGennes technique. We find that the
low-energy density of states is reduced, the superfluid stiffness is
significantly larger and off-diagonal long range order is more robust than the
self-consistent T-matrix prediction. These results are a consequence of the
inhomogeneous pairing amplitude in the ground state and of the low-lying
excitations formed by hybridized impurity resonances. These features, with
their nontrivial spatial structure, cannot be adequately described within the
conventional T-matrix approach.",0004481v1
2005-09-10,Microscopic Theory of Skyrmions in Quantum Hall Ferromagnets,"We present a microscopic theory of skyrmions in the monolayer quantum Hall
ferromagnet. It is a peculiar feature of the system that the number density and
the spin density are entangled intrinsically as dictated by the W$%_{\infty}$
algebra. The skyrmion and antiskyrmion states are constructed as W$_{\infty
}$-rotated states of the hole-excited and electron-excited states,
respectively. They are spin textures accompanied with density modulation that
decreases the Coulomb energy. We calculate their excitation energy as a
function of the Zeeman gap and compared the result with experimental data.",0509262v1
2005-09-16,Suppression of superfluid density in the superfluid-supersolid transition,"We show that the rather unexpected pressure dependence of superfluid density
observed near the superfluid-supersolid transition by Kim {\em et.al.}[M.H.W.
Chan, {\em private communication}], can be understood if the transition from
superfluid to supersolid state is a second order or weakly first order
transition from the superfluid state to a super-CDW state with non-uniform
Bose-condensation amplitude. The suppression of superfluid density is a direct
consequence of softening of phonon mode at finite wave-vector $|\vec{Q}|\sim
Q_0$ around the quantum phase transition.",0509428v3
1995-10-12,Neutron Drops and Skyrme Energy-Density Functionals,"The J$^{\pi}$=0$^+$ ground state of a drop of 8 neutrons and the lowest
1/2$^-$ and 3/2$^-$ states of 7-neutron drops, all in an external well, are
computed accurately with variational and Green's function Monte Carlo methods
for a Hamiltonian containing the Argonne $v_{18}$ two-nucleon and Urbana IX
three-nucleon potentials. These states are also calculated using Skyrme-type
energy-density functionals. Commonly used functionals overestimate the central
density of these drops and the spin-orbit splitting of 7-neutron drops.
Improvements in the functionals are suggested.",9510022v1
1998-07-14,Chiral dynamics of the nuclear equation of state,"We present a new chiral power expansion scheme for the nuclear equation of
state. The scheme is effective in the sense that it is constructed to work
around nuclear saturation density. The leading and subleading terms are
evaluated and are shown to provide an excellent equation of state. As a further
application we considered the chiral quark condensate in nuclear matter.
Already at nuclear saturation density we predict a substantially smaller
reduction of the condensate as compared to conventional approaches.",9807040v1
2003-04-28,Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices,"We present reduction theorems for the problem of optimal unambiguous state
discrimination (USD) of two general density matrices. We show that this problem
can be reduced to that of two density matrices that have the same rank $n$ and
are described in a Hilbert space of dimensions $2n$. We also show how to use
the reduction theorems to discriminate unambiguously between N mixed states (N
\ge 2).",0304179v2
2008-02-03,Non-Ergodic Mesoscopic Systems,"Suppose there is a mesoscopic system connected to single channel leads. If
the system is non-chaotic or non-ergodic then the thermodynamic and transport
properties do not depend on impurity averaged density of states. We show that
the partial density of states as well as density of states of a given system
can be determined exactly from the asymptotic wave-function (or scattering
matrix) at the resonances. The asymptotic wave-function can be determined
experimentally without any knowledge about the quantum mechanical potential
(including electron-electron interaction) or wave function in the interior of
the system. Some counter intuitive relations derived here can allow this.",0802.0290v2
2009-11-15,Edge reconstruction induces magnetic and metallic behavior in zigzag graphene nanoribbons,"The edge reconstruction of zigzag graphene nanoribbons to a stable line of
alternatively fused seven and five membered rings with hydrogen passivation has
been studied within density functional theory with both localized and extended
basis approximations. Reconstruction of both edges results in a nonmagnetic
metallic ground state, whereas the one edge reconstruction stabilizes the
system in a ferromagnetic metallic ground state. The reconstructed edge
suppresses the local spin density of atoms and contributes finite density of
states at Fermi energy. Our study paves a new way to fabricate the metallic
electrodes for semiconducting graphene devices with full control over the
magnetic behavior without any lattice mismatch between leads and the channel.",0911.2883v1
2015-10-03,Equation of state for tungsten over a wide range of densities and internal energies,"A caloric model, which describes the pressure--density--internal-energy
relationship in a broad region of condensed-phase states, is applied for
tungsten. As distinct from previously known caloric equations of state for this
material, a new form of the cold-compression curve at $T = 0$~K is used.
Thermodynamic characteristics along the cold curve and shock Hugoniots are
calculated for the metal and compared with some theoretical results and
experimental data available at high energy densities.",1510.00763v2
1998-02-24,Excitation spectrum and instability of a two-species Bose-Einstein condensate,"We numerically calculate the density profile and excitation spectrum of a
two-species Bose-Einstein condensate for the parameters of recent experiments.
We find that the ground state density profile of this system becomes unstable
in certain parameter regimes, which leads to a phase transition to a new stable
state. This state displays spontaneously broken cylindrical symmetry. This
behavior is reflected in the excitation spectrum: as we approach the phase
transition point, the lowest excitation frequency goes to zero, indicating the
onset of instability in the density profile. Following the phase transition,
this frequency rises again.",9802247v1
2002-01-04,Nonconstant electronic density of states tunneling inversion for A15 superconductors: Nb3Sn,"We re-examine the tunneling data on A15 superconductors by performing a
generalized McMillan-Rowell tunneling inversion that incorporates a nonconstant
electronic density of states obtained from band-structure calculations. For
Nb3Sn, we find that the fit to the experimental data can be slightly improved
by taking into account the sharp structure in the density of states, but it is
likely that such an analysis alone is not enough to completely explain the
superconducting tunneling characteristics of this material. Nevertheless, the
extracted Eliashberg function displays a number of features expected to be
present for the highest quality Nb3Sn samples.",0201048v1
2002-09-12,Ground-state properties of hard core bosons in one-dimensional harmonic traps,"The one-particle density matrices for hard core bosons in a one-dimensional
harmonic trap are computed numerically for systems with up to 160 bosons.
Diagonalization of the density matrix shows that the many-body ground state is
not Bose-Einstein condensed. The ground state occupation, the amplitude of the
lowest natural orbital, and the zero momentum peak height scale as powers of
the particle number, and the corresponding exponents are related to each other.
Close to its diagonal, the density matrix for hard core bosons is similar to
the one of noninteracting fermions.",0209300v2
2006-10-29,Local density of states subject to finite impurity concentration in graphene,"It is demonstrated that there is a characteristic impurity concentration, at
which variation with concentration and overall appearance of the local density
of states at the impurity site in graphene are changing their behavior.
Features that are prominent in the local density of states for the single
impurity are disappearing from it when impurity concentration far exceeds this
critical value. The impurity subsystem not only induces the rearrangement of
the electron spectrum in graphene, but also undergoes a substantial spectral
transformation by itself, which can be observed experimentally.",0610811v1
2010-05-27,Engineering the Photonic Density of States with metamaterials,"The photonic density of states (PDOS), like its' electronic coun- terpart, is
one of the key physical quantities governing a variety of phenom- ena and hence
PDOS manipulation is the route to new photonic devices. The PDOS is
conventionally altered by exploiting the resonance within a device such as a
microcavity or a bandgap structure like a photonic crystal. Here we show that
nanostructured metamaterials with hyperbolic dispersion can dramatically
enhance the photonic density of states paving the way for metamaterial based
PDOS engineering.",1005.5172v1
2022-07-08,Maximally Entangled Two-Qutrit Quantum Information States and De Gua's Theorem for Tetrahedron,"Geometric relations between separable and entangled two-qubit and two-qutrit
quantum information states are studied. To characterize entanglement of two
qubit states, we establish a relation between reduced density matrix and the
concurrence. For the rebit states, the geometrical meaning of concurrence as
double area of a parallelogram is found and for generic qubit states it is
expressed by determinant of the complex Hermitian inner product metric, where
reduced density matrix coincides with the inner product metric. In the case of
generic two-qutrit state, for reduced density matrix we find Pythagoras type
relation, where the concurrence is expressed by sum of all $2 \times 2$ minors
of $3\times3$ complex matrix. For maximally entangled two-retrit state, this
relation is just De Gua's theorem or a three-dimensional analog of the
Pythagorean theorem for triorthogonal tetrahedron areas. Generalizations of our
results for arbitrary two-qudit states are discussed",2207.03721v1
2012-08-17,Proof of an entropy conjecture for Bloch coherent spin states and its generalizations,"Wehrl used Glauber coherent states to define a map from quantum density
matrices to classical phase space densities and conjectured that for Glauber
coherent states the mininimum classical entropy would occur for density
matrices equal to projectors onto coherent states. This was proved by Lieb in
1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for
every angular momentum $J$. This conjecture is proved here. We also recall our
1991 extension of the Wehrl map to a quantum channel from $J$ to $K=J+1/2, J+1,
...$, with $K=\infty$ corresponding to the Wehrl map to classical densities.
For each $J$ and $J<K\leq \infty$ we show that the minimal output entropy for
these channels occurs for a $J$ coherent state. We also show that coherent
states both Glauber and Bloch minimize any concave functional, not just
entropy.",1208.3632v2
2008-03-06,Ground-state of graphene in the presence of random charged impurities,"We calculate the carrier density dependent ground state properties of
graphene in the presence of random charged impurities in the substrate taking
into account disorder and interaction effects non-perturbatively on an equal
footing in a self-consistent theoretical formalism. We provide detailed
quantitative results on the dependence of the disorder-induced spatially
inhomogeneous two-dimensional carrier density distribution on the external gate
bias, the impurity density, and the impurity location. We find that the
interplay between disorder and interaction is strong, particularly at lower
impurity densities. We show that for the currently available typical graphene
samples, inhomogeneity dominates graphene physics at low ($\lesssim 10^{12}$
cm$^{-2}$) carrier density with the density fluctuations becoming larger than
the average density.",0803.0963v2
2015-02-05,Negative energy densities in integrable quantum field theories at one-particle level,"We study the phenomenon of negative energy densities in quantum field
theories with self-interaction. Specifically, we consider a class of integrable
models (including the sinh-Gordon model) in which we investigate the
expectation value of the energy density in one-particle states. In this
situation, we classify the possible form of the stress-energy tensor from first
principles. We show that one-particle states with negative energy density
generically exist in non-free situations, and we establish lower bounds for the
energy density (quantum energy inequalities). Demanding that these inequalities
hold reduces the ambiguity in the stress-energy tensor, in some situations
fixing it uniquely. Numerical results for the lowest spectral value of the
energy density allow us to demonstrate how negative energy densities depend on
the coupling constant and on other model parameters.",1502.01714v3
2006-08-02,Excited-State Density Distributions of Neutron-Rich Unstable Nuclei,"We calculate densities of excited states in the quasiparticle random-phase
approximation (QRPA)with Skyrme interactions and volume pairing. We focus on
low-energy peaks/bumps in the strength functions of a range of Ca, Ni, and Sn
isotopes for J pi = 0+, 1-, and 2+. We define an ""emitted-neutron number"",
which we then use to distinguish localized states from scattering-like states.
The degree of delocalization either increases as the neutron-drip line is
approached or stays high between the stability line and the drip line. In the
2+ channel of Sn, however, the low-lying states, not even counting surface
vibrations, are still fairly well localized on average, even at the neutron
drip line.",0608007v1
2014-03-15,Entropy and entanglement bounds for reduced density matrices of fermionic states,"Unlike bosons, fermions always have a non-trivial entanglement. Intuitively,
Slater determinantal states should be the least entangled states. To make this
intuition precise we investigate entropy and entanglement of fermionic states
and prove some extremal and near extremal properties of reduced density
matrices of Slater determinantal states.",1403.3816v3
2022-02-18,Density Matrices of Seniority-Zero Geminal Wavefunctions,"Scalar products and density matrix elements of closed-shell pair geminal
wavefunctions are evaluated directly in terms of the pair amplitudes, resulting
in an analogue of Wick's theorem for fermions or bosons. This expression is in
general intractable, but it is shown how it becomes feasible in three distinct
ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and
the antisymmetrized product of strongly-orthogonal geminals. Dissociation
curves for hydrogen chains are computed with off-shell RG states and the
antisymmetrized product of interacting geminals. Both are near exact suggesting
that the incorrect results observed with ground state RG states are fixable
using a different RG state.",2202.09401v1
2010-11-05,Ab Initio Local Density Approximation Description of the Electronic Properties of Zinc Blende Cadmium Sulfide (zb-CdS),"Ab-initio, self-consistent electronic energy bands of zinc blende CdS are
reported within the local density functional approximation (LDA). Our first
principle, non-relativistic and ground state calculations employed a local
density potential and the linear combination of atomic orbitals (LCAO). Within
the framework of the Bagayoko, Zhao, and Williams (BZW) method, we solved
self-consistently both the Kohn-Sham equation and the equation giving the
ground state density in terms of the wave functions of the occupied states. Our
calculated, direct band gap of 2.39 eV, at the point, is in accord with
experiment. Our calculation reproduced the peaks in the conduction and valence
bands density of states, within experimental uncertainties. The calculated
electron effective mass agrees with experimental findings.",1011.1311v2
2010-11-11,Local Density Approximation Description of Electronic Properties of Wurtzite Cadmium Sulfide (w-CdS),"We present calculated, electronic and related properties of wurtzite cadmium
sulfide (w-CdS). Our ab-initio, non-relativistic calculations employed a local
density functional approximation (LDA) potential and the linear combination of
atomic orbitals (LCAO). Following the Bagayoko, Zhao, and Williams (BZW)
method, we solved self-consistently both the Kohn-Sham equation and the
equation giving the ground state density in terms of the wave functions of the
occupied states. Our calculated, direct band gap of 2.47 eV, at the point, is
in excellent agreement with experiment. So are the calculated density of states
and the electron effective mass. In particular, our results reproduce the peaks
in the conduction band density of states, within the experimental
uncertainties.",1011.2793v1
2014-11-01,A novel density of state method for complex action systems,"Recently, a new and efficient algorithm (the LLR method) has been proposed
for computing densities of states in statistical systems and gauge theories. In
this talk, we explore whether this novel density of states method can be
applied to numerical computations of observables in systems for which the
action is complex. To this purpose, we introduce a generalised density of
states, in terms of which integrals of oscillating observables can be
determined semi-analytically, and we define a strategy to compute it with the
LLR method. As a case study, we apply these ideas to the Z(3) spin model at
finite density, finding a remarkable agreement of our results for the phase
twist with those obtained with the worm algorithm for all explored chemical
potentials, including values for which there are cancellations over sixteen
orders of magnitude. These findings open new perspectives for dealing with the
sign problem on physically more relevant systems.",1411.0174v1
2020-09-18,"New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter","We present new equations of state for applications in core-collapse supernova
and neutron star merger simulations. We start by introducing an effective mass
parametrization that is fit to recent microscopic calculations up to twice
saturation density. This is important to capture the predicted thermal effects,
which have been shown to determine the proto-neutron star contraction in
supernova simulations. The parameter range of the energy-density functional
underlying the equation of state is constrained by chiral effective field
theory results at nuclear densities as well as by functional renormalization
group computations at high densities based on QCD. We further implement
observational constraints from measurements of heavy neutron stars, the
gravitational wave signal of GW170817, and from the recent NICER results.
Finally, we study the resulting allowed ranges for the equation of state and
for properties of neutron stars, including the predicted ranges for the neutron
star radius and maximum mass.",2009.08885v3
2019-06-19,Optical properties of magnetized transient low-pressure plasma,"A plasma under the influence of an external magnetic field changes the
optical properties due to the Zeeman splitting of the energy levels. This
splitting degenerates an initial single spectral line into a system of spectral
lines with different transition frequencies defined by the electronic structure
of the energy levels. Newly created magnetic sub-levels redefine the spectral
profile of the line emission and therefore radiation transport mechanism in
optically thick plasma. Self-absorption which defines the excited
state-densities is an important mechanism and can be used with other methods to
describe the state densities for an optically thick plasma. This method is an
established tool to retrieve state-density and plasma parameters. To measure
each magnetic sub-level density of argon 1s4 and 1s5 (in Paschen's notation) a
tunable diode laser absorption spectroscopy (TDLAS) was used. Based on
reconstructed excited state densities, the self-absorption coefficient was
calculated for individual magnetic sub-levels. A decrease in self-absorption
with an external magnetic field was noticed indicating a higher transparency of
the plasma. Furthermore a polarization dependent self-absorption was found. The
presented results can help to model optical properties and interpret the
absorption of a low-pressure optically thick magnetized plasma.",1906.08100v1
2012-12-05,Nonequilibrium density matrix for thermal transport in quantum field theory,"In these notes I explain how to describe one-dimensional quantum systems that
are simultaneously near to, but not exactly at, a critical point, and in a
far-from-equilibrium steady state. This description uses a density matrix on
scattering states (of the type of Hershfield's density matrix), or equivalently
a Gibbs-like ensemble of scattering states. The steady state I am considering
is one where there is a steady flow of energy along the chain, coming from the
steady draining / filling of two far-away reservoirs put at different
temperatures. The context I am using is that of massive relativistic quantum
field theory, which is the framework for describing the region near quantum
critical points in any universality class with translation invariance and with
dynamical exponent z equal to 1. I show, in this completely general setup, that
a particular steady-state density matrix occurs naturally from the physically
motivated Keldysh formulation of the steady state. In this formulation the
steady state occurs as a result of a large-time evolution from an initial state
where two halves of the system are separately thermalized. I also show how this
suggests a particular dependence (a ""factorization"") of the average current on
the left and right temperatures. The idea of this density matrix was proposed
already in a recent publication with my collaborator Denis Bernard, where we
studied it in the context of conformal field theory.",1212.1077v1
2010-05-27,First-principles prediction of spin-density-reflection symmetry driven magnetic transition of CsCl-type FeSe,"Based on results of density functional theory (DFT) calculations with the
local spin density approximation (LSDA) and the generalized gradient
approximation (GGA), we propose a new magnetic material, CsCl-type FeSe. The
calculations reveal the existence of ferromagnetic (FM) and antiferromagnetic
(AFM) states over a wide range of lattice constants. At 3.12\,{\AA} in the GGA,
the equilibrium state is found to be AFM with a local Fe magnetic moment of
$\pm 2.69\,\mu_\mathrm{B}$. A metastable FM state with Fe and Se local magnetic
moments of $2.00\,\mu_\mathrm{B}$ and $-0.032\,\mu_\mathrm{B}$, respectively,
lies 171.7\,{meV} above the AFM state. Its equilibrium lattice constant is
$\sim 2$\,{\%} smaller than that of the AFM state, implying that when the
system undergoes a phase transition from the AFM state to the FM one, the
transition is accompanied by volume contraction. Such an AFM-FM transition is
attributed to spin-density $z$-reflection symmetry; the symmetry driven AFM-FM
transition is not altered by spin-orbit coupling. The relative stability of
different magnetic phases is discussed in terms of the local density of states.
We find that CsCl-type FeSe is mechanically stable, but the magnetic states are
expected to be brittle.",1005.5112v2
2016-04-18,Topological density-wave states in a particle-hole symmetric Weyl metal,"We study the instabilities of a particle-hole symmetric Weyl metal with both
electron and hole Fermi surfaces (FS) around the Weyl points. For a repulsive
interaction, we find that the leading instability is towards a longitudinal
spin-density-wave order (SDW$_z$). Besides, there exist three degenerate
subleading instabilities: a charge-density-wave (CDW) instability and two
transverse spin-density-wave (SDW$_{x,y}$) instabilities. For an attractive
interaction the leading instabilities are towards two pair-density-wave orders
(PDW) which pair the two FS's separately. Both the PDW and SDW$_z$ order
parameters fully gap out FS's, while the CDW and SDW$_{x,y}$ ones leave line
nodes on both FS's. For the SDW$_z$ and the PDW states, the surface Fermi arc
in the metallic state evolves to a chiral Fermi line which passes the
projection of the Weyl points and traverses the full momentum space. For the
CDW state, the line node projects to a ""drumhead"" band localized on the
surface, which can lead to a topological charge polarization. We verify the
surface states by numerically simulating the angular-resolved photoemission
spectroscopy data.",1604.05311v2
2013-09-28,Collapsing Schrödinger Cats in the Density Matrix Renormalization Group,"In this paper, we propose a modified Density Matrix Renormalization Group
(DMRG) algorithm to preferentially select minimum entropy states (minimally
entangled states) in finite systems with asymptotic ground state degeneracy.
The algorithm adds a ""quench"" process to the conventional DMRG method, which
mimics the decoherence of physical systems, and collapses non-locally entangled
states such as Schr\""odinger cats. We show that the method works for
representative models with ground state degeneracy arising from either
topological order or spontaneous discrete symmetry breaking. In the minimal
entropy states thus obtained, properties associated with thermodynamic limit,
such as topological entanglement entropy and magnetic order parameters, can be
obtained directly and efficiently.",1309.7438v1
2023-09-07,Nonequilibrium Schwinger-Keldysh formalism for density matrix states: analytic properties and implications in cosmology,"Motivated by cosmological Hartle-Hawking and microcanonical density matrix
prescriptions for the quantum state of the Universe we develop
Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems
with the initial density matrix. We build the generating functional of in-in
Green's functions and expectation values for a generic density matrix of the
Gaussian type and show that the requirement of particle interpretation selects
a distinguished set of positive/negative frequency basis functions of the wave
operator of the theory, which is determined by the density matrix parameters.
Then we consider a special case of the density matrix determined by the
Euclidean path integral of the theory, which in the cosmological context can be
considered as a generalization of the no-boundary pure state to the case of the
microcanonical ensemble, and show that in view of a special reflection symmetry
its Wightman Green's functions satisfy Kubo-Martin-Schwinger periodicity
conditions which hold despite the nonequilibrium nature of the physical setup.
Rich analyticity structure in the complex plane of the time variable reveals
the combined Euclidean-Lorentzian evolution of the theory, which depending on
the properties of the initial density matrix can be interpreted as a decay of a
classically forbidden quantum state.",2309.03687v1
2009-10-03,Non-collinear spin-spiral phase for the uniform electron gas within Reduced-Density-Matrix-Functional Theory,"The non-collinear spin-spiral density wave of the uniform electron gas is
studied in the framework of Reduced-Density-Matrix-Functional Theory. For the
Hartree-Fock approximation, which can be obtained as a limiting case of
Reduced-Density-Matrix-Functional Theory, Overhauser showed a long time ago
that the paramagnetic state of the electron gas is unstable with respect to the
formation of charge or spin density waves. Here we not only present a detailed
numerical investigation of the spin-spiral density wave in the Hartree-Fock
approximation but also investigate the effects of correlations on the
spin-spiral density wave instability by means of a recently proposed
density-matrix functional.",0910.0534v1
2015-07-15,Minimum Density Hyperplanes,"Associating distinct groups of objects (clusters) with contiguous regions of
high probability density (high-density clusters), is central to many
statistical and machine learning approaches to the classification of unlabelled
data. We propose a novel hyperplane classifier for clustering and
semi-supervised classification which is motivated by this objective. The
proposed minimum density hyperplane minimises the integral of the empirical
probability density function along it, thereby avoiding intersection with high
density clusters. We show that the minimum density and the maximum margin
hyperplanes are asymptotically equivalent, thus linking this approach to
maximum margin clustering and semi-supervised support vector classifiers. We
propose a projection pursuit formulation of the associated optimisation problem
which allows us to find minimum density hyperplanes efficiently in practice,
and evaluate its performance on a range of benchmark datasets. The proposed
approach is found to be very competitive with state of the art methods for
clustering and semi-supervised classification.",1507.04201v3
2020-03-04,Parametrisations of relativistic energy density functionals with tensor couplings,"The relativistic density functional with minimal density dependent
nucleon-meson couplings for nuclei and nuclear matter is extended to include
tensor couplings of the nucleons to the vector mesons. The dependence of the
minimal couplings on either vector or scalar densities is explored. New
parametrisations are obtained by a fit to nuclear observables with
uncertainties that are determined self-consistently. The corresponding nuclear
matter parameters at saturation are determined including their uncertainties.
An improvement in the description of nuclear observables, in particular for
binding energies and diffraction radii, is found when tensor couplings are
considered, accompanied by an increase of the Dirac effective mass. The
equations of state for symmetric nuclear matter and pure neutron matter are
studied for all models. The density dependence of the nuclear symmetry energy,
the Dirac effective masses and scalar densities is explored. Problems at high
densities for parametrisations using a scalar density dependence of the
couplings are identified due to the rearrangement contributions in the scalar
self-energies that lead to vanishing Dirac effective masses.",2003.02085v2
2023-04-04,Denoising Diffusion Probabilistic Models to Predict the Density of Molecular Clouds,"We introduce the state-of-the-art deep learning Denoising Diffusion
Probabilistic Model (DDPM) as a method to infer the volume or number density of
giant molecular clouds (GMCs) from projected mass surface density maps. We
adopt magnetohydrodynamic simulations with different global magnetic field
strengths and large-scale dynamics, i.e., noncolliding and colliding GMCs. We
train a diffusion model on both mass surface density maps and their
corresponding mass-weighted number density maps from different viewing angles
for all the simulations. We compare the diffusion model performance with a more
traditional empirical two-component and three-component power-law fitting
method and with a more traditional neural network machine learning approach
(CASI-2D). We conclude that the diffusion model achieves an order of magnitude
improvement on the accuracy of predicting number density compared to that by
other methods. We apply the diffusion method to some example astronomical
column density maps of Taurus and the Infrared Dark Clouds (IRDCs) G28.37+0.07
and G35.39-0.33 to produce maps of their mean volume densities.",2304.01670v1
2004-03-31,Nonequilibrium electron transport using the density matrix renormalization group,"We extended the Density Matrix Renormalization Group method to study the real
time dynamics of interacting one dimensional spinless Fermi systems by applying
the full time evolution operator to an initial state. As an example we describe
the propagation of a density excitation in an interacting clean system and the
transport through an interacting nano structure.",0403759v1
2006-11-08,Optimum unambiguous discrimination of two mixed states and application to a class of similar states,"We study the measurement for the unambiguous discrimination of two mixed
quantum states that are described by density operators $\rho_1$ and $\rho_2$ of
rank d, the supports of which jointly span a 2d-dimensional Hilbert space.
Based on two conditions for the optimum measurement operators, and on a
canonical representation for the density operators of the states, two equations
are derived that allow the explicit construction of the optimum measurement,
provided that the expression for the fidelity of the states has a specific
simple form. For this case the problem is mathematically equivalent to
distinguishing pairs of pure states, even when the density operators are not
diagonal in the canonical representation. The equations are applied to the
optimum unambiguous discrimination of two mixed states that are similar states,
given by $\rho_2= U\rho_1 U^{\dag}$, and that belong to the class where the
unitary operator U can be decomposed into multiple rotations in the d mutually
orthogonal two-dimensional subspaces determined by the canonical
representation.",0611087v3
2013-02-06,Observation of an anomalous density-dependent energy gap of the $ν=5/2$ fractional quantum Hall state in the low density regime,"We have studied the $\nu=5/2$ fractional quantum Hall state in a
density-tunable sample at extremely low electron densities. For the densities
accessed in our experiment, the Landau level mixing parameter $\kappa$ spans
the $2.52<\kappa<2.82$ range. In the vicinity of $5.8 \times 10^{10}$~cm$^{-2}$
or $\kappa = 2.6$ an anomalously large change in the density dependence of the
energy gap is observed. Possible origins of such an anomaly are discussed,
including a topological phase transition in the $\nu=5/2$ fractional quantum
Hall state.",1302.1444v2
2008-07-28,Density-functional theory of nonequilibrium tunneling,"Nanoscale optoelectronics and molecular-electronics systems operate with
current injection and nonequilibrium tunneling, phenomena that challenge
consistent descriptions of the steady-state transport. The current affects the
electron-density variation and hence the inter- and intra-molecular bonding
which in turn determines the transport magnitude. The standard approach for
efficient characterization of steady-state tunneling combines ground-state
density functional theory (DFT) calculations (of an effective scattering
potential) with a Landauer-type formalism and ignores all actual many-body
scattering. The standard method also lacks a formal variational basis. This
paper formulates a Lippmann-Schwinger collision density functional theory
(LSC-DFT) for tunneling transport with full electron-electron interactions.
Quantum-kinetic (Dyson) equations are used for an exact reformulation that
expresses the variational noninteracting and interacting many-body scattering
T-matrices in terms of universal density functionals. The many-body
Lippmann-Schwinger (LS) variational principle defines an implicit equation for
the exact nonequilibrium density.",0807.4555v2
2024-02-21,Itinerant magnetism and magnetic polarons in the triangular lattice Hubbard model,"We use density matrix renormalization group to investigate the phase diagram
of the Fermi Hubbard model on a triangular lattice with densities above
half-filling, $1 \leq n < 2$. We discuss the important role of kinetic
magnetism and magnetic polarons. For strong interactions and low doublon
dopings, attractive interaction between polarons results in phase separation
between the fully polarized state at finite doping and the commensurate
spin-density wave state at half-filling. For intermediate interaction strength
and small doping, competition between antiferromagnetic superexchange and
kinetic magnetism gives rise to the incommensurate spin density wave (I-SDW)
phase. Fully polarized ferromagnetic (FPF) phase for weak interactions is
limited to dopings close to the van Hove singularity in the density of states.
With increasing interactions the FPF phase expands to lower dopings. For strong
interactions it reaches the low doping regime and is better understood as
arising from proliferation of Nagaoka-type ferromagnetic polarons. Other phases
that we find include a partially polarized phase, another type of I-SDW at high
densities, and M\""uller-Hartmann ferromagnetism close to the band insulating
regime.",2402.14074v1
2003-04-02,Color Ferromagnetism in Quark Matter,"We show a possibility that there exists a color ferromagnetic state in quark
matter, in which a color magnetic field is spontaneously generated. The state
arises between the hadronic state and the color superconducting state when the
density of quarks is varied.Although the state (Savvidy state) has been known
to involve unstablemodes of gluons, we show that the modes compose a quantum
Hall state to stabilize the ferromagnetic state. Such a quantum Hall statecan
arise only when quarks matter is present. We also show that the order of the
phase transition between the state andthe quark gluon plasma is of the first
order.",0304005v2
2014-05-17,Infrared properties of cuprates in the pseudogap state: A study of Mitrovic-Fiorucci and Sharapov-Carbotte scattering rates,"Frequency dependent scattering rate of generalized Drude model contains
important physics of the electronic structure and of scattering mechanisms. In
the present investigation, we study the frequency dependent scattering rate of
cuprates (Mitrovic-Fiorucci/ Sharapov-Carbotte scattering rate) in the
pseudogap phase using the non-constant energy dependent Yang-Rice-Zhang (YRZ)
density of states. First, with the energy dependent density of states, the
scattering rate gives the picture of depression formation coming from the
opening of the pseudogap. Second, the evolution of $1/\tau(\omega)$ with
temperature shows the increase of scattering rate with the temperature at lower
frequencies and the temperature independence of $1/\tau(\omega)$ at higher
frequencies. Third, the signature of thresholds due to boson density of states
and the electronic density of states also has been observed. These signatures
are qualitatively in accord with the experiments.",1405.4355v2
1994-10-07,Crossover from Spin-Density-Wave to Neel-like Ground state,"The characterization and evolution of a Spin Density Wave into the Quantum
Neel ground state is considered in the context of a weak coupling theory of the
half-filled Hubbard model. Magnetic properties obtained from this weak coupling
approach in one dimension compare favorably with exact results from Bethe
ansatz (BA). A study of the evolution of several length scales from weak to
strong coupling is also presented.",9410019v1
1996-08-07,Density of states for Bose-Einstein condensation in harmonic oscillator potentials,"We discuss how it is possible to obtain a reliable approximation for the
density of states for a system of particles in an anisotropic harmonic
oscillator potential. A direct application of the result to study Bose-Einstein
condensation of atomic gases in a potential trap can be given. In contrast to a
previous study, our method involves only analytic calculations.",9608032v1
1996-11-15,Interaction-induced oscillations of the tunneling density of states in a non-quantizing magnetic field,"We study tunneling into interacting disordered two-dimensional electron gas
in a non-quantizing magnetic field, which does not cause the standard de Haas--
van Alphen oscillations. Interaction induces a new type of oscillations in the
tunneling density of states with the characteristic period of cyclotron
quantum.",9611120v1
1998-10-13,Thermodynamic properties of spin-1/2 transverse XY chain with Dzyaloshinskii-Moriya interaction: Exact solution for correlated Lorentzian disorder,"We extend the consideration of the spin-1/2 transverse XY chain with
correlated Lorentzian disorder (Phys. Rev. B {\bf 55,} 14298 (1997)) for the
case of additional Dzyaloshinskii-Moriya interspin interaction. It is shown how
the averaged density of states can be calculated exactly. Results are presented
for the density of states and the transverse magnetization.",9810143v1
2000-07-21,Electron-electron interactions in graphene sheets,"The effects of the electron-electron interactions in a graphene layer are
investigated. It is shown that short range couplings are irrelevant, and scale
towards zero at low energies, due to the vanishing of density of states at the
Fermi level. Topological disorder enhances the density of states, and can lead
to instabilities. In the presence of sufficiently strong repulsive
interactions, p-wave superconductivity can emerge.",0007337v1
2002-08-16,A Diagonal Representation of Quantum Density Matrix Using q-Boson Oscillator Coherent States,"A q-analogue of Sudarshan's diagonal representation of the Quantum Mechanical
density matrix is obtained using q-boson coherent states. Earlier result of
Mehta and Sudarshan on the self reproducing property of rho(z',z) is also
generalized and a self-consistent self-reproducing kernel {K-tilde}(z',z) is
constructed.",0208128v1
2003-10-13,The thermodynamic limit of the Whitham equations,"The infinite-genus limit of the KdV-Whitham equations is derived. The limit
involves special scaling for the associated spectral surface such that the
integrated density of states remains finite as $N \to \infty$ (the
thermodynamic type limit). The limiting integro-differential system describes
slow evolution of the density of states and can be regarded as the kinetic
equation for a soliton gas.",0310014v1
2008-05-28,Reflectionless Herglotz functions and generalized Lyapunov exponents,"We study several related aspects of reflectionless Jacobi matrices. Our first
set of results deals with the singular part of reflectionless measures. We then
introduce and discuss Lyapunov exponents, density of states measures, and other
related quantities in a \textit{general} setting. This is related to the
previous material because the density of states measures are reflectionless on
certain sets.",0805.4439v1
2009-03-31,Lifshitz tails for the Interband Light Absorption Coefficient,"In this paper we consider the Interband Light Absorption Coefficient for
various models. We show that at the lower and upper edges of the spectrum the
Lifshitz tails behaviour of the density of states implies similar behaviour for
the ILAC at appropriate energies. The Lifshitz tails property is also exhibited
at some points corresponding to the internal band edges of the density of
states.",0903.5376v1
2009-07-26,Lower bound on the density of states for periodic Schrödinger operators,"We consider Schr\""odinger operators with smooth periodic potentials in
Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on
the density of states for large values of the spectral parameter.",0907.4465v1
2010-07-21,Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,"We measure the statistical distribution of the local density of optical
states (LDOS) on disordered semi-continuous metal films. We show that LDOS
fluctuations exhibit a maximum in a regime where fractal clusters dominate the
film surface. These large fluctuations are a signature of surface-plasmon
localization on the nanometer scale.",1007.3691v1
2012-06-25,Hölder Continuity of the Integrated Density of States for the Fibonacci Hamiltonian,"We prove H\""older continuity of the integrated density of states for the
Fibonacci Hamiltonian for any positive coupling, and obtain the asymptotics of
the H\""older exponents for large and small couplings.",1206.5561v1
2013-10-03,Integrated density of states for Poisson-Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket,"We prove the existence of the integrated density of states for subordinate
Brownian motions in presence of the Poissonian random potentials on the
Sierpi\'nski gasket.",1310.1027v2
2016-03-28,Transfer matrix approach to 1d random band matrices: density of states,"We study the special case of $n\times n$ 1D Gaussian Hermitian random band
matrices, when the covariance of the elements is determined by the matrix
$J=(-W^2\triangle+1)^{-1}$. Assuming that $n\ge CW\log W\gg 1$, we prove that
the averaged density of states coincides with the Wigner semicircle law up to
the correction of order $W^{-1}$.",1603.08476v1
2017-08-02,Multipartite separability of density matrices of graphs,"A new layers method is presented for multipartite separability of density
matrices from simple graphs. Full separability of tripartite states is studied
for graphs on degree symmetric premise. The models are generalized to
multipartite systems by presenting a class of fully separable states arising
from partially symmetric graphs.",1708.00883v2
2018-04-04,Luminescence and absorption in short period superlattices,"This paper applies analytical approximations for the luminescence of short
period semiconductor superlattices and analyses the low density regime,
demonstrating that the theory clearly connects with low density absorption with
ratios of oscillator strengths of bound and continuum states as expected from
the Elliott formula. A numerical study illustrates in detail the bleaching of
higher order bound state. The analytical expressions have potential for
systematic studies of controlled excitonic pathways characterized by THz
responses.",1804.01485v1
2016-07-21,Ground state energy density of the quantum harmonic oscillator,"The total energy of the ground state of the quantum harmonic oscillator is
obtained with minimal assumptions. The vacuum energy density of the universe is
derived and a cutoff frequency is obtained for the upper bound of the quantum
harmonic oscillator.",1608.06525v2
2019-09-23,The landscape law for the integrated density of states,"The present paper establishes non-asymptotic estimates from above and below
on the integrated density of states of the Schr\""odinger operator
$L=-\Delta+V$, using a counting function for the minima of the localization
landscape, a solution to the equation $Lu=1$.",1909.10558v2
2021-07-21,The density of states depends on the domain,"In this short note we demonstrate that the definition of the density of
states of a Schr\""{o}dinger operator with bounded potential in general depends
on the choice of the domain undergoing the thermodynamic limit.",2107.09828v1
2023-02-24,Derivation of the Weizsäcker Density Functional from Probability Theory,"We demonstrate that the Weizs\""acker potential is an exact term in the
universal functional in density functional theory (DFT) for the ground state of
a system with $N$ electrons. This proof uses no approximations or physical
arguments, and follows from the form of kinetic energy of the ground state and
probability theory. We also examine the form of the other terms in the kinetic
energy.",2302.12871v1
2002-12-31,Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay,"We determine the leading low-energy fall-off of the integrated density of
states of a magnetic Schroedinger operator with repulsive Poissonian random
potential in case its single impurity potential has a slow anisotropic decay at
infinity. This so-called magnetic Lifshits tail is shown to coincide with the
one of the corresponding classical integrated density of states.",0212078v1
2010-12-30,Exact ground state properties of the one-dimensional Coulomb gas,"The ground state properties of a single-component one-dimensional Coulomb gas
are investigated. We use Bose-Fermi mapping for the ground state wave function
which permits to solve the Fermi sign problem in the following respects (i) the
nodal surface is known, permitting exact calculations (ii) evaluation of
determinants is avoided, reducing the numerical complexity to that of a bosonic
system, thus allowing simulation of a large number of fermions. Due to the
mapping the energy and local properties in one-dimensional Coulomb systems are
exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground
state energy has been calculated in homogeneous and trapped geometries by using
the diffusion Monte Carlo method. We show that in the low-density Wigner
crystal limit an elementary low-lying excitation is a plasmon, which is to be
contrasted with the large-density ideal Fermi gas/Tonks-Girardeau limit, where
low lying excitations are phonons. Exact density profiles are confronted to the
ones calculated within the local density approximation which predicts a change
from a semicircular to inverted parabolic shape of the density profile as the
value of the charge is increased.",1101.0103v1
2019-12-04,Dissipative conductivity of a dirty superconductor with Dynes subgap states under a dc bias current up to the depairing current density,"We study the dissipative conductivity $\sigma_1$ of a dirty superconductor
with a finite Dynes parameter $\Gamma$ under a dc-biased weak time-dependent
field. The Usadel equation for the current-carrying state is solved to
calculate the pair potential, penetration depth, supercurrent density, and
quasiparticle spectrum. It is shown that, while the depairing current density
$j_d$ for $\Gamma=0$ is coincident with the Kupriyanov-Lukichev theory, a
finite $\Gamma$ decreases the superfluid density, resulting in a reduction of
$j_d$. The broadening of the peaks of the quasiparticle density of states
induced by a combination of a finite $\Gamma$ and a dc bias can reduce
$\sigma_1$ below that for the ideal dirty BCS superconductor with $\Gamma=0$,
while subgap states at Fermi level proportional to $\Gamma$ results in a
residual conductivity at $T\to 0$. We find the optimum combination of $\Gamma$
and the dc bias to minimize $\sigma_1$ by scanning all $\Gamma$ and all
currents up to $j_d$. By using the results, it is possible to improve $j_d$ and
reduce electromagnetic dissipation in various superconducting quantum devices.",1912.01822v1
2001-06-20,Comment on ``Critical current density from magnetization hysteresis data using the critical-state model'',"A recent paper [Physical Review {\bf B 64} 014508 (2001)] claims to present
an exact method to extract the critical current density J$_C$ from the M-H
hysteresis curve. We show that this claim appears unjustified.",0106391v1
1994-10-26,Continuously Diagonalized Density Operatorof Open Systems,"We showed several years ago that the density operator of Markovian open
systems can be diagonalized continuously in time. The resulting pure state jump
processes correspond to quantum trajectories proposed in recent quantum optics
calculations or, at fundamental level, to exact consistent histories.",9410037v1
1993-04-01,Two-dimensional Bose gas at low density,"We propose a new method to describe the interacting bose gas at zero
temperature. We use the decomposition of the logarithm of the wave function
into the irreducible $n$-point functions. We argue that in the low density
limit this expansion corresponds to the expansion of the ground-state energy in
powers of the small parameter. For three-dimensional system the correction to
the ground-state energy in density is reproduced. For two-dimensional dilute
bose gas the ground- state energy in the leading order in the parameter
$|\ln\a^2\rho|^{-1}$ where $\a$ is a scattering length is obtained.",9304001v1
1999-10-21,A semiclassical approach to the ground state and density oscillations of quantum dots,"A semiclassical Thomas-Fermi method, including a Weizs\""acker gradient term,
is implemented to describe ground states of two dimensional nanostructures of
arbitrary shape. Time dependent density oscillations are addressed in the same
spirit using the corresponding semiclassical time-dependent equations. The
validity of the approximations is tested, both for ground state and density
oscillations, comparing with the available microscopic Kohn-Sham solutions.",9910324v1
2000-12-18,The Non-Abelian Density Matrix Renormalization Group Algorithm,"We describe here the extension of the density matrix renormalization group
algorithm to the case where Hamiltonian has a non-Abelian global symmetry
group. The block states transform as irreducible representations of the
non-Abelian group. Since the representations are multi-dimensional, a single
block state in the new representation corresponds to multiple states of the
original density matrix renormalization group basis. We demonstrate the
usefulness of the construction via the one-dimensional Hubbard model as the
symmetry group is enlarged from $U(1) \times U(1)$, up to $SU(2) \times SU(2)$.",0012319v3
2001-08-13,Ground State Pressure and Energy Density of a Homogeneous Bose Gas in Two Dimensions,"We consider an interacting homogeneous Bose gas at zero temperature in two
spatial dimensions. The properties of the system can be calculated as an
expansion in powers of g, where g is the coupling constant. We calculate the
ground state pressure and the ground state energy density to second order in
the quantum loop expansion. The renormalization group is used to sum up leading
and subleading logarithms from all orders in perturbation theory. In the dilute
limit, the renormalization group improved pressure and energy density are
essentially expansions in powers of the T-matrix.",0108197v2
2002-06-02,Rippled state of double-layer quantum Hall systems,"The incommensurate phase of a bilayer quantum Hall state is found to have a
``rippled'' dipole charge density whenever the layers are unbalanced. This
tunable dipole-density-wave instability could be detected by sensitive
capacitance measurements and by anisotropic transport. We demonstrate this
explicitly by carrying out a Hartree-Fock calculation of the layer densities
and capacitance for a double-layer quantum Hall state at a total filling factor
of 1.",0206021v1
2003-12-31,Amorphous-like Density of Gap States in Single Crystal Pentacene,"We show that optical and electrical measurements on pentacene single crystals
can be used to extract the density of states in the HOMO-LUMO bandgap. It is
found that these highly purified crystals possess band tails broader than those
typically observed in inorganic amorphous solids. Results on field effect
transistors (FETs) fabricated from similar crystals are also compared. The FET
data imply that the gap state density is much larger within 5-10 nm of the gate
dielectric. These results are discussed in terms of both crystal phase domains
and structural disorder mechanisms.",0312722v1
2004-09-27,Competition Between Charge-Density Waves and Superconductivity in Striped Systems,"Switching on interchain coupling in a system of one-dimensional strongly
interacting chains often leads to an ordered state. Quite generally, there is a
competition between an insulating charge-density-wave and a superconducting
state. In the case of repulsive interactions, charge-density wave usually wins
over superconductivity. Here, we show that a suitable modulation in the form of
a period 4 bond-centered stripe can reverse this balance even in the repulsive
case and produce a superconducting state with relatively high temperature.",0409693v1
2005-10-12,Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime,"By minimizing the coupled mean-field energy functionals, we investigate the
ground-state properties of a rotating atomic boson-fermion mixture in a
two-dimensional parabolic trap. At high angular frequencies in the
mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic
condensate, and a finite number of degenerate fermions form the
maximum-density-droplet state. As the boson-fermion coupling constant
increases, the maximum density droplet develops into a lower-density state
associated with the phase separation, revealing characteristics of a
Landau-level structure.",0510301v2
2011-06-15,The Hartree-Fock phase diagram of the two-dimensional electron gas,"We calculate the ground state phase diagram of the homogeneous electron gas
in two dimensions within the Hartree-Fock approximation. At high density, we
find stable solutions, where the electronic charge and spin density form an
incommensurate crystal having more crystal sites than electrons, whereas the
commensurate Wigner crystal is favored at lower densities, rs> 1.22. Our
explicit calculations demonstrate that the homogeneous Fermi liquid state --
though being an exact stationary solution of the Hartree-Fock equations -- is
never the Hartree-Fock ground state of the electron gas.",1106.2939v2
2014-11-12,Local density of states in the superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br,"Low temperature scanning tunneling spectroscopy reveals the local density of
states of the organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br,
that was cut in-situ in ultra-high vacuum perpendicular to the superconducting
BEDT-TTF layers. The spectra confirm that superconductivity is confined to the
conducting BEDT-TTF layers, while the Cu[N(CN)$_2$]Br anion layers are
insulating. The density of states comprises a twofold superconducting gap,
which is attributed to the two separated bands crossing the Fermi surface.",1411.3181v1
2015-07-16,Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: application to silicon dioxide,"The liquid regime equation of state of silicon dioxide SiO$_2$ is calculated
via quantum molecular dynamics in the density range 5 to 15 g/cc and with
temperatures from 0.5 to 100 eV, including the $\alpha$-quartz and stishovite
phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density
functional theory (DFT), above 8 eV a new orbital-free DFT formulation,
presented here, based on matching Kohn-Sham DFT calculations is employed.
Recent experimental shock data is found to be in very good agreement with the
current results. Finally both experimental and simulation data are used in
constructing a new liquid regime equation of state table for SiO$_2$.",1507.04702v1
2018-02-07,Superfluid density of a photo-induced superconducting state,"Nonequilibrium conditions offer novel routes to superconductivity that are
not available at equilibrium. For example, by engineering nonequilibrium
electronic populations, pairing may develop between electrons in different
energy bands. A concrete proposal has been made to photo-induce
superconductivity in a semiconductor, where pairing occurs between electrons in
the conduction and valence bands, even for repulsive interactions. Here, we
calculate the superfluid density for such a nonequilibrium paired state, and
find it to be positive for repulsive interactions and interband pairing. The
positivity of the superfluid density implies the stability of the photo-induced
superconducting state as well as the existence of the Meissner effect.",1802.02593v1
2008-07-18,Exact low-temperature properties of a class of highly frustrated Hubbard models,"We study the repulsive Hubbard model both analytically and numerically on a
family of highly frustrated lattices which have one-electron states localized
on isolated trapping cells. We construct and count exact many-electron ground
states for a wide range of electron densities and obtain closed-form
expressions for the low-temperature thermodynamic quantities. Furthermore, we
find that saturated ferromagnetism is obtained only for sufficiently high
electron densities and large Hubbard repulsion $U$ while there is no finite
average moment in the ground states at lower densities.",0807.2991v2
2011-11-20,Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators,"We introduce and prove local Wegner estimates for continuous generalized
Anderson Hamiltonians, where the single-site random variables are independent
but not necessarily identically distributed. In particular, we get Wegner
estimates with a constant that goes to zero as we approach the bottom of the
spectrum. As an application, we show that the (differentiated) density of
states exhibits the same Lifshitz tails upper bound as the integrated density
of states.",1111.4674v2
2011-11-30,A New History-Driven Algorithm to Calculate the Density of States,"We present a new Monte Carlo algorithm applying a history-driven mechanism
for the calculation of the density of states for classical statistical models.
The new method is as efficient as the Wang-Landau method in sampling through
the energy range. With the new method, detailed balance is also naturally
satisfied in limit and the estimated density of state converges to the exact
value. The new method could be easily evolved into the multicanonical method to
achieve high accuracy.",1111.7059v1
2022-03-09,Ground and excited states of coupled exciton liquids in electron-hole quadrilayers,"Interlayer excitons are bound states of electrons and holes confined in
separate two-dimensional layers. Due to their repulsive dipolar interaction,
interlayer excitons can form a correlated liquid. If another electron-hole
bilayer is present, excitons from different bilayers can exhibit mutual
attraction. We study such a quadrilayer system by a hypernetted chain
formalism. We compute ground state energies, pair correlation functions, and
collective mode velocities as functions of the exciton densities. We estimate
the critical density for the transition to a paired biexciton phase. For a
strongly unbalanced (unequal density) system, the excitons in the more dilute
bilayer behave as polarons. We compute energies and effective masses of such
exciton-polarons.",2203.04504v1
2007-05-04,Phase transition in the two-component symmetric exclusion process with open boundaries,"We consider single-file diffusion in an open system with two species $A,B$ of
particles. At the boundaries we assume different reservoir densities which
drive the system into a non-equilibrium steady state. As a model we use an
one-dimensional two-component simple symmetric exclusion process with two
different hopping rates $D_A,D_B$ and open boundaries. For investigating the
dynamics in the hydrodynamic limit we derive a system of coupled non-linear
diffusion equations for the coarse-grained particle densities. The relaxation
of the initial density profile is analyzed by numerical integration. Exact
analytical expressions are obtained for the self-diffusion coefficients, which
turns out to be length-dependent, and for the stationary solution. In the
steady state we find a discontinuous boundary-induced phase transition as the
total exterior density gradient between the system boundaries is varied. At one
boundary a boundary layer develops inside which the current flows against the
local density gradient. Generically the width of the boundary layer and the
bulk density profiles do not depend on the two hopping rates. At the phase
transition line, however, the individual density profiles depend strongly on
the ratio $D_A/D_B$. Dynamic Monte Carlo simulation confirm our theoretical
predictions.",0705.0596v1
2007-05-07,Structure of the stationary state of the asymmetric target process,"We introduce a novel migration process, the target process. This process is
dual to the zero-range process (ZRP) in the sense that, while for the ZRP the
rate of transfer of a particle only depends on the occupation of the departure
site, it only depends on the occupation of the arrival site for the target
process. More precisely, duality associates to a given ZRP a unique target
process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of
a bias, both processes have the same stationary-state product measure. In this
work we focus our interest on the situation where the latter measure exhibits a
continuous condensation transition at some finite critical density $\rho_c$,
irrespective of the dimensionality. The novelty comes from the case of
asymmetric dynamics, where the target process has a nontrivial fluctuating
stationary state, whose characteristics depend on the dimensionality. In one
dimension, the system remains homogeneous at any finite density. An alternating
scenario however prevails in the high-density regime: typical configurations
consist of long alternating sequences of highly occupied and less occupied
sites. The local density of the latter is equal to $\rho_c$ and their
occupation distribution is critical. In dimension two and above, the asymmetric
target process exhibits a phase transition at a threshold density $\rho_0$ much
larger than $\rho_c$. The system is homogeneous at any density below $\rho_0$,
whereas for higher densities it exhibits an extended condensate elongated along
the direction of the mean current, on top of a critical background with density
$\rho_c$.",0705.0907v1
2021-03-10,Application of an ab-initio-inspired energy density functional to nuclei: impact of the effective mass and the slope of the symmetry energy on bulk and surface properties,"The YGLO (Yang-Grasso-Lacroix-Orsay) functional is applied for the first time
to investigate ground-state properties of different isotopic chains, from
Oxygen to Lead. Mean-field Hartree-Fock calculations are carried out to analyze
global trends for separation energies, binding energies, radii, neutron skins,
and density profiles. We have three objectives: i) we study whether this
functional leads to a reasonable description of ground-state properties
(despite the fact that it was not adjusted on nuclei) and we discuss the
associated limitations; ii) we investigate whether the correct description of
the low-density nuclear gas, which is the peculiarity of this functional, has
any relevant impact on predictions for nuclei; iii) we connect nuclear
energies, radii and density profiles with properties of the corresponding
equations of state of infinite matter. In particular, we identify a link
existing between the isoscalar effective mass and spatial properties in
neutron-deficient nuclei, namely proton radii and tails of proton densities. On
the other side, we show that the slope of the symmetry energy is connected with
spatial properties in neutron-rich nuclei: the slope computed at saturation
density is related to neutron skin thicknesses, as already well known, whereas
the slope calculated at lower densities is linked to the tails of neutron
densities. The YGLO effective mass turns out to be quite low. Directions to
improve this aspect are explored and suggested at the end of the manuscript.",2103.05996v2
2018-12-21,Optimization of flux-surface density variation in stellarator plasmas with respect to the transport of collisional impurities,"Avoiding impurity accumulation is a requirement for steady-state stellarator
operation. The accumulation of impurities can be heavily affected by variations
in their density on the flux-surface. Using recently derived semi-analytic
expressions for the transport of a collisional impurity species with high-$Z$
and flux-surface density-variation in the presence of a low-collisionality bulk
ion species, we numerically optimize the impurity density-variation on the
flux-surface to minimize the radial peaking factor of the impurities. These
optimized density-variations can reduce the core impurity density by $0.75^Z$
(with $Z$ the impurity charge number) in the Large Helical Device case
considered here, and by $0.89^Z$ in a Wendelstein 7-X standard configuration
case. On the other hand, when the same procedure is used to find
density-variations that maximize the peaking factor, it is notably increased
compared to the case with no density-variation. This highlights the potential
importance of measuring and controlling these variations in experiments.",1812.09194v2
2018-05-16,Geometric Phase using Diagonal Coherent State Representation,"Glauber-Sudarshan diagonal coherent state P-representation has been used to
determine geometric phase for non-classical states of light. For a given
density operator $\hat{\rho_1}$ of two mode optical beam, we evolve it in
complex projective ray space $(\cal R)$ to $\hat{\rho_2}$ and to $\hat{\rho_3}$
by changing its state of polarisation using unitary operator
$\mathrm{\hat{U}_p}(\theta)$. The diagonal coherent state basis has been
utilized to represent the density operators instead of fock state basis as in
the fock state basis the state vector in present work evolve under unitary
operator produe infinitely numerous terms which make the density operators very
messy to handle. This cumbersome situation can be easily avoided by using the
approach proposed above. The trace of the product of $\hat{\rho_1}$,
$\hat{\rho_2}$ and $\hat{\rho_3}$ is taken to get three vertex Bargmann
invariant. Argument of this gives the geometric phase which is represented in
terms of phase space variables containing a notion of symplectic area.",1805.06495v2
2020-05-23,Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States,"In a differential approach elaborated, we study the evolution of the
parameters of Gaussian, mixed, continuous variable density matrices, whose
dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of
the position and momentum operators or quadrature components. Specifically, we
obtain in generic form the differential equations for the covariance matrix,
the mean values, and the density matrix parameters of a multipartite Gaussian
state, unitarily evolving according to a Hamiltonian $\hat{H}$. We also present
the corresponding differential equations which describe the nonunitary
evolution of the subsystems. The resulting nonlinear equations are used to
solve the dynamics of the system instead of the Schr\""odinger equation. The
formalism elaborated allows us to define new specific invariant and
quasi-invariant states, as well as states with invariant covariance matrices,
i.e., states were only the mean values evolve according to the classical
Hamilton equations. By using density matrices in the position and in the
tomographic-probability representations, we study examples of these properties.
As examples, we present novel invariant states for the two-mode frequency
converter and quasi-invariant states for the bipartite parametric amplifier.",2005.11497v1
2023-06-02,Axis-symmetric Onsager Clustered States of Point Vortices in a Bounded Domain,"We study axis-symmetric Onsager clustered states of a neutral point vortex
system confined to a two-dimensional disc. Our analysis is based on the mean
field of bounded point vortices in the microcanonical ensemble. The clustered
vortex states are specified by the inverse temperature $\beta$ and the rotation
frequency $\omega$, which are the conjugate variables of energy $E$ and angular
momentum $L$, respectively. The formation of the axis-symmetric clustered
vortex states (azimuthal angle independent) involves the separating of vortices
with opposite circulation and the clustering of vortices with same circulation
around origin and edge. The state preserves $\rm SO(2)$ symmetry while breaks
$\mathbb Z_2$ symmetry. We find that, near the uniform state ($E=0$), the
rotation free state ($\omega=0$) emerges at particular values of $L^2/E$ and
$\beta$. At large energies, we obtain asymptotically exact vortex density
distributions, whose validity condition gives rise the lower bound of $\beta$
for the rotation free states. Noticeably, the obtained vortex density
distribution near the edge at large energies provides a novel exact vortex
density distribution for the corresponding chiral vortex system.",2306.01409v2
2008-11-07,Ground-state properties of interacting two-component Bose gases in a hard-wall trap,"We investigate ground-state properties of interacting two-component Bose
gases in a hard-wall trap using both the Bethe ansatz and exact numerical
diagonalization method. For equal intra- and inter-atomic interaction, the
system is exactly solvable. Thus the exact ground state wavefunction and
density distributions for the whole interacting regime can be obtained from the
Bethe ansatz solutions. Since the ground state is a degenerate state with total
spin S=N/2, the total density distribution are same for each degenerate state.
The total density distribution evolves from a Gauss-like Bose distribution to a
Fermi-like one as the repulsive interaction increases. The distribution of each
component is N_i/N of the total density distribution. This is approximately
true even in the experimental situation. In addition the numerical results show
that with the increase of interspecies interaction the distributions of two
Tonks-Girardeau gases exhibit composite fermionization crossover with each
component developing N peaks in the strongly interacting regime.",0811.1065v2
2012-07-16,When is a pure state of three qubits determined by its single-particle reduced density matrices?,"Using techniques from symplectic geometry, we prove that a pure state of
three qubits is up to local unitaries uniquely determined by its one-particle
reduced density matrices exactly when their ordered spectra belong to the
boundary of the, so called, Kirwan polytope. Otherwise, the states with given
reduced density matrices are parameterized, up to local unitary equivalence, by
two real variables. Given inevitable experimental imprecisions, this means that
already for three qubits a pure quantum state can never be reconstructed from
single-particle tomography. We moreover show that knowledge of the reduced
density matrices is always sufficient if one is given the additional promise
that the quantum state is not convertible to the Greenberger--Horne--Zeilinger
(GHZ) state by stochastic local operations and classical communication (SLOCC),
and discuss generalizations of our results to an arbitary number of qubits.",1207.3849v3
2002-03-01,On the density matrix of nonequilibrium steady-state statistical mechanics,"This paper derives a density matrix of the steady-state statistical mechanics
compatible with the steady-state thermodynamics proposed by Oono and Paniconi
[Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three
plausible basic assumptions for uniform steady states: (i) equivalence between
any two subsystems of the total, (ii) statistical independence between any two
subsystems, and (iii) additivity of energy. With a suitable definition of
energy, it is then shown that uniform steady states driven by mechanical forces
may be described by the Gibbs distribution.",0203005v1
2002-09-05,Lewenstein-Sanpera Decomposition for $2\otimes 2$ Systems,"As it is well known, every bipartite $2\otimes 2$ density matrix can be
obtained from Bell decomposable states via local quantum operations and
classical communications (LQCC). Using this fact, the Lewenstein-Sanpera
decomposition of an arbitrary bipartite $2\otimes 2$ density matrix has been
obtained through LQCC action upon Lewenstein-Sanpera decomposition of Bell
decomposable states of $2\otimes 2$ quantum systems, where the product states
introduced by Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245
(1998)] form the best separable approximation ensemble for Bell decomposable
states. It is shown that in these systems the average concurrence of the
Lewenstein-Sanpera decomposition is equal to the concurrence of these states.",0209045v1
2009-08-19,Density functional investigations of defect induced mid-gap states in graphane,"We have carried out ab initio electronic structure calculations on graphane
(hydrogenated graphene) with single and double vacancy defects. Our analysis of
the density of states reveal that such vacancies induce the mid gap states and
modify the band gap. The induced states are due to the unpaired electrons on
carbon atoms. Interestingly the placement and the number of such states is
found to be sensitive to the distance between the vacancies. Furthermore we
also found that in most of the cases the vacancies induce a local magnetic
moment.",0908.2730v1
2010-11-09,Surface density of states and topological edge states in non-centrosymmetric superconductors,"We study Andreev bound state (ABS) and surface density of state (SDOS) of
non-centrosymmetric superconductor where spin-singlet $d$-wave pairing mixes
with spin-triplet $p$ (or $f)$-wave one by spin-orbit coupling. For $d_{xy} +
p$-wave pairing, ABS appears as a zero energy state. The present ABS is a
Majorana edge mode preserving the time reversal symmetry. We calculate
topological invariant number and discuss the relevance to a single Majorana
edge mode. In the presence of the Majorana edge mode, the SDOS depends strongly
on the direction of the Zeeman field.",1011.2002v1
2018-09-08,Gapless Triplet Superconductivity in Magnetically Polarized Media,"We reveal that in a magnetically polarized medium, a specific commensurate
triplet pair density wave (TPDW) superconducting (SC) state, the staggered
d-wave $\Pi$-triplet state, may coexist with homogeneous triplet SC states and
even dominate eliminating them under generic conditions. When only this TPDW SC
state is present, we have the remarkable phenomenon of gapless
superconductivity. This may explain part of the difficulties in the realization
of the engineered localized Majorana fermion modes for topological quantum
computation. We point out qualitative characteristics of the tunneling density
of states, specific heat and charge susceptibility that identify the accessible
triplet SC regimes in a spinless medium.",1809.02879v1
2005-10-23,Bayesian prediction of the Gaussian states from n sample,"Recently quantum prediction problem was proposed in the Bayesian framework.
It is shown that Bayesian predictive density operators are the best predictive
density operators when we evaluate them by using the average relative entropy
based on a prior.As an illustrative example, we treat the Gaussian states
family adopting the Gaussian distribution as a prior and give the Bayesian
predictive density operator with the heterodyne measurement fixed. We show that
it is better than the plug-in predictive density operator based on the maximum
likelihood estimate by calculating each average relative entropy.",0510176v2
1995-02-22,Ground-State Dynamical Correlation Functions: An Approach from Density Matrix Renormalization Group Method,"A numerical approach to ground-state dynamical correlation functions from
Density Matrix Renormalization Group (DMRG) is developed. Using sum rules,
moments of a dynamic correlation function can be calculated with DMRG, and with
the moments the dynamic correlation function can be obtained by the maximum
entropy method. We apply this method to one-dimensional spinless fermion
system, which can be converted to the spin 1/2 Heisenberg model in a special
case. The dynamical density-density correlation function is obtained.",9502091v1
2000-08-03,Exchange Frequencies in the 2d Wigner crystal,"Using Path Integral Monte Carlo we have calculated exchange frequencies as
electrons undergo ring exchanges in a ``clean'' 2d Wigner crystal as a function
of density. The results show agreement with WKB calculations at very low
density, but show a more rapid increase with density near melting. Remarkably,
the exchange Hamiltonian closely resembles the measured exchanges in 2d He.
Using the resulting multi-spin exchange model we find the spin Hamiltonian for
r_s \leq 175 \pm 10 is a frustrated antiferromagnetic; its likely ground state
is a spin liquid. For lower density the ground state will be ferromagnetic.",0008062v1
1999-07-19,Negative energy density for a Dirac-Maxwell field,"It is well known that there can be negative energy densities in quantum field
theory. Most of the work done in this area has involved free non-interacting
systems. In this paper we show how a quantum state with negative energy density
can be formulated for a Dirac field interacting with an Electromagnetic field.
It will be shown that, for this case, there exist quantum states whose average
energy density over an arbitrary volume is a negative number with an
arbitrarily large magnitude.",9907060v1
2008-08-06,The Parts Determine the Whole except for n-Qubit Greenberger-Horne-Zeilinger States,"The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their
local unitary equivalents are the only pure states of n qubits that are not
uniquely determined (among arbitrary states, pure or mixed) by their reduced
density matrices of n-1 qubits. Thus, the generalized GHZ states are the only
ones containing information at the n-party level.",0808.0859v1
2012-10-16,Quantum entanglement and spin control in silicon nanocrystal,"Selective coherence control and electrically mediated exchange coupling of
single electron spin between triplet and singlet states using numerically
derived optimal control of proton pulses is demonstrated. We obtained spatial
confinement below size of the Bohr radius for proton spin chain FWHM. Precise
manipulation of individual spins and polarization of electron spin states are
analyzed via proton induced emission and controlled population of energy shells
in pure 29Si nanocrystal. Entangled quantum states of channeled proton
trajectories are mapped in transverse and angular phase space of 29Si axial
channel alignment in order to avoid transversal excitations. Proton density and
proton energy as impact parameter functions are characterized in single
particle density matrix via discretization of diagonal and nearest off-diagonal
elements. We combined high field and low densities (1 MeV/92 nm) to create
inseparable quantum state by superimposing the hyperpolarizationed proton spin
chain with electron spin of 29Si. Quantum discretization of density of states
(DOS) was performed by the Monte Carlo simulation method using numerical
solutions of proton equations of motion. Distribution of gaussian coherent
states is obtained by continuous modulation of individual spin phase and
amplitude. Obtained results allow precise engineering and faithful mapping of
spin states. This would provide the effective quantum key distribution (QKD)
and transmission of quantum information over remote distances between quantum
memory centers for scalable quantum communication network. Furthermore,
obtained results give insights in application of channeled protons subatomic
microscopy as a complete versatile scanning-probe system capable of both
quantum engineering of charged particle states and characterization of quantum
states below diffraction limit linear and in-depth resolution.",1210.4564v1
2004-03-02,Towards Density Functional Calculations from Nuclear Forces,"We propose a method for microscopic calculations of nuclear ground-state
properties in the framework of density functional theory. We discuss how the
density functional is equivalent to the effective action for the density,
thereby establishing a constructive framework for density functional
calculations from nuclear forces. The presented approach starts from
non-interacting nucleons in a background potential (a simple approximation for
the mean field). The nuclear forces are then gradually turned on, while the
background potential is removed. The evolution equation yields the ground-state
energy and density of a system of interacting nucleons, including
exchange-correlations beyond the RPA approximation. The method can start from
non-local low momentum (V_{low k}) or chiral interactions.",0403011v1
2021-03-25,Max Cuts in Triangle-free Graphs,"A well-known conjecture by Erd\H{o}s states that every triangle-free graph on
$n$ vertices can be made bipartite by removing at most $n^2/25$ edges. This
conjecture was known for graphs with edge density at least $0.4$ and edge
density at most $0.172$. Here, we will extend the edge density for which this
conjecture is true; we prove the conjecture for graphs with edge density at
most $0.2486$ and for graphs with edge density at least $0.3197$. Further, we
prove that every triangle-free graph can be made bipartite by removing at most
$n^2/23.5$ edges improving the previously best bound of $n^2/18$.",2103.14179v1
2018-06-30,Entanglement of extremal density matrices of 2-qubit Hamiltonian with Kramers degeneracy,"We establish a novel procedure to analyze the entanglement properties of
extremal density matrices depending on the parameters of a finite dimensional
Hamiltonian. It was applied to a general 2-qubit Hamiltonian which could
exhibit Kramers degeneracy. This is done through the extremal density matrix
formalism, which allows to extend the conventional variational principle to
mixed states. By applying the positive partial transpose criterion in terms of
the Correlation and Schlienz-Mahler matrices on the extremal density matrices,
we demonstrate that it is possible to reach both pure and mixed entangled
states, changing properly the parameters of the Hamiltonian. For time-reversal
invariant Hamiltonians, the extremal pure states can be entangled or not and we
prove that they are not time-reversal invariants. For extremal mixed states we
have in general 5 possible cases: three of them are entangled and the other two
separable.",1807.00227v1
2019-05-14,Magnetic phase diagram of the infinite-U Hubbard model with nearest- and next nearest-neighbor hoppings,"We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with
nearest (t) and next-nearest (t') neighbor hoppings by means of the
density-matrix renormalization group algorithm. In particular, we analyze the
stability of the Nagaoka state for several values of t' when we vary the
electron density $(\rho)$ from half-filling to the low-density limit. We build
the two-dimensional phase diagram, where the fully spin-polarized and
paramagnetic states prevail. We find that the inclusion of a non-frustrating
next nearest neighbor hopping stabilizes the fully spin-polarized phase up
until |t'/t|=0.5. Surprisingly, for this value of t', the ground state is fully
spin-polarized for almost any electron density 1 $\gtrsim \rho \gtrsim$ 0,
connecting the Nagaoka state to itinerant ferromagnetism at low density. Also,
we find that the previously found checkerboard insulator phase at t'=0 and
$\rho$=0.75 is unstable against t'.",1905.05838v1
2023-05-24,Transport phenomena of TiCoSb: Defects induced modification in structure and density of states,"TiCoSb1+x (x=0.0, 0.01, 0.02, 0.03, 0.04, 0.06) samples have been
synthesized, employing solid state reaction method followed by arc menting.
Theoretical calculations, using Density Functional Theory (DFT) have been
performed to estimate band structure and density of states (DOS). Further,
energitic calculations, using first principle have been carried out to reveal
the formation energy for vacancy, interstitial, anti-site defects. Detail
structural calculation, employing Rietveld refinement reveals the presence of
embedded phases, vacancy and interstitial atom, which is also supported by the
theoretical calculations. Lattice strain, crystalline size and dislocation
density have been estimated by Williamson-Hall and modified Williamson-Hall
methods. Thermal variation of resistivity [\r{ho}(T)] and thermopower [S(T)]
have been explained using Mott equation and density of states (DOS)
modification near the Fermi surface due to Co vancancy and embedded phases.
Figure of merit (ZT) has been calculated and 4 to 5 times higher ZT for TiCoSb
than earlier reported value is obtained at room temperature.",2305.15303v1
2023-06-09,Ordering in SU(4)-symmetric model of AA bilayer graphene,"We examine possible ordered states of AA stacked bilayer graphene arising due
to electron-electron coupling. We show that under certain assumptions the
Hamiltonian of the system possesses an SU(4) symmetry. The multicomponent order
parameter is described by a $4\times4$ matrix $\hat{Q}$, for which a mean-field
self-consistency equation is derived. This equation allows Hermitian and
non-Hermitian solutions. Hermitian solutions can be grouped into three
topologically-distinct classes. First class corresponds to the charge density
wave. Second class includes spin density wave, valley density wave, and
spin-valley density wave. An ordered state in the third class is a combination
of all the aforementioned density-wave types. For anti-Hermitian $\hat{Q}$ the
ordered states are characterized by spontaneous inter-layer loop currents
flowing in the bilayer. Depending on the topological class of the solution
these currents can carry charge, spin, valley, and spin-valley quanta. We also
discuss the special case when matrix $\hat{Q}$ is not Hermitian and not
anti-Hermitian. Utility and weak points of the proposed SU(4)-based
classification scheme of the ordered states are analyzed.",2306.05796v2
2007-11-01,Classification of quantum channels of information transfer,"Classification of states of quantum channels of information transfer is built
on the basis of unreducible representations of qubit state space group of
symmetry and properties of density matrix spectrum. It is shown that pure
disentangled states form two-dimensional surface, and the reason of state
disentanglement is in degeneration of non-zero density matrix eigenvalues",0711.0217v1
2003-11-12,Is the dynamics of open quantum systems always linear?,"We study the influence of the preparation of an open quantum system on its
reduced time evolution. In contrast to the frequently considered case of an
initial preparation where the total density matrix factorizes into a product of
a system density matrix and a bath density matrix the time evolution generally
is no longer governed by a linear map nor is this map affine. Put differently,
the evolution is truly nonlinear and cannot be cast into the form of a linear
map plus a term that is independent of the initial density matrix of the open
quantum system. As a consequence, the inhomogeneity that emerges in formally
exact generalized master equations is in fact a nonlinear term that vanishes
for a factorizing initial state. The general results are elucidated with the
example of two interacting spins prepared at thermal equilibrium with one spin
subjected to an external field. The second spin represents the environment. The
field allows the preparation of mixed density matrices of the first spin that
can be represented as a convex combination of two limiting pure states, i.e.
the preparable reduced density matrices make up a convex set. Moreover, the map
from these reduced density matrices onto the corresponding density matrices of
the total system is affine only for vanishing coupling between the spins. In
general, the set of the accessible total density matrices is nonconvex.",0311077v2
2016-03-29,Light-front representation of chiral dynamics with Delta isobar and large-N_c relations,"Transverse densities describe the spatial distribution of electromagnetic
current in the nucleon at fixed light-front time. At peripheral distances b =
O(M_pi^{-1}) the densities are governed by chiral dynamics and can be
calculated model-independently using chiral effective field theory (EFT).
Recent work has shown that the EFT results can be represented in
first-quantized form, as overlap integrals of chiral light-front wave functions
describing the transition of the nucleon to soft-pion-nucleon intermediate
states, resulting in a quantum-mechanical picture of the peripheral transverse
densities. We now extend this representation to include intermediate states
with Delta isobars and implement relations based on the large-N_c limit of QCD.
We derive the wave function overlap formulas for the Delta contributions to the
peripheral transverse densities by way of a three-dimensional reduction of
relativistic chiral EFT expressions. Our procedure effectively maintains
rotational invariance and avoids the ambiguities with higher-spin particles in
the light-front time-ordered approach. We study the interplay of pi-N and
pi-Delta intermediate states in the quantum-mechanical picture of the densities
in a transversely polarized nucleon. We show that the correct N_c-scaling of
the charge and magnetization densities emerges as the result of the particular
combination of currents generated by intermediate states with degenerate N and
Delta. The off-shell behavior of the chiral EFT is summarized in contact terms
and can be studied easily. The methods developed here can be applied to other
peripheral densities and to moments of the nucleon's generalized parton
distributions.",1603.08881v1
2004-03-04,Cosmic Coincidence with a new Type of Dark Matter,"A field theory is proposed where the regular fermionic matter and the dark
fermionic matter are different states of the same ""primordial"" fermion fields.
In regime of the fermion densities typical for normal particle physics, the
primordial fermions split into three families identified with regular fermions.
When fermion energy density becomes comparable with dark energy density, the
theory allows new type of states. The possibility of such Cosmo-Low Energy
Physics (CLEP) states is demonstrated by means of solutions of the field theory
equations describing FRW universe filled by homogeneous scalar field and
uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are
drawn into cosmological expansion by means of dynamically changing their own
parameters. One of the features of the fermions in CLEP state is that in the
late time universe their masses increase as a^{3/2} (a=a(t) is the scale
factor). The energy density of the cold dark matter consisting of neutrinos in
CLEP state scales as a sort of dark energy; this cold dark matter possesses
negative pressure and for the late time universe its equation of state
approaches that of the cosmological constant. The total energy density of such
universe is less than it would be in the universe free of fermionic matter at
all. The (quintessence) scalar field is coupled to dark matter but its coupling
to regular fermionic matter appears to be extremely strongly suppressed.",0403054v1
2019-06-04,Photoinduced hidden CDW state and relaxation dynamics of 1T-TaS_2 probed by time-resolved terahertz spectroscopy,"The dynamical properties of single crystal 1T-TaS$_{2}$ are investigated both
in commensurate charge density wave state (CCDW state) and hidden charge
density wave state (HCDW state). We develop a useful criterion in time-domain
transmission terahertz measurement to judge whether the compound is driven into
a metastable state or still in its virgin state. An increase of terahertz
conductivity by two orders of magnitude from CCDW state to HCDW state is
obtained by taking account of the penetration depth mismatch, which is in
agreement with reported \emph{dc} transport measurement. Upon weak pumping,
only transient processes with rapid decay dynamics are triggered in both CCDW
and HCDW states. We compare the conductivity increases in terahertz frequency
range between transient and HCDW states and suggest that fluctuated metallic
domain walls may develop in the transient states.",1906.01500v1
2024-01-03,Confinement-driven state transition and bistability in schooling fish,"We investigate the impact of confinement density (i.e the number of
individuals in a group per unit area of available space) on transitions from
polarized to milling state, using groups of rummy-nose tetrafish (Hemigrammus
rhodostomus) under controlled experimental conditions. We demonstrate for the
first time a continuous state transition controlled by confinement density in a
group of live animals. During this transition, the school exhibits a bistable
state, wherein both polarization and milling states coexist, with the group
randomly alternating between them. A simple two-state Markov process describes
the observed transition remarkably well. Importantly, the confinement density
influences the statistics of this bistability, shaping the distribution of
transition times between states. Our findings suggest that confinement plays a
crucial role in state transitions for moving animal groups, and, more
generally, they constitute a solid experimental benchmark for active matter
models of macroscopic, self-propelled, confined agents.",2401.01850v1
2020-05-12,London dispersion forces without density distortion: a path to first principles inclusion in density functional theory,"We analyse a path to construct density functionals for the dispersion
interaction energy from an expression in terms of the ground state densities
and exchange-correlation holes of the isolated fragments. The expression is
based on a constrained search formalism for a supramolecular wavefunction that
is forced to leave the diagonal of the many-body density matrix of each
fragment unchanged, and is exact for the interaction between one-electron
densities. We discuss several aspects: the needed features a density functional
approximation for the exchange-correlation holes of the monomers should have,
the optimal choice of the one-electron basis needed (named ""dispersals""), and
the functional derivative with respect to monomer density variations.",2005.05900v2
2023-06-01,Anomaly Detection with Variance Stabilized Density Estimation,"Density estimation based anomaly detection schemes typically model anomalies
as examples that reside in low-density regions. We propose a modified density
estimation problem and demonstrate its effectiveness for anomaly detection.
Specifically, we assume the density function of normal samples is uniform in
some compact domain. This assumption implies the density function is more
stable (with lower variance) around normal samples than anomalies. We first
corroborate this assumption empirically using a wide range of real-world data.
Then, we design a variance stabilized density estimation problem for maximizing
the likelihood of the observed samples while minimizing the variance of the
density around normal samples. We introduce an ensemble of autoregressive
models to learn the variance stabilized distribution. Finally, we perform an
extensive benchmark with 52 datasets demonstrating that our method leads to
state-of-the-art results while alleviating the need for data-specific
hyperparameter tuning.",2306.00582v1
2019-09-05,Accurate real-time evolution of electron densities and ground-state properties from generalized Kohn-Sham theory,"The exact static and time-dependent Kohn-Sham (KS) exchange-correlation (xc)
potential is extremely challenging to approximate as it is a local
multiplicative potential that depends on the electron density everywhere in the
system. The KS approach can be generalised by allowing part of the potential to
be spatially nonlocal. We take this nonlocal part to be that of unrestricted
Hartree-Fock theory. The additional local correlation potential in principle
ensures that the single-particle density exactly equals the many-body density.
In our case, the local correlation potential is predominantly nearsighted in
its dependence on the density and hence an (adiabatic) local density
approximation to this potential yields accurate ground-state properties and
real-time densities for one-dimensional test systems.",1909.02510v2
2014-07-09,Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study,"We develop an energy density matrix that parallels the one-body reduced
density matrix (1RDM) for many-body quantum systems. Just as the density matrix
gives access to the number density and occupation numbers, the energy density
matrix yields the energy density and orbital occupation energies. The
eigenvectors of the matrix provide a natural orbital partitioning of the energy
density while the eigenvalues comprise a single particle energy spectrum
obeying a total energy sum rule. For mean-field systems the energy density
matrix recovers the exact spectrum. When correlation becomes important, the
occupation energies resemble quasiparticle energies in some respects. We
explore the occupation energy spectrum for the finite 3D homogeneous electron
gas in the metallic regime and an isolated oxygen atom with ground state
quantum Monte Carlo techniques implemented in the QMCPACK simulation code. The
occupation energy spectrum for the homogeneous electron gas can be described by
an effective mass below the Fermi level. Above the Fermi level evanescent
behavior in the occupation energies is observed in similar fashion to the
occupation numbers of the 1RDM. A direct comparison with total energy
differences shows a quantitative connection between the occupation energies and
electron addition and removal energies for the electron gas. For the oxygen
atom, the association between the ground state occupation energies and particle
addition and removal energies becomes only qualitative. The energy density
matrix provides a new avenue for describing energetics with quantum Monte Carlo
methods which have traditionally been limited to total energies.",1407.2558v1
2013-03-01,The NDL Equation of State for Supernova Simulations,"We present an updated and improved equation of state (which we call the NDL
EoS) for use in neutron-star structure and supernova simulations. This EoS is
based upon a framework originally developed by Bowers & Wilson, but there are
numerous changes. Among them are: (1) a reformulation in the context of density
functional theory; (2) the possibility of the formation of material with a net
proton excess (Ye > 0.5); (3) an improved treatment of the nuclear statistical
equilibrium and the transition to heavy nuclei as the density approaches
nuclear matter density; (4) an improved treatment of the effects of pions in
the regime above nuclear matter density including the incorporation of all the
known mesonic and baryonic states at high temperature; (5) the effects of
3-body nuclear forces at high densities; and (6) the possibility of a
first-order or crossover transition to a QCD chiral symmetry restoration and
deconfinement phase at densities above nuclear matter density. This paper
details the physics of, and constraints on, this new EoS and describes its
implementation in numerical simulations. We show comparisons of this EoS with
other equations of state commonly used in supernova collapse simulations.",1303.0064v1
2003-11-08,Topological quantization of boundary forces and the integrated density of states,"For quantum systems described by Schr\""odinger operators on the half-space
$\RR^{d-1}\times\RR^{leq 0}$ the boundary force per unit area and unit energy
is topologically quantised provided the Fermi energy lies in a gap of the bulk
spectrum. Under this condition it is also equal to the integrated density of
states at the Fermi energy.",0311187v1
2005-02-01,Spatio-temporal conjecture for diffusion,"We present here a conjecture about the equivalence between the noise density
of states of a system governed by a generalized Langevin equation and the
fluctuation in the energy density of states in a Hamiltonian system. We present
evidence of this for a disordered Heisenberg system.",0502038v1
2005-11-14,Equation of state from lattice QCD,"Recent results on the equation of state from lattice QCD are reviewed. The
lattice technique and previous results are shortly discussed. New results for
physical quark masses and two sets of lattice spacings are presented. The
pressure, energy density, entropy density, speed of sound and quark number
susceptibilities are determined.",0511166v1
2002-08-18,Discontinuities of the integrated density of states for random operators on Delone sets,"Despite all the analogies with ""usual random"" models, tight binding operators
for quasicrystals exhibit a feature which clearly distinguishes them from the
former: the integrated density of states may be discontinuous. This phenomenon
is identified as a local effect, due to occurrence of eigenfunctions with
bounded support.",0208027v1
2009-05-06,Phonon spectroscopy through the electronic density of states in graphene,"We study how phonon structure manifests itself in the electronic density of
states of graphene. A procedure for extracting the value of the electron-phonon
renormalization $\lambda$ is developed. In addition, we identify direct phonon
structures. With increasing doping, these structures, along with $\lambda$,
grow in amplitude and no longer display particle-hole symmetry.",0905.0894v1
2012-09-20,Sampling the density of states,"It is shown that the algorithm introduced in [1] and conceived to deal with
continuous degrees of freedom models is well suited to compute the density of
states in models with a discrete energy spectrum too. The q=10 D=2 Potts model
is considered as a test case, and it is shown that using the Maxwell
construction the interface free energy can be obtained, in the thermodynamic
limit, with a good degree of accuracy.",1209.4443v1
2022-04-19,Smoothness of integrated density of states of the Anderson model on Bethe lattice in high disorder,"In this work we consider the Anderson model on Bethe lattice and prove that
the integrated density of states (IDS) is as smooth as the single site
distribution (SSD), in high disorder",2204.08660v2
1994-03-30,Asymptotic Level State Density for Parabosonic Strings,"Making use of some results concerning the theory of partitions, relevant in
number theory, the complete asymptotic behavior, for large $n$, of the level
density of states for a parabosonic string is derived. It is also pointed out
the similarity between parabosonic strings and membranes.",9403184v1
2006-12-13,What is the natural scale for a Lévy process in modelling term structure of interest rates?,"This paper gives examples of explicit arbitrage-free term structure models
with L\'evy jumps via state price density approach. By generalizing quadratic
Gaussian models, it is found that the probability density function of a L\'evy
process is a ""natural"" scale for the process to be the state variable of a
market.",0612341v1
2005-03-03,Differential geometry of density states,"We consider a geometrization, i.e., we identify geometrical structures, for
the space of density states of a quantum system. We also provide few comments
on a possible application of this geometrization for composite systems.",0503041v2
2009-03-01,Excitonic spin density wave state in iron pnictides,"We examine the appearance of a spin density wave in the FeAs parent compounds
due to an excitonic instability. Using a realistic four-band model, we show
that the magnetic state depends very sensitively upon the details of the band
structure. We demonstrate that an orthorhombic distortion of the crystal
enhances the stability of the antiferromagnetic order.",0903.0124v1
2010-09-10,The Integrated Density of States for the Wilson Dirac Operator,"It is shown that gauge field-dependent fermion Dirac operators from lattice
QCD form an ergodic operator family in the probabilistic sense, provided the
gauge field is an ergodic random field. As a consequence, the integrated
density of states of such Dirac operators in the thermodynamic limit exists and
is almost surely independent of the chosen gauge field configuration.",1009.1949v2
2010-12-02,Lipschitz-continuity of the integrated density of states for Gaussian random potentials,"The integrated density of states of a Schroedinger operator with random
potential given by a homogeneous Gaussian field whose covariance function is
continuous, compactly supported and has positive mean, is locally uniformly
Lipschitz-continuous. This is proven using a Wegner estimate.",1012.0393v2
2016-05-19,Fluctuation of density of states for 1d Schrödinger operators,"We consider the 1d Schr\""odinger operator with random decaying potential and
compute the 2nd term asymptotics of the density of states, which shows
substantial differences between the cases $\alpha > \frac 12$, $\alpha < \frac
12$ and $\alpha = \frac 12$.",1605.06030v2
2005-09-14,Physical Purification of Quantum States,"We introduce the concept of a physical process that purifies a mixed quantum
state, taken from a set of states, and investigate the conditions under which
such a purification map exists. Here, a purification of a mixed quantum state
is a pure state in a higher-dimensional Hilbert space, the reduced density
matrix of which is identical to the original state. We characterize all sets of
mixed quantum states, for which perfect purification is possible. Surprisingly,
some sets of two non-commuting states are among them. Furthermore, we
investigate the possibility of performing an imperfect purification.",0509100v3
2017-11-27,Partition of unity with mixed quantum states,"The completeness of quantum state space, is usually expressed as
\sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states
(basis). Density matrix |m><m| describes a pure quantum state. In this paper,
by virtue of the summation method within the normally ordered product of
operators we propose and show that the completeness relation can also be
represented or partitioned in terms of some mixed states, such as binomial
states and negative binomial states. Thus the view on the structure of Fock
space is widen and the connotation of Fock space is enriched. See the matter in
this sight, experimentalists may have interests to prepare the binomial- and
negative binomial states.",1711.09519v1
2002-07-18,The power of reduced quantum states,"In a system of n quantum particles, we define a measure of the degree of
irreducible n-way correlation, by which we mean the correlation that cannot be
accounted for by looking at the states of (n-1) particles. In the case of
almost all pure states of three qubits we show that there is no such
correlation: almost every pure state of three qubits is completely determined
by its two-particle reduced density matrices.",0207109v1
1999-08-23,Tails of Localized Density of States of Two-dimensional Dirac Fermions,"The density of states of Dirac fermions with a random mass on a
two-dimensional lattice is considered. We give the explicit asymptotic form of
the single-electron density of states as a function of both energy and
(average) Dirac mass, in the regime where all states are localized. We make use
of a weak-disorder expansion in the parameter g/m^2, where g is the strength of
disorder and m the average Dirac mass for the case in which the evaluation of
the (supersymmetric) integrals corresponds to non-uniform solutions of the
saddle point equation. The resulting density of states has tails which deviate
from the typical pure Gaussian form by an analytic prefactor.",9908318v1
2005-02-03,Local density of states at polygonal boundaries of d-wave superconductors,"Besides the well-known existence of Andreev bound states, the zero-energy
local density of states at the boundary of a d-wave superconductor strongly
depends on the boundary geometry itself. In this work, we examine the influence
of both a simple wedge-shaped boundary geometry and a more complicated
polygonal or faceted boundary structure on the local density of states. For a
wedge-shaped boundary geometry, we find oscillations of the zero-energy density
of states in the corner of the wedge, depending on the opening angle of the
wedge. Furthermore, we study the influence of a single Abrikosov vortex
situated near a boundary, which is of either macroscopic or microscopic
roughness.",0502073v1
2012-07-20,Energy of natural interface modes,"The paper is devoted to the thermodynamics of normal surface electromagnetic
fields within a nonuniform dispersive and absorptive system. This system is
formed by vacuum and lossy medium separated by a plane interface. As a medium,
we used dielectric and metal samples characterized by local and nonlocal
optical properties. Thermodynamic properties of surface eigenmodes of plane
interfaces are discussed. Various definitions of density of states and spectral
characteristics of surface polaritons in equilibrium at the interface formed by
vacuum and lossy medium are described and discussed. All formulas for
thermodynamic functions are represented in terms of density of states. The
generalized density of states is calculated based on the Barash-Ginzburg theory
and dispersion relations for the surface states in different approaches. It is
exemplified that different definitions of the density of states are identical
in the case of dissipationless materials. The spectral functions and integrated
over all frequencies thermodynamic characteristics and their temperature
dependences are demonstrated.",1207.5045v1
2014-10-08,Calculation of ground state energy of harmonically confined two dipolar fermions,"We calculate the ground state energies of a system of two dipolar fermions
trapped in a harmonic oscillator potential. The dipoles are assumed to be
aligned parallel to each other. We perform the calculations of ground state
energy as a function of strength of interaction between two fermions by
employing variational method with Hylleraas-like explicitly correlated wave
function. Furthermore, we perform calculations of ground state energy within
Hartree-Fock approximation and the magnitude of correlation energy is estimated
by subtracting these results from the corresponding wave function based
results. We also carry out calculations of ground state energies within the
realm of density functional theory by using recently reported expressions for
exchange and correlation energies under local density approximation. By
comparing correlated wave function based results with those obtained using
density functional theory approach we examine the role of fermion-fermion
correlation and assess the accuracy of local density approximation based
expression for the correlation energy functional.",1410.2078v1
2002-01-08,Parity Violating Measurements of Neutron Densities: Implications for Neutron Stars,"Parity violating electron scattering can measure the neutron density of a
heavy nucleus accurately and model independently. This is because the weak
charge of the neutron is much larger then that of the proton. The Parity Radius
Experiment (PREX) at Jefferson Laboratory aims to measure the root mean square
neutron radius of $^{208}$Pb with an absolute accuracy of 1% ($\pm 0.05$ Fm).
This is more accurate then past measurements with hadronic probes, which all
suffer from controversial strong interaction uncertainties. PREX should clearly
resolve the neutron-rich skin. Furthermore, this benchmark value for $^{208}$Pb
will provide a calibration for hadronic probes, such as proton scattering,
which can then be used to measure neutron densities of many exotic nuclei. The
PREX result will also have many implications for neutron stars. The neutron
radius of Pb depends on the pressure of neutron-rich matter: the greater the
pressure, the larger the radius as neutrons are pushed out against surface
tension. The same pressure supports a neutron star against gravity. The Pb
radius is sensitive to the equation of state at normal densities while the
radius of a 1.4 solar mass neutron star also depends on the equation of state
at higher densities. Measurements of the radii of a number of isolated neutron
stars such as Geminga and RX J185635-3754 should soon improve significantly. By
comparing the equation of state information from the radii of both Pb and
neutron stars one can search for a softening of the high density equation of
state from a phase transition to an exotic state. Possibilities include kaon
condensates, strange quark matter or color superconductors.",0201113v1
2001-04-14,A General Method for Obtaining a Lower Bound for the Ground State Entropy Density of the Ising Model With Short Range Interactions,"We present a general method for obtaining a lower bound for the ground state
entropy density of the Ising Model with nearest neighbor interactions. Then,
using this method, and with a random coupling constant configuration, we obtain
a lower bound for the ground state entropy density of the square, triangular,
and hexagonal two-dimensional lattices with free, cylindrical, and toroidal
boundary conditions.",0104020v1
2007-11-22,Neutron matter at finite temperature,"We calculate the neutron matter equation of state at finite temperature based
on low-momentum two- and three-nucleon interactions. The free energy is
obtained from a loop expansion around the Hartree-Fock energy, including
contributions from normal and anomalous diagrams. We focus on densities below
saturation density with temperatures T <= 10 MeV and compare our results to the
model-independent virial equation of state and to variational calculations.
Good agreement with the virial equation of state is found at low density. We
provide simple estimates for the theoretical error, important for
extrapolations to astrophysical conditions.",0711.3613v1
2008-03-18,Superconductivity in a model of two Hubbard chains coupled with ferromagnetic exchange interaction,"We study the ground-state properties of the double-chain Hubbard model
coupled with ferromagnetic exchange interaction by using the weak-coupling
theory, density-matrix renormalization group technique, and Lanczos
exact-diagonalization method. We determine the ground-state phase diagram in
the parameter space of the ferromagnetic exchange interaction and band filling.
We find that, in high electron density regime, the spin gap opens and the
spin-singlet $d_{xy}$-wave-like pairing correlation is most dominant, whereas
in low electron density regime, the fully-polarized ferromagnetic state is
stabilized where the spin-triplet $p_{y}$-wave-like pairing correlation is most
dominant.",0803.2590v1
2009-01-14,Dynamics of photoinduced Charge Density Wave-metal phase transition in K0.3MoO3,"We present first systematic studies of the photoinduced phase transition from
the ground charge density wave (CDW) state to the normal metallic (M) state in
the prototype quasi-1D CDW system K0.3MoO3. Ultrafast non-thermal CDW melting
is achieved at the absorbed energy density that corresponds to the electronic
energy difference between the metallic and CDW states. The results imply that
on the sub-picosecond timescale when melting and subsequent initial recovery of
the electronic order takes place the lattice remains unperturbed.",0901.1951v1
2019-09-27,Finite Horizon Density Steering for Multi-input State Feedback Linearizable Systems,"In this paper, we study the feedback synthesis problem for steering the joint
state density or ensemble subject to multi-input state feedback linearizable
dynamics. This problem is of interest to many practical applications including
that of dynamically shaping a robotic swarm. Our results here show that it is
possible to exploit the structural nonlinearities to derive the feedback
controllers steering the joint density from a prescribed shape to another while
minimizing the expected control effort to do so. The developments herein build
on our previous work, and extend the theory of the Schr\""{o}dinger bridge
problem subject to feedback linearizable dynamics.",1909.12511v2
2022-08-30,"Ground state correlations on ground state densities and total binding energies of 40Ca, 48Ca and 208Pb","Neutron and proton densities of doubly-closed shell nuclei 40Ca, 48Ca and
208Pb are studied based on a Hartree-Fock model with SAMi, SAMi-J27 and SAMi-T
energy density functionals (EDFs). The ground state correlations (GSC) induced
by isoscalar and isovector phonons are also evaluated by the second order
perturbation theory with a self-consistent random phase approximation (RPA). We
found that the interior part of the ground state densities is reduced by the
GSC in consistent with the experimental data. On the other hand, the GSC
enhances the neutron skin thickness of 48Ca and 208Pb. The effect of GSC on the
total binding energy is also evaluated by the quasi-boson approximation. The
effect of the tensor interaction is found small on both the density
distributions and the binding energies.",2208.13938v1
2022-09-23,Structure Optimization with Stochastic Density Functional Theory,"Linear-scaling techniques for Kohn-Sham density functional theory (KS-DFT)
are essential to describe the ground state properties of extended systems.
Still, these techniques often rely on the locality of the density matrix or on
accurate embedding approaches, limiting their applicability. In contrast,
stochastic density functional theory (sDFT) achieves linear- and
sub-linear-scaling by statistically sampling the ground state density without
relying on embedding or imposing localization. In return, ground state
observables, such as the forces on the nuclei, fluctuate in sDFT, making the
optimization of the nuclear structure a highly non-trivial problem. In this
work, we combine the most recent noise-reduction schemes for sDFT with
stochastic optimization algorithms to perform structure optimization within
sDFT. We compare the performance of the stochastic gradient descent (sGD)
approach and its variations (stochastic gradient descent with momentum (sGDM))
to stochastic optimization techniques that rely on the Hessian, such as the
stochastic Broyden-Fletcher-Goldfarb-Shanno (sBFGS) algorithm. We further
provide a detailed assessment of the computational efficiency and its
dependence on the optimization parameters for each methods for determining the
ground state structure of bulk silicon with varying supercell dimensions.",2209.11403v1
1999-02-02,Instabilities at [110] Surfaces of d_{x^2-y^2} Superconductors,"We compare different scenarios for the low temperature splitting of the
zero-energy peak in the local density of states at (110) surfaces of
d_{x^2-y^2}-wave superconductors, observed by Covington et al.
(Phys.Rev.Lett.79 (1997), 277). Using a tight binding model in the
Bogolyubov-de Gennes treatment we find a surface phase transition towards a
time-reversal symmetry breaking surface state carrying spontaneous currents and
an s+id-wave state. Alternatively, we show that electron correlation leads to a
surface phase transition towards a magnetic state corresponding to a local spin
density wave state.",9902026v1
2013-01-01,Layer Antiferromagnetic State in Bilayer Graphene : A First-Principle Investigation,"The ground state of bilayer graphene is investigated by the density
functional calculations with local spin density approximation. We find a ground
state with layer antiferromagnetic ordering, which has been suggested by former
studies based on simplified model. The calculations prove that the layer
antiferromagnetic state (LAF) is stable even if the remote hopping and nonlocal
Coulomb interaction are included. The gap of the LAF state is about 1.8 meV,
comparable to the experimental value. The surface magnetism in BLG is of the
order of $10^{-2} \mu_B /nm^2 $.",1301.0052v1
2013-03-05,Mapping densities in a noisy state space,"Weak noise smooths out fractals in a chaotic state space and introduces a
maximum attainable resolution to its structure. The balance of noise and
deterministic stretching/contraction in each neighborhood introduces local
invariants of the dynamics that can be used to partition the state space. We
study the local discrete-time evolution of a density in a two-dimensional
hyperbolic state space, and use the asymptotic eigenfunctions for the noisy
dynamics to formulate a new state space partition algorithm.",1303.0951v1
2024-02-18,Optimal Quantum State Tomography via Weak Value,"To improve the efficiency of the state tomography strategy via weak value, we
have searched the optimal coupling strength between the system and measuring
device. For an arbitrary d-dimensional quantum system, the optimal strengths
being used in measuring the real and imaginary parts of the density matrix are
obtained. The optimal efficiency of the state tomography has also been studied
by using mean square error. The minimal mean square errors in the reconstructed
density matrices have been derived. The state tomography strategy studied in
this article may be useful in the measurement of the unknown quantum states.",2402.11484v2
2013-10-31,Supersolid states in a hard-core Bose-Hubbard model on a layered triangular lattice,"We study ground-state properties in a hard-core Bose-Hubbard model on a
layered triangular lattice. Combining cluster mean-field theory with the
density matrix renormalization group method, we discuss the effect of the
interlayer coupling on the supersolid states realized in a single layered
model. By examining the distributions for the particle density and superfluid
order parameter, the rich phase diagram of the system is obtained. We find that
the supersolid states are widely stabilized at a commensurate filling, in
contrast to the case of the single layered model. The nature of the supersolid
states is also addressed.",1311.0005v1
2022-01-24,Quantum density estimation with density matrices: Application to quantum anomaly detection,"Density estimation is a central task in statistics and machine learning. This
problem aims to determine the underlying probability density function that best
aligns with an observed data set. Some of its applications include statistical
inference, unsupervised learning, and anomaly detection. Despite its relevance,
few works have explored the application of quantum computing to density
estimation. In this article, we present a novel quantum-classical density
matrix density estimation model, called Q-DEMDE, based on the expected values
of density matrices and a novel quantum embedding called quantum Fourier
features. The method uses quantum hardware to build probability distributions
of training data via mixed quantum states. As a core subroutine, we propose a
new algorithm to estimate the expected value of a mixed density matrix from its
spectral decomposition on a quantum computer. In addition, we present an
application of the method for quantum-classical anomaly detection. We evaluated
the density estimation model with quantum random and quantum adaptive Fourier
features on different data sets on a quantum simulator and a real quantum
computer. An important result of this work is to show that it is possible to
perform density estimation and anomaly detection with high performance on
present-day quantum computers.",2201.10006v5
2008-10-03,Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation,"We study the structure of the time evolution of the density matrix in contact
with a thermal bath in a standard projection operator sheme. The reduced
density matrix of the system in the steady state is obtained by tracing out the
degree of freedom of the thermal bath from the equilibrium density matrix of
the total system. This reduced density matrix is modified by the interaction,
and is different from that of the equilibrium of the system alone. We
explicitly calculate the contribution of each term in quantum master equation
to the realization of the steady state density matrix, and make clear roles of
each term. By making use of the role of each term, the properties of the
commonly used quantum master equation are examined.",0810.0626v1
2009-01-31,Density of States in the Magnetic Ground State of the Friedel-Anderson Impurity,"By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by
an order of magnitude the ground state of the Friedel-Anderson impurity is a
magnetic state. In recent years the author introduced the Friedel Artificially
Inserted Resonance (FAIR) method to investigate impurity properties. Within
this FAIR approach the magnetic ground state is derived. Its full excitation
spectrum and the composition of the excitations is calculated and numerically
evaluated. From the excitation spectrum the electron density of states is
calculated. Majority and minority d-resonances are obtained. The width of the
resonances is about twice as wide as the mean field theory predicts. This
broadening is due to the fact that any change of the occupation of the d-state
in one spin band changes the eigenstates in the opposite spin band and causes
transitions in both spin bands. This broadening reduces the height of the
resonance curve and therefore the density of states by a factor of two. This
yields an intuitive understanding for a previous result of the FAIR approach
that the critical value of the Coulomb interaction for the formation of a
magnetic moment is twice as large as the mean field theory predicts.",0902.0033v1
1999-08-19,Power densities for two-step gamma-ray transitions from isomeric states,"We have calculated the incident photon power density P_2 for which the
two-step induced emission rate from an isomeric nucleus becomes equal to the
natural isomeric decay rate. We have analyzed two-step transitions for isomeric
nuclei with a half-life greater than 10 min, for which there is an intermediate
state of known energy, spin and half-life, for which the intermediate state is
connected by a known gamma-ray transition to the isomeric state and to at least
another intermediate state, and for which the relative intensities of the
transitions to lower states are known. For the isomeric nucleus 166m-Ho, which
has a 1200 y isomeric state at 5.98 keV, we have found a value of P_2=6.3 x
10^7 W cm^{-2}, the intermediate state being the 263.8 keV level. We have found
power densities P_2 of the order of 10^{10} W cm^{-2} for several other
isomeric nuclei.",9908011v1
2015-03-03,Acceleration without Temperature,"We show that while some non-uniformly accelerating observers (NUAOs) do
indeed see a Bose-Einstein distribution of particles for the expectation value
of the number operator in the Minkowski vacuum state, the density matrix is
non-thermal and therefore a definition of temperature is not warranted. This is
due to the fact that our NUAOs do not see event horizons in the spacetime. More
specifically, the Minkowski vacuum state is perceived by our NUAOs as a
single-mode squeezed state as opposed to the two-mode squeezed state
characteristic of uniformly accelerating observers. Both single and two-mode
squeezed states are pure quantum states; however, tracing over degrees of
freedom in one of the modes of the two-mode squeezed state reduces the pure
density matrix to a thermal density matrix. It is this property in the two-mode
squeezed state that allows one to consistently define a temperature. In the
single-mode case, an equivalent tracing is neither required nor available.",1503.01152v1
2016-01-08,Enhancing multi-step quantum state tomography by PhaseLift,"Multi-photon system has been studied by many groups, however the biggest
challenge faced is the number of copies of an unknown state are limited and far
from detecting quantum entanglement. The difficulty to prepare copies of the
state is even more serious for the quantum state tomography. One possible way
to solve this problem is to use adaptive quantum state tomography, which means
to get a preliminary density matrix in the first step and revise it in the
second step. In order to improve the performance of adaptive quantum state
tomography, we develop a new distribution scheme of samples and extend it to
three steps, that is to correct it once again based on the density matrix
obtained in the traditional adaptive quantum state tomography. Our numerical
results show that the mean square error of the reconstructed density matrix by
our new method is improved to the level from $10^{-4}$ to $10^{-9}$ for several
tested states. In addition, PhaseLift is also applied to reduce the required
storage space of measurement operator.",1601.01873v2
2005-06-30,Localization Transition in a Ballistic Quantum Wire,"The many-body wave-function of an interacting one-dimensional electron system
is probed, focusing on the low-density, strong interaction regime. The
properties of the wave-function are determined using tunneling between two
long, clean, parallel quantum wires in a GaAs/AlGaAs heterostructure, allowing
for gate-controlled electron density. As electron density is lowered to a
critical value the many-body state abruptly changes from an extended state with
a well-defined momentum to a localized state with a wide range of momentum
components. The signature of the localized states appears as discrete tunneling
features at resonant gate-voltages, corresponding to the depletion of single
electrons and showing Coulomb-blockade behavior. Typically 5-10 such features
appear, where the one-electron state has a single-lobed momentum distribution,
and the few-electron states have double-lobed distributions with peaks at $\pm
k_F$. A theoretical model suggests that for a small number of particles (N<6),
the observed state is a mixture of ground and thermally excited spin states.",0506812v1
2012-10-05,The Interplay of Topological Surface and Bulk Electronic States in Bi2Se3,"In this Letter we present scanning tunneling microscopy density-of-states
measurements and electronic structure calculations of the topological insulator
Bi2Se3. The measurements show significant background states in addition to the
expected Dirac cone. Density functional calculations using a slab model and
analysis of the partial density-of-states show that the background is
consistent with bulk-like states with small amplitudes at the surface. The
topological surface states coexist with bulk-like states in the valence band,
appearing as a shoulder in the projected band structure. These results strongly
support the picture suggested by recent scattering experiments of the quantum
interference of topological and bulk-like surface states.",1210.1874v1
2004-04-14,New physics at low energies and dark matter-dark energy transmutation,"A field theory is proposed where the regular fermionic matter and the dark
fermionic matter can be different states of the same ""primordial"" fermion
fields. In regime of the fermion densities typical for normal particle physics,
the primordial fermions split into three families identified with regular
fermions. When fermion energy density becomes comparable with dark energy
density, the theory allows transition to new type of states. The possibility of
such Cosmo-Low Energy Physics (CLEP) states is demonstrated by means of
solutions of the field theory equations describing FRW universe filled with
homogeneous scalar field and uniformly distributed nonrelativistic neutrinos.
Neutrinos in CLEP state are drawn into cosmological expansion by means of
dynamically changing their own parameters. One of the features of the fermions
in CLEP state is that in the late time universe their masses increase as
a^{3/2} (a=a(t) is the scale factor). The energy density of the cold dark
matter consisting of neutrinos in CLEP state scales as a sort of dark energy;
this cold dark matter possesses negative pressure and for the late time
universe its equation of state approaches that of the cosmological constant.
The total energy density of such universe is less than it would be in the
universe free of fermionic matter at all.",0404099v1
2016-08-12,The Braess Paradox in a network of totally asymmetric exclusion processes,"We study the Braess paradox in the transport network as originally proposed
by Braess with totally asymmetric exclusion processes (TASEPs) on the edges.
The Braess paradox describes the counterintuitive situation in which adding an
edge to a road network leads to a user optimum with higher travel times for all
network users. Travel times on the TASEPs are nonlinear in the density, and
jammed states can occur due to the microscopic exclusion principle, leading to
a more realistic description of trafficlike transport on the network than in
previously studied linear macroscopic mathematical models. Furthermore, the
stochastic dynamics allows us to explore the effects of fluctuations on network
performance. We observe that for low densities, the added edge leads to lower
travel times. For slightly higher densities, the Braess paradox occurs in its
classical sense. At intermediate densities, strong fluctuations in the travel
times dominate the system's behavior due to links that are in a domain-wall
state. At high densities, the added link leads to lower travel times. We
present a phase diagram that predicts the system's state depending on the
global density and crucial path-length ratios.",1608.03753v2
2015-10-20,Adiabatic electronic flux density: a Born-Oppenheimer Broken Symmetry ansatz,"The Born-Oppenheimer approximation leads to the counterintuitive result of a
vanishing electronic flux density upon vibrational dynamics in the electronic
ground state. To circumvent this long known issue, we propose using pairwise
anti-symmetrically translated vibronic densities to generate a symmetric
electronic density that can be forced to satisfy the continuity equation
approximately. The so-called Born-Oppenheimer broken symmetry ansatz yields all
components of the flux density simultaneously while requiring only knowledge
about the nuclear quantum dynamics on the electronic adiabatic ground state
potential energy surface. The underlying minimization procedure is transparent
and computationally inexpensive, and the solution can be computed from the
standard output of any quantum chemistry program. Taylor series expansion
reveals that the implicit electron dynamics originates from non-adiabatic
coupling to the explicit Born-Oppenheimer nuclear dynamics. The new approach is
applied to the ${\rm H}_2^+$ molecular ion vibrating in its ${}^2\Sigma^+_g$
ground state. The electronic flux density is found to have the correct nodal
structure and symmetry properties at all times.",1510.05785v2
2016-03-18,Skyrmionic vortex lattices in coherently coupled three-component Bose-Einstein condensates,"We show numerically that a harmonically trapped and coherently Rabi-coupled
three-component Bose-Einstein condensate can host unconventional vortex
lattices in its rotating ground state. The discovered lattices incorporate
square and zig-zag patterns, vortex dimers and chains, and doubly quantized
vortices, and they can be quantitatively classified in terms of a skyrmionic
topological index, which takes into account the multicomponent nature of the
system. The exotic ground-state lattices arise due to the intricate interplay
of the repulsive density-density interactions and the Rabi couplings as well as
the ubiquitous phase frustration between the components. In the frustrated
state, domain walls in the relative phases can persist between some components
even at strong Rabi coupling, while vanishing between others. Consequently, in
this limit the three-component condensate effectively approaches a
two-component condensate with only density-density interactions. At
intermediate Rabi coupling strengths, however, we face unique vortex physics
that occurs neither in the two-component counterpart nor in the purely
density-density-coupled three-component system.",1603.05813v2
2006-08-25,Visualization of superposition of macroscopically distinct states,"We propose a method of visualizing superpositions of macroscopically distinct
states in many-body pure states. We introduce a visualization function, which
is a coarse-grained quasi joint probability density for two or more hermitian
additive operators. If a state contains superpositions of macroscopically
distinct states, one can visualize them by plotting the visualization function
for appropriately taken operators. We also explain how to efficiently find
appropriate operators for a given state. As examples, we visualize four states
containing superpositions of macroscopically distinct states: the ground state
of the XY model, that of the Heisenberg antiferromagnet, a state in Shor's
factoring algorithm, and a state in Grover's quantum search algorithm. Although
the visualization function can take negative values, it becomes non-negative
(hence becomes a coarse-grained joint probability density) if the
characteristic width of the coarse-graining function used in the visualization
function is sufficiently large.",0608196v1
1998-05-21,Decoherent Histories and Hydrodynamic Equations,"For a system consisting of a large collection of particles, a set of
variables that will generally become effectively classical are the local
densities (number, momentum, energy). That is, in the context of the decoherent
histories approach to quantum theory, it is expected that histories of these
variables will be approximately decoherent, and that their probabilites will be
strongly peaked about hydrodynamic equations. This possibility is explored for
the case of the diffusion of the number density of a dilute concentration of
foreign particles in a fluid. This system has the appealing feature that the
microscopic dynamics of each individual foreign particle is readily obtained
and the approach to local equilibrium may be seen explicitly. It is shown that,
for certain physically reasonable initial states, the probabilities for
histories of number density are strongly peaked about evolution according to
the diffusion equation. Decoherence of these histories is also shown for a
class of initial states which includes non-trivial superpositions of number
density. Histories of phase space densities are also discussed. The case of
histories of number, momentum and energy density for more general systems, such
as a dilute gas, is also discussed in outline. When the initial state is a
local equilibrium state, it is shown that the histories are trivally
decoherent, and that the probabilities for histories are peaked about
hydrodynamic equations. An argument for decoherence of more general initial
states is given.",9805062v2
2001-10-16,Analytical and numerical study of hardcore bosons in two dimensions,"We study various properties of bosons in two dimensions interacting only via
onsite hardcore repulsion. In particular, we use the lattice spin-wave
approximation to calculate the ground state energy, the density, the condensate
density and the superfluid density in terms of the chemical potential. We also
calculate the excitation spectrum, $\omega({\bf k})$. In addition, we performed
high precision numerical simulations using the stochastic series expansion
algorithm. We find that the spin-wave results describe extremely well the
numerical results over the {\it whole} density range $0\leq \rho \leq 1$. We
also compare the lattice spin-wave results with continuum results obtained by
summing the ladder diagrams at low density. We find that for $\rho \leq 0.1$
there is good agreement, and that the difference between the two methods
vanishes as $\rho^2$ for $\rho \to 0$. This offers the possibility of obtaining
precise continuum results by taking the continuum limit of the spin-wave
results for all densities. Finaly, we studied numerically the finite
temperature phase transition for the entire density range and compared with low
density predictions.",0110314v1
2006-12-02,Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics,"A forefront area of research concerns the exploration of the properties of
hadronic matter under extreme conditions of temperature and density, and the
determination of the equation of state--the relation between pressure,
temperature and density--of such matter. Experimentally, relativistic heavy-ion
collision experiments enable physicists to cast a brief glance at hot and
ultra-dense matter for times as little as about $10^{-22}$ seconds.
Complementary to this, the matter that exists in the cores of neutron stars,
observed as radio pulsars, X-ray pulsars, and magnetars, is at low temperatures
but compressed permanently to ultra-high densities that may be more than an
order of magnitude higher than the density of atomic nuclei. This makes pulsars
superb astrophysical laboratories for medium and high-energy nuclear physics,
as discussed in this paper.",0612054v1
2015-04-18,Tunneling density of states in quantum dots with anisotropic exchange,"We reexamine the tunneling density of states in quantum dots and
nanoparticles within the model which is extension of the universal Hamiltonian
to the case of uniaxial anisotropic exchange. We derive the exact analytical
result for the tunneling density of states in the case of arbitrary
single-particle energy spectrum. We find that, similar to the case of the
isotropic exchange, the tunneling density of states as a function of energy has
the maximum due to a finite value of the total spin of the ground state near
the Stoner instability. We demonstrate that there are no additional extrema
which have been predicted on the basis of perturbative analysis [M.N. Kiselev
and Y. Gefen, Phys. Rev. Lett. {\bf 96}, 066805 (2006)].",1504.04753v1
2019-01-23,Pauli Blocking in Degenerate Plasmas and the Separable Potential Approach,"The Mott effect describes the dissolution of bound states in a dense
partially ionized plasma. It happens when the ionization potential depression,
owing to effects of correlation and degeneracy, compensates the binding energy
of the bound state. At high densities and moderate temperatures, the Pauli
blocking becomes important and influences significantly the degree of
ionization in the region of degenerate plasmas. A quantum statistical approach
is used where the total density is decomposed in an uncorrelated, ""free"" part
and correlations, as a consequence of the cluster decomposition of the
self-energy. The contribution of correlations to the total density is given by
bound states and continuum correlations. Exact solutions for a separable
potential are compared to perturbation theory and numerical solutions of the
in-medium Schr\""odinger equation. The in-medium scattering phase shifts are
evaluated, and the role of continuum correlations is discussed. The Pauli
blocking of bound states and the density of states are considered for warm
dense matter conditions.",1901.08044v1
2019-10-29,Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms,"Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the
density of states counts the number of variable assignments that violate
exactly $e$ clauses, for all values of $e$. Thus, the density of states is a
histogram of the number of unsatisfied clauses over all possible assignments.
This computation generalizes both maximum-satisfiability (MAX-SAT) and model
counting problems and not only provides insight into the entire solution space,
but also yields a measure for the \emph{hardness} of the problem instance.
Consequently, in real-world scenarios, this problem is typically infeasible
even when using state-of-the-art algorithms. While finding an exact answer to
this problem is a computationally intensive task, we propose a novel approach
for estimating density of states based on the concentration of measure
inequalities. The methodology results in a quadratic unconstrained binary
optimization (QUBO), which is particularly amenable to quantum annealing-based
solutions. We present the overall approach and compare results from the D-Wave
quantum annealer against the best-known classical algorithms such as the
Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT)
solvers.",1910.13088v1
2023-12-09,Effect of Dispersion and Different Carrier Transitions on Absorption Characteristics of GaAs,"One of the basic optoelectronic characteristics is the absorption of any
optoelectronic device or material. We present the characteristics of pure GaAs
and the deviation of ideal spectra. Due to crystal defects, vacancies,
impurities, etc., energy states exist in the semiconductor other than the
allowed bands (conduction and valence bands). In this research, the effect of
transitions between these states on absorption spectra and how the absorption
coefficients change with the density and location of those states are analyzed
numerically. Among the cases of 0.07 eV, 0.12 eV, and 0.17 eV with the density
of 2%, 5%, 10%, 20%, and 30%, the minimum deviation occurs for the states
located 0.07 eV below the conduction band and when the energy states have the
minimum density of 2% and the deviation increases for the cases of 0.12 eV and
0.17 eV with higher densities.",2401.06773v1
2024-01-22,Not all Probability Density Functions are Tomograms,"This paper delves into the significance of the tomographic probability
density function (pdf) representation of quantum states, shedding light on the
special classes of pdfs that can be tomograms. Instead of using wave functions
or density operators on Hilbert spaces, tomograms, which are the true pdfs, are
used to completely describe the states of quantum systems. Unlike quasi-pdfs,
like the Wigner function, tomograms can be analysed using all the tools of
classical probability theory for pdf estimation, which can allow a better
quality of state reconstruction. This is particularly useful when dealing with
non-Gaussian states where the pdfs are multi-mode. The knowledge of the family
of distributions plays an important role in the application of both parametric
and non-parametric density estimation methods. We show that not all pdfs can
play the role of tomograms of quantum states and introduce the conditions that
must be fulfilled by pdfs to be ""quantum"".",2401.11966v1
2012-02-13,The Two States of Star Forming Clouds,"We examine the effects of self-gravity and magnetic fields on supersonic
turbulence in isothermal molecular clouds with high resolution simulations and
adaptive mesh refinement. These simulations use large root grids (512^3) to
capture turbulence and four levels of refinement to capture high density, for
an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two
super-Alfv\'enic and one trans-Alfv\'enic. We find that gravity splits the
clouds into two populations, one low density turbulent state and one high
density collapsing state. The low density state exhibits properties similar to
non-self-gravitating in this regime, and we examine the effects of varied
magnetic field strength on statistical properties: the density probability
distribution function is approximately lognormal; velocity power spectral
slopes decrease with field strength; alignment between velocity and magnetic
field increases with field; the magnetic field probability distribution can be
fit to a stretched exponential. The high density state is characterized by
self-similar spheres; the density PDF is a power-law; collapse rate decreases
with increasing mean field; density power spectra have positive slopes,
P({\rho},k) \propto k; thermal-to-magnetic pressure ratios are unity for all
simulations; dynamic-to-magnetic pressure ratios are larger than unity for all
simulations; magnetic field distribution is a power-law. The high Alfv\'en Mach
numbers in collapsing regions explain recent observations of magnetic influence
decreasing with density. We also find that the high density state is found in
filaments formed by converging flows, consistent with recent Herschel
observations. Possible modifications to existing star formation theories are
explored.",1202.2594v1
2016-10-07,Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field,"We study the quantum phases of bosons with repulsive contact interactions on
a two-leg ladder in the presence of a uniform Abelian gauge field. The model
realizes many interesting states, including Meissner phases, vortex-fluids,
vortex-lattices, charge-density-waves and the biased-ladder phase. Our work
focuses on the subset of these states that break a discrete symmetry. We use
density matrix renormalization group simulations to demonstrate the existence
of three vortex-lattice states at different vortex densities and we
characterize the phase transitions from these phases into neighboring states.
Furthermore, we provide an intuitive explanation of the chiral-current reversal
effect that is tied to some of these vortex lattices. We also study a
charge-density-wave state that exists at 1/4 particle filling at large
interaction strengths and flux values close to half a flux quantum. By changing
the system parameters, this state can transition into a completely gapped
vortex-lattice Mott-insulating state. We elucidate the stability of these
phases against nearest-neighbor interactions on the rungs of the ladder
relevant for experimental realizations with a synthetic lattice dimension. A
charge-density-wave state at 1/3 particle filling can be stabilized for flux
values close to half a flux-quantum and for very strong on-site interactions in
the presence of strong repulsion on the rungs. Finally, we analytically
describe the emergence of these phases in the low-density regime, and, in
particular, we obtain the boundaries of the biased-ladder phase, i.e., the
phase that features a density imbalance between the legs. We make contact to
recent quantum-gas experiments that realized related models and discuss
signatures of these quantum states in experimentally accessible observables.",1610.02435v2
2012-08-01,Local Control and v-Representability of Correlated Quantum Dynamics,"We present a local control scheme to construct the external potential v that,
for a given initial state, produces a prescribed time-dependent density in an
interacting quantum many-body system. The numerical method is efficient and
stable even for large and rapid density variations irrespective of the initial
state and the interactions. The method can at the same time be used to answer
fundamental v-representability questions in density-functional theory. In
particular, in the absence of interactions, it allows us to construct the exact
time-dependent Kohn-Sham potential for arbitrary initial states. We illustrate
the method in a correlated one-dimensional two-electron system with different
interactions, initial states and densities. For a Kohn-Sham system with a
correlated initial state we demonstrate the interplay between memory and
initial-state dependence as well as the failure of any adiabatic approximation.",1208.0226v2
2015-08-18,Phenomenological neutron star equations of state: 3-window modeling of QCD matter,"We discuss the 3-window modeling of cold, dense QCD matter equations of state
at density relevant to neutron star properties. At low baryon density, n_B < ~
2n_s (n_s: nuclear saturation density), we utilize purely hadronic equations of
state that are constrained by empirical observations at density n_B ~ n_s and
neutron star radii. At high density, n_B > ~ 5n_s, we use the percolated quark
matter equations of state which must be very stiff to pass the two-solar mass
constraints. The intermediate domain at 2 < n_B/n_s < 5 is described as neither
purely hadronic nor percolated quark matter, and the equations of state are
inferred by interpolating hadronic and percolated quark matter equations of
state. Possible forms of the interpolation are severely restricted by the
condition on the (square of) speed of sound, 0 < c_s^2 < 1. The characteristics
of the 3-window equation of state are compared with those of conventional
hybrid and self-bound quark matters. Using a schematic quark model for the
percolated domain, it is argued that the two-solar mass constraint requires the
model parameters to be as large as their vacuum values, indicating that the
gluon dynamics remains strongly non-perturbative to n_B ~ 10n_s. The hyperon
puzzle is also briefly discussed in light of quark descriptions.",1508.04408v2
2003-08-04,Tensor of coherences parameterization of multiqubit density operators for entanglement characterization,"For multiqubit densities, the tensor of coherences (or Stokes tensor) is a
real parameterization obtained by the juxtaposition of the affine Bloch vectors
of each qubit. While it maintains the tensorial structure of the underlying
space, it highlights the pattern of correlations, both classical and quantum,
between the subsystems and, due to the affine parameterization, it contains in
its components all reduced densities of all orders. The main purpose of our use
of this formalism is to deal with entanglement. For example, the detection of
bipartite entanglement is straightforward, as it is the synthesis of densities
having positive partial transposes between desired qubits. In addition, finding
explicit mixtures for families of separable states becomes a feasible issue for
few qubit symmetric densities (we compute it for Werner states) and, more
important, it provides some insight on the possible origin of entanglement for
such densities.",0308019v1
2013-08-01,"A comparison of the carrier density at the surface of quantum wells for different crystal orientations of silicon, gallium arsenide and indium arsenide","We report the carrier densities at the surface of single-crystal quantum
wells as a function of material, orientation and well width. We include wells
constructed from silicon, gallium arsenide and indium arsenide with three
crystal orientations, (100), (110) and (111), included for each material. We
find that the D2 states in a silicon (100) quantum well have the smallest
density near the surface of the slab. Inspection of the planar average of the
carrier densities reveals a characteristic shape that depends on the material
and orientation, which leads to a varying degree of suppression or enhancement
of the density near the surface. The physics responsible for the suppression or
enhancement of the density near the surface can be traced to a constraint
imposed by the symmetry of quantum well wavefunction on the phases of the bulk
Bloch states of the crystal from which it can be constructed.",1308.0360v1
2004-07-23,Superconducting and charge-density wave instabilities in ultrasmall-radius carbon nanotubes,"We perform a detailed analysis of the band structure, phonon dispersion, and
electron-phonon coupling of three types of small-radius carbon nanotubes
(CNTs): (5,0), (6,0), and (5,5) with diameters 3.9, 4.7, and 6.8 \AA
respectively. The large curvature of the (5,0) CNTs makes them metallic with a
large density of states at the Fermi energy. The density of states is also
strongly enhanced for the (6,0) CNTs compared to the results obtained from the
zone-folding method. For the (5,5) CNTs the electron-phonon interaction is
dominated by the in-plane optical phonons, while for the ultrasmall (5,0) and
(6,0) CNTs the main coupling is to the out-of-plane optical phonon modes. We
calculate electron-phonon interaction strengths for all three types of CNTs and
analyze possible instabilities toward superconducting and charge-density wave
phases. For the smallest (5,0) nanotube, in the mean-field approximation and
neglecting Coulomb interactions, we find that the charge-density wave
transition temperature greatly exceeds the superconducting one. When we include
a realistic model of the Coulomb interaction we find that the charge-density
wave is suppressed to very low temperatures, making superconductivity dominant
with the mean-field transition temperature around one K. For the (6,0) nanotube
the charge-density wave dominates even with the inclusion of Coulomb
interactions and we find the mean-field transition temperature to be around
five Kelvin. We find that the larger radius (5,5) nanotube is stable against
superconducting and charge-density wave orders at all realistic temperatures.",0407644v1
2021-05-13,"Bank Density, Population Density, and Economic Deprivation Across the United States","Recent research on the geographic locations of bank branches in the United
States has identified thresholds below which a given area can be considered to
be a ""banking desert."" Thus far, most analyses of the country as a whole have
tended to focus on minimum distances from geographic areas to the nearest bank,
while a recent density-based analysis focused only on the city of Chicago. As
such, there is not yet a nationwide study of bank densities for the entire
United States. This study calculates banks per square mile for U.S. Census
tracts over ten different ranges of population density. One main finding is
that bank density is sensitive to the measurement radius used (for example,
density in urban areas can be calculated as the number of banks within two
miles, while some rural areas require a 20-mile radius). This study then
compiles a set of lower 5- and 10-percent thresholds that might be used to
identify ""banking deserts"" in various urban, suburban, and rural areas; these
largely conform to the findings of previous analyses. Finally, adjusting for
population density using regression residuals, this paper examines whether an
index of economic deprivation is significantly higher in the five percent of
""desert"" tracts than in the remaining 95 percent. The differences are largest
-- and highly significant -- in the densest tracts in large urban areas.",2105.07823v1
2021-10-18,Mode I and Mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity,"In this study, we use the mechanism-based strain gradient plasticity theory
to evaluate both crack tip dislocation density behaviour and the coupled effect
of the material plastic properties and the intrinsic material length on
non-linear amplitude factors. The two planar classical stress-strain states are
examined, namely, plane strain and plane stress, both under pure mode I and
pure mode II loading conditions. The constitutive relations are based on
Taylor's dislocation model, which enables gaining insights into the role of the
increased dislocation density associated with large gradients in plastic strain
near cracks. The material model is implemented in a commercial finite element
(FE) software package using a user subroutine, and the nonlinear stress
intensity factors (SIF) are evaluated as a function of the intrinsic material
length, characterising the scale at which gradient effects become significant.
As a result of the FE calculations of dislocation density distributions, the
effects of both the fracture mode and the stress-strain state are determined.
In pure mode I, the geometrically necessary dislocation (GND) density is
located symmetrically with respect to the blunted crack tip. On the contrary,
under pure mode II, the GND density becomes concentrated in the blunted and
sharp parts of the crack tip. In this case, fracture initiation is shown to be
likely to occur near the blunted region of the crack tip, where both the stress
triaxiality and the GND density are at their maximum. The relation between the
equilibrium state of dislocation densities and the intrinsic material length as
well as the plastic SIF as a function of the work hardening exponent is
discussed.",2110.09211v1
2022-10-15,AMD-DBSCAN: An Adaptive Multi-density DBSCAN for datasets of extremely variable density,"DBSCAN has been widely used in density-based clustering algorithms. However,
with the increasing demand for Multi-density clustering, previous traditional
DSBCAN can not have good clustering results on Multi-density datasets. In order
to address this problem, an adaptive Multi-density DBSCAN algorithm
(AMD-DBSCAN) is proposed in this paper. An improved parameter adaptation method
is proposed in AMD-DBSCAN to search for multiple parameter pairs (i.e., Eps and
MinPts), which are the key parameters to determine the clustering results and
performance, therefore allowing the model to be applied to Multi-density
datasets. Moreover, only one hyperparameter is required for AMD-DBSCAN to avoid
the complicated repetitive initialization operations. Furthermore, the variance
of the number of neighbors (VNN) is proposed to measure the difference in
density between each cluster. The experimental results show that our AMD-DBSCAN
reduces execution time by an average of 75% due to lower algorithm complexity
compared with the traditional adaptive algorithm. In addition, AMD-DBSCAN
improves accuracy by 24.7% on average over the state-of-the-art design on
Multi-density datasets of extremely variable density, while having no
performance loss in Single-density scenarios. Our code and datasets are
available at https://github.com/AlexandreWANG915/AMD-DBSCAN.",2210.08162v2
2013-03-10,Suppression of Dielectronic Recombination Due to Finite Density Effects,"We have developed a general model for determining density-dependent effective
dielectronic recombination (DR) rate coefficients in order to explore
finite-density effects on the ionization balance of plasmas. Our model consists
of multiplying by a suppression factor those highly-accurate total zero-density
DR rate coefficients which have been produced from state-of-the-art theoretical
calculations and which have been benchmarked by experiment. The suppression
factor is based-upon earlier detailed collision-radiative calculations which
were made for a wide range of ions at various densities and temperatures, but
used a simplified treatment of DR. A general suppression formula is then
developed as a function of isoelectronic sequence, charge, density, and
temperature. These density-dependent effective DR rate coefficients are then
used in the plasma simulation code Cloudy to compute ionization balance curves
for both collisionally ionized and photoionized plasmas at very low (ne = 1
cm^-3) and finite (ne=10^10 cm^-3) densities. We find that the denser case is
significantly more ionized due to suppression of DR, warranting further studies
of density effects on DR by detailed collisional-radiative calculations which
utilize state-of-the-art partial DR rate coefficients. This is expected to
impact the predictions of the ionization balance in denser cosmic gases such as
those found in nova and supernova shells, accretion disks, and the broad
emission line regions in active galactic nuclei.",1303.2338v1
2023-08-07,Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe2,"Periodic spatial modulations of the superfluid density, or pair density
waves, have now been widely detected in unconventional superconductors, either
as the primary or the secondary states accompanying charge density waves.
Understanding how these density waves emerge, or conversely get suppressed by
external parameters, provides an important insight into their nature. Here we
use spectroscopic imaging scanning tunneling microscopy to study the evolution
of density waves in the heavy fermion spin-triplet superconductor UTe2 as a
function of temperature and magnetic field. We discover that charge
modulations, composed of three different wave vectors gradually weaken but
persist to a surprisingly high temperature T_CDW ~ 10-12 K. By tracking the
local amplitude of modulations, we find that these modulations become spatially
inhomogeneous, and form patches that shrink in size with higher temperature or
with applied magnetic field. Interestingly, one of the density wave vectors
along the mirror symmetry has a slightly different temperature onset, thus
revealing an unexpected decoupling of the three-component CDW state.
Importantly, T_CDW determined from our work matches closely to the temperature
scale believed to be related to magnetic fluctuations, providing the first
possible connection between density waves observed by surface probes and bulk
measurements. Combined with magnetic field sensitivity of the modulations, this
could point towards an important role of spin fluctuations or short-range
magnetic order in the formation of the primary charge density wave.",2308.03721v1
1998-03-06,The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain,"The density matrix renormalization group (DMRG) method introduced by White
for the study of strongly interacting electron systems is reviewed; the method
is variational and considers a system of localized electrons as the union of
two adjacent fragments A, B. A density matrix rho is introduced, whose
eigenvectors corresponding to the largest eigenvalues are the most significant,
the most probable states of A in the presence of B; these states are retained,
while states corresponding to small eigenvalues of rho are neglected. It is
conjectured that the decreasing behaviour of the eigenvalues is gaussian. The
DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene
(CH)_N up to N=34. A Hilbert space of dimension 5 x 10^+18 is explored. The
ground state energy is 10^-3 eV within the full CI value in the case N=18. The
DMRG method compares favourably also with coupled cluster approximations. The
unrestricted Hartree-Fock solution (which presents spin density waves) is
briefly reviewed, and a comparison is made with the DMRG energy values.
Finally, the spin-spin and density-density correlation functions are computed;
the results suggest that the antiferromagnetic order of the exact solution does
not extend up to large distances but exists locally. No charge density waves
are present.",9803071v1
2004-01-06,Ultrafast real-time spectroscopy of low dimensional charge density wave compounds,"We present a femtosecond time-resolved optical spectroscopy (TRS) as an
experimental tool to probe the changes in the low energy electronic density of
states as a result of short and long range charge density wave order. In these
experiments, a femtosecond laser pump pulse excites electron-hole pairs via an
interband transition in the material. These hot carriers rapidly release their
energy via electron-electron and electron-phonon collisions reaching states
near the Fermi energy within 10-100 fs. The presence of an energy gap in the
quasiparticle excitation spectrum inhibits the final relaxation step and
photoexcited carriers accumulate above the gap. The relaxation and
recombination processes of photoexcited quasiparticles are monitored by
measuring the time evolution of the resulting photoinduced absorption. This
way, the studies of carrier relaxation dynamics give direct information of the
temperature-dependent changes in the low energy density of states. Here we
present the application of the femtosecond time-resolved optical spectroscopy
for studying changes in the low energy electronic density of states in low
dimensional charge density wave systems associated with various charge density
wave (CDW) transitions and review some recent experiments on quasi 1D and 2D
CDW compounds.",0401059v1
2022-08-25,Sensitivity of Au+Au collisions to the symmetric nuclear matter equation of state at 2 -- 5 nuclear saturation densities,"We demonstrate that proton and pion flow measurements in heavy-ion collisions
at incident energies ranging from 1 to 20 GeV per nucleon in the fixed target
frame can be used for an accurate determination of the symmetric nuclear matter
equation of state at baryon densities equal 2--4 times nuclear saturation
density $n_0$. We simulate Au+Au collisions at these energies using a hadronic
transport model with an adjustable vector mean-field potential dependent on
baryon density $n_B$. We show that the mean field can be parametrized to
reproduce a given density-dependence of the speed of sound at zero temperature
$c_s^2(n_B, T = 0)$, which we vary independently in multiple density intervals
to probe the differential sensitivity of heavy-ion observables to the equation
of state at these specific densities. Recent flow data from the STAR experiment
at the center-of-mass energies $\sqrt{s_{NN}} = \{3.0, 4.5 \}\ $ GeV can be
described by our model, and a Bayesian analysis of these data indicates a hard
equation of state at $n_B \in (2,3) n_0$ and a possible phase transition at
$n_B \in (3,4) n_0$. More data at $\sqrt{s_{NN}} = 2-5$ GeV, as well as a more
thorough analysis of the model systematic uncertainties will be necessary for a
more precise conclusion.",2208.11996v4
2001-08-06,Quantal Andreev billiards: Semiclassical approach to mesoscale oscillations in the density of states,"Andreev billiards are finite, arbitrarily-shaped, normal-state regions,
surrounded by superconductor. At energies below the superconducting gap,
single-quasiparticle excitations are confined to the normal region and its
vicinity, the essential mechanism for this confinement being Andreev
reflection. This Paper develops and implements a theoretical framework for the
investigation of the short-wave quantal properties of these
single-quasiparticle excitations. The focus is primarily on the relationship
between the quasiparticle energy eigenvalue spectrum and the geometrical shape
of the normal-state region, i.e., the question of spectral geometry in the
novel setting of excitations confined by a superconducting pair-potential.
Among the central results of this investigation are two semiclassical trace
formulas for the density of states. The first, a lower-resolution formula,
corresponds to the well-known quasiclassical approximation, conventionally
invoked in settings involving superconductivity. The second, a
higher-resolution formula, allows the density of states to be expressed in
terms of: (i) An explicit formula for the level density, valid in the
short-wave limit, for billiards of arbitrary shape and dimensionality. This
level density depends on the billiard shape only through the set of
stationary-length chords of the billiard and the curvature of the boundary at
the endpoints of these chords; and (ii) Higher-resolution corrections to the
level density, expressed as a sum over periodic orbits that creep around the
billiard boundary. Owing to the fact that these creeping orbits are much longer
than the stationary chords, one can, inter alia, hear the stationary chords of
Andreev billiards.",0108102v1
1995-01-31,Destruction of density-wave states by a pseudo-gap in high magnetic fields: application to (TMTSF)$_2$ClO$_4$,"A model is presented for the destruction of density-wave states in
quasi-one-dimensional crystals by high magnetic fields. The model is consistent
with previously unexplained properties of the organic conductors
(TMTSF)$_2$ClO$_4$ and (BEDT-TTF)$_2$MHg(SCN)$_4$ (M=K,Rb,Tl). As the magnetic
field increases quasi-one-dimensional density-wave fluctuations increase,
producing a pseudo-gap in the electronic density of states near the transition
temperature. When the pseudo-gap becomes larger than the mean-field transition
temperature formation of a density-wave state is not possible.",9501135v2
2003-09-29,Mixing Property of Quantum Relative Entropy,"An analogue of the mixing property of quantum entropy is derived for quantum
relative entropy.It is applied to the final state of ideal measurement and to
the spectral form of the second density operator. Three cases of states on a
directed straight line of relative entropy are discussed.",0309211v1
2023-08-10,"Comment on ""Identification of the Mott Insulating Charge Density Wave State in $1T$-TaS$_2$""","The applicability of DFT+$U$ to the star-of-David phase of $1T$-TaS$_2$ is
examined. The viability of a Mott phase as a ground state for the bulk of this
material is briefly discussed in light of the available experimental evidence.",2308.05773v1
2004-11-12,Low-energy quasiparticle states at superconductor-CDW interfaces,"Quasiparticle bound states are found theoretically on transparent interfaces
of d-wave superconductors (dSC) with charge density wave solids (CDW), as well
as s-wave superconductors (sSC) with d-density waves (DDW). These bound states
represent a combined effect of Andreev reflection from the superconducting side
and an unconventional quasiparticle Q-reflection from the density wave solid.
If the order parameter for a density wave state is much less than the Fermi
energy, bound states with almost zero energy take place for an arbitrary
orientation of symmetric interfaces. For larger values of the order parameter,
dispersionless zero-energy states are found only on (110) interfaces. Two
dispersive energy branches of subgap quasiparticle states are obtained for
(100) symmetric interfaces. Andreev low-energy bound states, taking place in
junctions with CDW or DDW interlayers, result in anomalous junction properties,
in particular, the low-temperature behavior of the Josephson critical current.",0411351v1
2005-07-07,On the sharpness of the zero-entropy-density conjecture,"The zero-entropy-density conjecture states that the entropy density, defined
as the limit of S(N)/N at infinity, vanishes for all translation-invariant pure
states on the spin chain. Or equivalently, S(N), the von Neumann entropy of
such a state restricted to N consecutive spins, is sublinear. In this paper it
is proved that this conjecture cannot be sharpened, i.e., translation-invariant
states give rise to arbitrary fast sublinear entropy growth. The proof is
constructive, and is based on a class of states derived from quasifree states
on a CAR algebra. The question whether the entropy growth of pure quasifree
states can be arbitrary fast sublinear was first raised by Fannes et al. [J.
Math. Phys. 44, 6005 (2003)]. In addition to the main theorem it is also shown
that the entropy asymptotics of all pure shift-invariant nontrivial quasifree
states is at least logarithmic.",0507022v3
2019-07-30,Thermodynamic metric geometry of the two-state ST2 model for supercooled water,"Liquid water has anomalous liquid properties, such as its density maximum at
4\degree C. An attempt at theoretical explanation proposes a liquid-liquid
phase transition line in the supercooled liquid state, with coexisting
low-density (LDL) and high-density (HDL) liquid states. This line terminates at
a critical point. It is assumed that the LDL state possesses mesoscopic
tetrahedral structures that give it solid-like properties, while the HDL is a
regular random liquid. But the short-lived nature of these solid-like
structures make them difficult to detect directly. We take a thermodynamic
approach instead, and calculate the thermodynamic Ricci curvature scalar $R$ in
the metastable liquid regime. It is believed that solid-like structures signal
their presence thermodynamically by a positive sign for $R$, with a negative
sign typically present in less organized fluid states. Using thermodynamic data
from ST2 computer simulations fit to a mean field (MF) two state equation of
state, we find significant regimes of positive $R$ in the LDL state, supporting
the proposal of solid-like structures in liquid water. In addition, we review
the theory, compute critical exponents, demonstrate the large reach of the MF
critical regime, and calculate the Widom line using $R$.",1907.13192v1
2013-04-08,Energy and lifetime of resonant states with real basis sets,"Using a probabilistic interpretation of resonant states, we propose a formula
useful to calculate the lifetime of a resonance using square-integrable real
basis-set expansion techniques. Our approach does not require an estimation of
the density of states. The method is illustrated with calculations of $s$ and
$p$ resonant-state energies and lifetimes.",1304.2136v2
2002-05-23,Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?,"We discuss Coleman's theorem concerning the energy density of the ground
state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975).
According to this theorem the energy density of the ground state of the
sine-Gordon model should be unbounded from below for coupling constants beta^2
> 8 pi. The consequence of this theorem would be the non-existence of the
quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that
the energy density of the ground state in the sine-Gordon model is bounded from
below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's
theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and
soliton-soliton scattering in the sine-Gordon model.",0205249v3
2013-07-03,Invariance of reduced density matrices under Local Unitary operations,"We derive necessary and sufficient conditions for local unitary (LU)
operators to leave invariant the set of 1-qubit reduced density matrices of a
multi-qubit state. LU operators with this property are tensor products of {\it
cyclic local} operators, and form a subgroup, the centralizer subgroup of the
set of reduced states, of the Lie group $SU(2)^{\otimes n}$. The dimension of
this subgroup depends on the type of reduced density matrices. It is maximum
when all reduced states are maximally mixed and it is minimum when none of them
is maximally mixed. For any given multi-qubit state, pure or mixed, we compute
the LU operators that fix the corresponding reduced density matrices and
determine the equivalence class of the given state.",1307.0948v2
2023-02-26,Classification of magnetic order from electronic structure by using machine learning,"Identifying the magnetic state of materials is of great interest in a wide
range of applications, but direct identification is not always straightforward
due to limitations in neutron scattering experiments. In this work, we present
a machine-learning approach using decision-tree algorithms to identify
magnetism from the spin-integrated excitation spectrum, such as the density of
states. The dataset was generated by Hartree-Fock mean-field calculations of
candidate antiferromagnetic orders on a Wannier Hamiltonian, extracted from
first-principle calculations targeting BaOsO$_3$. Our machine learning model
was trained using various types of spectral data, including local density of
states, momentum-resolved density of states at high-symmetry points, and the
lowest excitation energies from the Fermi level. Although the density of states
shows good performance for machine learning, the broadening method had a
significant impact on the model's performance. We improved the model's
performance by designing the excitation energy as a feature for machine
learning, resulting in excellent classification of antiferromagnetic order,
even for test samples generated by different methods from the training samples
used for machine learning.",2302.13329v2
2023-10-11,Wigner crystallization in Bernal bilayer graphene,"In Bernal bilayer graphene (BBG), a perpendicular displacement field flattens
the bottom of the conduction band and thereby facilitates the formation of
strongly-correlated electron states at low electron density. Here, we focus on
the Wigner crystal (WC) state, which appears in a certain regime of
sufficiently large displacement field, low electron density, and low
temperature. We first consider a model of BBG without trigonal warping, and we
show theoretically that Berry curvature leads to a new kind of WC state in
which the electrons acquire a spontaneous orbital magnetization when the
displacement field exceeds a critical value. We then consider the effects of
trigonal warping in BBG, and we show that they lead to an unusual ``doubly
re-entrant"" behavior of the WC phase as a function of density. The rotational
symmetry breaking associated with trigonal warping leads to a nontrivial
``minivalley order"" in the WC state, which changes abruptly at a critical value
of displacement field. In both cases, we estimate the phase boundary of the WC
state in terms of density, displacement field, and temperature.",2310.07751v1
2007-09-09,L^2-spectral invariants and convergent sequences of finite graphs,"Using the spectral theory of weakly convergent sequences of finite graphs, we
prove the uniform existence of the integrated density of states for a large
class of infinite graphs.",0709.1261v1
2004-08-17,Extended RPA with ground-state correlations in a solvable model,"The ground states and excited states of the Lipkin model hamiltonian are
calculated using a new theoretical approach which has been derived from an
extended time-dependent Hartree-Fock theory known as the time-dependent
density-matrix theory (TDDM). TDDM enables us to calculate correlated ground
states, and its small amplitude limit (STDDM), which is a version of extended
RPA theories based on a correlated ground state, can be used to calculate
excited states. It is found that this TDDM plus STDDM approach gives much
better results for both the ground states and the excited states than the
Hartree-Fock ground state plus RPA approach.",0408042v1
2014-01-01,Recent Advances in the Microscopic Calculations of Level Densities by the Shell Model Monte Carlo Method,"The shell model Monte Carlo (SMMC) method enables calculations in model
spaces that are many orders of magnitude larger than those that can be treated
by conventional methods, and is particularly suitable for the calculation of
level densities in the presence of correlations. We review recent advances and
applications of SMMC for the microscopic calculation of level densities. Recent
developments include (i) a method to calculate accurately the ground-state
energy of an odd-mass nucleus, circumventing a sign problem that originates in
the projection on an odd number of particles, and (ii) a method to calculate
directly level densities, which, unlike state densities, do not include the
spin degeneracy of the levels. We calculated the level densities of a family of
nickel isotopes $^{59-64}$Ni and of a heavy deformed rare-earth nucleus
$^{162}$Dy and found them to be in close agreement with various experimental
data sets.",1401.0236v1
2019-11-05,Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes,"The dynamics of two-dimensional (2D) topological quadrupole insulator (TQI)
and Chern insulator (CI) after the real-space configuration is transformed from
a cylinder or Mobius strip to open boundary condition (OBC) and vice versa is
analyzed. Similar dynamics of both models are observed, but the quadrupole
corner states of the TQI makes the signatures more prominent. After the systems
transform from a cylinder or Mobius strip to OBC, the occupation of the corner
state of the TQI and the edge state of the CI exhibits steady-state behavior.
The steady-state values depend on the ramping rate of the configuration
transformation, manifesting a type of quantum memory effect. On the other hand,
oscillatory density ripples from the merging of edge states persist after the
systems transform from OBC to a cylinder or Mobius strip. If the final
configuration is a cylinder, the density ripples are along the edges of the
cylinder. In contrast, the density ripples can traverse the bulk after the
systems transform from OBC to a Mobius strip. The transformation of real-space
topology thus can be inferred from the dynamical signatures of the topological
edge states.",1911.01620v1
2022-07-24,Landau-Zener transition with energy-dependent decay rate of the excited state,"A remarkable feature of the Landau-Zener transition is insensitivity of the
survival probability to the decay rate, of the excited state. Namely, the
probability for a particle, which is initially in the ground state, to remain
in the same state is insensitive to decay, which is due to e.g. coupling to
continuum [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)]. This
insensitivity was demonstrated for the case when the density of states in the
continuum is energy-independent. We study the opposite limit when the density
of states in the continuum is a step-like function of energy. As a result of
this step-like behavior of the density of states, the decay rate of a driven
excited level experiences a jump as a function of time at certain moment t_0.
We take advantage of the fact that the analytical solution at t<t_0 and at
t>t_0 is known. We show that the decay enters the survival probability when t_0
is comparable to the transition time.",2207.11849v1
2000-03-07,Double-Layer Systems at Zero Magnetic Field,"We investigate theoretically the effects of intralayer and interlayer
exchange in biased double-layer electron and hole systems, in the absence of a
magnetic field. We use a variational Hartree-Fock-like approximation to analyze
the effects of layer separation, layer density, tunneling, and applied gate
voltages on the layer densities and on interlayer phase coherence. In agreement
with earlier work, we find that for very small layer separations and low layer
densities, an interlayer-correlated ground state possessing spontaneous
interlayer coherence (SILC) is obtained, even in the absence of interlayer
tunneling. In contrast to earlier work, we find that as a function of total
density, there exist four, rather than three, distinct noncrystalline phases
for balanced double-layer systems without interlayer tunneling. The newly
identified phase exists for a narrow range of densities and has three
components and slightly unequal layer densities, with one layer being spin
polarized, and the other unpolarized. An additional two-component phase is also
possible in the presence of sufficiently strong bias or tunneling. The
lowest-density SILC phase is the fully spin- and pseudospin-polarized
``one-component'' phase discussed by Zheng {\it et al.} [Phys. Rev. B {\bf 55},
4506 (1997)]. We argue that this phase will produce a finite interlayer Coulomb
drag at zero temperature due to the SILC. We calculate the particle densities
in each layer as a function of the gate voltage and total particle density, and
find that interlayer exchange can reduce or prevent abrupt transfers of charge
between the two layers. We also calculate the effect of interlayer exchange on
the interlayer capacitance.",0003109v1
2002-10-14,Transposition of a local-density-dependent pion-nucleus potential to an effective density-linear potential - generalized Seki-Masutani relations,"We have shown that a local-density-dependent term, $F[\rho(r)] \rho(r)$, of
the pion-nucleus potential with a nuclear density, $\rho(r)$, can be transposed
to a conventional density-linear term, $F(\rho_e) \rho(r)$, with an effective
nuclear density, $\rho_e$, which is close to $\sim 0.6 \rho(0)$ for most
$\pi^-$ bound states. The presently found relations, {\it generalized
Seki-Masutani relations}, for the density-quadratic term, the medium-modified
isovector term and the double-scattering isoscalar term of the s-wave
pion-nucleus interaction assure that the constant parameters in the
conventional pion-nucleus potential are interpreted as being effective ones in
the light of density-dependent effects.",0210040v2
2018-01-20,Structured Inhomogeneous Density Map Learning for Crowd Counting,"In this paper, we aim at tackling the problem of crowd counting in extremely
high-density scenes, which contain hundreds, or even thousands of people. We
begin by a comprehensive analysis of the most widely used density map-based
methods, and demonstrate how easily existing methods are affected by the
inhomogeneous density distribution problem, e.g., causing them to be sensitive
to outliers, or be hard to optimized. We then present an extremely simple
solution to the inhomogeneous density distribution problem, which can be
intuitively summarized as extending the density map from 2D to 3D, with the
extra dimension implicitly indicating the density level. Such solution can be
implemented by a single Density-Aware Network, which is not only easy to train,
but also can achieve the state-of-art performance on various challenging
datasets.",1801.06642v1
2020-11-16,Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations,"We present accurate many-body results of the electronic densities in several
solid materials, including Si, NaCl, and Cu. These results are obtained using
the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a
plane-wave basis with norm-conserving, multiple-projector pseudopotentials.
AFQMC has been shown to be an excellent many-body total energy method.
Computation of observables and correlation functions other than the
ground-state energy requires back-propagation, whose adaption and
implementation in the plane-wave basis AFQMC framework are discussed in the
present paper. This development allows us to compute correlation functions,
electronic densities and interatomic forces, paving the way for geometry
optimizations and calculations of thermodynamic properties in solids. Finite
supercell size effects are considerably more subtle in the many-body framework
than in independent-electron calculations. We analyze the convergence of the
electronic density, and obtain best estimates for the thermodynamic limit. The
densities from several typical density functionals are benchmarked against our
near-exact results. The electronic densities we have obtained can also be used
to help construct improved density functionals.",2011.08335v2
2022-01-13,Stationary States of the One-Dimensional Discrete-Time Facilitated Symmetric Exclusion Process,"We describe the extremal translation invariant stationary (ETIS) states of
the facilitated exclusion process on $\mathbb{Z}$. In this model all particles
on sites with one occupied and one empty neighbor jump at each integer time to
the empty neighbor site, and if two particles attempt to jump into the same
empty site we choose one randomly to succeed. The ETIS states are qualitatively
different for densities $\rho<1/2$, $\rho=1/2$, and $1/2<\rho<1$, but in each
density region we find states which may be grouped into families, each of which
is in natural correspondence with the set of all ergodic measures on
$\{0,1\}^{\mathbb{Z}}$. For $\rho<1/2$ there is one such family, containing all
the ergodic states in which the probability of two adjacent occupied sites is
zero. For $\rho=1/2$ there are two families, in which configurations translate
to the left and right, respectively, with constant speed 2. For the high
density case there is a continuum of families. We show that all ETIS states at
densities $\rho\le1/2$ belong to these families, and conjecture that also at
high density there are no other ETIS states. We also study the possible ETIS
states which might occur if the conjecture fails.",2201.05175v1
2014-07-03,Strange Quark Star Model with Quadratic Equation of State,"In this paper, we studied the behaviour of compact relativistic objects with
anisotropic matter distribution considering quadratic equation of state of
Feroze and Siddiqui (2011). We specify the gravitational potential Z(x) in
order to integrate the fields equations and there has been calculated the
energy density, the radial pressure, the anisotropy and the mass function. The
new solutions to the Einstein-Maxwell system of equations are found in term of
elementary functions. For n=2, we have obtained the expressions for mass
function, energy density, radius and metric functions of the model of
Thirukkanesh and Ragel (2012) with polytropic equation of state.",1407.0760v1
2006-10-17,Local Density of States around an Impurity in a Strong Magnetic Field. I. a Two-Dimensional System with Parabolic Dispersion,"Bound states around an impurity are investigated for a two dimensional
electron system in a strong magnetic field. Long-range Coulomb potential and
related potentials are considered. Schr\""odinger equation is solved numerically
to obtain the bound states. The energy and wave function of these bound states
are indirectly observed by the scanning tunneling spectroscopy as local density
of states (LDOS). Theoretically obtained LDOS is compared with experiment.
Reasonable agreement is obtained.",0610461v1
2010-12-03,Entangled Qubits in a non-Gaussian Quantum State,"We experimentally generate and tomographically characterize a mixed,
genuinely non-Gaussian bipartite continuous-variable entangled state. By
testing entanglement in 2$\times$2-dimensional two-qubit subspaces, entangled
qubits are localized within the density matrix, which, firstly, proves the
distillability of the state and, secondly, is useful to estimate the efficiency
and test the applicability of distillation protocols. In our example, the
entangled qubits are arranged in the density matrix in an asymmetric way, i.e.
entanglement is found between diverse qubits composed of different photon
number states, although the entangled state is symmetric under exchanging the
modes.",1012.0686v2
2021-08-19,Chiral pair density wave states generated by spin supercurrents,"We report that spin supercurrents in magnetic superconductors and
superconductor/ferromagnetic insulator bilayers can induce the
Dzyaloshinskii-Moriya interaction which strength is proportional to the
superconducting order parameter amplitude. This effect leads to the existence
of inhomogeneous parity-breaking ground states combining the chiral magnetic
helix and the pair density wave orders. The formation of such states takes
place via the penetration of chiral domain walls at the threshold temperature
below the superconducting transition. We find regimes with both the single and
the re-entrant transitions into the inhomogeneous states with decreasing
temperature. The predicted hybrid chiral states can be found in the existing
structures with realistic parameters and materials combinations.",2108.08862v1
2004-07-15,Checkerboard density of states in strong-coupling superconductors,"The Bogoliubov-de Gennes (BdG) equations are solved in the strong-coupling
limit, where real-space (preformed) pairs bose-condense with finite
center-of-mass momenta. There are two energy scales in this regime, a
temperature independent incoherent gap $\Delta_p$ and a temperature dependent
coherent gap $\Delta_c (T)$, modulated in real space. The single-particle
density of states (DOS) reveals checkerboard modulations similar to the
tunnelling DOS in cuprates.",0407401v1
2005-12-22,The Density of States Method at Finite Chemical Potential,"We study the density of states method to explore the phase diagram of the
chiral transition on the temperature and quark chemical potential plane. Four
quark flavors are used in the analysis. Though the method is quite expensive
small lattices show an indication for a triple-point connecting three different
phases on the phase diagram.",0512032v1
2005-08-31,Elliptic Faulhaber polynomials and Lamé densities of states,"A generalisation of the Faulhaber polynomials and Bernoulli numbers related
to elliptic curves is introduced and investigated. This is applied to compute
the density of states for the classical Lam\'e operators.",0508066v1
2006-07-24,Ground state of a confined Yukawa plasma,"The ground state of an externally confined one-component Yukawa plasma is
derived analytically. In particular, the radial density profile is computed.
The results agree very well with computer simulations on three-dimensional
spherical Coulomb crystals. We conclude in presenting an exact equation for the
density distribution for a confinement potential of arbitrary geometry.",0607203v1
1999-09-06,Probability distributions consistent with a mixed state,"A density matrix $\rho$ may be represented in many different ways as a
mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper
characterizes the class of probability distributions $(p_i)$ that may appear in
such a decomposition, for a fixed density matrix $\rho$. Several illustrative
applications of this result to quantum mechanics and quantum information theory
are given.",9909020v1
2011-01-30,Local unitary equivalent consistence for n-party states and their (n-1)-party reduced density matrices,"We present that the local unitary equivalence of n-party pure states is
consistent with the one of their (n-1)-party reduced density matrices. As an
application, we obtain the local invariants for a class of tripartite pure
qudits.",1101.5736v1
2017-09-16,Hopping charge transport in amorphous semiconductors with the spatially correlated exponential density of states,"Hopping charge transport in amorphous semiconductors having spatially
correlated exponential density of states has been considered. Average carrier
velocity is exactly calculated for the quasi-equilibrium (nondispersive)
transport regime. We suggest also a heuristic approach for the consideration of
the carrier velocity for the non-equilibrium dispersive regime.",1709.05500v1
1997-01-25,"Comment on ""Nonzero Fermi Level Density of States for a Disordered d-wave superconductor in 2D"" by Ziegler et al. PRL 77, 3013 (1996)","In their paper Ziegler et al. claim that the model of 2D Dirac fermions in a
random gauge potential has a finite density of states at zero energy. We point
out that the approach used in this paper fails to reproduce the perturbation
theory results for this problem.",9701191v1
2015-09-08,Ground-state electronic structure of quasi-one-dimensional wires in semiconductor heterostructures,"We apply density functional theory, in the local density approximation, to a
quasi-one-dimensional electron gas in order to quantify the effect of Coulomb
and correlation effects in modulating, and therefore patterning, the charge
density distribution. Our calculations are presented specifically for
surface-gate-defined quasi-one-dimensional quantum wires in a GaAs-AlGaAs
heterostructure but we expect our results to apply more generally for other low
dimensional semiconductor systems. We show that at high densities with strong
confinement, screening of electrons in the direction transverse to the wire is
efficient and density modulations are not visible. In the low-density,
weak-confinement regime, the exchange-correlation potential induces small
density modulations as the electrons are depleted from the wire. At the weakest
confinements and lowest densities, the electron density splits into two rows
thereby forming a pair of quantum wires that lie beneath the surface gates. An
additional double-well external potential forms at very low density which
enhances this row splitting phenomenon. We produce phase diagrams that show a
transition between the presence of a single quantum wire in a split-gate
structure and two quantum wires. We suggest that this phenomenon can be used to
pattern and modulate the electron density in low-dimensional structures with
particular application to systems where a proximity effect from a surface gate
would be valuable.",1509.02457v3
2021-12-29,VDPC: Variational Density Peak Clustering Algorithm,"The widely applied density peak clustering (DPC) algorithm makes an intuitive
cluster formation assumption that cluster centers are often surrounded by data
points with lower local density and far away from other data points with higher
local density. However, this assumption suffers from one limitation that it is
often problematic when identifying clusters with lower density because they
might be easily merged into other clusters with higher density. As a result,
DPC may not be able to identify clusters with variational density. To address
this issue, we propose a variational density peak clustering (VDPC) algorithm,
which is designed to systematically and autonomously perform the clustering
task on datasets with various types of density distributions. Specifically, we
first propose a novel method to identify the representatives among all data
points and construct initial clusters based on the identified representatives
for further analysis of the clusters' property. Furthermore, we divide all data
points into different levels according to their local density and propose a
unified clustering framework by combining the advantages of both DPC and
DBSCAN. Thus, all the identified initial clusters spreading across different
density levels are systematically processed to form the final clusters. To
evaluate the effectiveness of the proposed VDPC algorithm, we conduct extensive
experiments using 20 datasets including eight synthetic, six real-world and six
image datasets. The experimental results show that VDPC outperforms two
classical algorithms (i.e., DPC and DBSCAN) and four state-of-the-art extended
DPC algorithms.",2201.00641v1
1997-07-27,Statistical Mechanics of Vibration-Induced Compaction of Powders,"We propose a theory which describes the density relaxation of loosely packed,
cohesionless granular material under mechanical tapping. Using the compactivity
concept we develope a formalism of statistical mechanics which allows us to
calculate the density of a powder as a function of time and compactivity. A
simple fluctuation-dissipation relation which relates compactivity to the
amplitude and frequency of a tapping is proposed. Experimental data of
E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of
initially deposited in a fluffy state powder evolves under carefully controlled
tapping towards a random close packing (RCP) density. Ramping the vibration
amplitude repeatedly up and back down again reveals the existence of reversible
and irreversible branches in the response. In the framework of our approach the
reversible branch (along which the RCP density is obtained) corresponds to the
steady state solution of the Fokker-Planck equation whereas the irreversible
one is represented by a superposition of ""excited states"" eigenfunctions. These
two regimes of response are analyzed theoretically and a qualitative
explanation of the hysteresis curve is offered.",9707276v3
2022-05-17,Deep learning density functionals for gradient descent optimization,"Machine-learned regression models represent a promising tool to implement
accurate and computationally affordable energy-density functionals to solve
quantum many-body problems via density functional theory. However, while they
can easily be trained to accurately map ground-state density profiles to the
corresponding energies, their functional derivatives often turn out to be too
noisy, leading to instabilities in self-consistent iterations and in
gradient-based searches of the ground-state density profile. We investigate how
these instabilities occur when standard deep neural networks are adopted as
regression models, and we show how to avoid it using an ad-hoc convolutional
architecture featuring an inter-channel averaging layer. The testbed we
consider is a realistic model for noninteracting atoms in optical speckle
disorder. With the inter-channel average, accurate and systematically
improvable ground-state energies and density profiles are obtained via
gradient-descent optimization, without instabilities nor violations of the
variational principle.",2205.08367v2
2000-11-14,Odd-Frequency Density Waves: Non-Fermi-Liquid Metals with an Order Parameter,"We consider states with a charge- or spin-density wave order parameter which
is odd in frequency, so that the order parameter vanishes at zero frequency and
there is a conventional Fermi surface. Such states break translational symmetry
and, therefore, are not conventional Fermi liquids. In the odd-frequency
spin-density wave case, there are Goldstone bosons and the low-energy spectrum
is manifestly different from that of a Fermi liquid. We discuss a simple model
which gives rise to such ordered states. The frequency-dependence of the gap
leads to an unusual temperature dependence for various thermodynamic and
transport properties, notably the resistivity.",0011234v2
2006-08-17,Bound states in ab initio approaches to quantum transport: A time-dependent formulation,"In this work we study the role of bound electrons in quantum transport. The
partition-free approach by Cini is combined with time-dependent density
functional theory (TDDFT) to calculate total currents and densities in
interacting systems. We show that the biased electrode-device-electrode system
with bound states does not evolve towards a steady regime. The density
oscillates with history-dependent amplitudes and, as a consequence, the
effective potential of TDDFT oscillates too. Such time dependence might open
new conductive channels, an effect which is not accounted for in any
steady-state approach and might deserve further investigations.",0608401v2
2004-12-01,Neutron matter on the lattice with pionless effective field theory,"We study neutron matter by combining pionless effective field theory with
non-perturbative lattice methods. The neutron contact interaction is determined
by zero temperature scattering data. We simulate neutron matter on the lattice
at temperatures 4 and 8 MeV and densities below one-fifth normal nuclear matter
density. Our results at different lattice spacings agree with one another and
match bubble chain calculations at low densities. The equation of state of pure
neutron matter obtained from our simulations agrees quantitatively with
variational calculations based on realistic potentials.",0412002v1
2018-12-11,Saturation and alternate pathways in four-wave mixing in rubidium,"We have examined the frequency spectrum of the blue light generated via
four-wave mixing in a rubidium vapor cell inside a ring cavity. At high atomic
density and input laser power, two distinct frequency components separated by
$116 \pm 4$ MHz are observed, indicating alternate four-wave mixing channels
through the $6p_{3/2}$ hyperfine states. The dependence of the generated light
on excitation intensity and atomic density are explored, and indicate the
primary process has saturated. This saturation results when the excitation rate
through the 6p state becomes equal to the rate through the 5p state, giving no
further gain with atomic density while a quadratic intensity dependence
remains.",1812.04465v1
2023-07-20,Chiral currents in Bose-Einstein condensates subject to current-density interactions,"Persistent currents in quasi-one-dimensional Bose-Einstein condensates become
chiral in the presence of current-density interactions. This phenomenon is
explored in ultracold atoms loaded in a rotating ring geometry, where diverse
current-carrying stationary states are analytically found to generalize
previously known solutions to the mean-field equations of motion. Their
dynamical stability is tested by numerical simulations that show stable
currents for states with both constant and modulated density profiles, while
decaying currents appear only beyond a unidirectional velocity threshold.
Recent experiments in the field make these states within experimental reach.",2307.10977v1
2014-04-09,Bottomonium states in hot asymmetric strange hadronic matter,"We calculate the in-medium masses of the bottomonium states ($\Upsilon(1S)$,
$\Upsilon(2S)$, $\Upsilon(3S)$ and $\Upsilon(4S)$) in isospin asymmetric
strange hadronic matter at finite temperatures. The medium modifications of the
masses arise due to the interaction of these heavy quarkonium states with the
gluon condensates of QCD. The gluon condensates in the hot hadronic matter are
computed from the medium modification of a scalar dilaton field within a chiral
SU(3) model, introduced in the hadronic model to incorporate the broken scale
invariance of QCD. There is seen to be drop in the masses of the bottomonium
states and mass shifts are observed to be quite considerable at high densities
for the excited states. The effects of density, isospin asymmetry, strangeness
as well as temperature of the medium on the masses of the $\Upsilon$-states are
investigated. The effects of the isospin asymmetry as well as strangeness
fraction of the medium are seen to be appreciable at high densities and small
temperatures. The density effects are the most dominant medium effects which
should have observable consequences in the compressed baryonic matter (CBM) in
the heavy ion collision experiments in the future facility at FAIR, GSI. The
study of the $\Upsilon$ states will however require access to energies higher
than the energy regime planned at CBM experiment. The density effects on the
bottomonium masses should also show up in the dilepton spectra at the SPS
energies, especially for the excited states for which the mass drop is observed
to quite appreciable.",1404.2517v2
2022-05-25,Robust optimal density control of robotic swarms,"In this paper, we propose a computationally efficient, robust density control
strategy for the mean-field model of a robotic swarm. We formulate a static
optimal control problem (OCP) that computes a robot velocity field which drives
the swarm to a target equilibrium density, and we prove the stability of the
controlled system in the presence of transient perturbations and uncertainties
in the initial conditions. The density dynamics are described by a linear
elliptic advection-diffusion equation in which the control enters bilinearly
into the advection term. The well-posedness of the state problem is ensured by
an integral constraint. We prove the existence of optimal controls by embedding
the state constraint into the weak formulation of the state dynamics. The
resulting control field is space-dependent and does not require any
communication between robots or costly density estimation algorithms. Based on
the properties of the primal and dual systems, we first propose a method to
accommodate the state constraint. Exploiting the properties of the state
dynamics and associated controls, we then construct a modified dynamic OCP to
speed up the convergence to the target equilibrium density of the associated
static problem. We then show that the finite-element discretization of the
static and dynamic OCPs inherits the structure and several useful properties of
their infinite-dimensional formulations. Finally, we demonstrate the
effectiveness of our control approach through numerical simulations of
scenarios with obstacles and an external velocity field.",2205.12592v2
2002-01-25,Density of States Monte Carlo Method for Simulation of Fluids,"A Monte Carlo method based on a density-of-states sampling is proposed for
study of arbitrary statistical mechanical ensembles in a continuum. A random
walk in the two-dimensional space of particle number and energy is used to
estimate the density of states of the system; this density of states is
continuously updated as the random walk visits individual states. The validity
and usefulness of the method are demonstrated by applying it to the simulation
of a Lennard-Jones fluid. Results for its thermodynamic properties, including
the vapor-liquid phase coexistence curve, are shown to be in good agreement
with high-accuracy literature data.",0201470v1
2003-05-09,An improved Monte Carlo method for direct calculation of the density of states,"We present an efficient Monte Carlo algorithm for determining the density of
states which is based on the statistics of transition probabilities between
states. By measuring the infinite temperature transition probabilities--that
is, the probabilities associated with move proposal only--we are able to
extract excellent estimates of the density of states. When this estimator is
used in conjunction with a Wang-Landau sampling scheme [F. Wang and D. P.
Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling
of macrostates (e.g., energies) and systematically refine the calculated
density of states. This approach requires only potential energy evaluations,
continues to improve the statistical quality of its results as the simulation
time is extended, and is applicable to both lattice and continuum systems. We
test the algorithm on the Lennard-Jones liquid and demonstrate good statistical
convergence properties.",0305210v3
2006-12-14,Expansion of a mesoscopic Fermi system from a harmonic trap,"We study quantum dynamics of an atomic Fermi system with a finite number of
particles, N, after it is released from a harmonic trapping potential. We
consider two different initial states: The Fermi sea state and the paired state
described by the projection of the grand-canonical BCS wave function to the
subspace with a fixed number of particles. In the former case, we derive exact
and simple analytic expressions for the dynamics of particle density and
density-density correlation functions, taking into account the level
quantization and possible anisotropy of the trap. In the latter case of a
paired state, we obtain analytic expressions for the density and its
correlators in the leading order with respect to the ratio of the trap
frequency and the superconducting gap (the ratio assumed small). We discuss
several dynamic features, such as time evolution of the peak due to pair
correlations, which may be used to distinguish between the Fermi sea and the
paired state.",0612376v2
2005-07-20,Bounds on the energy densities of ground states on static spacetimes of compact objects,"In this paper we investigate quantum fields propagating on given, static,
spherically symmetric spacetimes, which are isometric to a part of the
Schwarzschild spacetime. Without specifying the internal geometry we show, that
there exist bounds on the energy densities of ground states of a quantum scalar
field on such spacetimes. The bounds (from above and below) come from the
so-called Quantum Energy Inequalities, and are centered around the energy
density of the Boulware state (the ground state for Schwarzschild spacetime).
The specific value of the bound from below depends critically on the distance
$\ell$ from the horizon, where the spacetimes of compact objects cease to be
isometric to the Schwarzschild spacetime. In the limit of small $\ell$ we
prove, that the energy densities of ground states cannot be below the Boulware
level.",0507089v1
2003-10-29,On the monotonicity conjecture for the curvature of the Kubo-Mori metric,"The canonical correlation or Kubo-Mori scalar product on the state space of a
finite quantum system is a natural generalization of the classical Fisher
metric. This metric is induced by the von Neumann entropy or the relative
entropy of the quantum mechanical states. An important conjecture of Petz that
the scalar curvature of the state space with Kubo-Mori scalar product as
Riemannian metric is monotone with respect to the majorisation relation of
states: the scalar curvature is increases if one goes to more mixed states. We
give an appropriate grouping for the summands in the expression for the scalar
curvature. The conjecture will follows from the monotonicity of the summands.
We prove the monotonicity for some of these summands and we give numerical
evidences that the remaining terms are monotone too. Note that the real density
matrices form a submanifold of the complex density matrices. We prove that if
Petz's conjecture true for complex density matrices then it is true for real
density matrices too.",0310064v1
2008-04-15,Gap opening with ordering in PrFe4P12 studied by local tunneling spectroscopy,"We present measurements of the local tunneling density of states in the low
temperature ordered state of PrFe4P12. The temperature dependencies of the
Fermi level density of states and of the integrated density of states at low
bias voltages show anomalies at T=6.5 K, the onset of multipolar ordering as
detected by specific heat and other macroscopic measurements. In the ordered
phase, we find a local density of states with a V-shape form, indicating a
partial gap opening over the Fermi surface. The size of the gap according to
the tunneling spectra is about 2 meV.",0804.2312v1
2013-07-01,Phonon structure in dispersion curves and density of states of massive Dirac Fermions,"Dirac fermions exist in many solid state systems including graphene, silicene
and other two dimensional membranes such as are found in group VI
dichalcogenides, as well as on the surface of some insulators where such states
are protected by topology. Coupling of those fermions to phonons introduces new
structures in their dispersion curves and, in the case of massive Dirac
fermions, can shift and modify the gap. We show how these changes present in
angular-resolved photoemission spectroscopy of the dressed charge carrier
dispersion curves and scanning tunneling microscopy measurements of their
density of states. In particular we focus on the region around the band gap. In
this region the charge carrier spectral density no longer consists of a
dominant quasiparticle peak and a smaller incoherent phonon related background.
The quasiparticle picture has broken down and this leads to important
modification in both dispersion curves and density of states.",1307.0422v1
2017-12-06,The hierarchical Green function approach to the two-dimensional Hubbard model,"By introducing multipe-site correlation functions, we propose a hierarchical
Green function approach, and apply it to study the characteristic properties of
a 2D square lattice Hubbard model by solving the equation of motions of a
one-particle Green function and related multipe-site correlation functions.
Under a cut-off approximation and taking the Fourier representation of
multipe-site correlation functions, we obtain an analytical expression of
one-particle Green function with static correlation functions. Then we
calculate the spectral density function of electrons, and obtain that besides
two main peaks corresponding to the lower and upper Hubbard bands in the
spectral density function, there emerge some novel states between these two
main peaks, and the total spectral weight of these emerged states is
proportional to the hole doping concentration . Meanwhile, there also emerge
some collective modes related to possible charge/spin density wave and/or
electronic pairing density wave ordering states. This calculation is completely
consistent with the spectroscopy observations of the cuprate superconductors in
normal states. On the other hand, the appearence of the static correlation
functions in the one-particle Green function can be used to describe the
intertwined orders observed in the normal state of the cuprate superconductors.",1712.02002v1
2018-09-26,Cavity-induced superconducting and $4k_F$ charge-density-wave states,"We propose two experimental setups for fermionic atoms in a high-finesse
optical resonator in which either a superconducting state with s-wave symmetry
of the pairs or a 4k F charge density wave can self-organize. In order to
stabilize the s-wave pairing, a two component attractively in- teracting
fermionic gas is confined to a one dimensional chain structure by an optical
lattice. The tunneling of the atoms along the chains is suppressed initially by
an energy offset between neighbor- ing sites. A Raman transition using the
cavity mode and a transversal pump laser then reintroduces a cavity-assisted
tunneling. The feedback mechanism between the cavity field and the atoms leads
to a spontaneous occupation of the cavity field and of a state of the fermionic
atoms which is dominated by s-wave pairing correlations. Extending the setup to
a quasi-one-dimensional ladder structure where the tunneling of atoms along the
rungs of the ladder is cavity-assisted, the repul- sively interacting fermionic
atoms self-organize into a 4k F charge density wave. We use adiabatic
elimination of the cavity field combined with state-of-the-art density matrix
renormalization group methods in finite systems in order to identify the steady
state phases of the system.",1809.09884v1
2021-01-14,Direct measurement of density-matrix elements using a phase-shifting technique Tianfeng,"A direct measurement protocol allows reconstructing specific elements of the
density matrix of a quantum state without using quantum state tomography.
However, the direct measurement protocols to date are primarily based on weak
or strong measurements with an ancillary pointer, which interacts with the
investigated system to extract information about the specified elements. Here,
we present a direct measurement scheme based on phase-shifting operations which
do not need ancillary pointers. In this method, estimates of at most six
expectation values of projective observables suffice to determine any specific
element of an unknown quantum density matrix. A concrete quantum circuit to
implement this direct measurement protocol for multiqubit states is provided,
which is composed of just single-qubit gates and two multiqubit
controlled-phase gates. This scheme is also extended for the direct measurement
of the density matrix of continuous-variable quantum states. Our method can be
used in quantum information applications where only partial information about
the quantum state needs to be extracted, for example, problems such as
entanglement witnessing, fidelity estimation of quantum systems, and quantum
coherence estimation.",2101.05556v3
2023-03-27,Exact Excited-State Functionals of the Asymmetric Hubbard Dimer,"The exact functionals associated with the (singlet) ground and the two
singlet excited states of the asymmetric Hubbard dimer at half-filling are
calculated using both Levy's constrained search and Lieb's convex formulation.
While the ground-state functional is, as commonly known, a convex function with
respect to the density (or, more precisely, the site occupation), the
functional associated with the (highest) doubly-excited state is found to be
concave. Also, because the density of the first-excited state is
non-invertible, its ``functional'' is a partial, multi-valued function composed
of one concave and one convex branch that correspond to two separate sets of
values of the external potential. Remarkably, it is found that, although the
one-to-one mapping between density and external potential may not apply (as in
the case of the first excited state), each state-specific energy and
corresponding universal functional are ``functions'' whose derivatives are each
other's inverse, just as in the ground state formalism. These findings offer
insight into the challenges of developing state-specific excited-state density
functionals for general applications in electronic structure theory.",2303.15084v5
2013-05-01,Densities and energies of nuclei in dilute matter,"We explore the ground-state properties of nuclear clusters embedded in a gas
of nucleons with the help of Skyrme-Hartree-Fock microscopic calculations. Two
alternative representations of clusters are introduced, namely coordinate-space
and energy-space clusters. We parameterize their density profiles in spherical
symmetry in terms of basic properties of the energy density functionals used
and propose an analytical, Woods-Saxon density profile whose parameters depend,
not only on the composition of the cluster, but also of the nucleon gas. We
study the clusters' energies with the help of the local-density approximation,
validated through our microscopic results. We find that the volume energies of
coordinate-space clusters are determined by the saturation properties of
matter, while the surface energies are strongly affected by the presence of the
gas. We conclude that both the density profiles and the cluster energies are
strongly affected by the gas and discuss implications for the nuclear EoS and
related perspectives. Our study provides a simple, but microscopically
motivated modeling of the energetics of clusterized matter at subsaturation
densities, for direct use in consequential applications of astrophysical
interest.",1305.0282v1
2000-11-15,Separable approximations of density matrices of composite quantum systems,"We investigate optimal separable approximations (decompositions) of states
rho of bipartite quantum systems A and B of arbitrary dimensions MxN following
the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261
(1998)]. Such approximations allow to represent in an optimal way any density
operator as a sum of a separable state and an entangled state of a certain
form. For two qubit systems (M=N=2) the best separable approximation has a form
of a mixture of a separable state and a projector onto a pure entangled state.
We formulate a necessary condition that the pure state in the best separable
approximation is not maximally entangled. We demonstrate that the weight of the
entangled state in the best separable approximation in arbitrary dimensions
provides a good entanglement measure. We prove in general for arbitrary M and N
that the best separable approximation corresponds to a mixture of a separable
and an entangled state which are both unique. We develop also a theory of
optimal separable approximations for states with positive partial transpose
(PPT states). Such approximations allow to decompose any density operator with
positive partial transpose as a sum of a separable state and an entangled PPT
state. We discuss procedures of constructing such decompositions.",0011066v2
2021-04-12,QCD sum rule analysis of Bottomonium ground states,"The in-medium masses of the bottomonium ground states [$1S$ ($\Upsilon (1S),
\eta_b$) and $1P$ ($\chi_{b0},\chi_{b1}$)] are investigated in the magnetized
vacuum (nuclear medium), using the QCD sum rule framework. In QCD sum rule
approach, the mass modifications are calculated in terms of the medium
modifications of the scalar and twist-2 gluon condensates, which are obtained
in the nuclear medium, from the medium change of a scalar dilaton field, $\chi$
within a chiral effective model. The in-medium masses of the bottomonium ground
states are observed to decrease with increasing density. P-wave states are
observed to have more appreciable mass-shifts than the S-wave states. In the
present investigation, the effects of spin-mixing between 1S bottomonium
states, $\Upsilon(1S)$ and $\eta_b$ are taking into account in presence of an
external magnetic field. The contribution of magnetic fields are seen to be
dominant via spin-magnetic field interaction effects, which leads to an
appreciable rise and drop in the in-medium masses of the longitudinal component
of vector $1S$ state ($\Upsilon$) and pseudoscalar state ($\eta_b$)
respectively. For zero magnetic field, the effects of baryon density on the
bottomonium ground states in isospin asymmetric nuclear medium are observed to
be quite appreciable. These should have observable consequences for the
production of the open and hidden bottom meson states resulting from high
energy asymmetric nuclear collisions in facilities which probe high density
baryonic matter. There is observed to be large contributions to the masses of
the longitudinal component of the vector bottomonium state, $\Upsilon (1S)$ and
pesudoscalar state $\eta_b$ in strong magnetic fields.",2104.05471v1
2014-01-15,Something special at the event horizon,"We calculate the free-fall energy density of scalar fields semi-classically
by employing the trace anomaly on a two-dimensional Schwarzschild black hole
with respect to various black hole states in order to clarify whether something
special at the horizon happens or not. For the Boulware state, the energy
density at the horizon is always negative divergent, which is independent of
initial free-fall positions. However, in the Unruh state the initial free-fall
position is responsible for the energy density at the horizon and there is a
critical point to determine the sign of the energy density at the horizon. In
particular, a huge negative energy density appears when the freely falling
observer is dropped just near the horizon. For the Hartle-Hawking state, it may
also be positive or negative depending on the initial free-fall position, but
it is always finite. Finally, we discuss physical consequences of these
calculations.",1401.3501v4
2015-06-12,Criticality at the Haldane-insulator charge-density-wave quantum phase transition,"Exploiting the entanglement concept within a matrix-product-state based
infinite density-matrix renormalization group approach, we show that the
spin-density-wave and bond-order-wave ground states of the one-dimensional
half-filled extended Hubbard model give way to a symmetry-protected topological
Haldane state in case an additional alternating ferromagnetic spin interaction
is added. In the Haldane insulator the lowest entanglement level features a
characteristic twofold degeneracy. Increasing the ratio between
nearest-neighbor and local Coulomb interaction $V/U$, the enhancement of the
entanglement entropy, the variation of the charge, spin and neutral gaps, and
the dynamical spin/density response signal a quantum phase transition to a
charge-ordered state. Below a critical point, which belongs to the universality
class of the tricritical Ising model with central charge 7/10, the model is
critical with $c=1/2$ along the transition line. Above this point, the
transition between the Haldane insulator and charge-density-wave phases becomes
first order.",1506.04003v2
2022-04-28,Local Rotational Jamming and Multi-Scale Hyperuniformities in an Active Spinner System,"An active system consisting of many self-spinning dimers is simulated, and a
distinct local rotational jamming transition is observed as the density
increases. In the low density regime, the system stays in an absorbing state,
in which each dimer rotates independently subject to the applied torque. While
in the high density regime, a fraction of the dimers become rotationally jammed
into local clusters, and the system exhibits spinodal-decomposition like
two-phase morphologies. For high enough densities, the system becomes
completely jammed in both rotational and translational degrees of freedom. Such
a simple system is found to exhibit rich and multiscale disordered
hyperuniformities among the above phases: the absorbing state shows a critical
hyperuniformity of the strongest class and subcritically preserves the
vanishing density-fluctuation scaling up to some length scale; the
locally-jammed state shows a two-phase hyperuniformity conversely beyond some
length scale with respect to the phase cluster sizes; the totally jammed state
appears to be a monomer crystal, but intrinsically loses large-scale
hyperuniformity. These results are inspiring for designing novel
phase-separation and disordered hyperuniform systems through dynamical
organization.",2204.13391v1
2023-08-22,"Pair density wave, unconventional superconductivity, and non-Fermi liquid quantum critical phase in frustrated Kondo lattice","Motivated by the recent discovery of an intermediate quantum critical phase
between the antiferromagnetic order and the Fermi liquid in the frustrated
Kondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated
$J_1$-$J_2$ XXZ interactions among local spins using the density matrix
renormalization group method. Our simulations reveal a global phase diagram
with rich ground states including the antiferromagnetic order, the
valence-bond-solid and bond-order-wave orders, the pair density wave state, the
uniform superconducting state, and the Luttinger liquid state. We show that
both the pair density wave and uniform superconductivity belong to the family
of Luther-Emery liquids and may arise from pair instability of an intermediate
quantum critical phase with medium Fermi volume in the presence of strong
quantum fluctuations, while the Luttinger liquid has a large Fermi volume. This
suggests a deep connection between the pair density wave, the unconventional
superconductivity, and the non-Fermi liquid quantum critical phase.",2308.11414v2
2006-02-08,Orbital densities functional,"Local density approximation (LDA) to the density functional theory (DFT) has
continuous derivative of total energy as a number of electrons function and
continuous exchange-correlation potential, while in exact DFT both should be
discontinuous as number of electrons goes through an integer value. We propose
orbital densities functional (ODF) (with orbitals defined as Wannier functions)
that by construction obeys this discontinuity condition. By its variation
one-electron equations are obtained with potential in the form of projection
operator. The operator increases a separation between occupied and empty bands
thus curing LDA deficiency of energy gap value systematic underestimation.
Orbital densities functional minimization gives ground state orbital and total
electron densities. The ODF expression for the energy of orbital densities
fluctuations around the ground state values defines ODF fluctuation Hamiltonian
that allows to treat correlation effects. Dynamical mean-field theory (DMFT)
was used to solve this Hamiltonian with quantum Monte Carlo (QMC) method for
effective impurity problem. We have applied ODF method to the problem of
metal-insulator transition in lanthanum trihydride LaH_{3-x}. In LDA
calculations ground state of this material is metallic for all values of
hydrogen nonstoichiometry x while experimentally the system is insulating for x
< 0.3. ODF method gave paramagnetic insulator solution for LaH_3 and LaH_{2.75}
but metallic state for LaH_{2.5}.",0602204v1
2021-06-12,Stiffening of matter in quark-hadron continuity,"We discuss stiffening of matter in quark-hadron continuity. We introduce a
model that relates quark wave functions in a baryon and the occupation
probability of states for baryons and quarks in dense matter. In a dilute
regime, the confined quarks contribute to the energy density through the masses
of baryons, but do not directly contribute to the pressure; hence, the
equations of state are very soft. This dilute regime continues until the low
momentum states for quarks get saturated; this may happen even before baryons
fully overlap, possibly at density slightly above the nuclear saturation
density. After the saturation the pressure grows rapidly while changes in
energy density are modest, producing a peak in the speed of sound. If we use
baryonic descriptions for quark distributions near the Fermi surface, we reach
a description similar to the quarkyonic matter model of McLerran and Reddy.
With a simple adjustment of quark interactions to get the nucleon mass, our
model becomes consistent with the constraints from 1.4-solar mass neutron
stars, but the high density part is too soft to account for two-solar mass
neutron stars. We delineate the relation between the saturation effects and
short range interactions of quarks, suggesting interactions that leave low
density equations of state unchanged but stiffen the high density part.",2106.06687v3
2009-09-09,Spin density in frustrated magnets under mechanical stress: Mn-based antiperovskites,"In this paper we present results of our calculations of the non-collinear
spin density distribution in the systems with frustrated triangular magnetic
structure (Mn-based antiperovskite compounds, Mn_{3}AN (A=Ga, Zn)) in the
ground state and under external mechanical strain. We show that the spin
density in the (111)-plane of the unit cell forms a ""domain"" structure around
each atomic site but it has a more complex structure than the uniform
distribution of the rigid spin model, i.e. Mn atoms in the (111)-plane form
non-uniform ""spin clouds"", with the shape and size of these ""domains"" being
function of strain. We show that both magnitude and direction of the spin
density change under compressive and tensile strains, and the orientation of
""spin domains"" correlates with the reversal of the strain, i.e. switching
compressive to tensile strain (and vice versa) results in ""reversal"" of the
domains. We present analysis for the intra-atomic spin-exchange interaction and
the way it affects the spin density distribution. In particular, we show that
the spin density inside the atomic sphere in the system under mechanical stress
depends on the degree of localization of electronic states.",0909.1825v1
1999-05-28,Identification of the Chemical Potential of an Open System at 0 K with Functional Derivatives of the Integer-State Energy Density Functionals,"Open-system density functional theory may be formulated in terms of ensemble
averages arising from interaction with a bath. The system is allowed to
exchange particles with the bath and the states in the ensemble average are
those corresponding to integer numbers of particles. The weights in the
ensemble average are typically equated with time-averaged values of the
occupation numbers of the various states comprising the open system. As a
result, there are two constraints on the occupation numbers: (1) Their sum must
be unity so that the ensemble average is a probability function and (2) The sum
of the occupation numbers times the number of particles for the associated
state must equal the time-averaged number of particles.
  By solving explicitly the first constraint we arrive at an expression for the
energy having a form structurally equivalent to a Gibbs thermodynamic function.
  From this form follows both chemical potential equalization and the
identification of the functional derivative of the energy for a particular
state with respect to its integer-state density as the chemical potential. We
highlight a distinction between functional derivatives of the time-averaged and
the integer-state energies with respect to integer-state densities. From this
we can restate the jump discontinuity behavior of the exchange-correlation
functional in terms of integer-state behavior.",9905414v1
2008-10-27,Particle production in models with helicity-0 graviton ghost in de Sitter spacetime,"We revisit the problem of the helicity-0 ghost mode of massive graviton in
the de Sitter background. In general, the presence of a ghost particle, which
has negative energy, drives the vacuum to be unstable through pair production
of ghost particles and ordinary particles. In the case that the vacuum state
preserves the de Sitter invariance, the number density created by the pair
production inevitably diverges due to unsuppressed ultra-violet(UV)
contributions. In such cases one can immediately conclude that the model is not
viable. However, in the massive gravity theory we cannot construct a vacuum
state which respects the de Sitter invariance. Therefore the presence of a
ghost does not immediately mean the breakdown of the model. Explicitly
estimating the number density and the energy density of particles created by
the pair production of two conformal scalar particles and one helicity-0 ghost
graviton, we find that these densities both diverge. However, since models with
helicity-0 ghost graviton have no de Sitter invariant vacuum state, it is
rather natural to consider a UV cutoff scale in the three-dimensional momentum
space. Then, even if we take the cutoff scale as large as the Planck scale, the
created number density and energy density are well suppressed. In many models
the cutoff scale is smaller than the Planck scale. In such models the created
number density and the energy density are negligiblly small as long as only the
physics below the cutoff scale is concerned.",0810.4811v1
2002-04-15,Existence of the density of states for some alloy type models with single site potentials of changing sign,"We study spectral properties of ergodic random Schr\""odinger operators on
$L^2 (\RR^d)$. The density of states is shown to exist for a certain class of
alloy type potentials with single site potentials of changing sign. The Wegner
estimate we prove implies Anderson localization under certain additional
assumptions. For some examples we discuss briefly some properties of the common
and conditional densities of the random coupling constants used in the proof of
the Wegner estimate.",0204031v1
2014-01-22,Heavy-ion Collisions: Direct and indirect probes of the density and temperature dependence of Esym,"Heavy-ion collisions provide a versatile terrestrial probe of the nuclear
equation of state through the formation of nuclear matter at a wide variety of
temperatures, densities, and pressures. Direct and indirect approaches for
constraining the density dependence of the symmetry energy using heavy-ion
collisions have been developed. The direct approach relies on scaling methods
which attempt to connect isotopic fragment distributions to the symmetry
energy. Using the indirect approach constraints on the equation of state are
extracted from comparison of experimental results and theoretical transport
calculations which utilize effective nucleon-nucleon interactions. Besides
exploring the density dependence of the equation of state, heavy-ion collisions
are simultaneously probing different temperature gradients of nuclear matter
allowing for the temperature dependence of the symmetry energy to be examined.
The current progress and open questions related to constraining the density and
temperature dependence of the symmetry energy with heavy-ion collisions are
discussed in the review.",1401.5533v1
2015-01-16,Magnetic dichroism study on Mn$_{1.8}$Co$_{1.2}$Ga thin film using a combination of X-ray absorption and photoemission spectroscopy,"Using circularly polarised radiation and a combination of bulk-sensitive hard
X-ray photoelectron spectroscopy and X-ray-absorption spectroscopy (XAS) we
studied the electronic and magnetic structure of epitaxial
Mn$_{1.8}$Co$_{1.2}$Ga thin films. Spin resolved Bloch spectral functions,
density of states as well as charge and magnetisation densities were
investigated by a first-principles analysis of full potential, fully
relativistic Korringa--Kohn--Rostoker calculations of the electronic structure.
The valence states were experimentally investigated by using linear dichroism
in the angular distribution and comparing the results to spin-resolved
densities of states. The linear dichroism in the valence band enabled a
symmetry analysis of the contributing states. The spectra were in good
agreement with the theoretical partial density of states. The element-specific,
spin-resolved, unoccupied densities of states for Co and Mn were analysed by
using XAS and X-ray magnetic circular dichroism (XMCD) at the $L_{3,2}$ edges.
The spectra were influenced by strong correlation effects. XMCD was used to
extract the site resolved magnetic moments. The experimental values of $m_{\rm
Mn}=0.7\:\mu_B$ and $m_{\rm Co}=1.05\:\mu_B$ agree very well with the
calculated magnetic moments. Magnetic circular dichroism in angle-resolved
photoelectron spectroscopy at the Mn and Co $2p$ core level exhibited a
pronounced magnetic dichroism and confirmed the localised character of the Mn
$d$ valence states.",1501.03962v1
2016-01-21,Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator,"Results are presented for the occupation probabilities and current densities
of bulk and edge states of half-filled graphene in a cylindrical geometry, and
irradiated by a circularly polarized laser. It is assumed that the system is
closed, and that the laser has been switched on as a quench. Laser parameters
corresponding to some representative topological phases are studied: one where
the Chern number of the Floquet bands equals the number of chiral edge modes, a
second where anomalous edge states appear in the Floquet Brillouin zone
boundaries, and a third where the Chern number is zero, yet topological edge
states appear at the center and boundaries of the Floquet Brillouin zone.
Qualitative differences are found for the high frequency off-resonant and low
frequency on-resonant laser with edge states arising due to resonant processes
occupied with a high effective temperature on the one hand, while edge states
arising due to off-resonant processes occupied with a low effective temperature
on the other. For an ideal half-filled system where only one of the bands in
the Floquet Brillouin zone is occupied and the other empty, particle-hole and
inversion symmetry of the Floquet Hamiltonian implies zero current density.
However the laser switch-on protocol breaks the inversion symmetry, resulting
in a net cylindrical sheet of current density at steady-state. Due to the
underlying chirality of the system, this current density profile is associated
with a net charge imbalance between the top and bottom of the cylinders.",1601.05732v3
2020-11-28,Defect State Density and Orbital Localization in a-Si:H/c-Si Heterojunction and the Role of H,"In this paper, we explore the effect of H and its bonding configurations on
the defect state density and orbital localization of hydrogenated amorphous Si
(a-Si:H)/crystalline Si (c-Si) heterostructures using density functional theory
(DFT) studies of model interfaces between amorphous silicon (a- Si)/a-Si:H and
c-Si. To model the atomic configuration of a-Si on c-Si, melting and quenching
simulations were performed using classical molecular dynamics (MD). Different
hydrogen contents were inserted into the a-Si in different bonding
configurations followed by DFT relaxation to create the stable structures of
a-Si:H representative of hydrogenated a-Si on crystalline Si surfaces. In
contrast to crystalline heterojunctions (where the interface density is a
maximum at the interface), we find that, in the most energetically stable
configurations of H atoms, the defect state density is relatively low at the
interface and maximum at the middle of a-Si layer. Our structural analysis
shows that in these configurations, H atoms do not necessarily bond to dangling
bonds or to interface atoms. However, they are able to significantly change the
atomic structure of the heterostructure and consequently decrease the density
of defect states and orbital localization at the a-Si layer and more
significantly at the interface of a-Si/c-Si. The general form of the modeled
defect state distribution demonstrates the passivating role of a-Si:H on c-Si
substrates.",2011.14158v1
2021-03-29,Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory,"The Reduced Density Matrix Functional Theory (RDMFT) is a remarkable tool for
studying properties of ground states of strongly interacting quantum many body
systems. As it gives access to the one-particle reduced density matrix of the
ground state, it provides a perfectly tailored approach to studying the
Bose-Einstein condensation or systems of strongly correlated electrons. In
particular, for homogeneous Bose-Einstein condensates as well as for the
Bose-Hubbard dimer it has been recently shown that the relevant density
functional exhibits a repulsive gradient (called the Bose-Einstein condensation
force) which diverges when the fraction of non-condensed bosons tends to zero.
In this paper, we show that the existence of the Bose-Einstein condensation
force is completely universal for any type of pair-interaction and also in the
non-homogeneous gases. To this end, we construct a universal family of
variational trial states which allows us to suitably approximate the relevant
density functional in a finite region around the set of the completely
condensed states. We also show the existence of an analogous repulsive gradient
in the fermionic RDMFT for the $N$-fermion singlet sector in the vicinity of
the set of the Hartree-Fock states. Finally, we show that our approximate
functional may perform well in electron transfer calculations involving low
numbers of electrons. This is demonstrated numerically in the Fermi-Hubbard
model in the strongly correlated limit where some other approximate functionals
are known to fail.",2103.17069v6
2023-04-11,Building an Equation of State Density Ladder,"The confluence of major theoretical, experimental, and observational advances
are providing a unique perspective on the equation of state of dense
neutron-rich matter -- particularly its symmetry energy -- and its imprint on
the mass-radius relation for neutron stars. In this contribution we organize
these developments in an equation of state density ladder. Of particular
relevance to this discussion is the impact of the various rungs on the equation
of state and the identification of possible discrepancies among the various
methods. A preliminary analysis identifies a possible tension between
laboratory measurements and gravitational-wave detections that could indicate
the emergence of a phase transition in the stellar core.",2304.05441v1
2005-03-21,Continuous optimal ensembles I: A geometrical characterization of robustly separable quantum states,"A geometrical characterization of robustly separable (that is, remaining
separable under sufficiently small variiations) mixed states of a bipartite
quantum system is given. It is shown that the density matrix of any such state
can be represented as a normal vector to a hypersurface in the Euclidean space
of all self-adjoint operators in the state space of the whole system. The
expression for this hypersurface is provided.",0503173v1
2012-07-16,Quantum properties and dynamics of X states,"X states are a broad class of two-qubit density matrices that generalize many
states of interest in the literature. In this work, we give a comprehensive
account of various quantum properties of these states, such as entanglement,
negativity, quantum discord and other related quantities. Moreover, we discuss
the transformations that preserve their structure both in terms of continuous
time evolution and discrete quantum processes.",1207.3689v1
2019-03-03,Symplectic tomography of nonlinear coherent states of a trapped ion,"Squeezed and rotated quadrature of an ion in a Paul trap is discussed in
connection with reconstructing its quantum state using symplectic-tomography
method. Marginal distributions of the quadrature for squeezed and correlated
states and for nonlinear coherent states of a trapped ion are obtained and the
density matrices in the Fock basis are expressed explicitly in terms of these
marginal distributions.",1903.00882v1
2005-07-04,A 2-Dimensional Cellular Automaton for Agents Moving from Origins to Destinations,"We develop a two-dimensional cellular automaton (CA) as a simple model for
agents moving from origins to destinations. Each agent moves towards an empty
neighbor site corresponding to the minimal distance to its destination. The
stochasticity or noise ($p$) is introduced in the model dynamics, through the
uncertainty in estimating the distance from the destination. The friction
parameter $""\mu""$ is also introduced to control the probability that the
movement of all agents involved to the same site (conflict) is denied at one
time step. This model displays two states; namely the freely moving and the
jamming state. If $\mu$ is large and $p$ is low, the system is in the jamming
state even if the density is low. However, if $\mu$ is large and $p$ is high, a
freely moving state takes place whenever the density is low. The cluster size
and the travel time distributions in the two states are studied in detail. We
find that only very small clusters are present in the freely moving state while
the jamming state displays a bimodal distribution. At low densities, agents can
take a very long time to reach their destinations if $\mu$ is large and $p$ is
low (jamming state); but long travel times are suppressed if $p$ becomes large
(freely moving state).",0507012v1
1998-12-28,Electronic Density of States of Atomically Resolved Single-Walled Carbon Nanotubes: Van Hove Singularities and End States,"The electronic density of states of atomically resolved single-walled carbon
nanotubes have been investigated using scanning tunneling microscopy. Peaks in
the density of states due to the one-dimensional nanotube band structure have
been characterized and compared with the results of tight-binding calculations.
In addition, tunneling spectroscopy measurements recorded along the axis of an
atomically-resolved nanotube exhibit new, low-energy peaks in the density of
states near the tube end. Calculations suggest that these features arise from
the specific arrangement of carbon atoms that close the nanotube end.",9812408v1
2002-10-01,Quantum Disorder and Quantum Chaos in Andreev Billiards,"We investigate the crossover from the semiclassical to the quantum
description of electron energy states in a chaotic metal grain connected to a
superconductor. We consider the influence of scattering off point impurities
(quantum disorder) and of quantum diffraction (quantum chaos) on the electron
density of states. We show that both the quantum disorder and the quantum chaos
open a gap near the Fermi energy. The size of the gap is determined by the mean
free time in disordered systems and by the Ehrenfest time in clean chaotic
systems. Particularly, if both times become infinitely large, the density of
states is gapless, and if either of these times becomes shorter than the
electron escape time, the density of states is described by random matrix
theory. Using the Usadel equation, we also study the density of states in a
grain connected to a superconductor by a diffusive contact.",0210033v1
2008-09-03,Alpha-Particle Condensation in Nuclear Systems,"The onset of quartetting, i.e. alpha-particle condensation, in symmetric
nuclear matter is studied with the help of an in-medium modified four nucleon
equation. It is found that at very low density quartetting wins over pairing,
because of the strong binding of the alpha-particles. The critical temperature
can reach values up to around 6 MeV. Also the disappearance of alpha-particles
with increasing density, i.e. the Mott transition, is investigated. In finite
nuclei the Hoyle state, that is the 0_2^+ of 12C, is identified as an
""alpha-particle condensate"" state. It is conjectured that such states also
exist in heavier n alpha-nuclei, like 16O, 20Ne, etc. For instance the 6-th 0^+
state of 16O at 15.1 MeV is identified from a theoretical analysis as being a
strong candidate for an alpha condensate state. Exploratory calculations are
performed for the density dependence of the alpha condensate fraction at zero
temperature to address the suppression of the four-particle condensate below
nuclear-matter density. Possible quartet condensation in other systems is
discussed briefly",0809.0542v1
2014-09-09,Anomalous density of states in multiband superconductors near Lifshitz transition,"We consider a multiband metal with deep primary bands and a shallow secondary
one. In the normal state the system undergoes Lifshitz transition when the
bottom of the shallow band crosses the Fermi level. In the superconducting
state Cooper pairing in the shallow band is induced by the deep ones. As a
result, the density of electrons in the shallow band remains finite even when
the bottom of the band is above the Fermi level. We study the density of states
in the system and find qualitatively different behaviors on the two sides of
the Lifshitz transition. On one side of the transition the density of states
diverges at the energy equal to the induced gap, whereas on the other side it
vanishes. We argue that this physical picture describes the recently measured
gap structure in shallow bands of iron pnictides and selenides.",1409.2807v2
2021-11-03,Proof of the universal density of charged states in QFT,"We prove a recent conjecture by Harlow and Ooguri concerning a universal
formula for the charged density of states in QFT at high energies for global
symmetries associated with finite groups. An equivalent statement, based on the
entropic order parameter associated with charged operators in the thermofield
double state, was proven in a previous article by Casini, Huerta, Pontello, and
the present author. Here we describe how the statement about the entropic order
parameter arises, and how it gets transformed into the universal density of
states. The use of the certainty principle, relating the entropic order and
disorder parameters, is crucial for the proof. We remark that although the
immediate application of this result concerns charged states, the origin and
physics of such density can be understood by looking at the vacuum sector only.
We also describe how these arguments lie at the origin of the so-called entropy
equipartition in these type of systems, and how they generalize to QFT's on
non-compact manifolds.",2111.02418v2
2022-04-21,Normalization procedure for obtaining the local density of states from high-bias scanning tunneling spectroscopy,"Differential conductance spectroscopy performed in the high bias regime -- in
which the applied voltage exceeds the sample work function -- is a poor measure
of the local density of states due to the effects of the changing tunnel
barrier. Additionally, the large applied voltage oftentimes makes
constant-height measurement experimentally impractical, lending
constant-current spectroscopy an advantageous edge; but the differential
conductance in that case is even further removed from the local density of
states due to the changing tip height. Here, we present a normalization scheme
for extracting the local density of states from high bias scanning tunneling
spectroscopy, obtained in either constant-current or constant-height mode. We
extend this model to account for the effects of the in-plane momentum of the
probed states to the overall current. We demonstrate the validity of the
proposed scheme by applying it to laterally confined field-emission resonances,
which appear as peak-shaped spectroscopic features with a well-defined in-plane
momentum.",2204.09929v2
2013-07-22,Topological quantum phase transition in Kane-Mele-Kondo lattice model,"We systematically explore the ground-state phase diagram of the
Kane-Mele-Kondo lattice model on the honeycomb lattice, in particular, we focus
on its magnetic properties which has not been studied in the previous
publication[Feng, Dai, Chung, and Si, Phys. Rev. Lett. \textbf{111}, 016402
(2013)]. Beside the Kondo insulator found in that paper, two kinds of
antiferromagnetic spin-density-wave phases are identified. One is the normal
antiferromagnetic spin-density-wave state and the other is a nontrivial
topological antiferromagnetic spin-density-wave state with a quantized spin
Hall conductance and a helical edge-state. The quantum spin Hall insulator is
found to be absent since it is always unstable to antiferromagnetic
spin-density-wave states at least at the mean-field level in our model.
Furthermore, the transition between the two spin-density-wave phases are
topological quantum phase transition described by the three-dimensional quantum
electrodynamics, in which conduction electrons contribute to the low-energy
Dirac fermions while the spin-wave fluctuation of local spins gives rise to an
effective dynamic U(1) gauge-field. Such nontrivial transition shows radical
critical thermodynamic, transport and single-particle behaviors, which provide
a fingerprint for this transition. Additionally, the transition of
antiferromagnetic spin-density-wave states to the Kondo insulator is found to
be first-order. The introduction of two novel magnetic phases and their
topological quantum phase transition show rich and intrinsic physics involving
in the Kane-Mele-Kondo lattice model.",1307.5627v2
2010-09-05,Current Developments in Nuclear Density Functional Methods,"Density functional theory (DFT) became a universal approach to compute
ground-state and excited configurations of many-electron systems held together
by an external one-body potential in condensed-matter, atomic, and molecular
physics. At present, the DFT strategy is also intensely studied and applied in
the area of nuclear structure. The nuclear DFT, a natural extension of the
self-consistent mean-field theory, is a tool of choice for computations of
ground-state properties and low-lying excitations of medium-mass and heavy
nuclei. Over the past thirty-odd years, a lot of experience was accumulated in
implementing, adjusting, and using the density-functional methods in nuclei.
This research direction is still extremely actively pursued. In particular,
current developments concentrate on (i) attempts to improve the performance and
precision delivered by the nuclear density-functional methods, (ii) derivations
of density functionals from first principles rooted in the low-energy
chromodynamics and effective theories, and (iii) including effects of
low-energy correlations and symmetry restoration. In this study, we present an
overview of recent results and achievements gained in nuclear
density-functional methods.",1009.0899v1
2021-10-11,Density-Based Clustering with Kernel Diffusion,"Finding a suitable density function is essential for density-based clustering
algorithms such as DBSCAN and DPC. A naive density corresponding to the
indicator function of a unit $d$-dimensional Euclidean ball is commonly used in
these algorithms. Such density suffers from capturing local features in complex
datasets. To tackle this issue, we propose a new kernel diffusion density
function, which is adaptive to data of varying local distributional
characteristics and smoothness. Furthermore, we develop a surrogate that can be
efficiently computed in linear time and space and prove that it is
asymptotically equivalent to the kernel diffusion density function. Extensive
empirical experiments on benchmark and large-scale face image datasets show
that the proposed approach not only achieves a significant improvement over
classic density-based clustering algorithms but also outperforms the
state-of-the-art face clustering methods by a large margin.",2110.05096v3
2014-05-14,Quantum Mechanics Without State Vectors,"It is proposed to give up the description of physical states in terms of
ensembles of state vectors with various probabilities, relying instead solely
on the density matrix as the description of reality. With this definition of a
physical state, even in entangled states nothing that is done in one isolated
system can instantaneously effect the physical state of a distant isolated
system. This change in the description of physical states opens up a large
variety of new ways that the density matrix may transform under various
symmetries, different from the unitary transformations of ordinary quantum
mechanics. Such new transformation properties have been explored before, but so
far only for the symmetry of time translations into the future, treated as a
semi-group. Here new transformation properties are studied for general symmetry
transformations forming groups, rather than semi-groups. Arguments are given
that such symmetries should act on the density matrix as in ordinary quantum
mechanics, but loopholes are found for all of these arguments.",1405.3483v1
2017-06-06,Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions,"We report results of the first systematic simulation of proton and neutron
density distributions in central heavy-ion collisions within the beam energy
range of $ E_{\rm beam} \leq 800 \, \text{MeV/nucl}$ using pBUU and TDHF
models. The symmetric $^\text{40}$Ca +$^\text{40}$Ca, $^\text{48}$Ca
+$^\text{48}$Ca, $^\text{100}$Sn +$^\text{100}$Sn and $^\text{120}$Sn +
$^\text{120}$Sn and asymmetric $^\text{40}$Ca +$^\text{48}$Ca and
$^\text{100}$Sn +$^\text{120}$Sn systems were chosen for the simulations. We
find limits on the maximum proton and neutron densities and the related
proton-neutron asymmetry $\delta$ as a function of the initial state, beam
energy, system size and a symmetry energy model. While the maximum densities
are almost independent of these parameters, our simulation reveals, for the
first time, their subtle impact on the proton-neutron asymmetry. Most
importantly, we find that variations in the proton-neutron asymmetry at maximum
densities are related at most at 50\% level to the details in the symmetry
energy at supranormal density. The reminder is due to the details in the
symmetry energy at subnormal densities and its impact on proton and neutron
distributions in the initial state. This result puts to forefront the need of a
proper initialization of the nuclei in the simulation, but also brings up the
question of microscopy, such as shell effects, that affect initial proton and
neutron densities, but cannot be consistently incorporated into semiclassical
transport models.",1706.01582v1
2021-04-01,Ground state features and spectral properties of large polaron liquids from low to high charge densities,"A new variational approach is proposed at zero temperature for a finite
density of charge carriers in order to study ground state features of the
Frohlich model including electron-electron and electron-phonon interactions.
Within the intermediate electron-phonon coupling regime characteristic of large
polarons, the approach takes into account on the same footing polaron formation
and polaron-polaron correlations which play a relevant role going from low to
high charge densities. Including fluctuations on top of the variational
approach, the electronic spectral function is calculated from the weak to the
intermediate electron-phonon coupling regime finding a peak-dip-hump line
shape. The spectra are characterized by a transfer of spectral weight from the
incoherent hump to the coherent peak with decreasing the electron-phonon
coupling constant or with increasing the particle density. Three different
density regimes stem out: the first, at low densities, where the features of a
single large polaron with a substantial incoherent spectral weight are not
modified by charge carrier interactions; a second one, at intermediate
densities, where the polaronic liquid shows a rapid crossover from incoherent
to coherent dynamics; the third one, at high densities, where screening effects
are so prominent that the system presents a conventional metallic phase. The
results obtained in the low to intermediate density regime turn out to be
relevant for the interpretation of recent tunneling and photoemission
experiments in SrTiO3-based systems.",2104.00469v1
2018-04-24,The Mass and Absorption Columns of Galactic Gaseous Halos II -- The High Ionization State Ions,"The high ionization-state ions trace the hot gases in the universe, of which
gaseous halos around galaxies are a major contributor. Following Qu & Bregman
(2018), we calculate the gaseous halo contribution to the observed column
density distributions for these ions by convolving the gaseous halo model with
the observed stellar mass function. The predicted column density distribution
reproduces the general shape of the observed column density distribution -- a
broken power law with the break point at $\log N=14.0$ for {\OVI}. Our modeling
suggests that the high column density systems originate from galaxies for which
the virial temperature matches the temperature of the ionization fraction peak.
Specifically, this mass range is $\log M_\star=8.5-10$ for {\OVI}, $\log
M_\star=9.5-10.5$ for {\NeVIII}, and higher for higher ionization state ions
(assuming $T_{\rm max}=2T_{\rm vir}$). A comparison with the observed {\OVI}
column density distribution prefers a large radius model, where the maximum
radius is twice the virial radius. This model may be in conflict with the more
poorly defined {\NeVIII} column density distribution, suggesting further
observations are warranted. The redshift evolution of the high column density
systems is dominated by the change of the cosmic star formation rate, which
decreases from $z=1.0$ to the local universe. Some differences at lower columns
between our models and observations indicate that absorption by the intra-group
(cluster) medium and intergalactic medium are also contributors to the total
column density distributions.",1804.08784v2
2022-09-19,Alpha-particle formation and clustering in nuclei,"The nucleonic localization function has been used for a decade to study the
formation of alpha-particles in nuclei, by providing a measure of having
nucleons of a given spin in a single place. However, differences in
interpretation remain, compared to the nucleonic density of the nucleus. In
order to better understand the respective role of the nucleonic localization
function and the densities in the alpha-particle formation in cluster states or
in alpha-decay mechanism, both an analytic approximation and microscopic
calculations, using energy density functionals, are undertaken. The nucleonic
localization function is shown to measure the anti-centrifugal effect, and is
not sensitive to the level of compactness of the alpha-particle itself. It
probes the purity of the spatial overlap of four nucleons in the four possible
(spin, isospin) states. The density provides, in addition, information on the
compactness of an alpha-particle cluster. The respective roles of the nucleonic
localization function and the density are also analyzed in the case of
alpha-particle emission. More generally, criteria to assess the prediction of
alpha-cluster in nuclear states are provided.",2209.08888v2
2006-05-23,Electronic structure of BaIrO3: A first principle study using local spin-density approximations,"We investigate the electronic structure of BaIrO3, an interesting compound
exhibiting charge density wave transition in its insulating phase and
ferromagnetic transition at the same temperature, using full potential
linearized augmented plane wave method within the local spin density
approximations. The ferromagnetic ground state could exactly be described in
these calculations and the calculated spin magnetic moment is found to be small
as observed in the magnetic measurements. Interestingly, no signature of
exchange splitting is observed in the density of states corresponding to Ir 5d
and/or any other electronic states. The small spin moment appears essentially
due to unequal population of the up- and down-spin Ir 5d bands. Comparison of
the valence band density of states with the experimental spectral functions
suggests that a rigid shift of the Fermi level towards higher energies in the
calculated density of states provides a good description of the experimental
spectra. This indicates that the intrinsic oxygen non-stoichiometry leads to
electron doping in the system and plays the primary role in determining the
electronic structure rather than the electron correlation effects as often
observed in other systems. The calculated results for Ba 5p core levels show
that the Madelung potential of one of the three non-equivalent Ba atoms is
different from that of other two as predicted in the recent experiments.",0605555v1
1999-08-08,Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable,"Given a bipartite quantum system represented by a tensor product of two
Hilbert spaces, we give an elementary argument showing that if either component
space is infinite-dimensional, then the set of nonseparable density operators
is trace-norm dense in the set of all density operators (and the separable
density operators nowhere dense). This result complements recent detailed
investigations of separability, which show that when both component Hilbert
spaces are finite-dimensional, there is a separable neighborhood (perhaps very
small for large dimensions) of the maximally mixed state.",9908028v1
2017-10-02,Investigation of the electronic properties of the surface and bulk forms of gold and palladium,"The density of electronic states for bulk metals Au and Pd, their surfaces in
the form of polycrystalline surface layers of nanometer thickness is
investigated. The calculations were performed using density functional theory
with pseudopotential in full relativistic approximation. Approximations have
been found that provide calculations the density of electronic states of noble
metal surfaces that describe the experimentally observed features of XPS
spectra of the valence band of these metals.",1710.00789v1
2007-05-17,The tripartite separability of density matrices of graphs,"The density matrix of a graph is the combinatorial laplacian matrix of a
graph normalized to have unit trace. In this paper we generalize the
entanglement properties of mixed density matrices from combinatorial laplacian
matrices of graphs discussed in Braunstein {\it et al.} Annals of
Combinatorics, {\bf 10}(2006)291 to tripartite states. Then we proved that the
degree condition defined in Braunstein {\it et al.} Phys. Rev. A {\bf 73},
(2006)012320 is sufficient and necessary for the tripartite separability of the
density matrix of a nearest point graph.",0705.2561v2
1999-01-29,Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons,"We study the ground state of a system of Bose hard-spheres trapped in an
isotropic harmonic potential to investigate the effect of the interatomic
correlations and the accuracy of the Gross-Pitaevskii equation. We compare a
local density approximation, based on the energy functional derived from the
low density expansion of the energy of the uniform hard sphere gas, and a
correlated wave function approach which explicitly introduces the correlations
induced by the potential. Both higher order terms in the low density expansion,
beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of
the order of percent when the number of trapped particles becomes similar to
that attained in recent experiments.",9901342v1
2012-09-11,Spinodal amplification of density fluctuations in fluid-dynamical simulations of relativistic nuclear collisions,"Extending a previously developed two-phase equation of state, we simulate
head-on relativistic lead-lead collisions with fluid dynamics, augmented with a
finite-range term, and study the effects of the phase structure on the
evolution of the baryon density. For collision energies that bring the bulk of
the system into the mechanically unstable spinodal region of the phase diagram,
the density irregularities are being amplified significantly. The resulting
density clumping may be exploited as a signal of the phase transition, possibly
through an enhanced production of composite particles.",1209.2462v2
2008-12-04,Neutral H density at the termination shock: a consolidation of recent results,"We discuss a consolidation of determinations of the density of neutral
interstellar H at the nose of the termination shock carried out with the use of
various data sets, techniques, and modeling approaches. In particular, we focus
on the determination of this density based on observations of H pickup ions on
Ulysses during its aphelion passage through the ecliptic plane. We discuss in
greater detail a novel method of determination of the density from these
measurements and review the results from its application to actual data. The H
density at TS derived from this analysis is equal to 0.087 \pm 0.022 cm-3, and
when all relevant determinations are taken into account, the consolidated
density is obtained at 0.09 \pm 0.022 cm-3. The density of H in CHISM based on
literature values of filtration factor is then calculated at 0.16 \pm 0.04
cm-3.",0812.0839v1
2005-06-24,The correlation energy as an explicit functional of the one-particle density matrix from a determinantal reference state,"Using an approach based on many body perturbation theory, the correlation
energy $\cEco$ is expressed as an explicit functional of $\rho_1$, $v$, and
$v_s$, where $\rho_1$ is the one-particle density matrix from the
noninteracting, or reference, determinantal-state; $v$ is the external
potential from the interacting, or target, state; $v_s$ is the (kernel of the)
external potential from the noninteracting determinantal-state. In other words
we have $\cEco[\rho_1,v,v_s]$. Anther possibility is the following explicit
functional: $\cEco[\rho_1,v_{\text{co}},v_s]$, where $v_{\text{co}}$ is the
(kernel of the) correlation potential from the noninteracting Hamiltonian. The
proposed method can, in principle, be used to compute $\cEco$ in a very
accurate and efficient manner, since, like the Kohn--Sham approach, there are
no virtual orbitals to consider. However, in contrast to the Kohn--Sham
approach, $\cEco$ is a known, explicit functional that can be approximated in a
systematic manner. For simplicity, we only consider noninteracting closed-shell
states and target states that are nondegenerate, singlet ground-states; so, in
that case, $\rho_1$ denotes the spin-less one-particle density matrix from the
determinantal reference state.",0506186v2
2007-01-01,Negativity as a distance from a separable state,"The computable measure of the mixed-state entanglement, the negativity, is
shown to admit a clear geometrical interpretation, when applied to
Schmidt-correlated (SC) states: the negativity of a SC state equals a distance
of the state from a pertinent separable state. As a consequence, a SC state is
separable if and only if its negativity vanishes. Another remarkable
consequence is that the negativity of a SC can be estimated ""at a glance"" on
the density matrix. These results are generalized to mixtures of SC states,
which emerge in certain quantum-dynamical settings.",0701005v1
2020-02-18,Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires,"In the topological phase of spin-orbit coupled nanowires Majorana bound
states are known to localize at the nanowire edges and to exhibit a spin
density orthogonal to both the magnetic field and the spin-orbit field. By
investigating a nanowire exposed to a uniform magnetic field with an interface
between regions with different spin-orbit couplings, we find that the
orthogonal spin density is pinned at the interface even when both interface
sides are in the topologically trivial phase, and even when no bound state is
present at all. A trivial bound state may additionally appear at the interface,
especially if the spin-orbit coupling takes opposite signs across the
interface. However, it can be destroyed by a smoothening of the spin-orbit
profile or by a magnetic field component parallel to the spin-orbit field. In
contrast, the orthogonal spin density persists in various and realistic
parameter ranges. We also show that, while the measurement of bulk equilibrium
spin currents has been elusive so far, such robust orthogonal spin density peak
may provide a way to detect spin current variations across interfaces.",2002.07779v2
1998-05-25,Zero-energy peak of the density of states and localization properties of a one-dimensional Frenkel exciton: Off-diagonal disorder,"We study a one-dimensional Frenkel Hamiltonian with off-diagonal disorder,
focusing our attention on the physical nature of the zero-energy peak of the
density of states. The character of excitonic states (localized or delocalized)
is also examined in the vicinity of this peak. It is shown that the state being
responsible for the peak is localized. A detailed comparison of the
nearest-neighbor approach with the long-range dipole-dipole coupling is
performed.",9805316v1
2016-12-16,Observation of spin-charge separation and boundary bound states via the local density of states,"We numerically calculate the local density of states (LDOS) of a
one-dimensional Mott insulator with open boundaries, which is modelled
microscopically by a (extended) Hubbard chain at half filling. In the Fourier
transform of the LDOS we identify several dispersing features corresponding to
propagating charge and spin degrees of freedom, thus providing a visualisation
of the spin-charge separation in the system. We also consider the effect of an
additional boundary potential, which, if sufficiently strong, leads to the
formation of a boundary bound state which is clearly visible in the LDOS as a
non-dispersing feature inside the Mott gap.",1612.05597v1
1998-01-10,Phase Transition in ν=2 Bilayer Quantum Hall State,"The Hall-plateau width and the activation energy were measured in the bilayer
quantum Hall state at filling factor \nu=2, 1 and 2/3, by changing the total
electron density and the density ratio in the two quantum wells. Their behavior
are remarkably different from one to another. The \nu=1 state is found stable
over all measured range of the density difference, while the \nu=2/3$ state is
stable only around the balanced point. The \nu=2 state, on the other hand,
shows a phase transition between these two types of the states as the electron
density is changed.",9801085v1
1997-04-25,Boundary States and Black Hole Entropy,"Black hole entropy is derived from a sum over boundary states. The boundary
states are labeled by energy and momentum surface densities, and parametrized
by the boundary metric. The sum over state labels is expressed as a functional
integral with measure determined by the density of states. The sum over metrics
is expressed as a functional integral with measure determined by the universal
expression for the inverse temperature gradient at the horizon. The analysis
applies to any stationary, nonextreme black hole in any theory of gravitational
and matter fields.",9704071v1
1996-08-17,Quantum Hall effect in single wide quantum wells,"We study the quantum Hall states in the lowest Landau level for a single wide
quantum well. Due to a separation of charges to opposite sides of the well, a
single wide well can be modelled as an effective two level system. We provide
numerical evidence of the existence of a phase transition from an
incompressible to a compressible state as the electron density is increased for
specific well width. Our numerical results show a critical electron density
which depends on well width, beyond which a transition incompressible double
layer quantum Hall state to a mono-layer compressible state occurs. We also
calculate the related phase boundary corresponding to destruction of the
collective mode energy gap. We show that the effective tunneling term and the
interlayer separation are both renormalised by the strong magnetic field. We
also exploite the local density functional techniques in the presence of strong
magnetic field at $\nu=1$ to calculate renormalized $\Delta_{SAS}$. The
numerical results shows good agreement between many-body calculations and local
density functional techniques in the presence of a strong magnetic field at
$\nu=1$. we also discuss implications of this work on the $\nu=1/2$
incompressible state observed in SWQW.",9608072v1
2016-01-16,Electronic and Optical Properties of the Narrowest Armchair Graphene Nanoribbons Studied by Density Functional Methods,"In the present study, a series of planar poly(p-phenylene) (PPP) oligomers
with n phenyl rings (n = 1 - 20), designated as n-PP, are taken as finite-size
models of the narrowest armchair graphene nanoribbons with hydrogen
passivation. The singlet-triplet energy gap, vertical ionization potential,
vertical electron affinity, fundamental gap, optical gap, and exciton binding
energy of n-PP are calculated using Kohn-Sham density functional theory and
time-dependent density functional theory with various exchange-correlation
density functionals. The ground state of n-PP is shown to be singlet for all
the chain lengths studied. In contrast to the lowest singlet state (i.e., the
ground state), the lowest triplet state and the ground states of the cation and
anion of n-PP are found to exhibit some multi-reference character. Overall, the
electronic and optical properties of n-PP obtained from the omegaB97 and
omegaB97X functionals are in excellent agreement with the available
experimental data.",1601.04205v2
2016-10-18,Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization,"The real-time broadening of density profiles starting from non-equilibrium
states is at the center of transport in condensed-matter systems and dynamics
in ultracold atomic gases. Initial profiles close to equilibrium are expected
to evolve according to linear response, e.g., as given by the current
correlator evaluated exactly at equilibrium. Significantly off equilibrium,
linear response is expected to break down and even a description in terms of
canonical ensembles is questionable. We unveil that single pure states with
density profiles of maximum amplitude yield a broadening in perfect agreement
with linear response, if the structure of these states involves randomness in
terms of decoherent off-diagonal density-matrix elements. While these states
allow for spin diffusion in the XXZ spin-1/2 chain at large exchange
anisotropies, coherences yield entirely different behavior.",1610.05778v2
2021-03-12,Entropy minimization for many-body quantum systems,"The problem considered here is motivated by a work by B. Nachtergaele and
H.T. Yau where the Euler equations of fluid dynamics are derived from manybody
quantum mechanics, see [10]. A crucial concept in their work is that of local
quantum Gibbs states, which are quantum statistical equilibria with prescribed
particle, current, and energy densities at each point of space (here R d , d
$\ge$ 1). They assume that such local Gibbs states exist, and show that if the
quantum system is initially in a local Gibbs state, then the system stays, in
an appropriate asymptotic limit, in a Gibbs state with particle, current, and
energy densities now solutions to the Euler equations. Our main contribution in
this work is to prove that such local quantum Gibbs states can be constructed
from prescribed densities under mild hypotheses, in both the fermionic and
bosonic cases. The problem consists in minimizing the von Neumann entropy in
the quantum grand canonical picture under constraints of local particle,
current, and energy densities. The main mathematical difficulty is the lack of
compactness of the minimizing sequences to pass to the limit in the
constraints. The issue is solved by defining auxiliary constrained optimization
problems, and by using some monotonicity properties of equilibrium entropies.",2103.07310v1
2021-06-30,Self-consistent state and measurement tomography with fewer measurements,"We describe a technique for self consistently characterizing both the quantum
state of a single qubit system, and the positive-operator-valued measure (POVM)
that describes measurements on the system. The method works with only ten
measurements. We assume that a series of unitary transformations performed on
the quantum state are fully known, while making minimal assumptions about both
the density operator of the state and the POVM. The technique returns
maximum-likely estimates of both the density operator and the POVM. To
experimentally demonstrate the method, we perform reconstructions of over 300
state-measurement pairs and compare them to their expected density operators
and POVMs. We find that 95% of the reconstructed POVMs have fidelities of 0.98
or greater, and 92% of the density operators have fidelities that are 0.98 or
greater.",2107.00121v1
2005-09-14,Synchronized flow and wide moving jams from balanced vehicular traffic,"Recently we proposed an extension to the traffic model of Aw, Rascle and
Greenberg. The extended traffic model can be written as a hyperbolic system of
balance laws and numerically reproduces the reverse $\lambda$ shape of the
fundamental diagram of traffic flow. In the current work we analyze the steady
state solutions of the new model and their stability properties. In addition to
the equilibrium flow curve the trivial steady state solutions form two
additional branches in the flow-density diagram. We show that the
characteristic structure excludes parts of these branches resulting in the
reverse $\lambda$ shape of the flow-density relation. The upper branch is
metastable against the formation of synchronized flow for intermediate
densities and unstable for high densities, whereas the lower branch is unstable
for intermediate densities and metastable for high densities. Moreover, the
model can reproduce the typical speed of the downstream front of wide moving
jams. It further reproduces a constant outflow from wide moving jams, which is
far below the maximum free flow. Applying the model to simulate traffic flow at
a bottleneck we observe a general pattern with wide moving jams traveling
through the bottleneck.",0509124v2
2012-05-29,Electronic Energy Functionals: Levy-Lieb principle within the Ground State Path Integral Quantum Monte Carlo,"We propose a theoretical/computational protocol based on the use of the
Ground State (GS) Path Integral (PI) Quantum Monte Carlo (QMC) for the
calculation of the kinetic and Coulomb energy density for a system of $N$
interacting electrons in an external potential. The idea is based on the
derivation of the energy densities via the $N-1$-conditional probability
density within the framework of the Levy-Lieb constrained search principle. The
consequences for the development of energy functionals within the context of
Density Functional Theory (DFT) are discussed. We propose also the possibility
of going beyond the energy densities and extend this idea to a computational
procedure where the $N-1$-conditional probability is an implicit functional of
the electron density, independently from the external potential. In principle,
such a procedure paves the way for an {\it on-the-fly} determination of the
energy functional for any system.",1205.6503v1
2016-06-13,Electronic quasiparticles in the quantum dimer model: density matrix renormalization group results,"We study a recently proposed quantum dimer model for the pseudogap metal
state of the cuprates. The model contains bosonic dimers, representing a
spin-singlet valence bond between a pair of electrons, and fermionic dimers,
representing a quasiparticle with spin-$1/2$ and charge $+e$. By density matrix
renormalization group calculations on a long but finite cylinder, we obtain the
ground-state density distribution of the fermionic dimers for a number of
different total densities. From the Friedel oscillations at open boundaries, we
deduce that the Fermi surface consists of small hole pockets near $(\pi/2,
\pi/2)$, and this feature persists up to a doping density of $1/16$. We also
compute the entanglement entropy and find that it closely matches the sum of
the entanglement entropies of a critical boson and a low density of free
fermions. Our results support the existence of a fractionalized Fermi liquid in
this model.",1606.04105v2
2021-09-07,Thermal near-field energy density and LDOS in topological 1D SSH chains and 2D SSH lattices of plasmonic nanoparticles,"We derive a general expression for electric and magnetic part of the
near-field energy density of $N$ dipoles of temperatures $T_1, \ldots, T_N$
immersed in a background field having a different temperature $T_b$. In
contrast to former expressions this inclusion of the background field allows
for determining the energy density of heated or cooled isotropic dipolar
objects within an arbitrary environment which is thermalized at a different
temperature. Furthermore, we show how the energy density is related to the
local density of states. We use this general expression to study the near-field
enhanced energy density at the edges and corners of 1D Su-Schrieffer-Heeger
chains and 2D Su-Schrieffer-Heeger lattices of plasmonic InSb nanoparticles
when the phase transition from a topological trivial to a topological
non-trivial state is made. We discuss the robustness of these modes when adding
defects and the possibility to measure the topological edge and corner modes.",2109.03073v2
1998-09-17,Density-matrix renormalization using three classes of block states,"An extension of the the density matrix renormalization group (DMRG) method is
presented. Besides the two groups or classes of block states considered in
White's formulation, the retained $m$ states and the neglected ones, we
introduce an intermediate group of block states having the following $p$
largest eigenvalues $\lambda_i$ of the reduced density matrix: $\lambda_1 \ge
>... \lambda_m \ge \lambda_{m+1}\ge ... \ge \lambda_{m+p}$. These states are
taken into account when they contribute to intrablock transitions but are
neglected when they participate in more delocalized interblock fluctuations.
Applications to one-dimensional models (Heisenberg, Hubbard and dimerized
tight-binding) show that in this way the involved computer resources can be
reduced without significant loss of accuracy. The efficiency and accuracy of
the method is analyzed by varying $m$ and $p$ and by comparison with standard
DMRG calculations. A Hamiltonian-independent scheme for choosing $m$ and $p$
and for extrapolating to the limit where $m$ and $p$ are infinite is provided.
Finally, an extension of the 3-classes approach is outlined, which incorporates
the fluctuations between the $p$ states of different blocks as a
self-consistent dressing of the block interactions among the retained $m$
states.",9809233v1
2007-08-24,The Friedel-Anderson and Kondo Impurity Problem for Arbitrary s-Band Density of States and Exchange Interaction,"In his renormalization paper of the Kondo effect Wilson replaced the full
band of s-electrons by a small number of ''Wilson states''. He started from a
rather artificial symmetric band with constant density of states and constant
interaction with the impurity. It is shown in the present paper that with a
minor modification the Wilson states are optimally suited to treat the
interaction of an impurity with an arbitrary s-band. Each Wilson state
represents electrons of a whole energy range. It carries the interaction of all
these electrons with the impurity. All the other electron states in this energy
range have zero interaction with the impurity and are neglected in the
calculation. The resulting error is minor. As an example the singlet-triplet
excitation energy of a Kondo impurity is numerically calculated for a
tight-binding band with a strongly energy dependent density of states.",0708.3267v1
2015-06-24,"""Photonic"" cat states from strongly interacting matter waves","We consider ultracold quantum gases of scalar bosons, residing in a coupling
strength--density regime in which they constitute a twofold fragmented
condensate trapped in a single well. It is shown that the corresponding quantum
states are, in the appropriate Fock space basis, identical to the photon cat
states familiar in quantum optics, which correspond to superpositions of
coherent states of the light field with a phase difference of $\pi$. In marked
distinction to photon cat states, the very existence of matter wave cat states
however crucially depends on the many-body correlations of the constituent
particles. We consequently establish that the quadratures of the effective
""photons,"" expressing the highly nonclassical nature of the macroscopic matter
wave superposition state, can be experimentally accessed by measuring the
density-density correlations of the interacting quantum gas.",1506.07478v2
2013-02-27,Equation of state of hypernuclear matter: impact of hyperon--scalar-meson couplings,"We study the equation of state and composition of hypernuclear matter within
a relativistic density functional theory with density-dependent couplings. The
parameter space of hyperon--scalar-meson couplings is explored by allowing for
mixing and breaking of SU(6) symmetry, while keeping the nucleonic couplings
constant fixed. The subset of equations of state, which corresponds to small
values of hyperon--scalar-meson couplings allows for massive M < 2.25 M_solar
compact stars; the radii of hypernuclear stars are within the range 12--14 km.
We also study the equation of state of hot neutrino-rich and neutrinoless
hypernuclear matter and confirm that neutrinos stiffen the equation of state
and dramatically change the composition of matter by keeping the fractions of
charged leptons nearly independent of the density prior to the onset of
neutrino transparency. We provide piecewise polytropic fits to six
representative equations of state of hypernuclear matter, which are suitable
for applications in numerical astrophysics.",1302.6925v3
2023-05-15,Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions,"We show that chemically-accurate potential energy surfaces (PESs) can be
generated from quantum computers by measuring the density along an adiabatic
transition between different molecular geometries. In lieu of using phase
estimation, the energy is evaluated by performing line-integration using the
inverted TDDFT Kohn-Sham potential obtained from the time-varying densities.
The accuracy of this method depends on the validity of the adiabatic evolution
itself and the potential inversion process (which is theoretically exact but
can be numerically unstable), whereas total evolution time is the defining
factor for the precision of phase estimation. We examine the method with a
one-dimensional system of two electrons for both the ground and first triplet
state in first quantization, as well as the ground state of three- and four-
electron systems in second quantization. It is shown that few accurate
measurements can be utilized to obtain chemical accuracy across the full
potential energy curve, with shorter propagation time than may be required
using phase estimation for a similar accuracy. We also show that an accurate
potential energy curve can be calculated by making many imprecise density
measurements (using few shots) along the time evolution and smoothing the
resulting density evolution. We discuss how one can generate full PESs using
either sparse grid representations or machine learning density functionals
where it is known that training the functional using the density (along with
the energy) generates a more transferable functional than only using the
energy. Finally, it is important to note that the method is able to classically
provide a check of its own accuracy by comparing the density resulting from a
time-independent Kohn-Sham calculation using the inverted potential, with the
measured density.",2305.08837v1
2021-03-24,Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials,"Disordered hyperuniformity (DHU) is a recently discovered novel state of
many-body systems that is characterized by vanishing normalized
infinite-wavelength density fluctuations similar to a perfect crystal, yet
possesses an amorphous structure like a liquid or glass. Here we investigate
equilibrium DHU states of Brownian particles induced by external potentials. In
particular, we analytically derive sufficient conditions on the external
potentials in order to achieve distinct classes of DHU density distributions of
Brownian particles in thermal equilibrium, based on the stationary-state
solutions of the corresponding Smoluchowski equation. We show for a wide
spectrum of tight-binding potentials, the desirable DHU states of Brownian
particles can be controlled and achieved by imposing proper hyperuniformity
conditions on the potentials. Moreover, we find that thermal motions in these
systems tend to enhance hyperuniformity. We also analyze the evolution dynamics
of an initial density distribution (hyperuniform or non-hyperuniform) to the
desirable equilibrium DHU state determined by the prescribed external
potentials, which is shown to be coupled with the full spectra of the force
fields associated with the imposed potentials. We find that although the
transient density distribution can rapidly develop local patterns reminiscent
of those in the equilibrium distribution, which is governed by the fast
dynamics induced by the external potential, the overall distribution is still
modulated by the initial density fluctuations which are relaxed through slow
diffusive dynamics. Our study has implications for the fabrication of designer
DHU materials.",2103.12952v1
2002-07-02,Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons,"The recent experimental realisation of a one-dimensional Bose gas of ultra
cold alkali atoms has renewed attention on the theoretical properties of the
impenetrable Bose gas. Of primary concern is the ground state occupation of
effective single particle states in the finite system, and thus the tendency
for Bose-Einstein condensation. This requires the computation of the density
matrix. For the impenetrable Bose gas on a circle we evaluate the density
matrix in terms of a particular Painlev\'e VI transcendent in $\sigma$-form,
and furthermore show that the density matrix satisfies a recurrence relation in
the number of particles. For the impenetrable Bose gas in a harmonic trap, and
with Dirichlet or Neumann boundary conditions, we give a determinant form for
the density matrix, a form as an average over the eigenvalues of an ensemble of
random matrices, and in special cases an evaluation in terms of a transcendent
related to Painlev\'e V and VI. We discuss how our results can be used to
compute the ground state occupations.",0207005v2
2020-12-02,Compression modulus and symmetry energy of nuclear matter with KIDS density functional,"Equation of state of dense nuclear matter is explored in the KIDS density
functional theory. Parameters of the equation of state which are coefficients
of the energy density expanded in powers of $(\rho - \rho_0)/3\rho_0$ where
$\rho$ is the nuclear matter density and $\rho_0$ is its density at saturation
are constrained by using both nuclear data and the mass-radius relation of the
neutron star determined from the modern astronomy. We find that the combination
of both data can reduce the uncertainty in the equation of state parameters
significantly. We confirm that the newly constrained parameters reproduce the
basic properties of spherical magic nuclei with high accuracy. Neutron drip
lines, on the other hand, show non-negligible dependence on the uncertainty of
the nuclear symmetry energy.",2012.00930v1
2019-10-18,Solving the measurement problem within standard quantum theory,"A misunderstanding of entangled states has spawned decades of concern about
quantum measurements and a plethora of quantum interpretations. The
""measurement state"" or ""Schrodinger's cat state"" of a superposed quantum system
and its detector is nonlocally entangled, suggesting that we turn to
nonlocality experiments for insight into measurements. By studying the full
range of superposition phases, these experiments show precisely what the
measurement state does and does not superpose. These experiments reveal that
the measurement state is not, as had been supposed, a paradoxical superposition
of detector states. It is instead a nonparadoxical superposition of two
correlations between detector states and system states. In this way, the
experimental results resolve the problem of definite outcomes (""Schrodinger's
cat""), leading to a resolution of the measurement problem. However, this
argument does not yet resolve the measurement problem because it is based on
the results of experiments, while measurement is a theoretical problem: How can
standard quantum theory explain the definite outcomes seen experimentally?
Thus, we summarize the nonlocality experiments' supporting theory, which
rigorously predicts the experimental results directly from optical paths.
Several previous theoretical analyses of the measurement problem have relied on
the reduced density operators derived from the measurement state, but these
solutions have been rejected due to criticism of reduced density operators.
Because it avoids reduced density operators, the optical-path analysis is
immune to such criticism.",1910.08591v2
2007-04-12,Temperature-driven transition from the Wigner Crystal to the Bond-Charge-Density Wave in the Quasi-One-Dimensional Quarter-Filled band,"It is known that within the interacting electron model Hamiltonian for the
one-dimensional 1/4-filled band, the singlet ground state is a Wigner crystal
only if the nearest neighbor electron-electron repulsion is larger than a
critical value. We show that this critical nearest neighbor Coulomb interaction
is different for each spin subspace, with the critical value decreasing with
increasing spin. As a consequence, with the lowering of temperature, there can
occur a transition from a Wigner crystal charge-ordered state to a spin-Peierls
state that is a Bond-Charge-Density Wave with charge occupancies different from
the Wigner crystal. This transition is possible because spin excitations from
the spin-Peierls state in the 1/4-filled band are necessarily accompanied by
changes in site charge densities. We apply our theory to the 1/4-filled band
quasi-one-dimensional organic charge-transfer solids in general and to 2:1
tetramethyltetrathiafulvalene (TMTTF) and tetramethyltetraselenafulvalene
(TMTSF) cationic salts in particular. We believe that many recent experiments
strongly indicate the Wigner crystal to Bond-Charge-Density Wave transition in
several members of the TMTTF family. We explain the occurrence of two different
antiferromagnetic phases but a single spin-Peierls state in the generic phase
diagram for the 2:1 cationic solids. The antiferromagnetic phases can have
either the Wigner crystal or the Bond-Charge-Spin-Density Wave charge
occupancies. The spin-Peierls state is always a Bond-Charge-Density Wave.",0704.1656v2
2009-08-09,Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids,"Much of the discussion in the literature of the low frequency part of the
density of states of amorphous solids was dominated for years by comparing
measured or simulated density of states to the classical Debye model. Since
this model is hardly appropriate for the materials at hand, this created some
amount of confusion regarding the existence and universality of the so- called
``Boson Peak'' which results from such comparisons. We propose that one should
pay attention to the different roles played by different aspects of disorder,
the first being disorder in the interaction strengths, the second positional
disorder, and the third coordination disorder. These have different effects on
the low-frequency part of the density of states. We examine the density of
states of a number of tractable models in one and two dimensions, and reach a
clearer picture of the softening and redistribution of frequencies in such
materials. We discuss the effects of disorder on the elastic moduli and the
relation of the latter to frequency softening, reaching the final conclusion
that the Boson peak is not universal at all.",0908.1228v1
2004-05-13,"Continuum corrections to the level density and its dependence on excitation energy, n-p asymmetry, and deformation","In the independent-particle model, the nuclear level density is determined
from the neutron and proton single-particle level densities. The
single-particle level density for the positive-energy continuum levels is
important at high excitation energies for stable nuclei and at all excitation
energies for nuclei near the drip lines. This single-particle level density is
subdivided into compound-nucleus and gas components. Two methods were
considered for this subdivision. First in the subtraction method, the
single-particle level density is determined from the scattering phase shifts.
In the Gamov method, only the narrow Gamov states or resonances are included.
The level densities calculated with these two methods are similar, both can be
approximated by the backshifted Fermi-gas expression with level-density
parameters that are dependent on A, but with very little dependence on the
neutron or proton richness of the nucleus. However, a small decrease in the
level-density parameter was predicted for some nuclei very close to the drip
lines. The largest difference between the calculations using the two methods
was the deformation dependence on the level density. The Gamov method predicts
a very strong peaking of the level density at sphericity for high excitation
energies. This leads to a suppression of deformed configurations and,
consequently, the fission rate predicted by the statistical model is reduced in
the Gamov method.",0405041v1
2022-08-02,Fast Kernel Density Estimation with Density Matrices and Random Fourier Features,"Kernel density estimation (KDE) is one of the most widely used nonparametric
density estimation methods. The fact that it is a memory-based method, i.e., it
uses the entire training data set for prediction, makes it unsuitable for most
current big data applications. Several strategies, such as tree-based or
hashing-based estimators, have been proposed to improve the efficiency of the
kernel density estimation method. The novel density kernel density estimation
method (DMKDE) uses density matrices, a quantum mechanical formalism, and
random Fourier features, an explicit kernel approximation, to produce density
estimates. This method has its roots in the KDE and can be considered as an
approximation method, without its memory-based restriction. In this paper, we
systematically evaluate the novel DMKDE algorithm and compare it with other
state-of-the-art fast procedures for approximating the kernel density
estimation method on different synthetic data sets. Our experimental results
show that DMKDE is on par with its competitors for computing density estimates
and advantages are shown when performed on high-dimensional data. We have made
all the code available as an open source software repository.",2208.01206v2
2002-05-09,Structure and Parametrization of Generic Stochastic Maps of Density Matrices,"The most general evolution of the density matrix of a quantum system with a
finite-dimensional state space is by stochastic maps which take a density
matrix linearly into the set of density matrices. These dynamical stochastic
maps form a linear convex set that may be viewed as supermatrices. The property
of hermiticity of density matrices renders an associated supermatrix hermitian
and hence diagonalizable. The positivity of the density matrix does not make
the associated supermatrix positive though. If the map itself is positive, it
is called completely positive and they have a simple parameterization. This is
extended to all positive (not completely positive) maps. A general dynamical
map that does not preserve the norm of the density matrices it acts on can be
thought of as the contraction of a norm-preserving map of an extended system.
The reconstruction of such extended dynamics is also given.",0205051v2
2023-10-19,On the contact conditions for the density and charge profiles in the theory of electrical double layer: From planar to spherical and cylindrical geometry,"In this paper, starting from the Bogoliubov-Born-Green-Yvon equations of the
liquid-state theory, we formulate two equivalent approaches for the calculation
of the total density profile and of the charge density profile of ionic fluids
near nonplanar charged surfaces. In the framework of these approaches, we
establish exact conditions, that a particular point of these profiles should
satisfy, in the form of contact theorems. These contact theorems for the total
density profile and the charge density profile are obtained by direct
integration of a system of equations derived from the
Bogoliubov-Born-Green-Yvon equations. The contact theorems for both profiles
have nonlocal character. It is shown that the contact value of the total
density profile for uncharged surfaces is characterized by the bulk pressure
and the surface tension. The contact theorems are applied to the cases of
spherical and cylindrical surfaces. It is shown that the contact theorem for
the total density profile coincides with the recent results obtained by W.
Silvester-Alcantara, D. Henderson and L.B. Bhuiyan Mol. Phys., 113, 3403, 2015",2310.12783v1
1998-01-29,Density of States and Energy Gap in Andreev Billiards,"We present numerical results for the local density of states in semiclassical
Andreev billiards. We show that the energy gap near the Fermi energy develops
in a chaotic billiard. Using the same method no gap is found in similar square
and circular billiards.",9801310v1
2005-08-18,Lower Bound for the Ground-State Energy Density of a 1D Quantum Spin System,"We present a simple method to calculate systematic lower bounds for the
ground-state energy density of a 1D quantum spin system.",0508428v2
2011-07-21,Raising Tc in charge density wave superconductor ZrTe3 by Ni intercalation,"We report discovery of bulk superconductivity in Ni0.05ZrTe3 at Tc = 3.1 K,
obtained through Ni intercalation. Superconductivity coexists with charge
density wave (CDW) state with TCDW = 41 K. When compared to parent material
ZrTe3, filamentary superconducting transition is substantially increased
whereas TCDW was suppressed. The analysis of superconducting state indicates
that Ni0.05ZrTe3 is an intermediately coupled superconductor.",1107.4355v1
2015-01-21,Some Estimates Regarding Integrated density of States for Random Schrödinger Operator with decaying Random Potentials,"We investigate some bounds for the density of states in the pure point regime
for the random Schr\""{o}dinger operators
$H^{\omega}=-\Delta+\displaystyle\sum_{n\in\mathbb{Z}^d}a_nq_n(\omega)$, acting
on $\ell^2(\mathbb{Z}^d)$, where $\{q_n\}$ are iid random variables and
$a_n\simeq|n|^{-\alpha}~~\alpha>0$.",1501.05055v2
2015-02-05,Optical lattice with heterogeneous atomic density,"The possibility is considered for the formation in optical lattices of a
heterogeneous state characterized by a spontaneous mesoscopic separation of the
system into the spatial regions with different atomic densities. It is shown
that such states can arise, if there are repulsive interactions between atoms
in different lattice sites and the filling factor is less than one-half.",1502.01634v1
2008-01-12,Possible Metastable State Triggered by Competition of Peierls State and Charge Ordered State,"We examine a Peierls ground state and its competing metastable state in the
one-dimensional quarter-filled Peierls-Hubbard model with the nearest-neighbor
repulsive interaction V and the electron-phonon interaction (\propto 1/K with K
being the elastic constant). From the mean-field approach, we obtain the phase
diagram for the ground state on the plane of parameters V and K. The coexistent
state of the spin-density wave and the charge ordering is realized for large V
and K. With decreasing K, it exhibits a first-order phase transition to the
unconventional Peierls state which is described by the bond-centered
charge-density-wave state. In the large region of the Peierls ground state in
the phase diagram, there exists the metastable state where the energy takes a
local minimum with respect to the lattice distortion. On the basis of the
present calculation, we discuss the photoinduced phase observed in the
(EDO-TTF)_{2}PF_{6} compound.",0801.1889v1
2011-03-02,Entropic Entanglement Criteria for Fermion Systems,"Entanglement criteria for general (pure or mixed) states of systems
consisting of two identical fermions are introduced. These criteria are based
on appropriate inequalities involving the entropy of the global density matrix
describing the total system, on the one hand, and the entropy of the one
particle reduced density matrix, on the other one. A majorization-related
relation between these two density matrices is obtained, leading to a family of
entanglement criteria based on R\'enyi's entropic measure. These criteria are
applied to various illustrative examples of parametrized families of mixed
states. The dependence of the entanglement detection efficiency on R\'enyi's
entropic parameter is investigated. The extension of these criteria to systems
of $N$ identical fermions is also considered.",1103.0569v1
2015-08-22,Covariant energy density functionals: the assessment of global performance across the nuclear landscape,"The assessment of the global performance of the state-of-the-art covariant
energy density functionals and related theoretical uncertainties in the
description of ground state observables has recently been performed. Based on
these results, the correlations between global description of binding energies
and nuclear matter properties of covariant energy density functionals have been
studied in this contribution.",1508.05526v1
2017-10-02,I-Love-Q to the extreme,"Certain bulk properties of neutron stars, in particular their moment of
inertia, rotational quadrupole moment and tidal Love number, when properly
normalized, are related to one another in a nearly equation of state
independent way. The goal of this paper is to test these relations with extreme
equations of state at supranuclear densities constrained to satisfy only a
handful of generic, physically sensible conditions. By requiring that the
equation of state be (i) barotropic and (ii) its associated speed of sound be
real, we construct a piecewise function that matches a tabulated equation of
state at low densities, while matching a stiff equation of state parametrized
by its sound speed in the high-density region. We show that the I-Love-Q
relations hold to 1 percent with this class of equations of state, even in the
extreme case where the speed of sound becomes superluminal and independently of
the transition density. We also find further support for the interpretation of
the I-Love-Q relations as an emergent symmetry due to the nearly constant
eccentricity of isodensity contours inside the star. These results reinforce
the robustness of the I-Love-Q relations against our current incomplete picture
of physics at supranuclear densities, while strengthening our confidence in the
applicability of these relations in neutron star astrophysics.",1710.00919v1
2002-08-28,Spectral densities of Kondo impurities in nanoscopic systems,"We present results for the spectral properties of Kondo impurities in
nanoscopic systems. Using Wilson's renormalization group we analyze the
frequency and temperature dependence of the impurity spectral density for
impurities in small systems that are either isolated or in contact with a
reservoir. We have performed a detailed analysis of the structure of the
impurity spectral density for energies around the Fermi energy for different
Fermi energies relative to the intrinsic structure of the local density of
states. We show how the electron confinement energy scales introduce new
features in the frequency and temperature dependence of the impurity spectral
properties.",0208570v1
2002-11-15,Collective modes in unconventional density waves,"We have investigated the collective modes of unconventional charge and spin
density waves (UCDW, USDW) in quasi-one dimensional systems in random phase
approximation. The density correlator regains its normal state form due to the
phase degree of freedom of the condensate. The possible effect of impurities is
also discussed. From this, the current-current correlation function is
evaluated through charge conservation. The spin susceptibility of USDW remains
anisotropic an spite of the lack of any periodic modulation of the spin
density. In UCDW, the spin response gets weaker in all three directions as the
temperature is lowered.",0211316v1
2008-02-06,Nuclear Energy Density Functionals Constrained by Low-Energy QCD,"A microscopic framework of nuclear energy density functionals is reviewed,
which establishes a direct relation between low-energy QCD and nuclear
structure, synthesizing effective field theory methods and principles of
density functional theory. Guided by two closely related features of QCD in the
low-energy limit: a) in-medium changes of vacuum condensates, and b)
spontaneous breaking of chiral symmetry; a relativistic energy density
functional is developed and applied in studies of ground-state properties of
spherical and deformed nuclei.",0802.0838v1
2010-02-05,Instabilities in the Nuclear Energy Density Functional,"In the field of Energy Density Functionals (EDF) used in nuclear structure
and dynamics, one of the unsolved issues is the stability of the functional.
Numerical issues aside, some EDFs are unstable with respect to particular
perturbations of the nuclear ground-state density. The aim of this contribution
is to raise questions about the origin and nature of these instabilities, the
techniques used to diagnose and prevent them, and the domain of density
functions in which one should expect a nuclear EDF to be stable.",1002.1321v1
2012-11-23,The effect of isoscalar-isovector coupling in infinite nuclear matter,"Working on the framework of Relativistic Mean Field theory, we exposed the
effect of nonlinear isoscalar-isovector coupling on G2 parameter set on the
density dependence of nuclear symmetry energy in infinite nuclear matter. The
observables like symmetric energy and few related coefficients are studied
systematically. We presented the results of stiff symmetry energy at
sub-saturation densities and a soft variation at normal densities. Correlation
between the symmetric energy and the isoscalar-isovector coupling parameter
fully demonstrated for wide range of density. The work further extended to the
octet system and showed the effect of coupling over the equation of state.",1211.5461v1
2015-09-23,Metric space analysis of systems immersed in a magnetic field,"Understanding the behavior of quantum systems subject to magnetic fields is
of fundamental importance and underpins quantum technologies. However, modeling
these systems is a complex task, because of many-body interactions and because
many-body approaches such as density functional theory get complicated by the
presence of a vector potential into the system Hamiltonian. We use the metric
space approach to quantum mechanics to study the effects of varying the
magnetic vector potential on quantum systems. The application of this technique
to model systems in the ground state provides insight into the fundamental
mapping at the core of current density functional theory, which relates the
many-body wavefunction, particle density and paramagnetic current density. We
show that the role of the paramagnetic current density in this relationship
becomes crucial when considering states with different magnetic quantum
numbers, $m$. Additionally, varying the magnetic field uncovers a richer
complexity for the ""band structure"" present in ground state metric spaces, as
compared to previous studies varying scalar potentials. The robust nature of
the metric space approach is strengthened by demonstrating the gauge invariance
of the related metric for the paramagnetic current density. We go beyond ground
state properties and apply this approach to excited states. The results suggest
that, under specific conditions, a universal behavior may exist for the
relationships between the physical quantities defining the system.",1509.07010v1
2001-06-27,Strongly correlated hopping and many-body bound states,"We study a system in which the quantum dynamics of electrons depend on the
particle density in their neighborhood. For any on-site repulsive interaction,
we show that the exact two-body and three-body ground states are bound states.
We also discuss the finite density case in a mean-field framework and we show
that the system can undergo an unusual transition from an effective attractive
interaction to a repulsive one, when varying the electron density.",0106571v2
2003-09-08,Chiral d+is superconducting state in the two dimensional t-t' Hubbard model,"Applying the recently developed variational approach to Kohn-Luttinger
superconductivity to the t-t' Hubbard model in two dimensions, we have found,
for sizeable next-nearest neighbor hopping, an electron density controlled
quantum phase transition between a d-wave superconducting state close to half
filling and an s-wave superconductor at lower electron density. The transition
occurs via an intermediate time reversal breaking d+is superconducting phase,
which is characterized by nonvanishing chirality and density-current
correlation. Our results suggest the possibility of a bulk time reversal
symmetry breaking state in overdoped cuprates.",0309183v1
2003-03-19,Polariton condensation and lasing in optical microcavities - the decoherence driven crossover,"We explore the behaviour of a system which consists of a photon mode dipole
coupled to a medium of two-level oscillators in a microcavity in the presence
of decoherence. We consider two types of decoherence processes which are
analogous to magnetic and non-magnetic impurities in superconductors. We study
different phases of this system as the decoherence strength and the excitation
density is changed. For a low decoherence we obtain a polariton condensate with
comparable excitonic and photonic parts at low densities and a BCS-like state
with bigger photon component due to the fermionic phase space filling effect at
high densities. In both cases there is a large gap in the density of states. As
the decoherence is increased the gap is broadened and suppressed, resulting in
a gapless condensate and finally a suppression of the coherence in a low
density regime and a laser at high density limit. A crossover between these
regimes is studied in a self-consistent way analogous to the Abrikosov and
Gor'kov theory of gapless superconductivity.",0303392v1
2005-11-15,Ground state structure and conductivity of quantum wires of infinite length and finite width,"We have studied the ground state structure of quantum strips within the local
spin-density approximation, for a range of electronic densities between $\sim$
5$\times10^4$ and 2$\times10^6$ cm$^{-1}$ and several strengths of the lateral
confining potential. The results have been used to address the conductance $G$
of quantum strips. At low density, when only one subband is occupied, the
system is fully polarized and $G$ takes a value which is close to
0.7(2e$^2/h$), decreasing with increasing electron density in agreement with
experiments. At higher densities the system becomes paramagnetic and $G$ takes
a value near (2e$^2/h$), showing a similar decreasing behaviour with increasing
electron density. In both cases, the physical parameter that determines the
value of the conductance is the ratio $K/K_0$ of the compressibility of the
system over the free one.",0511378v1
2016-06-07,Landau theory of nuclear level density and its application in description of nuclear level density in the region of discrete and s-wave neutron resonance energies,"In this work, the reliability of the Landau expression for the nuclear level
density calculations is tested, for the first-time, to describe nuclear level
densities of some light, intermediate mass and heavy nuclei at excitations
corresponding to discrete and s-wave neutron resonance energies. The chi-2
minimizing method is used in treatment of the experimental data for the two
suggested energy range of discrete energies given by Nuclear Data Sheet [1] and
by the systematic for nuclear level density parametrization in [2]. Our
comparison with the related data in the discrete energy range has shown that
the results obtained by the Landau expression are better than those of
back-shifted Fermi-gas model and constant temperature approximation. This
result is also valid for some nuclei of interest when the s-wave neutron
resonance level density is included to check theoretical prescriptions in the
energy range from initial bound states to unbound states near the neutron
binding energy.",1606.02575v1
2018-01-30,Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature,"In this work, we establish a general theory of phase transitions and quantum
entanglement in the equilibrium state at arbitrary temperatures. First, we
derived a set of universal functional relations between the matrix elements of
two-body reduced density matrix of the canonical density matrix and the
Helmholtz free energy of the equilibrium state, which implies that the
Helmholtz free energy and its derivatives are directly related to entanglement
measures because any entanglement measures are defined as a function of the
reduced density matrix. Then we show that the first order phase transitions are
signaled by the matrix elements of reduced density matrix while the second
order phase transitions are witnessed by the first derivatives of the reduced
density matrix elements. Near second order phase transition point, we show that
the first derivative of the reduced density matrix elements present universal
scaling behaviors. Finally we establish a theorem which connects the phase
transitions and entanglement at arbitrary temperatures. Our general results are
demonstrated in an experimentally relevant many-body spin model.",1801.09830v1
2018-02-21,Density-aware Single Image De-raining using a Multi-stream Dense Network,"Single image rain streak removal is an extremely challenging problem due to
the presence of non-uniform rain densities in images. We present a novel
density-aware multi-stream densely connected convolutional neural network-based
algorithm, called DID-MDN, for joint rain density estimation and de-raining.
The proposed method enables the network itself to automatically determine the
rain-density information and then efficiently remove the corresponding
rain-streaks guided by the estimated rain-density label. To better characterize
rain-streaks with different scales and shapes, a multi-stream densely connected
de-raining network is proposed which efficiently leverages features from
different scales. Furthermore, a new dataset containing images with
rain-density labels is created and used to train the proposed density-aware
network. Extensive experiments on synthetic and real datasets demonstrate that
the proposed method achieves significant improvements over the recent
state-of-the-art methods. In addition, an ablation study is performed to
demonstrate the improvements obtained by different modules in the proposed
method. Code can be found at: https://github.com/hezhangsprinter",1802.07412v1
2023-11-24,Nuclear level density from relativistic density functional theory and combinatorial method,"Nuclear level density is calculated with the combinatorial method based on
the relativistic density functional theory including pairing correlations. The
Strutinsky method is adopted to smooth the total state density in order to
refine the prediction at low excitation energy. The impacts of pairing
correlations and moments of inertia on the nuclear level density are discussed
in detail. Taking $\mathrm{^{112}Cd}$ as an example, it is demonstrated that
the nuclear level density based on the relativistic density functional PC-PK1
can reproduce the experimental data at the same level as or even better than
the previous approaches.",2311.14250v2
2013-10-12,Role of Anion Ordering in the Coexistence of Spin-Density-Wave and Superconductivity in (TMTSF)2ClO4,"Using various transport and magnetotransport probes we study the coexistence
of spin-density wave and superconductor states in (TMTSF)2ClO4 at various
degrees of ClO4 anions ordering. In the two-phase complex state when both
superconductivity and spin-density wave are observed in transport, we find
prehistory effects, enhancement of the superconducting critical field, and
strong spatial anisotropy of the superconducting state. These features are
inconsistent with the conventional model of structural inhomogeneities produced
by anion ordering transition. We reveal instead that superconductor and
spin-density wave regions overlap on the temperature -- dimerization gap V
phase diagram, where V is varied by anion ordering. The effect of anion
ordering on (TMTSF)2ClO4 properties is thus analogous to that of pressure on
(TMTSF)2X (X=PF6 or AsF6), thereby unifying general picture of the coexistence
of superconductivity and spin-density wave in these compounds.",1310.3434v1
2014-09-18,Density-wave instabilities of fractionalized Fermi liquids,"Recent experiments in the underdoped regime of the hole-doped cuprates have
found evidence for an incommensurate charge density wave state. We present an
analysis of the charge ordering instabilities in a metal with antiferromagnetic
correlations, where the electronic excitations are coupled to the
fractionalized excitations of a quantum fluctuating antiferromagnet on the
square lattice. The resulting charge density wave state emerging out of such a
fractionalized Fermi-liquid (FL*) has wavevectors of the form $(\pm Q_0,0),
(0,\pm Q_0)$, with a predominantly $d$-form factor, in agreement with
experiments on a number of different families of the cuprates. In contrast, as
previously shown, the charge density wave instability of a nearly
antiferromagnetic metal with a large Fermi surface, interacting via short-range
interactions, has wavevectors of the type $(\pm Q_0,\pm Q_0)$. Our results show
that the observed charge density wave appears as a low-energy instability of a
fractionalized metallic state linked to the proximity to an antiferromagnetic
insulator, and the pseudogap regime can be described by such a metal at least
over intermediate length and energy scales.",1409.5430v2
2015-06-17,Characteristic density contrasts in the evolution of superclusters. The case of A2142 supercluster,"The formation and evolution of the cosmic web in which galaxy superclusters
are the largest relatively isolated objects is governed by a gravitational
attraction of dark matter and antigravity of dark energy (cosmological
constant). We study the characteristic density contrasts in the spherical
collapse model for several epochs in the supercluster evolution and their
dynamical state. We analysed the density contrasts for the turnaround, future
collapse and zero gravity in different LCDM models and applied them to study
the dynamical state of the supercluster A2142 with an almost spherical main
body. The analysis of the supercluster A2142 shows that its high-density core
has already started to collapse. The zero-gravity line outlines the outer
region of the main body of the supercluster. In the course of future evolution
the supercluster may split into several collapsing systems. The various density
contrasts presented in our study and applied to the supercluster A2142 offer a
promising way to characterise the dynamical state and expected future evolution
of galaxy superclusters.",1506.05252v2
2019-01-23,"Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence","What is the quantum state of the universe? Although there have been several
interesting suggestions, the question remains open. In this paper, I consider a
natural choice for the universal quantum state arising from the Past
Hypothesis, a boundary condition that accounts for the time-asymmetry of the
universe. The natural choice is given not by a wave function (representing a
pure state) but by a density matrix (representing a mixed state).
  I begin by classifying quantum theories into two types: theories with a
fundamental wave function and theories with a fundamental density matrix. The
Past Hypothesis is compatible with infinitely many initial wave functions, none
of which seems to be particularly natural. However, once we turn to density
matrices, the Past Hypothesis provides a natural choice---the normalized
projection onto the Past Hypothesis subspace in the Hilbert space.
Nevertheless, the two types of theories can be empirically equivalent. To
provide a concrete understanding of the empirical equivalence, I provide a
novel subsystem analysis in the context of Bohmian theories. Given the
empirical equivalence, it seems empirically underdetermined whether the
universe is in a pure state or a mixed state. Finally, I discuss some
theoretical payoffs of the density-matrix theories and present some open
problems for future research.",1901.08053v1
1996-08-29,The Post-Decoherence Density Matrix Propagator for Quantum Brownian Motion,"Using the path integral representation of the density matrix propagator of
quantum Brownian motion, we derive its asymptotic form for times greater than
the localization time, $ (\hbar / \gamma k T )^{\half}$, where $\gamma$ is the
dissipation and $T$ the temperature of the thermal environment. The
localization time is typically greater than the decoherence time, but much
shorter than the relaxation time, $\gamma^{-1}$. We use this result to show
that the reduced density operator rapidly evolves into a state which is
approximately diagonal in a set of generalized coherent states. We thus
reproduce, using a completely different method, a result we previously obtained
using the quantum state diffusion picture (Phys.Rev. D52, 7294 (1995)). We also
go beyond this earlier result, in that we derive an explicit expression for the
weighting of each phase space localized state in the approximately diagonal
density matrix, as a function of the initial state. For sufficiently long times
it is equal to the Wigner function, and we confirm that the Wigner function is
positive for times greater than the localization time (multiplied by a number
of order 1).",9608046v1
2014-07-31,Equation of state at finite net-baryon density using Taylor coefficients up to sixth order,"We employ the lattice QCD data on Taylor expansion coefficients up to sixth
order to construct an equation of state at finite net-baryon density. When we
take into account how hadron masses depend on lattice spacing and quark mass,
the coefficients evaluated using the p4 action are equal to those of hadron
resonance gas at low temperature. Thus the parametrised equation of state can
be smoothly connected to the hadron resonance gas equation of state. We see
that the equation of state using Taylor coefficients up to second order is
realistic only at low densities, and that at densities corresponding to s/n_B >
40, the expansion converges by the sixth order term.",1407.8532v1
2000-06-12,Structure of the density matrix providing the minimum of generalized uncertainty relation for mixed states,"For configurational space of arbitrary dimension a strict form of the
uncertainty principle has been obtained, which takes into account the
dependence of inequality limit on the effective number of pure states present
in given statistical mixture. It is shown that in a state with minimal
uncertainty the density operators eigenfunctions coincide with the stationary
wavefunctions of a multidimensional harmonic oscillator. The mixed state
obtained has a permutational symmetry which is typical for a system of
identical bosons.",0006055v1
2012-02-14,Equation of state at non-zero baryon density based on lattice QCD,"We employ the lattice QCD data on Taylor expansion coefficients to extend our
previous parametrization of the equation of state to finite baryon density.
When we take into account lattice spacing and quark mass dependence of the
hadron masses, the Taylor coefficients at low temperature are equal to those of
hadron resonance gas. Parametrized lattice equation of state can thus be
smoothly connected to the hadron resonance gas equation of state at low
temperatures.",1202.3104v2
2023-11-02,On linear (in)stability of steady states for the free boundary hard phase model in general relativity,"The hard phase model describes a relativistic barotropic fluid with sound
speed equal to the speed of light. In the framework of general relativity, the
motion of the fluid is coupled to the Einstein equations which describe the
structure of the underlying spacetime. This model admits a $1$-parameter family
of steady states with spherical symmetry. In this work, for perturbations
within spherical symmetry, we study the linear stability and instability of
this family. We prove that the linearized operator around steady states with
large central density admits a growing mode, while such growing modes do not
exist for steady states with small central density.",2311.00955v1
2003-05-29,Image resonance in the many-body density of states at a metal surface,"The electronic properties of a semi-infinite metal surface without a bulk gap
are studied by a formalism able to account for the continuous spectrum of the
system. The density of states at the surface is calculated within the $GW$
approximation of many-body perturbation theory. We demonstrate the presence of
an unoccupied surface resonance peaked at the position of the first image
state. The resonance encompasses the whole Rydberg series of image states and
cannot be resolved into individual peaks. Its origin is the shift in spectral
weight when many-body correlation effects are taken into account.",0305678v1
2000-11-01,Branch points in the complex plane and information loss in quantum systems at high level density,"The mechanism of avoided level crossings in quantum systems is studied. It is
traced back to the existence of branch points in the complex plane which
influence the properties of resonance states as well as of discrete states. An
avoided level crossing of two states causes not only an exchange of the two
wave functions but, above all, correlations between them. The correlations play
an important role at high level density since they cause the loss of
information on the individual properties of the states.",0011008v1
2009-09-21,Equation of state for supernova matter,"We provide an equation of state for high density supernova matter by applying
a momentum-dependent effective interaction. We focus on the study of the
equation of state of high-density and high-temperature nuclear matter
containing leptons (electrons and neutrinos) under the chemical equilibrium
condition. Thermal effects on the properties and equation of state of nuclear
matter are evaluated and analyzed in the framework of the proposed effective
interaction model. Since supernova matter is characterized by a constant
entropy we also present the thermodynamic properties for the isentropic case.",0909.3739v1
2020-10-07,Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas,"We consider the homogeneous Bose gas on a unit torus in the mean-field regime
when the interaction strength is proportional to the inverse of the particle
number. In the limit when the number of particles becomes large, we derive a
two-term expansion of the one-body density matrix of the ground state. The
proof is based on a cubic correction to Bogoliubov's approximation of the
ground state energy and the ground state.",2010.03595v2
2019-12-16,A measure of qubit environment entanglement for pure dephasing evolutions,"We propose a qubit-environment entanglement measure which is tailored for
evolutions that lead to pure dephasing of the qubit, such as are abundant in
solid state scenarios. The measure can be calculated directly form the density
matrix without minimization of any kind. In fact it does not require the
knowledge of the full density matrix, and it is enough to know the initial
qubit state and the states of the environment conditional on qubit pointer
states. This yields a computational advantage over standard entanglement
measures, which becomes large when there are no correlations between
environmental components in the conditional environmental states. In contrast
to all other measures of mixed state entanglement, the measure has a
straightforward physical interpretation directly linking the amount of
information about the qubit state which is contained in the environment to the
amount of qubit-environmnent entanglement. This allows for a direct extension
of the pure state interpretation of entanglement generated during pure
dephasing to mixed states, even though pure-state conclusions about qubit
decoherence are not transferable.",1912.07317v2
2021-12-17,Entropic Density Functional Theory: Entropic Inference and the Equilibrium State of Inhomogeneous Fluids,"A unified formulation of the density functional theory is constructed on the
foundations of entropic inference in both the classical and the quantum
regimes. The theory is introduced as an application of entropic inference for
inhomogeneous fluids in thermal equilibrium. It is shown that entropic
inference reproduces the variational principle of DFT when information about
expected density of particles is imposed. In the classical regime, this process
introduces a family of trial density-parametrized probability distributions,
and consequently a trial entropy, from which the preferred one is found using
the method of Maximum Entropy (MaxEnt). In the quantum regime, similarly, the
process involves introduction of a family of trial density-parametrized density
matrices, and consequently a trial entropy, from which the preferred density
matrix is found using the method of quantum MaxEnt. As illustrations some known
approximation schemes of the theory are discussed.",2112.09577v1
2020-01-25,Properties of $Z_c(3900)$ tetraquark in a cold nuclear matter,"The study of medium effects on properties of particles embedded in nuclear
matter is of great importance for understanding the nature and internal
quark-gluon organization as well as exact determination of the quantum numbers,
especially of the exotic states. In this context, we study the physical
properties of one of the famous charmonium-like states, $Z_c(3900)$, in a cold
dense matter. We investigate the possible shifts in the mass and current-meson
coupling of the $Z_c(3900)$ state due to the dense medium at saturation
density, $ \rho^{sat} $, by means of the in-medium sum rules. We also estimate
the vector self-energy of this state at saturation nuclear matter density. We
discuss the behavior of the spectroscopic parameters of this state with respect
to the density up to a high density corresponding to the core of neutron stars,
$\rho\approx 5\rho^{sat}$. Both the mass and current-coupling of this state
show nonlinear behavior and decrease with respect to the density of the medium:
the mass reaches roughly $30\%$ of its vacuum value at $ \rho=5\rho^{sat} $,
while the current-coupling approaches zero at $ \rho\approx2.1\rho^{sat} $,
when the central values of the auxiliary and other input parameters are used.",2001.09356v3
2014-05-23,Competing quantum Hall phases in the second Landau level in low density limit,"We present in this Letter the results from two high quality, low density GaAs
quantum wells. In sample A of electron density n=5.0x10^10 cm^-2, anisotropic
electronic transport behavior was observed at \nu=7/2 in the second Landau
level. We believe that the anisotropy is due to the large Landau level mixing
effect in this sample. In sample B of density 4.1x10^10 cm^-2, strong 8/3, 5/2,
and 7/3 fractional quantum Hall states were observed. Furthermore, our energy
gap data suggest that, similar to the 8/3 state, the 5/2 state may also be spin
unpolarized in the low density limit. The results from both samples show that
the strong electron-electron interactions and a large Landau level mixing
effect play an import role in the competing ground states in the second landau
level.",1405.6188v2
2015-05-28,Genesis of charge orders in high temperature superconductors,"One of the most puzzling facts about cuprate high-temperature superconductors
in the lightly doped regime is the coexistence of uniform superconductivity
and/or antiferromagnetism with many low-energy charge-ordered states in a
unidirectional charge density wave or a bidirectional checkerboard structure.
Recent experiments have discovered that these charge density waves exhibit
different symmetries in their intra-unit-cell form factors for different
cuprate families. Using a renormalized mean-field theory for a well-known,
strongly correlated model of cuprates, we obtain a number of charge-ordered
states with nearly degenerate energies without invoking special features of the
Fermi surface. All of these self-consistent solutions have a pair density wave
intertwined with a charge density wave and sometimes a spin density wave. Most
of these states vanish in the underdoped regime, except for one with a large
d-form factor that vanishes at approximately 19% doping of the holes, as
reported by experiments. Furthermore, these states could be modified to have a
global superconducting order, with a nodal-like density of states at low
energy.",1505.07728v5
2014-06-19,Massive Neutron Stars with Antikaon Condensates in a Density Dependent Hadron Field Theory,"The measurement of $1.97 \pm 0.04 M_{solar}$ for PSR J1614-2230 and $2.01 \pm
0.04M_{solar}$ for PSR J0348+0432 puts a strong constraint on the neutron star
equation of state and its exotic composition at higher densities. In this
paper, we investigate the possibility of exotic equation of state within the
observational mass constraint of $2M_{solar}$ in the framework of relativistic
mean field model with density-dependent couplings. We particularly study the
effect of antikaon condensates in the presence of hyperons on the mass-radius
relationship of the neutron star.",1406.4961v1
1995-03-29,New Phases of High Temperature Superconductors in High Magnetic Field,"Fluctuation behavior of high temperature superconductors in high magnetic
field is studied within the Ginzburg-Landau theory. Landau level degeneracy of
Cooper pairs enhances fluctuations which destroy the familiar Abrikosov vortex
lattice for D=2,3. Instead, a charge-density wave of Cooper pairs (SCDW) is the
new low-temperature phase of the theory. SCDW has no condensate, but differs
from the normal state by a periodic modulation of the Cooper pair density. In
presence of disorder, the Abrikosov state is revived and both superconducting
and density-wave phases are possible.",9503156v1
1998-04-09,On the Dynamical Meaning of Spectral Dimensions,"Time averaging over the trajectory of a wavepacket up to time T defines a
statistical operator (density matrix). The corresponding (Von Neumann) entropy
is proven to asymptotically increase with time like D.log T, with D the
Hausdorff dimension of the Local Density of States, at least if the latter
measure has good scaling properties. In more general cases, spectral upper and
lower bounds for the increase of entropy are given, in terms of the Hausdorff
and of the Fractal Dimension of the Local Density of States.",9804009v1
2016-01-11,Current induced and interaction driven Dirac-point drag of massless quasi-relativistic fermions,"We study the quasiparticle properties of two-dimensional massless Dirac
Fermions when the many-body states possess a finite momentum density in the
clean limit. The lack of Galilean invariance endows the many-body states at
finite momentum density with qualitative differences from those of the system
at rest. At finite carrier densities we demonstrate the appearance of a
current-induced distortion of the pseudospin texture in momentum space that can
be viewed as a drag of the Dirac point and the origin of which lies entirely in
electron-electron interactions. We discuss the potential observation of this
effect in graphene.",1601.02619v2
2017-08-16,Isothermal Equation of State of Three Dimensional Yukawa Gas,"Molecular Dynamics (MD) simulation is carried out to examine the effect of
particle confinement on the pressure of 3D Yukawa gas. Confinement effects are
taken into account by using perfectly reflecting boundary condition in MD
simulations. An equation of state relating pressure to number density is
obtained. The results of the MD simulations show that in weak coupling regime
pressure of confined Yukawa gas is much bigger than the kinetic pressure and
scales quadratically with number density. Results are compared with earlier
theories and experiments which show quadratic scaling of dust pressure with
density.",1708.04874v2
2019-01-16,Models of a protoplanetary disk forming in-situ the Galilean and smaller nearby satellites before Jupiter is formed,"We fit an isothermal oscillatory density model of Jupiter's protoplanetary
disk to the present-day Galilean and other nearby satellites and we determine
the radial scale length of the disk, the equation of state and the central
density of the primordial gas, and the rotational state of the Jovian nebula.
Although the radial density profile of Jupiter's disk was similar to that of
the solar nebula, its rotational support against self-gravity was very low, a
property that also guaranteed its long-term stability against self-gravity
induced instabilities for millions of years.",1901.05131v2
1997-05-01,Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics,"A one-dimensional driven lattice gas with disorder in the particle hopping
probabilities is considered. It has previously been shown that in the version
of the model with random sequential updating, a phase transition occurs from a
low density inhomogeneous phase to a high density congested phase. Here the
steady states for both parallel (fully synchronous) updating and ordered
sequential updating are solved exactly and the phase transition shown to
persist in both cases. For parallel dynamics and forward ordered sequential
dynamics the phase transition occurs at the same density but for backward
ordered sequential dynamics it occurs at a higher density. In both cases the
critical density is higher than that for random sequential dynamics. In all the
models studied the steady state velocity is related to the fugacity of a Bose
system suggesting a principle of minimisation of velocity. A generalisation of
the dynamics where the hopping probabilities depend on the number of empty
sites in front of the particles, is also solved exactly in the case of parallel
updating. The models have natural interpretations as simplistic descriptions of
traffic flow. The relation to more sophisticated traffic flow models is
discussed.",9705006v1
1997-01-23,From quantum Bayesian inference to quantum tomography,"We derive an expression for a density operator estimated via Bayesian quantum
inference in the limit of an infinite number of measurements.
  This expression is derived under the assumption that the reconstructed system
is in a pure state. In this case the estimation corresponds to an averaging
over a generalized microcanonical ensemble of pure states satisfying a set of
constraints imposed by the measured mean values of the observables under
consideration. We show that via the ``purification'' ansatz, statistical
mixtures can also be consistently reconstructed via the quantum Bayesian
inference scheme. In this case the estimation corresponds to averaging over the
generalized canonical ensemble of states satisfying the given constraints, and
the reconstructed density operator maximizes the von Neumann entropy (i.e.,
this density operator is equal to the generalized canonical density operator
which follows from the Jaynes principle of maximum entropy). We study in detail
the reconstruction of the spin-1/2 density operator and discuss the logical
connection between the three reconstruction schemes, i.e., (1) quantum Bayesian
inference, (2) reconstruction via the Jaynes principle of maximum entropy, and
(3) discrete quantum tomography.",9701029v1
2015-03-17,Density of states method for the Z(3) spin model,"We apply the density of states approach to the Z(3) spin model with a
chemical potential mu. For determining the density of states we use restricted
Monte Carlo simulations on small intervals of the variable for the density. In
each interval we probe the response of the system to the variation of a free
parameter in the Boltzmann factor. This response is a known function which we
fit to the Monte Carlo data and the parameters of the density are obtained from
that fit (functional fit approch; FFA). We evaluate observables related to the
particle number and the particle number susceptibility, as well as the free
energy. We find that for a surprisingly large range of mu the results from the
FFA agree very well with the results from a reference simulation in the dual
formulation of the Z(3) spin model which is free of the complex action problem.",1503.04947v2
2016-06-17,Ground State Properties of Anti-Ferromagnetic Spinor Bose gases in One Dimension,"We investigate the ground state properties of anti-ferromagnetic spin-1 Bose
gases in one dimensional harmonic potential from the weak repulsion regime to
the strong repulsion regime. By diagonalizing the Hamiltonian in the Hilbert
space composed of the lowest eigenstates of single particle and spin
components, the ground state wavefunction and therefore the density
distributions, magnetization distribution, one body density matrix, and
momentum distribution for each components are obtained. It is shown that the
spinor Bose gases of different magnetization exhibit the same total density
profiles in the full interaction regime, which evolve from the single peak
structure embodying the properties of Bose gases to the fermionized shell
structure of spin-polarized fermions. But each components display different
density profiles, and magnetic domains emerge in the strong interaction limit
for $M=0.25$. In the strong interaction limit, one body density matrix and the
momentum distributions exhibit the same behaviours as those of spin-polarized
fermions. The fermionization of momentum distribution takes place, in contrast
to the $\delta$-function-like distribution of single component Bose gases in
the full interaction region.",1606.05461v1
2020-06-02,Intercalated phosphorene for improved spintronic applications,"In this work we study the intercalation of monolayer phosphorene with
nitrogen, lithium and calcium for exploring prospects of spintronic
applications. The electronic and the magnetic properties of the intercalated
structure are investigated via density functional theory to obtain the band
structure and the spin polarized density of states. Albeit the band structure
data show vanishing band gap, a noticeable difference emerges in the densities
of the up and the down spin states induced by the intercalants. To evaluate the
performance of the intercalated phosphorene, the spintronic order parameter,
measuring the asymmetry among the up and the down spin densities of states, is
computed which clearly shows evolution of improved spintronic properties at
large intercalant densities. Further, larger atomic numbers of the intercalants
seem to aid the performance of phosphorene as a spintronic material.",2006.01577v1
2021-02-04,On the equivalence of self-consistent equations for nonuniform liquids: a unified description of the various modifications,"A variety of self-consistent (SC) equations have been proposed for
non-uniform states of liquid particles under external fields, including
adsorbed states at solid substrates and confined states in pores. External
fields represent not only confining geometries but also fixed solutes. We
consider SC equations ranging from the modified Poisson-Boltzmann equations for
the Coulomb potential to the hydrostatic linear response equation for the
equilibrium density distribution of Lennard-Jones fluids. Here, we present a
unified equation that explains the apparent diversity of previous forms and
proves the equivalence of various SC equations. This unified description of SC
equations is obtained from a hybrid method combining the conventional density
functional theory and statistical field theory. The Gaussian approximation of
density fluctuations around a mean-field distribution is performed based on the
developed hybrid framework, allowing us to derive a novel form of the
grand-potential density functional that provides the unified SC equation for
equilibrium density.",2102.02495v1
2024-03-25,Tensor network formulation of symmetry protected topological phases in mixed states,"We define and classify symmetry-protected topological (SPT) phases in mixed
states based on the tensor network formulation of the density matrix. In one
dimension, we introduce strong injective matrix product density operators
(MPDO), which describe a broad class of short-range correlated mixed states,
including the locally decohered SPT states. We map strong injective MPDO to a
pure state in the doubled Hilbert space and define the SPT phases according to
the cohomology class of the symmetry group in the doubled state. Although the
doubled state exhibits an enlarged symmetry, the possible SPT phases are also
constrained by the Hermiticity and the semi-positivity of the density matrix.
We here obtain a complete classification of SPT phases with a direct product of
strong $G$ and weak $K$ unitary symmetry given by the cohomology group
$\mathcal{H}^2(G, \text{U}(1))\oplus\mathcal{H}^1(K, \mathcal{H}^1(G,
\text{U}(1)))$. The SPT phases in our definition are preserved under symmetric
local circuits consisting of non-degenerate channels. This motivates an
alternative definition of SPT phases according to the equivalence class of
mixed states under a ``one-way"" connection using symmetric non-degenerate
channels. In locally purifiable MPDO with strong symmetry, we prove that this
alternative definition reproduces the cohomology classification. We further
extend our results to two-dimensional mixed states described by strong
semi-injective tensor network density operators and classify the possible SPT
phases.",2403.17069v1
1996-03-22,Relativistic Mean-Field Theory and the High-Density Nuclear Equation of State,"The properties of high-density nuclear and neutron matter are studied using a
relativistic mean-field approximation to the nuclear matter energy functional.
Based on ideas of effective field theory, nonlinear interactions between the
fields are introduced to parametrize the density dependence of the energy
functional. Various types of nonlinearities involving scalar-isoscalar
($\sigma$), vector-isoscalar ($\omega$), and vector-isovector ($\rho$) fields
are studied. After calibrating the model parameters at equilibrium nuclear
matter density, the model and parameter dependence of the resulting equation of
state is examined in the neutron-rich and high-density regime. It is possible
to build different models that reproduce the same observed properties at normal
nuclear densities, but which yield maximum neutron star masses that differ by
more than one solar mass. Implications for the existence of kaon condensates or
quark cores in neutron stars are discussed.",9603037v1
2008-10-08,Saturation of Two Level Systems and Charge Noise in Josephson Junction Qubits,"We study the charge noise $S_Q$ in Josephson qubits produced by fluctuating
two level systems (TLS) with electric dipole moments in the substrate. The TLS
are driven by an alternating electric field of angular frequency $\Omega$ and
electric field intensity $I$. It is not widely appreciated that TLS in small
qubits can easily be strongly saturated if $I\gg I_c$, where $I_c$ is the
critical electric field intensity. To investigate the effect of saturation on
the charge noise, we express the noise spectral density in terms of density
matrix elements. To determine the dependence of the density matrix elements on
the ratio $I/I_c$, we find the steady state solution for the density matrix
using the Bloch-Redfield differential equations. We then obtain an expression
for the spectral density of charge fluctuations as a function of frequency $f$
and the ratio $I/I_c$. We find $1/f$ charge noise at low frequencies, and that
the charge noise is white (constant) at high frequencies. Using a flat density
of states, we find that TLS saturation has no effect on the charge noise at
either high or low frequencies.",0810.1334v2
2014-11-25,FFLO order in ultra-cold atoms in three-dimensional optical lattices,"We investigate different ground-state phases of attractive spin-imbalanced
populations of fermions in 3-dimensional optical lattices. Detailed numerical
calculations are performed using Hartree-Fock-Bogoliubov theory to determine
the ground-state properties systematically for different values of density,
spin polarization and interaction strength. We first consider the high density
and low polarization regime, in which the effect of the optical lattice is most
evident. We then proceed to the low density and high polarization regime where
the effects of the underlying lattice are less significant and the system
begins to resemble a continuum Fermi gas. We explore the effects of density,
polarization and interaction on the character of the phases in each regime and
highlight the qualitative differences between the two regimes. In the
high-density regime, the order is found to be of Larkin-Ovchinnikov type,
linearly oriented with one characteristic wave vector but varying in its
direction with the parameters. At lower densities the order parameter develops
more structures involving multiple wave vectors.",1411.6967v1
2018-07-26,Novel Superconductivity in Endohedral Gallide Mo8Ga41,"We report on synthesis and characterization of gallide cluster based Mo8Ga41
superconductor. Transport and magnetization measurements confirm the
superconducting transition temperature to be 9.8 K. The upper critical field,
lower critical field, Ginzburg-Landau coherence length and penetration depth
are estimated to be 11.8T, 150G, 5.2nm, 148nm respectively. The electronic band
structure, density of states and phonon dispersion curve calculations are
obtained by using Density Functional Theory. The core level X-ray Photoelectron
Spectroscopy (XPS) reveals the binding energy information of the constituting
elements Mo and Ga in Mo8Ga41. The valence band spectra from XPS is in good
agreement with calculated density of states (DOS). The zero field critical
current density (Jc) at T = 2 K is ~ 3*10^5 A/cm^2 which is indicative of
efficient flux pinning in the as grown compound. About two fold enhancement in
critical current density with application of external pressure (1.1 GPa) is
observed with marginal decrease in transition temperature. The fitting of
current density to double exponential model confirms possibility of two gap
superconductivity in Mo8Ga41.",1807.09988v1
2019-09-22,Moments of the ground state density for the $d$-dimensional Fermi gas in an harmonic trap,"We consider properties of the ground state density for the $d$-dimensional
Fermi gas in an harmonic trap. Previous work has shown that the $d$-dimensional
Fourier transform has a very simple functional form. It is shown that this fact
can be used to deduce that the density itself satisfies a third order linear
differential equation, previously known in the literature but from other
considerations. It is shown too how this implies a closed form expression for
the $2k$-th non-negative integer moments of the density, and a second order
recurrence. Both can be extended to general Re$\, k > -d/2$. The moments, and
the smoothed density, permit expansions in $1/\tilde{M}^2$, where $\tilde{M} =
M + (d+1)/2$, with $M$ denoting the shell label. The moment expansion
substituted in the second order recurrence gives a generalisation of the
Harer--Zagier recurrence, satisfied by the coefficients of the $1/N^2$
expansion of the moments of the spectral density for the Gaussian unitary
ensemble in random matrix theory.",1909.09918v4
2020-06-30,Operando Control of Skyrmion Density in a Lorentz Transmission Electron Microscope with Current Pulses,"Magnetic skyrmions hold promise for spintronic devices. To explore the
dynamical properties of skyrmions in devices, a nanoscale method to image spin
textures in response to a stimulus is essential. Here, we apply a technique for
operando electrical current pulsing of chiral magnetic devices in a Lorentz
transmission electron microscope. In ferromagnetic multilayers with interfacial
Dzyaloshinskii-Moriya interaction (DMI), we study the creation and annihilation
of skyrmions localized by point-like pinning sites due to defects. Using a
combination of experimental and micromagnetic techniques, we establish a
thermal contribution for the creation and annihilation of skyrmions in our
study. Our work reveals a mechanism for controlling skyrmion density, which
enables an examination of skyrmion magnetic field stability as a function of
density. We find that high-density skyrmion states are more stable than
low-density states or isolated skyrmions resisting annihilation over a magnetic
field range that increases monotonically with density.",2006.16780v1
2021-07-19,Gauge-invariant perturbation expansion in powers of electric charge for the density-of-states of a network model for charged-particle motion in a uniform background magnetic flux density,"An explicitly-gauge-invariant expansion in powers of $e/\hbar$ times the
magnetic flux density is formally obtained for the density of states (as
characterized by the trace of the resolvent $\widehat G$ = $(\omega - \hat
h)^{-1}$) of a charged particle moving on a Hermitian quantum network that is
embedded in a Euclidean background that supports a uniform magnetic flux
density. The explicit expressions, given here up to third order in the flux
density, are also valid for the ``local trace'' (the trace of $\widehat P_i
\widehat G$, where $\widehat P_i$ is the projector on a network node), and do
not appear to have been previously given.",2107.08672v1
2021-12-21,DensityTool: A post-processing tool for space- and spin-resolved density of states from VASP,"The knowledge of the local electronic structure of heterogeneous solid
materials is crucial for understanding their electronic, magnetic, transport,
optical, and other properties. VASP, one of the mostly used packages for
density-functional calculations, provides local electronic structure either by
projecting the electronic wave functions on atomic spheres, or as a
band-decomposed partial charge density. Here, we present a simple tool which
takes the partial charge density and the energy eigenvalues calculated by VASP
as input and constructs local charge and spin densities. The new data provides
a much better spatial resolution than the projection on the atomic spheres. It
can be visualized directly in the real space e.g. with Vesta, or averaged along
planes spanned by two of the lattice vectors of the periodic unit cell. The
plane-averaged local (spin) density of states can be easily plotted e.g. as
color-coded data using almost any plotting program. DensityTool can be applied
to manipulate, visualize, and understand the local electronic structure of any
system calculated with VASP. We expect it to be useful especially for
researchers concerned with inhomogeneous systems, such as interfaces, defects,
surfaces, adsorbed molecules, or hybrid inorganic-organic composites.",2112.11050v1
2022-09-12,Enhanced dilepton emission from a phase transition in dense matter,"It is demonstrated that the presence of a phase transition in heavy ion
collisions, at beam energies that probe dense QCD matter, leads to a
significant enhancement of the dilepton yield per produced pion due to the
extended emission time. In addition, the temperature of low mass dileptons
shows a modest decrease due to the mixed phase. The emission of dileptons in
the SIS18-SIS100 beam energies range is studied by augmenting the UrQMD
transport model with a realistic density dependent equation of state, as well
as two different phase transitions. This is achieved by extending the molecular
dynamics interaction part of the UrQMD model to a density dependent interaction
potential with a high density minimum leading to a phase transition and
metastable coexisting high density states. Together with a high precision
measurement these simulations will be able to constrain the existence of a
phase transition in QCD up to densities of several times nuclear saturation
density.",2209.05267v1
2005-06-11,Phase Diagram and Spectroscopy of FFLO states of two-dimensional d-wave superconductors,"Experimental evidence suggests that the Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state may be realized in the unconventional, heavy-fermion
superconductor CeCoIn$_5$. We present a self-consistent calculation of the
field versus temperature phase diagram and order parameter structures for the
FFLO states of quasi-two-dimensional d-wave superconductors. We calculate the
spatially nonuniform order parameter, free energy density, and local density of
states for magnetic fields parallel to the superconducting planes. We predict
that the lower critical magnetic field transition between the spatially uniform
and nonuniform FFLO state is second order. We discuss the signatures of the
nonuniform FFLO state which should be observable in scanning tunneling
microscopy measurements of the local density of states.",0506257v1
2023-05-09,Tomography of Quantum States from Structured Measurements via quantum-aware transformer,"Quantum state tomography (QST) is the process of reconstructing the state of
a quantum system (mathematically described as a density matrix) through a
series of different measurements, which can be solved by learning a
parameterized function to translate experimentally measured statistics into
physical density matrices. However, the specific structure of quantum
measurements for characterizing a quantum state has been neglected in previous
work. In this paper, we explore the similarity between highly structured
sentences in natural language and intrinsically structured measurements in QST.
To fully leverage the intrinsic quantum characteristics involved in QST, we
design a quantum-aware transformer (QAT) model to capture the complex
relationship between measured frequencies and density matrices. In particular,
we query quantum operators in the architecture to facilitate informative
representations of quantum data and integrate the Bures distance into the loss
function to evaluate quantum state fidelity, thereby enabling the
reconstruction of quantum states from measured data with high fidelity.
Extensive simulations and experiments (on IBM quantum computers) demonstrate
the superiority of the QAT in reconstructing quantum states with favorable
robustness against experimental noise.",2305.05433v2
2016-06-14,Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study,"In nuclear physics, Density Functional Theory (DFT) provides the basis for
state-of-the art studies of ground-state properties of heavy nuclei. However,
the direct relation of the density functional underlying these calculations and
the microscopic nuclear forces is not yet fully understood. We present a
combination of DFT and Renormalization Group (RG) techniques which allows to
study selfbound many-body systems from microscopic interactions. We discuss its
application with the aid of systems of identical fermions interacting via a
long-range attractive and short-range repulsive two-body force in one
dimension. We compute ground-state energies, intrinsic densities, and density
correlation functions of these systems and compare our results to those
obtained from other methods. In particular, we show how energies of excited
states as well as the absolute square of the ground-state wave function can be
extracted from the correlation functions within our approach. The relation
between many-body perturbation theory and our DFT-RG approach is discussed and
illustrated with the aid of the calculation of the second-order energy
correction for a system of $N$ identical fermions interacting via a general
two-body interaction. Moreover, we discuss the control of spuriously emerging
fermion self-interactions in DFT studies within our framework. In general, our
approach may help to guide the development of energy functionals for future
quantitative DFT studies of heavy nuclei from microscopic interactions.",1606.04388v1
2006-08-31,An orbital-free density functional method based on inertial fields,"In this paper we revisit the Levy-Perdew-Sahni equation. We establish that
the relation implicitly contains the conservation of energy density at every
point of the system. The separate contributions to the total energy density are
described in detail, and it is shown that the key difference to standard
density functional methods is the existence of a general exchange-correlation
potential, which does not explicitly depend on electron charge. We derive
solutions for the hydrogen-like atoms and analyse local properties. It is found
that these systems are stable due to the existence of a vector potential ${\bf
A}$, related to electron motion, which leads to two general effects: (i) The
root of the charge density acquires an additional complex phase; and (ii) for
single electrons, the vector potential cancels the effect of electrostatic
repulsions. We determine the density of states of a free electron gas based on
this model and find that the vectorpotential also accounts for the Pauli
exclusion principle. Implications of these results for direct methods in
density functional theory are discussed. It seems that the omission of vector
potentials in formulating the kinetic energy density functionals may be the
main reason that direct methods so far are not generally applicable. Finally,
we provide an orbital free self-consistent formulation for determining the
groundstate charge density in a local density approximation.",0608713v1
2008-06-18,The QSO proximity effect at redshift <z>=2.6 with the FLO approach,"We revisit the proximity effect produced by QSOs at redshifts 2.1-3.3
applying the FLO approach (Saitta et al. 2008) to a sample of ~6300 Ly-alpha
lines fitted in 21 high resolution, high signal-to-noise spectra. This new
technique allows to recover the hydrogen density field from the HI column
densities of the lines in the Ly-alpha forest, on the basis of simple
assumptions on the physical state of the gas. To minimize the systematic
uncertainties that could affect the density recovering in the QSO vicinity, we
carefully determined the redshifts of the QSOs in our sample and modelled in
detail their spectra to compute the corresponding ionising fluxes. The mean
density field obtained from the observed spectra shows a significant
over-density in the region within 4 proper Mpc from the QSO position,
confirming that QSOs are hosted in high density peaks. The absolute value of
rho/<rho> for the peak is uncertain by a factor of ~3, depending on the assumed
QSO spectral slope and the minimum HI column density detectable in the spectra.
We do not confirm the presence of a significant over-density extending to
separations of ~15 proper Mpc from the QSO, claimed in previous works at
redshifts <z>=2.5 and 3.8. Our best guess for the UV background ionisation rate
based on the IGM mean density recovered by FLO is Gamma_UVB ~ 10^{-12} s^{-1}.
However, values of Gamma_UVB ~ 3x10^{-12} s^{-1} could be viable if an inverted
temperature-density relation with index alpha=-0.5 is adopted.",0806.3075v1
2009-09-07,Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory,"We investigate the approach to the universal regime of the dilute unitary
Fermi gas as the density is reduced to zero in a lattice model. To this end we
study the chemical potential, superfluid order parameter and internal energy of
the attractive Hubbard model in three different lattices with densities of
states (DOS) which share the same low-energy behavior of fermions in
three-dimensional free space: a cubic lattice, a ""Bethe lattice"" with a
semicircular DOS, and a ""lattice gas"" with parabolic dispersion and a sharp
energy cut-off that ensures the normalization of the DOS. The model is solved
using Dynamical Mean-Field Theory, that treats directly the thermodynamic limit
and arbitrarily low densities, eliminating finite-size effects. At densities of
the order of one fermion per site the lattice and its specific form dominate
the results. The evolution to the low-density limit is smooth and it does not
allow to define an unambiguous low-density regime. Such finite-density effects
are significantly reduced using the lattice gas, and they are maximal for the
three-dimensional cubic lattice. Even though dynamical mean-field theory is
bound to reduce to the more standard static mean field in the limit of zero
density due to the local nature of the self-energy and of the vertex functions,
it compares well with accurate Monte Carlo simulations down to the lowest
densities accessible to the latter.",0909.1298v1
2014-12-13,Decay and structure of the Hoyle state,"The first $0^+$ resonant state of the $^{12}$C nucleus ${}^{12}$C$(0_2^+)$,
so called the Hoyle state, is investigated in a three-$\alpha$-particle
(3-$\alpha$) model. A wave function for the photodisintegration reaction of a
$^{12}$C bound state to 3-$\alpha$ final states is defined and calculated by
the Faddeev three-body formalism, in which three-body bound- and continuum
states are treated consistently. From the wave function at the Hoyle state
energy, I calculated distributions of outgoing $\alpha$-particles and density
distributions at interior region of the Hoyle state. Results show that a
process through a two-$\alpha$ resonant state is dominant in the decay and
contributions of the rest process are very small, less than 1 \%. There appear
some peaks in the interior density distribution corresponding to configurations
of an equilateral- and an isosceles triangles. It turns out that these results
are obtained independently of the choice of $\alpha$-particle interaction
models, when they are made to reproduce the Hoyle state energy.",1412.4176v1
2012-08-31,The Temperature-Density Relation in the Intergalactic Medium at Redshift <z>=2.4,"We present new measurements of the temperature-density (T-rho) relation for
neutral hydrogen in the 2.0 < z < 2.8 intergalactic medium (IGM) using a sample
of ~6000 individual HI absorbers fitted with Voigt profiles constrained in all
cases by multiple Lyman series transitions. We find model independent evidence
for a positive correlation between the column density of HI (NHI) and the
minimum observed velocity width of absorbers (bmin). With minimal
interpretation, this implies that the temperature-density relation in the IGM
is not ""inverted"", contrary to many recent studies. Fitting bmin as a function
of NHI results in line width - column density dependence of the form bdmin =
b_0 [NHI/N_(HI,0)]^(Gamma-1) with a minimum line width at mean density rhobar
[N_(HI, 0) = 10^13.6 cm^-2] of b_0 = 17.9 +- 0.2 km/s and a power-law index of
(Gamma-1) = 0.15 +- 0.02. Using analytic arguments, these measurements imply an
""equation of state"" for the IGM at <z>= 2.4 of the form T = T_0
(rho/rhobar)^(gamma-1) with a temperature at mean density of T_0 = (1.94 +-
0.05) x 10^4 K and a power-law index (gamma -1) = 0.46 +- 0.05.",1209.0005v1
2016-02-11,Energy density distribution of shaped waves inside scattering media mapped onto a complete set of diffusion modes,"We show that the spatial distribution of the energy density of optimally
shaped waves inside a scattering medium can be described by considering only a
few of the lowest eigenfunctions of the diffusion equation. Taking into account
only the fundamental eigenfunction, the total internal energy inside the sample
is underestimated by only 2%. The spatial distribution of the shaped energy
density is very similar to the fundamental eigenfunction, up to a cosine
distance of about 0.01. We obtained the energy density inside a quasi-1D
disordered waveguide by numerical calculation of the joined scattering matrix.
Computing the transmission-averaged energy density over all transmission
channels yields the ensemble averaged energy density of shaped waves. From the
averaged energy density obtained, we reconstruct its spatial distribution using
the eigenfunctions of the diffusion equation. The results from our study have
exciting applications in controlled biomedical imaging, efficient light
harvesting in solar cells, enhanced energy conversion in solid-state lighting,
and low threshold random lasers.",1602.03921v1
2016-09-23,Shear viscosity of nuclear matter,"Shear viscosity $\eta$ is calculated for the nuclear matter described as a
system of interacting nucleons with the van der Waals (VDW) equation of state.
The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of
the collective overdamped motion. In the frequent-collision regime, the shear
viscosity depends on the particle-number density $n$ through the mean-field
parameter $a$, which describes attractive forces in the VDW equation. In the
temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the
entropy density $s$ is smaller than 1 at the nucleon number density $n =(0.5 -
1.5)\,n^{}_0$, where $n^{}_0=0.16\,$fm$^{-3}$ is the particle density of
equilibrium nuclear matter at zero temperature. A minimum of the $\eta/s$ ratio
takes place somewhere in a vicinity of the critical point of the VDW system.
Large values of $\eta/s\gg 1$ are, however, found in both the low-density,
$n\ll n^{}_0$, and high-density, $n>2n^{}_0$, regions. This makes the ideal
hydrodynamic approach inapplicable for these densities.",1609.07453v2
2018-04-12,Screening and anti-screening of the pairing interaction in low-density neutron matter,"We study pairing in low-density neutron matter including the screening
interaction due to the exchange of particle-hole and RPA excitations. As bare
force we employ the effective low-momentum interaction $V_{low\,k}$, while the
Fermi-liquid parameters are taken from a phenomenological energy density
functional (SLy4) which correctly reproduces the equation of state of neutron
matter. At low density, we find screening, i.e., pairing is reduced, while at
higher densities, we find anti-screening, i.e., pairing is enhanced. This
enhancement is mostly due to the strongly attractive Landau parameter $f_0$. We
discuss in detail the critical temperature $T_c$ in the limit of low densities
and show that the suppression of $T_c$ predicted by Gor'kov and
Melik-Barkhudarov can only be reproduced if the cutoff of the $V_{low\,k}$
interaction is scaled with the Fermi momentum. We also discuss the effect of
non-condensed pairs on the density dependence of $T_c$ in the framework of the
Nozi\`eres-Schmitt-Rink theory.",1804.04332v2
2021-02-06,Inhomogeneous activity enhances density phase separation in active model B,"We study the binary phase separation in active model B, on a two-dimensional
substrate with inhomogeneous activity. The activity was introduced with a
maximum value at the center of the box and spread as a Bivariate-Gaussian
distribution as we move away from the center. The system was studied for three
different intensities of the distribution. Towards the boundary of the box,
activity is zero or the model is similar to the passive model B. We start from
the random homogeneous distribution of density of particles, and the system
evolves towards a structured distribution of density. With time, density starts
to phase separately with maximum density at the center of the box and decreases
as we move away from the center of the box. The width of the density profile at
the center increases as a power lawexponent{\alpha}(t) remains close between
2/3 to 3/4 up to some moderate time and then decays to zero in the steady
state. Hence, our result shows the response of density in an active binary
system with respect to the patterned substrate. It can be used to design
devices useful for the trapping and segregation of active particles.",2102.03600v2
2006-06-30,Joint density-functional theory for electronic structure of solvated systems,"We introduce a new form of density functional theory for the {\em ab initio}
description of electronic systems in contact with a molecular liquid
environment. This theory rigorously joins an electron density-functional for
the electrons of a solute with a classical density-functional theory for the
liquid into a single variational principle for the free energy of the combined
system. A simple approximate functional predicts, without any fitting of
parameters to solvation data, solvation energies as well as state-of-the-art
quantum-chemical cavity approaches, which require such fitting.",0606817v2
1997-01-21,One-dimensional classical adjoint SU(2) Coulomb Gas,"The equation of state of a one-dimensional classical nonrelativistic Coulomb
gas of particles in the adjoint representation of SU(2) is given. The problem
is solved both with and without sources in the fundamental representation at
either end of the system. The gas exhibits confining properties at low
densities and temperatures and deconfinement in the limit of high densities and
temperatures. However, there is no phase transition to a regime where the
string tension vanishes identically; true deconfinement only happens for
infinite densities and temperatures. In the low density, low temperature limit,
a new type of collective behavior is observed.",9701105v1
1993-10-18,Quasiparticle properties and the dynamics of high-density nuclear matter,"The energy spectrum of nucleons in high-density nuclear matter is
investigated in the framework of relativistic meson-nucleon many-body theory,
employing the $1/N$ expansion method. The coupling of the nucleon with the
particle-hole excitations in the medium flattens the spectra in the vicinity of
the Fermi surface. The effect grows logarithmically for increasing density and
eventually leads to instability of the normal state. The validity of the
mean-field theory at high density is criticized.",9310023v1
2001-11-07,Discerning the neutron density distribution of 208Pb from nucleon elastic scattering,"We seek a measure of the neutron density of 208Pb from analyses of
intermediate energy nucleon elastic scattering. The pertinent model for such
analyses is based on coordinate space nonlocal optical potentials obtained from
model nuclear ground state densities. Those potentials give predictions of
integral observables and of angular distributions which show sensitivity to the
neutron density. When compared with experiment, and correlated with analyses of
electron scattering data, the results suggest that 208Pb has a neutron skin
thickness ~0.17 fm.",0111020v2
2015-06-08,Quantum walks in the density operator picture,"A new approach to quantum walks is presented. Considering a quantum system
undergoing some unitary discrete-time evolution in a directed graph G, we think
of the vertices of G as sites that are occupied by the quantum system, whose
internal state is described by density operators. To formulate the unitary
evolution, we define reflections in the tensor product of an internal Hilbert
space and a spatial Hilbert space. We then construct unitary channels that
govern the evolution of the system in the graph. The discrete dynamics of the
system (called quantum walks) is obtained by iterating the unitary channel on
the density operator of the quantum system. It turns out that in this
framework, the action of the unitary channel on a density operator is described
by the usual matrix multiplication.",1506.02493v1
2015-11-22,Charge-density-wave phases of the generalized t-V model,"The one-dimensional extended t-V model of fermions on a lattice is a model
with repulsive interactions of finite range that exhibits a transition between
a Luttinger liquid conducting phase and a Mott insulating phase. It is known
that by tailoring the potential energy of the insulating system, one can force
a phase transition into another insulating phase. We show how to construct all
possible charge-density-wave phases of the system at low critical densities in
the atomic limit. Higher critical densities are investigated by a brute-force
analysis of the possible finite unit cells of the Fock states.",1511.07043v2
2023-01-24,Casimir Self-Interaction Energy Density of Quantum Electrodynamic Fields,"Quantum electrodynamic fields possess fluctuations corresponding to transient
particle/antiparticle dipoles, which can be characterized by a non-vanishing
polarizability density. Here, we extend a recently proposed quantum scaling law
to describe the volumetric and radial polarizability density of a quantum field
corresponding to electrons and positrons and derive the Casimir
self-interaction energy (SIE) density of the field, $\bar{E}_{\rm{SIE}}$, in
terms of the fine-structure constant. The proposed model obeys the cosmological
equation of state $w=-1$ and the magnitude of the calculated
$\bar{E}_{\rm{SIE}}$ lies in between the two recent measurements of the
cosmological constant $\Lambda$ obtained by the Planck Mission and the Hubble
Space Telescope.",2301.10151v1
1995-03-08,"Quantum State Diffusion, Density Matrix Diagonalization and Decoherent Histories: A Model","We analyse the quantum evolution of a particle moving in a potential in
interaction with an environment of harmonic oscillators in a thermal state,
using the quantum state diffusion (QSD) picture of Gisin and Percival, in which
one associates the usual Markovian master equation for the density operator
with a class of stochastic non-linear Schr\""odinger equations. We find
stationary solutions to the Ito equation which are Gaussians, localized around
a point in phase space undergoing classical Brownian motion. We show that every
initial state approaches these stationary solutions in the long time limit. We
recover the density operator corresponding to these solutions, and thus show,
for this particular model, that the QSD picture effectively supplies a
prescription for approximately diagonalizing the density operator in a basis of
phase space localized states. The rate of localization is related to the
decoherence time, and also to the timescale on which thermal and quantum
fluctuations become comparable. We use these results to exemplify the general
connection between the QSD picture and the decoherent histories approach.",9503008v1
2015-02-27,Solid-state diffusion in amorphous zirconolite,"We discuss how structural disorder and amorphization affects solid-state
diffusion, and consider zirconolite as a currently important case study. By
performing extensive molecular dynamics simulations, we disentangle the effects
of amorphization and density, and show that a profound increase of solid-state
diffusion takes place as a result of amorphization. Importantly, this can take
place at the same density as in the crystal, representing an interesting
general insight regarding solid-state diffusion. We find that decreasing the
density in the amorphous system increases pre-factors of diffusion constants,
but not decreasing the activation energy. We also find that atomic species in
zirconolite are affected differently by amorphization and density change. Our
microscopic insights are relevant for understanding how solid-state diffusion
changes due to disorder and for building predictive models of operation of
materials to be used to encapsulate nuclear waste.",1502.07912v1
2007-12-10,Excitation energies from ground-state density-functionals by means of generator coordinates,"The generator-coordinate method is a flexible and powerful reformulation of
the variational principle. Here we show that by introducing a generator
coordinate in the Kohn-Sham equation of density-functional theory, excitation
energies can be obtained from ground-state density functionals. As a viability
test, the method is applied to ground-state energies and various types of
excited-state energies of atoms and ions from the He and the Li isoelectronic
series. Results are compared to a variety of alternative DFT-based approaches
to excited states, in particular time-dependent density-functional theory with
exact and approximate potentials.",0712.1586v2
2017-12-16,"Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers","A new calculation using off-shell matrix elements with TMD parton densities
supplemented with a newly developed initial state TMD parton shower is
described. The calculation is based on the KaTie package for an automated
calculation of the partonic process in high-energy factorization, making use of
TMD parton densities implemented in TMDlib. The partonic events are stored in
an LHE file, similar to the conventional LHE files, but now containing the
transverse momenta of the initial partons. The LHE files are read in by the
CASCADE package for the full TMD parton shower, final state shower and
hadronization from PYTHIA where events in HEPMC format are produced. We have
determined a full set of TMD parton densities and developed an initial state
TMD parton shower, including all flavors following the TMD distribution. As an
example of application we have calculated the azimuthal de-correlation of high
pt dijets as measured at the LHC and found very good agreement with the
measurement when including initial state TMD parton showers together with
conventional final state parton showers and hadronization.",1712.05932v1
2020-10-20,Study of Yu-Shiba-Rusinov bound states by tuning the electron density at the Fermi energy,"Magnetic atoms can break the Cooper pairs of superconductors, leading to the
formation of Yu-Shiba-Rusinov (YSR) bound states inside superconducting gaps.
Theory predicts that the YSR bound states can be controlled by tuning the
electron density at the Fermi energy, but it has not been studied deeply. In
this work, we studied the nature of YSR bound states in response to the
potential scattering U by tuning the electron density at the Fermi energy. By
comparing two systems, Mn-phthalocyanine molecules on Pb(111) and Co atoms on
PbSe/Pb(111), we demonstrate that the sign of U can be unambiguously determined
by varying the electron density at the Fermi energy. We also show that U
competes with the exchange interaction JS in the formation of YSR bound states.
Our work provides insights into the interactions between magnetic atoms and
superconductors at a fundamental level.",2010.10120v1
2018-04-08,Mean-field model for the density of states of jammed soft spheres,"We propose a class of mean-field models for the isostatic transition of
systems of soft spheres, in which the contact network is modeled as a random
graph and each contact is associated to $d$ degrees of freedom. We study such
models in the hypostatic, isostatic, and hyperstatic regimes. The density of
states is evaluated by both the cavity method and exact diagonalization of the
dynamical matrix. We show that the model correctly reproduces the main features
of the density of states of real packings and, moreover, it predicts the
presence of localized modes near the lower band edge. Finally, the behavior of
the density of states $D(\omega)\sim\omega^\alpha$ for $\omega\to 0$ in the
hyperstatic regime is studied. We find that the model predicts a nontrivial
dependence of $\alpha$ on the details of the coordination distribution.",1804.02705v2
2023-04-24,Evolution of Flat Band and Van Hove Singularities with Interlayer Coupling in Twisted Bilayer Graphene,"Here we present a theoretical analysis (applicable to all twist angles of
TBG) of band dispersion and density of states in TBG relating evolution of flat
band and Van-Hove singularities with evolution of interlayer coupling in TBG. A
simple tight binding Hamiltonian with environment dependent interlayer hopping
and incorporated with internal configuration of carbon atoms inside a supercell
is used to calculate band dispersion and density of states in TBG. Various
Hamiltonian parameters and functional form of interlayer hopping applicable to
a wide range of twist angles in TBG is estimated by fitting calculated
dispersion and density of states with available experimentally observed
dispersion and density of states in Graphene, AB-stacked bilayer graphene and
some TBG systems. Computationally obtained band dispersion reveal that flat
band in TBG occurs very close to Dirac point of graphene and only along linear
dimension of two-dimensional wave vector space connecting two closest Dirac
points of two graphene layers of TBG.",2304.12279v1
2010-02-23,T>0 ensemble state density functional theory revisited,"A logical foundation of equilibrium state density functional theory in a
Kohn-Sham type formulation is presented on the basis of Mermin's treatment of
the grand canonical state. it is simpler and more satisfactory compared to the
usual derivation of ground state theory, and free of remaining open points of
the latter. It may in particular be relevant with respect to cases of
spontaneous symmetry breaking like non-collinear magnetism and orbital order.",1002.4267v1
2010-10-27,Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte-Carlo simulations,"We use replica exchange Monte-Carlo simulations to measure the equilibrium
equation of state of the disordered fluid state for a binary hard sphere
mixture up to very large densities where standard Monte-Carlo simulations do
not easily reach thermal equilibrium. For the moderate system sizes we use (up
to N=100), we find no sign of a pressure discontinuity near the location of
dynamic glass singularities extrapolated using either algebraic or simple
exponential divergences, suggesting they do not correspond to genuine
thermodynamic glass transitions. Several scenarios are proposed for the fate of
the fluid state in the thermodynamic limit.",1010.5607v1
2010-11-10,Nondistillability of distillable qutrit-qutrit states under depolarizing noise,"We study the effects of decoherence on some particular bipartite qutrit
states under the influence of global, collective, local and multilocal
depolarizing noise. We show that certain free entangled distillable qutrit
density matrices become bound entangled or separable and hence convert into
nondistillable density matrices in global noise. The collective noise increases
the degree of entanglement of the qutrit bipartite states. Furthermore, we show
that some particular local operation cannot avoid the Nondistillability of the
distillable states.",1011.2484v4
2012-03-02,Edge states of graphene bilayer strip,"The electronic structure of the zig-zag bilayer strip is analyzed. The
electronic spectra of the bilayer strip is computed. The dependence of the edge
state band flatness on the bilayer width is found. The density of states at the
Fermi level is analytically computed. It is shown that it has the singularity
which depends on the width of the bilayer strip. There is also asymmetry in the
density of states below and above the Fermi energy.",1203.0437v1
2015-02-09,Inequalities for purity parameters for multipartite and single qudit states,"We analyze a recently found inequality for eigenvalues of the density matrix
and purity parameter describing either a bipartite system state or a single
qudit state. The Minkowski type trace inequality for the density matrices of
the qudit states is rewritten in terms of the purities. The properties of the
obtained inequality are discussed. The $X$-states of the two qubits and the
single qudit are considered in detail. A study of the relation of the obtained
purity inequalities with the entanglement is presented.",1502.02371v1
2016-06-06,"The Electron-pair Density Distribution of the ${^{1,3}Π_u}$ Excited States of H$_2$","The non-monotonic behavior of the electron repulsion energy and the
interelectronic distance, as a function of the internuclear separation, in the
$^{3}\Pi_{u}$ excited state of the hydrogen molecule has been assessed by
explicitly calculation and analysis of the electron-pair density distribution
functions from high level ab initio Full Configuration Interaction wave
functions, for both the $^{3}\Pi_{u}$ and the $^{1}\Pi_{u}$ states.
Additionally, the Hund's rule as applied to these two states has been accounted
for in terms of simple electronic shielding effects induced by wave function
antisymmetrization.",1606.01821v1
2014-06-05,The Density of Surface States in Weyl Semimetals,"Weyl semimetal is a three-dimensional material with a conical spectrum near
an even number of point nodes, where two bands touch each other. Here we study
spectral properties of surface electron states in such a system. We show that
the density of surface states possesses a logarithmic singularity for the
energy $\varepsilon \to 0$. It decreases linearly at the intermediate energy of
surface electron states and approaches zero as $\sqrt{1-\varepsilon}$ for
$\varepsilon \to 1$. This universal behavior is a hallmark of the topological
order that offers a new wide range of applications.",1406.1507v1
2023-12-30,Ultrafast X-ray Diffraction Probe of Coherent Spin-state Dynamics in Molecules,"We propose an approach to probe coherent spin-state dynamics of molecules
using circularly polarized hard x-ray pulses. For the dynamically aligned
nitric oxide molecules in a coherent superposition spin-orbit coupled
electronic state that can be prepared through stimulated Raman scattering, we
demonstrate the capability of ultrafast x-ray diffraction to not only reveal
the quantum beating of the coherent spin-state wave packet, but also image the
spatial spin density of the molecule. With circularly polarized ultrafast x-ray
diffraction signal, we show that the electronic density matrix can be
retrieved. The spatio-temporal resolving power of ultrafast x-ray diffraction
paves the way for tracking transient spatial wave function in molecular
dynamics involving spin degree of freedom.",2401.00259v1
2024-02-02,Distribution of the entanglement entropy of a non-ergodic quantum state,"We theoretically derive the probability densities of the entanglement
measures of a pure non-ergodic many-body state, represented in a bipartite
product basis and with its reduced density matrix described by a generalized,
multi-parametric Wishart ensemble with unit trace. Our results indicate
significant fluctuations of the measures around their average behavior
(specifically for the states away from separability and maximum entanglement
limits). The information is relevant not only for hierarchical arrangement of
entangled states (e.g., revealing the flaws in their characterization based on
average behavior) but also for phase transition studies of many body systems.",2402.01102v1
2001-08-13,"Extended state floating up in a lattice model: Bona fide levitation fingerprints, irrespective of the correlation length","The evolution of extended states with magnetic field and disorder intensities
is investigated for 2D lattice models. The floating-up picture is revealed when
the shift of the extended state, relative to the density of states, is properly
taken into account, either for white-noise or correlated disorder.",0108211v1
2007-02-02,Concurrence-based entanglement measure for Werner States,"We give explicit expressions for entanglement measures of Werner states in
arbitrary dimensions in terms of concurrence and tangle. We show that an
optimal ensemble decomposition for a joint density matrix of a Werner state can
achieve the minimum average concurrence and tangle simultaneously. Furthermore,
the same decomposition also attains entanglement of formation for Werner
states.",0702017v1
2007-11-03,Local Indistinguishability and Possibility of Hiding cbits in Activable Bound Entangled States,"In this letter we prove local indistinguishability of four orthogonal
activable bound entangled states shared among even number of parties. All
reduced density matrices of such states are maximally mixed. We further proceed
to establish a multipartite quantum data hiding scheme on those states and
explore its power and limitations.",0711.0475v1
2012-07-06,Detection of $k$-nonseparable $n$-partite quantum states,"The detection of multipartite entanglement in arbitrary dimensional systems
is investigated. We derive useful $k$-separability criteria of mixed
$n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite
quantum states. Our criteria can be expressed by the elements of the density
matrix, which allows a simple and practical evaluation and computation. They
are experimentally accessible without quantum state tomography.",1207.1596v2
2024-01-05,Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state,"Spin-1/2 kagome antiferromagnet (AFM) is one of the most studied models in
frustrated magnetism since it is a promising candidate to host exotic spin
liquid states. However, despite numerous studies using both analytical and
numerical approaches, the nature of the ground state and low-energy excitations
in this system remain elusive. This is related to the difficulty in determining
the spin gap in various calculations. We present the results of our
investigation of the Kagome AFM using the recently developed group equivariant
convolutional neural networks - an advanced machine learning technique for
studying strongly frustrated models. The approach, combined with variational
Monte Carlo, introduces significant improvement of the achievable results
accuracy in comparison with approaches based on other neural network
architectures that lack generalization quality for frustrated spin systems.
Contrary to the results obtained previously with various methods, that
predicted Z_2 or U(1) Dirac spin liquid states, our results strongly indicate
that the ground state of the kagome lattice antiferromagnet is a spinon pair
density wave that does not break time-reversal symmetry or any of the lattice
symmetries. The found state appears due to the spinon Cooper pairing
instability close to two Dirac points in the spinon energy spectrum and
resembles the pair density wave state studied previously in the context of
underdoped cuprate superconductors in connection with the pseudogap phase. The
state has significantly lower energy than the lowest energy states found by the
SU(2) symmetric density matrix renormalization group calculations and other
methods.",2401.02866v1
2004-02-12,Developments for Reference--State One--Particle Density--Matrix Theory,"Brueckner orbitals, and the density of the Brueckner reference-state, are
shown to satify the same cusp condition -- involving the nuclear charges -- as
natural- and Hartree--Fock-orbitals. Using the cusp condition, the density of a
determinantal state can be used to determine the external potential, if the
determinantal state is from either Hartee--Fock or Brueckner-orbital theory, as
well as, determinant states obtained by many other formalisms that are defined
by a one-body operator, if a portion of the one-body operator -- the portion
not associated with the kinetic energy or external potential -- generates a
well behaved function when acting on an occupied orbital. Using this
relationship involving a determinant and its external potential, a variation of
Reference--State One--Particle Density--Matrix Theory (physics/0308056) is
formulated, where the trial wavefunctions are universal, in the Kohn-Sham
sense, since they do not depend on the external potential. The resulting
correlation-energy functionals, are also, universal, except for a relatively
small term involving the portion of the expectation value of the external
potential with the trial wavefunctions that appears beyond the first order. The
same approximate energy functionals that were shown to be valid for the
previous v-dependent, Reference--State One--Particle Density--Matrix Theory
(physics/0308084), are shown to be valid for the current approach, except that
the use of the LYP and Colle--Salvetti functional appear more natural within
the current approach, since these functionals are universal ones. And since the
BLYP and B3LYP functionals contain the LYP functional, these approaches are
also better suited with the current approach.",0402059v1
2007-05-09,Improved Quantum Hard-Sphere Ground-State Equations of State,"The London ground-state energy formula as a function of number density for a
system of identical boson hard spheres, corrected for the reduced mass of a
pair of particles in a sphere-of-influence picture, and generalized to fermion
hard-sphere systems with two and four intrinsic degrees of freedom, has a
double-pole at the ultimate \textit{regular} (or periodic, e.g.,
face-centered-cubic) close-packing density usually associated with a
crystalline branch. Improved fluid branches are contructed based upon exact,
field-theoretic perturbation-theory low-density expansions for many-boson and
many-fermion systems, appropriately extrapolated to intermediate densities, but
whose ultimate density is irregular or \textit{random} closest close-packing as
suggested in studies of a classical system of hard spheres. Results show
substantially improved agreement with the best available Green-function Monte
Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder,
variational Fermi hypernetted chain, and so-called L-expansion data for
two-component fermions.",0705.1191v2
2014-10-07,The Z3 model with the density of states method,"In this contribution we apply a new variant of the density of states method
to the Z3 spin model at finite density. We use restricted expectation values
evaluated with Monte Carlo simulations and study their dependence on a control
parameter lambda. We show that a sequence of one-parameter fits to the
Monte-Carlo data as a function of lambda is sufficient to completely determine
the density of states. We expect that this method has smaller statistical
errors than other approaches since all generated Monte Carlo data are used in
the determination of the density. We compare results for magnetization and
susceptibility to a reference simulation in the dual representation of the Z3
spin model and find good agreement for a wide range of parameters.",1410.1645v1
2012-01-05,Constraining mean-field models of the nuclear matter equation of state at low densities,"An extension of the generalized relativistic mean-field (gRMF) model with
density dependent couplings is introduced in order to describe thermodynamical
properties and the composition of dense nuclear matter for astrophysical
applications. Bound states of light nuclei and two-nucleon scattering
correlations are considered as explicit degrees of freedom in the
thermodynamical potential. They are represented by quasiparticles with
medium-dependent properties. The model describes the correct low-density limit
given by the virial equation of state (VEoS) and reproduces RMF results around
nuclear saturation density where clusters are dissolved. A comparison between
the fugacity expansions of the VEoS and the gRMF model provides consistency
relations between the quasiparticles properties, the nucleon-nucleon scattering
phase shifts and the meson-nucleon couplings of the gRMF model at zero density.
Relativistic effects are found to be important at temperatures that are typical
in astrophysical applications. Neutron matter and symmetric matter are studied
in detail.",1201.1078v2
2019-12-19,Microscopic calculations of nuclear level densities with the Lanczos method,"A new method for computing the density of states in nuclei making use of an
extrapolated form of the tri-diagonal matrix obtained from the Lanczos method
is presented. It will be shown that the global, average properties of the
entire Lanczos matrix can be predicted from just four Lanczos iterations. The
extrapolated Lanczos matrix (ELM) approach provides for an accurate computation
of the density of states described within the configuration space, which, in
some cases, is sufficient to accurately calculate the density of states at, or
near, the neutron separation energy. Comparisons between theory and experiment
are shown for $^{57}$Fe, $^{74}$Ge, and $^{76}$Ge. In addition, we show results
for the $J$-dependence of moments and the level density for these three nuclei.",1912.08973v1
2022-11-24,A Multivariate Non-Gaussian Bayesian Filter Using Power Moments,"In this paper, we extend our results on the univariate non-Gaussian Bayesian
filter using power moments to the multivariate systems, which can be either
linear or nonlinear. Doing this introduces several challenging problems, for
example a positive parametrization of the density surrogate, which is not only
a problem of filter design, but also one of the multiple dimensional Hamburger
moment problem. We propose a parametrization of the density surrogate with the
proofs to its existence, Positivstellensatz and uniqueness. Based on it, we
analyze the errors of moments of the density estimates by the proposed density
surrogate. A discussion on continuous and discrete treatments to the
non-Gaussian Bayesian filtering problem is proposed to motivate the research on
continuous parametrization of the system state. Simulation results on
estimating different types of multivariate density functions are given to
validate our proposed filter. To the best of our knowledge, the proposed filter
is the first one implementing the multivariate Bayesian filter with the system
state parameterized as a continuous function, which only requires the true
states being Lebesgue integrable.",2211.13374v3
2019-05-09,Best-scored Random Forest Density Estimation,"This paper presents a brand new nonparametric density estimation strategy
named the best-scored random forest density estimation whose effectiveness is
supported by both solid theoretical analysis and significant experimental
performance. The terminology best-scored stands for selecting one density tree
with the best estimation performance out of a certain number of purely random
density tree candidates and we then name the selected one the best-scored
random density tree. In this manner, the ensemble of these selected trees that
is the best-scored random density forest can achieve even better estimation
results than simply integrating trees without selection. From the theoretical
perspective, by decomposing the error term into two, we are able to carry out
the following analysis: First of all, we establish the consistency of the
best-scored random density trees under $L_1$-norm. Secondly, we provide the
convergence rates of them under $L_1$-norm concerning with three different tail
assumptions, respectively. Thirdly, the convergence rates under
$L_{\infty}$-norm is presented. Last but not least, we also achieve the above
convergence rates analysis for the best-scored random density forest. When
conducting comparative experiments with other state-of-the-art density
estimation approaches on both synthetic and real data sets, it turns out that
our algorithm has not only significant advantages in terms of estimation
accuracy over other methods, but also stronger resistance to the curse of
dimensionality.",1905.03729v1
2023-03-11,Enhanced K-Radar: Optimal Density Reduction to Improve Detection Performance and Accessibility of 4D Radar Tensor-based Object Detection,"Recent works have shown the superior robustness of four-dimensional (4D)
Radar-based three-dimensional (3D) object detection in adverse weather
conditions. However, processing 4D Radar data remains a challenge due to the
large data size, which require substantial amount of memory for computing and
storage. In previous work, an online density reduction is performed on the 4D
Radar Tensor (4DRT) to reduce the data size, in which the density reduction
level is chosen arbitrarily. However, the impact of density reduction on the
detection performance and memory consumption remains largely unknown. In this
paper, we aim to address this issue by conducting extensive hyperparamter
tuning on the density reduction level. Experimental results show that
increasing the density level from 0.01% to 50% of the original 4DRT density
level proportionally improves the detection performance, at a cost of memory
consumption. However, when the density level is increased beyond 5%, only the
memory consumption increases, while the detection performance oscillates below
the peak point. In addition to the optimized density hyperparameter, we also
introduce 4D Sparse Radar Tensor (4DSRT), a new representation for 4D Radar
data with offline density reduction, leading to a significantly reduced raw
data size. An optimized development kit for training the neural networks is
also provided, which along with the utilization of 4DSRT, improves training
speed by a factor of 17.1 compared to the state-of-the-art 4DRT-based neural
networks. All codes are available at: https://github.com/kaist-avelab/K-Radar.",2303.06342v1
2008-08-19,Localized states and interaction induced delocalization in Bose gases with quenched disorder,"Very diluted Bose gas placed into a disordered environment falls into a
fragmented localized state. At some critical density the repulsion between
particles overcomes the disorder. The gas transits into a coherent superfluid
state. In this article the geometrical and energetic characteristics of the
localized state at zero temperature and the critical density at which the
quantum phase transition from the localized to the superfluid state proceeds
are found.",0808.2565v2
2003-08-14,Reference-State One-Particle Density-Matrix Theory,"A density-matrix formalism is developed based on the one-particle
density-matrix of a single-determinantal reference-state. The v-representable
problem does not appear in the proposed method, nor the need to introduce
functionals defined by a constrained search. The correlation-energy functionals
are not universal; they depend on the external potential. Nevertheless, model
systems can still be used to derive universal energy-functionals. In addition,
the correlation-energy functionals can be partitioned into individual terms
that are -- to a varying degree -- universal; yielding, for example, an
electron gas approximation. Variational and non-variational energy functionals
are introduced that yield the target-state energy when the reference state --
or its corresponding one-particle density matrix -- is constructed from
Brueckner orbitals. Using many-body perturbation theory, diagrammatic
expansions are given for the non-variational energy-functionals, where the
individual diagrams explicitly depend on the one-particle density-matrix.
Non-variational energy-functionals yield generalized Hartree--Fock equations
involving a non-local correlation-potential and the Hartree--Fock exchange;
these equations are obtained by imposing the Brillouin--Brueckner condition.
The same equations -- for the most part -- are obtained from variational
energy-functionals using functional minimizations, yielding the (kernel of)
correlation potential as the functional derivative of correlation-energy
functionals. Approximations for the correlation-energy functions are
introduced, including a one-particle-density-matrix variant of the
local-density approximation (LDA) and a variant of the Lee--Yang--Parr (LYP)
functional.",0308056v1
2005-12-23,Local virial relation and velocity anisotropy in self-gravitating system,"We investigate the merging process in N-body self-gravitating system from the
viewpoints of the local virial relation which is the relation between the local
kinetic energy and the local potential. We compare both the density profile and
the phase space density profile in cosmological simulations with the critical
solutions of collisionless static state satisfying the local virial (LV)
relation. We got the results that the critical solution can explain the
characteristic density profile with the appropriate value of anisotropy
parameter $\beta \sim 0.5$. It can also explain the power law of the phase
space density profile in the outer part of a bound state. However, it fails in
explaining the central low temperature part which is connected to the scale
invariant phase space density. It can be well fitted to the critical solution
with the higher value of$\beta \sim 0.75$. These results indicate that the LV
relation is not compatible with the scale invariant phase space density in
cosmological simulation.",0512587v1
2012-10-29,Glueball spectral densities from the lattice,"The propagator of a physical degree of freedom ought to obey a
K\""{a}ll\'{e}n-Lehmann spectral representation, with positive spectral density.
The latter quantity is directly related to a cross section based on the optical
theorem. The spectral density is a crucial ingredient of a quantum field theory
with elementary and bound states, with a direct experimental connection as the
masses of the excitations reflect themselves into (continuum)
$\delta$-singularities. In usual lattice simulational approaches to the QCD
spectrum the spectral density itself is not accessed. The (bound state) masses
are extracted from the asymptotic exponential decay of the two-point function.
Given the importance of the spectral density, each nonperturbative continuum
approach to QCD should be able to adequately describe it or to take into proper
account. In this work, we wish to present a first trial in extracting an
estimate for the scalar glueball spectral density in SU(3) gluodynamics using
lattice gauge theory.",1210.7794v1
2013-10-05,Computational complexity of time-dependent density functional theory,"Time-dependent density functional theory (TDDFT) is rapidly emerging as a
premier method for solving dynamical many-body problems in physics and
chemistry. The mathematical foundations of TDDFT are established through the
formal existence of a fictitious non-interacting system (known as the Kohn-Sham
system), which can reproduce the one-electron reduced probability density of
the actual system. We build upon these works and show that on the interior of
the domain of existence, the Kohn-Sham system can be efficiently obtained given
the time-dependent density. Since a quantum computer can efficiently produce
such time-dependent densities, we present a polynomial time quantum algorithm
to generate the time-dependent Kohn-Sham potential with controllable error
bounds. As a consequence, in contrast to the known intractability result for
ground state density functional theory (DFT), the computation of the necessary
time-dependent potentials given the initial state is in the complexity class
described by bounded error quantum computation in polynomial time (BQP).",1310.1428v2
2015-12-23,Linking density functional and mode coupling models for supercooled liquids,"We compare predictions from two familiar models of the metastable supercooled
liquid respectively constructed with thermodynamic and dynamic approach. In the
so called density functional theory (DFT) the free energy $F[\rho]$ of the
liquid is a functional of the inhomogeneous density $\rho({\bf r})$. The
metastable state is identified as a local minimum of $F[\rho]$. The sharp
density profile characterizing $\rho({\bf r})$ is identified as a single
particle oscillator, whose frequency is obtained from the parameters of the
optimum density function. On the other hand, a dynamic approach to supercooled
liquids is taken in the mode coupling theory (MCT) which predict a sharp
ergodicity-nonergodicity transition at a critical density. The single particle
dynamics in the non-ergodic state, treated approximately, represents a
propagating mode whose characteristic frequency is computed from the
corresponding memory function of the MCT. The mass localization parameters in
the above two models (treated in their simplest forms) are obtained
respectively in terms of the corresponding natural frequencies depicted and are
shown to have comparable magnitudes.",1512.07588v1
2022-03-03,Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations,"The properties of hydrogen under extreme conditions are important for many
applications, including inertial confinement fusion and astrophysical models. A
key quantity is given by the electronic density response to an external
perturbation, which is probed in X-ray Thomson scattering (XRTS) experiments --
the state of the art diagnostics from which system parameters like the free
electron density $n_e$, the electronic temperature $T_e$, and the charge state
$Z$ can be inferred. In this work, we present highly accurate path integral
Monte Carlo (PIMC) results for the electronic density response of hydrogen. We
obtain the exchange-correlation (XC) kernel $K_{xc}$, which is of central
relevance for many applications, such as time-dependent density functional
theory (TD-DFT). This gives us a first unbiased look into the electronic
density response of hydrogen in the warm-dense matter regime, thereby opening
up a gamut of avenues for future research.",2203.01797v1
2011-01-27,Momentum Dependent Higher Partial Wave Interactions in Bose Einstein condensate,"We have investigated the role of momentum dependent s-wave and higher partial
wave strong interactions to determine the ground state properties and the
column densities in the Bose-Einstein condensate (BEC) for large scattering
length (a) such that ka >>1 even for small values of momentum where the
momentum p=(h/2pi)k and k is the wave number. Since the scattering length is
large we have included the first correction (Lee-Huang-Yang correction) both
for the k-dependent (s-wave + higher partial wave) interactions and
k-independent contact interactions (s-wave). We have derived the
time-independent equations from the corresponding energy functionals and found
that the ground state properties and the column densities differ significantly
for these two types of interactions even for moderate values of scattering
length (a = 3000 a_0) in BEC of cylindrically trapped 85Rb atoms at 100 nK. The
effect of higher partial wave (d-wave) increases with increase in a and it is >
20% for peak density at a= 8700 a_0 which can be experimentally detected.
Dependence of column density on particle number density has been studied.
Column densities have been compared with experimental results.",1101.5264v1
2022-11-20,Magnetic trapping of ultracold molecules at high density,"Trapping ultracold molecules in conservative traps is essential for
applications -- such as quantum state-controlled chemistry, quantum
simulations, and quantum information processing. These applications require
high densities or phase-space densities. We report magnetic trapping of NaLi
molecules in the triplet ground state at high density ($\approx 10^{11} \;
\rm{cm}^{-3}$) and ultralow temperature ($\approx 1\;{\rm \mu K}$). Magnetic
trapping at these densities allows studies on both atom-molecule and
molecule-molecule collisions in the ultracold regime in the absence of trapping
light, which has often lead to undesired photo-chemistry. We measure the
inelastic loss rates in a single spin sample and spin-mixtures of fermionic
NaLi as well as spin-stretched NaLi$+$Na mixtures. We demonstrate sympathetic
cooling of NaLi molecules in the magnetic trap by radio frequency evaporation
of co-trapped Na atoms and observe an increase in the molecules' phase-space
density by a factor of $\approx 16$.",2211.11120v2
2023-06-22,Unconventional superfluidity of superconductivity on Penrose lattice,"We theoretically investigate the gap function, superfluid density and the
transition temperature of the superconductivity (SC) on semi-periodic Penrose
lattice, where an attractive Hubbard model is adopted as an example. Firstly,
we clarify that the gap function, density of states and superfluid density are
all positively correlate to the extended degree of single particle states
around the Fermi energy. Secondly, we identify that the paramagnetic component
of the superfluid density does not decay to zero in the thermodynamic limit,
which is completely different from the periodic system. The difference between
the diamagnetic and paramagnetic currents keeps stable with whatever scaling,
which is consistent with recent experimental results that although the
superfluid density is lower than that of the periodic system, the system has
bulk SC. Thirdly, we find that both the superfluid density and SC transition
temperature can be boosted with the increase of disorder strength, which should
be general to quasicrystal but unusual to periodic systems, reflecting the
interplay between the underlying geometry and disorder.",2306.12641v1
2010-10-13,Density profiles of a colloidal liquid at a wall under shear flow,"Using a dynamical density functional theory we analyze the density profile of
a colloidal liquid near a wall under shear flow. Due to the symmetries of the
system considered, the naive application of dynamical density functional theory
does not lead to a shear induced modification of the equilibrium density
profile, which would be expected on physical grounds. By introducing a
physically motivated dynamic mean field correction we incorporate the missing
shear induced interparticle forces into the theory. We find that the shear flow
tends to enhance the oscillations in the density profile of hard-spheres at a
hard-wall and, at sufficiently high shear rates, induces a nonequilibrium
transition to a steady state characterized by planes of particles parallel to
the wall. Under gravity, we find that the center-of-mass of the density
distribution increases with shear rate, i.e., shear increases the potential
energy of the particles.",1010.2629v1
2012-05-31,"Response functions of cold neutron matter: density, spin and current fluctuations","We study the response of a single-component pair-correlated baryonic
Fermi-liquid to density, spin, and their current perturbations. A complete set
of response functions is derived in the low-temperature regime both within an
effective theory based on a small momentum transfer expansion and within a
numerical scheme valid for arbitrary momentum transfers. A comparison of these
two approaches validates the perturbative approximation within the domain of
its convergence. We derive the spectral functions of collective excitations
associated with the density, density-current, spin, and spin-current
perturbations. The dispersion relations of density and spin fluctuations are
derived and it is shown that the density fluctuations lead to exciton-like
undamped bound states, whereas the spin excitations correspond to diffusive
modes above the pair-breaking threshold. The contribution of the collective
pair-breaking modes to the specific heat of neutron matter at subnuclear
densities is computed and is shown to be comparable to that of the degenerate
electron gas at not too low temperatures.",1205.6902v2
1997-04-07,Effects of Umklapp Scattering on Electronic States in One Dimension,"The effects of Umklapp scattering on electronic states are studied in one
spatial dimension at absolute zero. The model is basically the Hubbard model,
where parameters characterizing the normal ($U$) and Umklapp ($V$) scattering
are treated independently. The density of states is calculated in the t-matrix
approximation by taking only the forward and Umklapp scattering into account.
It is found that the Umklapp scattering causes the global splitting of the
density of states. In the presence of sufficiently strong Umklapp scattering, a
pole in the t-matrix appears in the upper half plane, signalling an instability
towards the '$G/2-$pairing' ordered state ($G$ is the reciprocal lattice
vector), whose consequences are studied in the mean field approximation. It
turns out that this ordered state coexists with spin-density-wave state and
also brings about Cooper-pairs. A phase diagram is determined in the plane of
$V$ and electron filling $n$.",9704049v4
2020-12-18,Transition density matrices of Richardson-Gaudin states,"Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer
Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a
wavefunction ansatz for strong correlation. This wavefunction physically
represents a mean-field of pairs of electrons (geminals) with a constant
pairing strength. To move beyond the mean-field, one must develop the
wavefunction in the basis of all the RG states. This requires both practical
expressions for transition density matrices and an idea of which states are
most important in the expansion. In this contribution, we present expressions
for the transition density matrix elements and calculate them numerically for
half-filled picket fence models. There are no Slater-Condon rules for RG
states, though an analogue of the aufbau principle proves to be useful in
choosing which states are important.",2012.10477v1
2021-03-15,Loop Quantum Gravity's Boundary Maps,"In canonical quantum gravity, the presence of spatial boundaries naturally
leads to a boundary quantum states, representing quantum boundary conditions
for the bulk fields. As a consequence, quantum states of the bulk geometry
needs to be upgraded to wave-functions valued in the boundary Hilbert space:
the bulk become quantum operator acting on boundary states. We apply this to
loop quantum gravity and describe spin networks with 2d boundary as
wave-functions mapping bulk holonomies to spin states on the boundary. This
sets the bulk-boundary relation in a clear mathematical framework, which allows
to define the boundary density matrix induced by a bulk spin network states
after tracing out the bulk degrees of freedom. We ask the question of the bulk
reconstruction and prove a boundary-to-bulk universal reconstruction procedure,
to be understood as a purification of the mixed boundary state into a pure bulk
state. We further perform a first investigation in the algebraic structure of
induced boundary density matrices and show how correlations between bulk
excitations, i.e. quanta of 3d geometry, get reflected into the boundary
density matrix.",2103.08409v1
2023-03-06,Light-activated microtubule-based 2D active nematic,"We characterize two-dimensional (2D) microtubule-based active nematics driven
by light-responsive kinesin motor clusters. We assess two constructs of
optogenetic kinesin: opto-K401, a processive motor, and opto-K365, a
non-processive motor. Measurements reveal an order of magnitude improvement in
the contrast of nematic flow speeds between maximally- and
minimally-illuminated states for opto-K365 motors. Focusing on opto-K365
nematics, we characterize both the steady-state flow and defect density as a
function of applied light and examine the transient behavior between
steady-states. The steady-state nematic flow and defect densities are set by
the applied light intensity across centimeter-sized samples, independent of
initial conditions. Although nematic flow reaches steady-state within tens of
seconds, the defect density exhibits transient behavior for 4 to 10 minutes,
showing a separation between small-scale active reorganization and system-scale
structural states. This work establishes an experimental platform to test
theoretical frameworks which exploit spatiotemporally-heterogeneous patterns of
activity to generate targeted dynamical states.",2303.02945v1
2006-07-27,"The Density of States in the Two-Dimensional Electron Gas and Quantum Dots (Ph.D. thesis, Cornell University, January 1991)","This thesis describes capacitance and tunneling experiments performed on
two-dimensional electron gas (2DEG) and quantum dot systems. It develops a
system of equations that allow determination, by means of capacitance
measurements, of the electronic density of states, the electron density, and
the chemical potential in a 2DEG. The thesis describes the use of these
techniques in the observation of a magnetic field induced energy gap to
tunneling in the 2DEG and the single electron addition spectrum in arrays of
quantum dots.",0607739v1
2008-11-19,Unscreening Effect on Fe-Pnictide Superconductor,"We study a microscopic mechanism of Fe-pnictide superconductor, considering
the screening effects of Coulomb interaction in addition to the conventional
spin-fluctuation mechanism. It is shown that, by electron doping, the
transition temperature of superconductivity increases due to the ""unscreening""
effect even though the density of states decrease, while that of spin-density
wave rapidly decreases due to breaking of nesting conditions. Our results give
a clear interpretation to the mystery of interrelation between T_c and the
density of states observed in the Fe-pnictide superconductors.",0811.3052v1
2010-01-26,Quantum capacitance and density of states of graphene,"We report on measurements of the quantum capacitance in graphene as a
function of charge carrier density. A resonant LC-circuit giving high
sensitivity to small capacitance changes is employed. The density of states,
which is directly proportional to the quantum capacitance, is found to be
significantly larger than zero at and around the charge neutrality point. This
finding is interpreted to be a result of potential fluctuations with amplitudes
of the order of 100 meV in good agreement with scanning single-electron
transistor measurements on bulk graphene and transport studies on nanoribbons.",1001.4690v1
2011-11-06,Phase diagram and density large deviations of a nonconserving ABC model,"The effect of particle-nonconserving processes on the steady state of driven
diffusive systems is studied within the context of a generalized ABC model. It
is shown that in the limit of slow nonconserving processes, the large deviation
function of the overall particle density can be computed by making use of the
steady state density profile of the conserving model. In this limit one can
define a chemical potential and identify first order transitions via Maxwell's
construction, similarly to what is done in equilibrium systems. This method may
be applied to other driven models subjected to slow nonconserving dynamics.",1111.1430v2
2020-02-12,Density of States of an Electron in the Image Field and Blocking Electric Field,"The motion of an electron in an image field and a blocking electric field is
considered in semiclassical approximation. An exact analytical expression is
found for the density of the energy spectrum of states. The dependence of
spectral density on energy is obtained in a wide range of electric field
strengths. The energy ranges with a qualitatively different structure of the
spectrum are determined.",2002.05192v1
2021-10-28,On the global approximate controllability in small time of semiclassical 1-D Schrödinger equations between two states with positive quantum densities,"In this paper, we study, in the semiclassical sense, the global approximate
controllability in small time of the quantum density and quantum momentum of
the 1-D semiclassical cubic Schr\""odinger equation with two controls between
two states with positive quantum densities. We first control the asymptotic
expansions of the zeroth and first order of the physical observables via
Agrachev-Sarychev's method. Then we conclude the proof through techniques of
semiclassical approximation of the nonlinear Schr\""odinger equation.",2110.15299v1
2022-04-27,Quasiparticle spectrum in mesoscopic superconducting junctions with weak magnetization,"We theoretically investigate the effects of the weak magnetization on the
local density of states of mesoscopic proximity structures, where two
superconducting terminals are attached to a side surface of the diffusive
ferromagnet wire with a phase difference. When there is no phase difference,
the local density of states is significantly modified by the magnetization in
both spin-singlet $s$-wave and spin-triplet $p$-wave cases. When the phase
difference is $\pi$, the local density of stets is less modified by the
magnetization compared with the in-phase case because of the destructive
interference of Cooper pairs.",2204.12887v1
2023-01-04,Thermodynamic and transport properties of plasmas: low-density benchmarks,"Physical properties of plasmas such as equations of state and transport
coefficients are expressed in terms of correlation functions, which can be
calculated using various approaches (analytical theory, numerical simulations).
The method of Green's functions provides benchmark values for these properties
in the low-density limit. For the equation of state and electrical
conductivity, expansions with respect to density (virial expansions) are
considered. Comparison of analytical results with numerical simulations is used
to verify theory, to prove the accuracy of simulations, and to establish
interpolation formulas.",2301.01499v1
2023-08-16,Accuracy of Kohn-Sham density functional theory for warm- and hot-dense matter equation of state,"We study the accuracy of Kohn-Sham density functional theory (DFT) for warm-
and hot-dense matter (WDM and HDM). Specifically, considering a wide range of
systems, we perform accurate ab initio molecular dynamics simulations with
temperature-independent local/semilocal density functionals to determine the
equations of state at compression ratios of 3x--7x and temperatures near 1 MK.
We find very good agreement with path integral Monte Carlo (PIMC) benchmarks,
while having significantly smaller error bars and smoother data, demonstrating
the fidelity of DFT for the study of WDM and HDM.",2308.08132v1
2023-11-13,Neutron stars in a uniform density approximation,"Models of neutron stars are considered in the case of a uniform density
distribution. An algebraic equation, valid for any equation of state, is
obtained. This equation allows one to find the approximate mass of a star of a
given density without resorting to the integration of differential equations.
The solutions presented in the paper for various equations of state, including
more realistic ones, differ from the exact solutions obtained by the numerical
integration of differential equations by at most ~20%",2311.07220v1
2016-03-17,Observation of charge density wave order in 1D mirror twin boundaries of single-layer MoSe2,"Properties of two-dimensional transition metal dichalcogenides are highly
sensitive to the presence of defects in the crystal structure. A detailed
understanding of defect structure may lead to control of material properties
through defect engineering. Here we provide direct evidence for the existence
of isolated, one-dimensional charge density waves at mirror twin boundaries in
single-layer MoSe2. Our low-temperature scanning tunneling
microscopy/spectroscopy measurements reveal a substantial bandgap of 60 - 140
meV opening at the Fermi level in the otherwise one dimensional metallic
structure. We find an energy-dependent periodic modulation in the density of
states along the mirror twin boundary, with a wavelength of approximately three
lattice constants. The modulations in the density of states above and below the
Fermi level are spatially out of phase, consistent with charge density wave
order. In addition to the electronic characterization, we determine the atomic
structure and bonding configuration of the one-dimensional mirror twin boundary
by means of high-resolution non-contact atomic force microscopy. Density
functional theory calculations reproduce both the gap opening and the
modulations of the density of states.",1603.05558v1
2002-04-02,Metastability and uniqueness of vortex states at depinning,"We present results from numerical simulations of transport of vortices in the
zero-field cooled (ZFC) and the field-cooled (FC) state of a type-II
superconductor. In the absence of an applied current $I$, we find that the FC
state has a lower defect density than the ZFC state, and is stable against
thermal cycling. On the other hand, by cycling $I$, surprisingly we find that
the ZFC state is the stable state. The FC state is metastable as manifested by
increasing $I$ to the depinning current $I_{c}$, in which case the FC state
evolves into the ZFC state. We also find that all configurations acquire a
unique defect density at the depinning transition independent of the history of
the initial states.",0204039v3
2014-08-07,A New Method of Classification of Pure Tripartite Quantum States,"The classification of the multipartite entanglement is an important problem
in quantum information theory. We propose a class of two qubit mixed states
$\sigma_{AB}=
p|\chi_{1}\rangle\langle\chi_{1}|\otimes\rho_{1}+(1-p)|\chi_{2}\rangle\langle\chi_{2}|\otimes\rho_{2}$,
where $|\chi_{1}\rangle=\alpha|0\rangle+\beta|1\rangle$,
$|\chi_{2}\rangle=\beta|0\rangle+(-1)^{n}\alpha|1\rangle$. We have shown that
the state $\sigma_{AB}$ represent a classical state when $n$ is odd while it
represent a non-classical state when $n$ is even. The purification of the state
$\sigma_{AB}$ is studied and found that the purification is possible if the
spectral decomposition of the density matrices $\rho_{1}$ and $\rho_{2}$
represent pure states. We have established a relationship between three tangle,
which measures the amount of entanglement in three qubit system and the
quantity $\langle\chi_{1}|\chi_{2}\rangle$, which identifies whether the two
qubit mixed state is classical or non-classical. The three qubit purified state
is then classified as a separable or biseparable or W-type or GHZ-type state
using the quantum correlation, measured by geometric discord, of its reduced
two qubit density matrix.",1408.1539v1
1995-10-11,Diffusion with critically correlated traps and the slow relaxation of the longest wavelength mode,"We study diffusion on a substrate with permanent traps distributed with
critical positional correlation, modeled by their placement on the perimeters
of a critical percolation cluster. We perform a numerical analysis of the
vibrational density of states and the largest eigenvalue of the equivalent
scalar elasticity problem using the method of Arnoldi and Saad. We show that
the critical trap correlation increases the exponent appearing in the stretched
exponential behavior of the low frequency density of states by approximately a
factor of two as compared to the case of no correlations. A finite size scaling
hypothesis of the largest eigenvalue is proposed and its relation to the
density of states is given. The numerical analysis of this scaling postulate
leads to the estimation of the stretch exponent in good agreement with the
density of states result.",9510056v1
1997-06-25,Characterization of the Local Density of States Fluctuations near the Integer Quantum Hall Transition in a Quantum Dot Array,"We present a calculation for the second moment of the local density of states
in a model of a two-dimensional quantum dot array near the quantum Hall
transition. The quantum dot array model is a realistic adaptation of the
lattice model for the quantum Hall transition in the two-dimensional electron
gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and
Grinstein. We make use of a Dirac fermion representation for the Green
functions in the presence of fluctuations for the quantum dot energy levels. A
saddle-point approximation yields non-perturbative results for the first and
second moments of the local density of states, showing interesting fluctuation
behaviour near the quantum Hall transition. To our knowledge we discuss here
one of the first analytic characterizations of chaotic behaviour for a
two-dimensional mesoscopic structure. The connection with possible experimental
investigations of the local density of states in the quantum dot array
structures (by means of NMR Knight-shift or single-electron-tunneling
techniques) and our work is also established.",9706256v1
2007-02-02,On the nature of the spin-polarized hole states in a quasi-two-dimensional GaMnAs ferromagnetic layer,"A self-consistent calculation of the density of states and the spectral
density function is performed in a two-dimensional spin-polarized hole system
based on a multiple-scattering approximation. Using parameters corresponding to
GaMnAs thin layers, a wide range of Mn concentrations and hole densities have
been explored to understand the nature, localized or extended, of the
spin-polarized holes at the Fermi level for several values of the average
magnetization of the Mn ystem. We show that, for a certain interval of Mn and
hole densities, an increase on the magnetic order of the Mn ions come together
with a change of the nature of the states at the Fermi level. This fact
provides a delocalization of spin-polarized extended states anti-aligned to the
average Mn magnetization, and a higher spin-polarization of the hole gas. These
results are consistent with the occurrence of ferromagnetism with relatively
high transition temperatures observed in some thin film samples and
multilayered structures of this material.",0702053v1
2003-03-20,Linking Vibrational Dynamics to Local Electronic Structure: Local Analysis of Dynamics of the relaxed Si$_{87}$ Cluster,"A flexible scheme for decomposing the vibrational density of states in terms
of pair vibrational density of states is presented. This scheme provides the
linkage between the site vibrational density of states and pair vibrational
density of states so that vibrational modes, in particular localized modes, can
be conveniently examined in terms of the correlation between the vibration at a
given site and those at its neighboring sites. Furthermore, within the
framework of a total energy vibrational spectrum study, this scheme allows the
analysis of vibrational modes in terms of their electronic origin. A case study
of the vibrational dynamics of the relaxed Si$_{87}$ cluster is carried out to
demonstrate the flexibility of the scheme in analyzing the properties of
vibrational modes, particularly for complex systems with reduced or no
symmetry.",0303088v1
2007-08-24,Do we know eventually p(e)?,"A quasi-particle model is employed to derive from available lattice QCD
calculations an equation of state useable in hydrodynamical simulations of the
expansion stage of strongly interacting matter created in ultra-relativistic
heavy-ion collisions. Various lattice results give an astonishing agreement of
the pressure as a function of energy density at large energy densities supposed
the pseudo-critical temperature is in the range $170 \pm 15$ MeV, while in the
transition region the equation of state is not yet well constrained. Therefore,
one can construct a family of equations of state by bridging the uncertain
region from the uniquely given high-energy density region part to a hadronic
equation of state by suitable interpolation together with the extrapolation to
non-zero baryon density by means of the quasi-particle model. We present a
series of tests of the model, discuss the chiral extrapolation and the role of
Landau damping. We also briefly sketch the path of cosmic matter in the early
universe in the phase diagram.",0708.3322v1
2010-11-09,Density of states of a graphene in the presence of strong point defects,"The density of states near zero energy in a graphene due to strong point
defects with random positions are computed. Instead of focusing on density of
states directly, we analyze eigenfunctions of inverse T-matrix in the unitary
limit. Based on numerical simulations, we find that the squared magnitudes of
eigenfunctions for the inverse T-matrix show random-walk behavior on defect
positions. As a result, squared magnitudes of eigenfunctions have equal {\it a
priori} probabilities, which further implies that the density of states is
characterized by the well-known Thomas-Porter type distribution. The numerical
findings of Thomas-Porter type distribution is further derived in the
saddle-point limit of the corresponding replica field theory of inverse
T-matrix. Furthermore, the influences of the Thomas-Porter distribution on
magnetic and transport properties of a graphene, due to its divergence near
zero energy, are also examined.",1011.1968v1
2010-11-16,The role of bandstructure in the thermodynamic properties of itinerant metamagnets,"It is known that itinerant metamagnetic transitions can be driven by features
in the electronic density of states. We study the signatures of these
transitions in the entropy and specific heat for a variety of different cases,
identifying the key features which differ from naive expectations, such as
enhanced critical fields and non-Fermi liquid temperature dependencies. We
begin with the generic case of a logarithmically divergent density of states,
as caused by a two dimensional van Hove singularity. We then study a specific
model for the bandstructure of Sr3Ru2O7, a material with a well-studied
metamagnetic transition and quantum critical endpoint. We consider how far the
behaviour of the system can be explained by the density of states rather than
quantum fluctuations, and the distinctive features of this mechanism. One of
the characteristic features of Sr3Ru2O7 is an unusual phase with a higher
entropy than its surroundings, we consider how this may arise in the context of
a density of states picture and find that we can reproduce the thermodynamic
behaviour and first-order phase transitions.",1011.3733v1
2012-12-22,Spectral footprints of impurity scattering in graphene nanoribbons,"We report a detailed investigation of the interplay between size quantization
and local scattering centers in graphene nanoribbons, as seen in the local
density of states. The spectral signatures, obtained after Fourier
transformation of the local density of states, include characteristic peaks
that can be related to the transverse modes of the nanoribbon. In armchair
ribbons, the Fourier transformed density of states of one of the two
inequivalent sublattices takes a form similar to that of a quantum channel in a
two-dimensional electron gas, modified according to the differences in
bandstructure. After addition of the second sublattice contribution, a
characteristic modulation of the pattern due to superposition is obtained,
similar to what has been obtained in spectra due to single impurity scattering
in large-area graphene. We present analytic results for the electron propagator
in armchair nanoribbons in the Dirac approximation, including a single
scattering center within a T-matrix formulation. For comparison, we have
extended the investigation with numerics obtained with an atomistic recursive
Green's function approach. The spectral signatures of the atomistic approach
include the effects of trigonal warping. The impurity induced oscillations in
the local density of states are not decaying at large distance in few-mode
nanoribbons.",1212.5730v1
2016-12-10,Calculation of density of states of transition metals: from bulk sample to nanocluster,"The technique is presented of restoring the electronic density of states of
the valence band from data of X-ray photoelectron spectroscopy. The originality
of the technique consists in using a stochastic procedure to solve an integral
equation relating the density of states and the experimental X-ray
photoelectron spectra. The results are presented for bulk sample of gold and
nanoclusters of tantalum; the possibility of using the results to determine the
density of states of low-dimensional structures, including ensembles of metal
nanoclusters, is demonstrated.",1612.03288v1
2021-02-02,Direct tomography of high-dimensional density matrices for general quantum states of photons,"Quantum state tomography is the conventional method used to characterize
density matrices for general quantum states. However, the data acquisition time
generally scales linearly with the dimension of the Hilbert space, hindering
the possibility of dynamic monitoring of a high-dimensional quantum system.
Here, we demonstrate a direct tomography protocol to measure density matrices
of photons in the position basis through the use of a polarization-resolving
camera, where the dimension of density matrices can be as large as
580$\times$580 in our experiment. The use of the polarization-resolving camera
enables parallel measurements in the position and polarization basis and as a
result, the data acquisition time of our protocol does not increase with the
dimension of the Hilbert space and is solely determined by the camera exposure
time (on the order of 10 ms). Our method is potentially useful for the
real-time monitoring of the dynamics of quantum states and paves the way for
the development of high-dimensional, time-efficient quantum metrology
techniques.",2102.01271v2
2012-03-08,On the quantum statistics of bound states within the Rutherford model of matter,"The quantum statistical treatment of the Rutherford model, considering matter
as a system of point charges (electrons and nuclei) is analyzed. First, in the
historical context, the solutions of different fundamental problems, such as
the divergence of the partition function, elaborated by Herzfeld, Planck,
Brillouin and Rompe - most of the relevant papers published in the Annalen der
Physik, are discussed. Beyond this, the modern state of art is presented and
new results are given which explain, why bound states according to a discrete
part of the spectra occur only in a valley in the temperature-density plane.
Based on the actual state of the quantum statistics of Coulomb systems, virial
expansions within the canonical ensemble and the grand ensemble and
combinations are derived. The following transitions along isotherms are
studied: (i) the formation of bound states occurring by increasing the density
from low to moderate values, (ii) the disappearance of bound state effects at
higher densities due to medium effects. Within the physical picture we
calculate isotherms of pressure for Hydrogen in a broad density region and show
that in the region between $20\, 000$ K and $100\, 000$ K and particle
densities below $10^{22}$ cm$^{-3}$ the cross-over from full to partial
ionization may be well described by the contributions of extended ring diagrams
and ladder diagrams.",1203.1708v1
2023-07-12,Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states,"While topology is a property of a quantum state itself, most existing methods
for characterizing the topology of interacting phases of matter require direct
knowledge of the underlying Hamiltonian. We offer an alternative by utilizing
the one-particle density matrix formalism to extend the concept of the Chern,
chiral, and Chern-Simons markers to include interactions. The one-particle
density matrix of a free-fermion state is a projector onto the occupied bands,
defining a Brillouin zone bundle of the given topological class. This is no
longer the case in the interacting limit, but as long as the one-particle
density matrix is gapped, its spectrum can be adiabatically flattened,
connecting it to a topologically equivalent projector. The corresponding
topological markers thus characterize the topology of the interacting phase.
Importantly, the one-particle density matrix is defined in terms of a given
state alone, making the local markers numerically favorable, and providing an
invaluable tool for characterizing topology of interacting systems when only
the state itself is available. To demonstrate the practical use of the markers
we use the chiral marker to identify the topology of the ground state of the
Majorana-XYZ model as well as the midspectrum eigenstates of the Ising-Majorana
chain across the transition between the ergodic and many-body localized phases.",2307.06447v1
2002-10-25,Ground State Phase Diagram of 2D Electrons in High Magnetic Field,"The ground state of 2D electrons in high magnetic field is studied by the
density matrix renormalization group method. The ground state energy,
excitation gap, and pair correlation functions are systematically calculated at
various fillings in the lowest and the second lowest Landau levels. The ground
state phase diagram, which consists of incompressible liquid state,
compressible liquid state, stripe state, pairing state, and Wigner crystal is
determined.",0210569v2
2013-04-30,Geometry of quantum dynamics and optimal control for mixed states,"Geometric effects make evolution time vary for different evolution curves
that connect the same two quantum states. Thus, it is important to be able to
control along which path a quantum state evolve to achieve maximal speed in
quantum calculations. In this paper we establish fundamental relations between
Hamiltonian dynamics and Riemannian structures on the phase spaces of unitarily
evolving finite-level quantum systems. In particular, we show that the
Riemannian distance between two density operators equals the infimum of the
energy dispersions of all possible evolution curves connecting the two density
operators. This means, essentially, that the evolution time is a controllable
quantity. The paper also contains two applied sections. First, we give a
geometric derivation of the Mandelstam-Tamm estimate for the evolution time
between two distinguishable mixed states. Secondly, we show how to equip the
Hamiltonians acting on systems whose states are represented by invertible
density operators with control parameters, and we formulate conditions for
these that, when met, makes the Hamiltonians transport density operators along
geodesics.",1304.8103v1
2001-10-15,Color Superconducting State of Quarks,"An introductory review of physics of color superconducting state of matter is
presented. Comparison with superconductivity in electron systems reveals
difficulties involved in formulating color superconductivity theory at
moderately ultra-nuclear density.",0110197v1
2008-12-02,Bipartite states of low rank are almost surely entangled,"We show that a bipartite state on a tensor product of two matrix algebras is
almost surely entangled if its rank is not greater than that of one of its
reduced density matrices.",0812.0405v1
2015-08-19,Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases,"Stealthy potentials, a family of long-range isotropic pair potentials,
produce infinitely degenerate disordered ground states at high densities and
crystalline ground states at low densities in d-dimensional Euclidean space
R^d. In the previous paper in this series, we numerically studied the
entropically favored ground states in the canonical ensemble in the
zero-temperature limit across the first three Euclidean space dimensions. In
this paper, we investigate using both numerical and theoretical techniques
metastable stacked-slider phases, which are part of the ground-state manifold
of stealthy potentials at densities in which crystal ground states are favored
entropically. Our numerical results enable us to devise analytical models of
this phase in two, three, and higher dimensions. Utilizing this model, we
estimated the size of the feasible region in configuration space of the
stacked-slider phase, finding it to be smaller than that of crystal structures
in the infinite-system-size limit, which is consistent with our recent previous
work. In two dimensions, we also determine exact expressions for the pair
correlation function and structure factor of the analytical model of
stacked-slider phases and analyze the connectedness of the ground-state
manifold of stealthy potentials in this density regime. We demonstrate that
stacked-slider phases are distinguishable states of matter; they are
nonperiodic, statistically anisotropic structures that possess long-range
orientational order but have zero shear modulus. We outline some possible
future avenues of research to elucidate our understanding of this unusual phase
of matter.",1508.04728v1
2001-09-25,Charge-density waves in one-dimensional Hubbard superlattices,"We study the formation of charge density waves (CDW's) in one-dimensional
Hubbard superlattices, modeled by a repeated pattern of repulsive (U>0) and
free (U=0) sites. By means of Lanczos diagonalizations for the ground state, we
calculate the charge structure factor. Our results show that while the
superlattice structure affects the modulation of the charge density waves, the
periodicity can still be predicted through an effective density. We also show
that, for a fixed repulsive layer thickness, the periodicity of the CDW is an
oscillatory function of the free layer thickness.",0109467v1
1998-03-08,Meaning of the Density Matrix,"Protective measurement, which was proposed as a method of observing the
wavefunction of a single system, is extended to the observation of the density
matrix of a single system. d'Espagnat's definition of `proper mixture' is shown
to be improper because it does not allow for appropriate fluctuations. His
claim that there could be different mixtures corresponding to the same density
matrix is critically examined. These results provide a new meaning to the
density matrix, which gives it the same ontological status as the wavefunction
describing a pure state. This also enables quantum entropy to be associated
with a single system.",9803018v1
1999-10-01,Exact Solutions of the Caldeira-Leggett Master Equation: A Factorization Theorem For Decoherence,"Exact solutions of the Caldeira-Leggett Master equation for the reduced
density matrix for a free particle and for a harmonic oscillator system coupled
to a heat bath of oscillators are obtained for arbitrary initial conditions.
The solutions prove that the Fourier transform of the density matrix at time t
with respect to (x + x')/2, where x and x' are the initial and final
coordinates, factorizes exactly into a part depending linearly on the initial
density matrix and a part independent of it. The theorem yields the exact
initial state dependence of the density operator at time t and its eventual
diagonalization in the energy basis.",9910004v1
2005-03-09,Theory of Games on Quantum Objects,"Effect of replacing the classical game object with a quantum object is
analyzed. We find this replacement requires a throughout reformation of the
framework of Game Theory. If we use density matrix to represent strategy state
of players, they are full-structured density matrices with off-diagonal
elements for the new games, while reduced diagonal density matrix will be
enough for the traditional games on classical objects. In such formalism, the
payoff function of every player becomes Hermitian Operator acting on the
density matrix. Therefore, the new game looks really like Quantum Mechanics
while the traditional game becomes Classical Mechanics.",0503094v2
2007-02-15,Asymptotics of random density matrices,"We investigate random density matrices obtained by partial tracing larger
random pure states. We show that there is a strong connection between these
random density matrices and the Wishart ensemble of random matrix theory. We
provide asymptotic results on the behavior of the eigenvalues of random density
matrices, including convergence of the empirical spectral measure. We also
study the largest eigenvalue (almost sure convergence and fluctuations).",0702154v3
2014-09-08,Exciton formation in strongly correlated electron-hole systems near the semimetal-semiconductor transition,"The region surrounding the excitonic insulator phase is a three-component
plasma composed of electrons, holes, and excitons. Due to the extended nature
of the excitons, their presence influences the surrounding electrons and holes.
We analyze this correlation. To this end, we calculate the density of bound
electrons, the density of electrons in the correlated state, the
momentum-resolved exciton density, and the momentum-resolved density of
electron-hole pairs that are correlated but unbound. We find qualitative
differences in the electron-hole correlations between the weak-coupling and the
strong-coupling regime.",1409.2230v1
2016-01-27,Does the method of quasi-averages lead to the periodic density in a crystal?,"Since the Gibbs distribution function always yields a density of particles
constant in space, in order to obtain the periodic density characteristic of a
crystal it is usual to mention the method of quasi-averages. In the present
paper it is shown that the method of quasi-averages does not lead to the
periodic density as well as the initial Gibbs distribution. It is also
discussed how the crystalline state can be investigated by means of statistical
mechanics.",1601.07546v1
2014-06-11,"Thermal conductivity of hemp concretes: Variation with formulation, density and water content","This study investigates the effect of formulation, density and water content
on the thermal conductivity of hemp concretes. The investigations are based on
experimental measurements and on self-consistent scheme modelling. The thermal
conductivity of studied materials ranges from 90 to 160 mW/(m.K) at (23 degrees
C; 50%HR). The impact of density on thermal conductivity is much more important
than the impact of moisture content. It is shown that the thermal conductivity
increases by about 54 % when the density increases by 2/3 while it increases by
less than 15 % to 20 % from dry state to 90%RH.",1406.3310v1
2017-06-10,Phase-diagram and dynamics of Rydberg-dressed fermions in two-dimensions,"We investigate the ground-state properties and the collective modes of a
two-dimensional two-component Rydberg-dressed Fermi liquid in the
dipole-blockade regime. We find instability of the homogeneous system toward
phase separated and density ordered phases, using the Hartree-Fock and
random-phase approximations, respectively. The spectral weight of collective
density oscillations in the homogenous phase also signals the emergence of
density-wave instability. We examine the effect of exchange-hole on the
density-wave instability and on the collective mode dispersion using the
Hubbard local-field factor.",1706.03222v1
2017-11-27,Statistical mechanics of Landau damping,"Landau damping is the tendency of solutions to the Vlasov equation towards
spatially homogeneous distribution functions. The distribution functions
however approach the spatially homogeneous manifold only weakly, and Boltzmann
entropy is not changed by Vlasov equation. On the other hand, density and
kinetic energy density, which are integrals of the distribution function,
approach spatially homogeneous states strongly, which is accompanied by growth
of the hydrodynamic entropy. Such a behavior can be seen when Vlasov equation
is reduced to the evolution equations for density and kinetic energy density by
means of the Ehrenfest reduction.",1711.10022v1
2020-11-30,Compact Objects in Entangled Relativity,"We describe the first numerical Tolman-Oppenheimer-Volkoff solutions of
compact objects in entangled relativity, which is an alternative to the
framework of general relativity that does not have any additional free
parameter. Assuming a simple polytropic equation of state and the conservation
of the rest-mass density, we notably show that, for any given density, compact
objects are always heavier (up to $\sim 8\%$) in entangled relativity than in
general relativity -- for any given central density within the usual range of
neutron stars' central densities, or for a given radius of the resulting
compact object.",2011.14629v1
2022-01-07,On the definition of local spatial densities in hadrons,"We show that the matrix element of a local operator between hadronic states
gives rise to an unambiguous definition of the associated spatial density. As
an explicit example, we consider the charge density of a spinless particle in
the rest and moving frames and clarify its relationship to the electric form
factor. Our results suggest that the interpretation of the spatial densities of
local operators and their moments such as the mean square charge radius needs
to be revised.",2201.02565v1
2023-03-03,The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory,"Exact conditions have long been used to guide the construction of density
functional approximations. But hundreds of empirical-based approximations
tailored for chemistry are in use, many of which neglect these conditions in
their design. We analyze well-known conditions and revive several obscure ones.
Two crucial distinctions are drawn: that between necessary and sufficient
conditions, and between all electronic densities and the subset of realistic
Coulombic ground states. Simple search algorithms find that many empirical
approximations satisfy many exact conditions for realistic densities and
non-empirical approximations satisfy even more conditions than those enforced
in their construction. The role of exact conditions in developing
approximations is revisited.",2303.01766v2
2024-03-28,Gyrokinetic limit of the 2D Hartree equation in a large magnetic field,"We study the dynamics of two-dimensional interacting fermions submitted to a
homogeneous transverse magnetic field. We consider a large magnetic field
regime, with the gap between Landau levels set to the same order as that of
potential energy contributions. Within the mean-field approximation, i.e.
starting from Hartree's equation for the first reduced density matrix, we
derive a drift equation for the particle density. We use vortex coherent states
and the associated Husimi function to define a semi-classical density almost
satisfying the limiting equation. We then deduce convergence of the density of
the true Hartree solution by a Dobrushin-type stability estimate for the
limiting equation.",2403.19226v1
2023-04-17,Relativistic probability densities for location,"Imposing the Born rule as a fundamental principle of quantum mechanics would
require the existence of normalizable wave functions also for relativistic
particles. Indeed, the Fourier transforms of normalized k-space amplitudes
yield normalized x-space wave packets which reproduce the standard k-space
expectation values for energy and momentum from local momentum
pseudo-densities. However, in the case of bosonic fields, the wave packets are
nonlocally related to the corresponding relativistic quantum fields, and
therefore the canonical local energy-momentum densities differ from the
pseudo-densities and appear nonlocal in terms of the wave packets. We examine
the relation between the canonical energy density, the canonical charge
density, the energy pseudo-density, and the Born density for the massless free
Klein-Gordon field. We find that those four proxies for particle location are
tantalizingly close even in this extremely relativistic case: In spite of their
nonlocal mathematical relations, they are mutually local in the sense that
their maxima do not deviate beyond a common position uncertainty $\Delta x$.
Indeed, they are practically indistinguishable in cases where we would expect a
normalized quantum state to produce particle-like position signals, viz. if we
are observing quanta with momenta $p\gg\Delta p\ge\hbar/2\Delta x$. We also
translate our results to massless Dirac fields. Our results confirm and
illustrate that the normalized energy density provides a suitable measure for
positions of bosons, whereas normalized charge density provides a suitable
measure for fermions.",2304.08540v1
2018-07-22,Applying constrained simulations for low temperature lattice QCD at finite baryon chemical potential,"We study the density of states method as well as reweighting to explore the
low temperature phase diagram of QCD at finite baryon chemical potential. We
use four flavors of staggered quarks, a tree-level Symanzik improved gauge
action and four stout smearing steps on lattices with $N_s=4,6,8$ and $N_t=6 -
16$. We compare our results to that of the phase quenched ensemble and also
determine the pion and nucleon masses. In the density of states approach we
applied pion condensate or gauge action density fixing. We found that the
density of states method performs similarly to reweighting. At $T \approx 100$
MeV, we found an indication of the onset of the quark number density at around
$\mu/m_N \sim 0.16 - 0.18$ on $6^4$ lattices at $\beta=2.9$.",1807.08326v2
2019-09-08,High-density electron doping of SmNiO$_3$ from first principles,"Recent experimental work has realized a new insulating state of samarium
nickelate (SmNiO$_3$), accessible in a reversible manner via high-density
electron doping. To elucidate this behavior, we use the first-principles
density functional theory (DFT) + U method to study the effect of added
electrons on the crystal and electronic structure of SmNiO$_3$. First, we track
the changes in the crystal and electronic structure with added electrons
compensated by a uniform positive background charge at concentrations of
$\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, and 1 electrons per Ni. The change
in electron concentration does not rigidly shift the Fermi energy; rather, the
added electrons localize on NiO$_6$ octahedra causing an on-site Mott
transition and a change in the density of states resulting in a large gap
between the occupied and unoccupied Ni $e_g$ orbitals at full doping. This
evolution of the density of states is essentially unchanged when the added
electrons are introduced by doping with interstitial H or Li ions.",1909.03425v2
2020-04-08,Density of states approach for lattice gauge theory with a $θ$-term,"We discuss a new strategy for treating the complex action problem of lattice
field theories with a $\theta$-term based on density of states (DoS) methods.
The key ingredient is to use open boundary conditions where the topological
charge is not quantized to integers and the density of states is sufficiently
well behaved such that it can be computed precisely with recently developed DoS
techniques. After a general discussion of the approach and the role of the
boundary conditions, we analyze the method for 2-d U(1) lattice gauge theory
with a $\theta$-term, a model that can be solved in closed form. We show that
in the continuum limit periodic and open boundary conditions describe the same
physics and derive the DoS, demonstrating that only for open boundary
conditions the density is sufficiently well behaved for a numerical evaluation.
We conclude our proof of principle analysis with a small test simulation where
we numerically compute the density and compare it with the analytical result.",2004.03837v2
2002-01-07,High Density Neutron Star Equation of State from 4U 1636-53 Observations,"A bound on the compactness of the neutron star in the low mass x-ray binary
4U 1636-53 is used to estimate the equation of state of neutron star matter at
high density. Observations of 580 Hz oscillations during the rising phase of
x-ray bursts from this system appear to be due to two antipodal hot spots on
the surface of an accreting neutron star rotating at 290 Hz, implying the
compactness of the neutron star is less than 0.163 at the 90% confidence level.
The equation of state of high density neutron star matter estimated from this
compactness limit is significantly stiffer than extrapolations to high density
of equations of state determined by fits of experimental nucleon-nucleon
scattering data and properties of light nuclei to two- and three-body
interaction potentials.",0201099v1
2010-10-12,Vibrational density of states of silicon nanoparticles,"The vibrational density of states of silicon nanoparticles in the range from
2.3 to 10.3 nm is studied with the help of molecular-dynamics simulations. From
these simulations the vibrational density of states and frequencies of
bulk-like vibrational modes at high-symmetry points of the Brillouin-zone have
been derived. The results show an increase of the density of states at low
frequencies and a transfer of modes from the high-frequency end of the spectrum
to the intermediate range. At the same time the peak of transverse optical
modes is shifted to higher frequencies. These observations are in line with
previous simulation studies of metallic nanoparticles and they provide an
explanation for a previously observed discrepancy between experimental and
theoretical data [C. Meier et al., Physica E, 32, 155 (2006)].",1010.2271v2
2006-04-17,Electronic states and Landau levels in graphene stacks,"We analyze, within a minimal model that allows analytical calculations, the
electronic structure and Landau levels of graphene multi-layers with different
stacking orders. We find, among other results, that electrostatic effects can
induce a strongly divergent density of states in bi- and tri-layers,
reminiscent of one-dimensional systems. The density of states at the surface of
semi-infinite stacks, on the other hand, may vanish at low energies, or show a
band of surface states, depending on the stacking order.",0604396v1
2008-03-06,Bound States in Time-Dependent Quantum Transport: Oscillations and Memory Effects in Current and Density,"The presence of bound states in a nanoscale electronic system attached to two
biased, macroscopic electrodes is shown to give rise to persistent,
non-decaying, localized current oscillations which can be much larger than the
steady part of the current. The amplitude of these oscillations depends on the
entire history of the applied potential. The bound-state contribution to the
{\em static} density is history-dependent as well. Moreover, the time-dependent
formulation leads to a natural definition of the bound-state occupations out of
equilibrium.",0803.0914v1
2008-09-24,Fermi-liquid effects in the gapless state of marginally thin superconducting films,"We present low temperature tunneling density-of-states measurements in Al
films in high parallel magnetic fields. The thickness range of the films, t=6-9
nm, was chosen so that the orbital and Zeeman contributions to their parallel
critical fields were comparable. In this quasi-spin paramagnetically limited
configuration, the field produces a significant suppression of the gap, and at
high fields the gapless state is reached. By comparing measured and calculated
tunneling spectra we are able to extract the value of the antisymmetric
Fermi-liquid parameter G^0 and thereby deduce the quasiparticle density
dependence of the effective parameter G^0_{eff} across the gapless state.",0809.4077v1
2010-08-27,Non existence of vortices in the small density region of a condensate,"In this paper, we answer a question raised by Len Pitaevskii and prove that
the ground state of the Gross-Pitaevskii energy describing a Bose Einstein
condensate at low rotation does not have vortices in the low density region.
Therefore, the first ground state with vortices has its vortices in the bulk.
This is obtained by proving that for small rotational velocities, the ground
state is multiple of the ground state with zero rotation. We rely on sharp
bounds of the decay of the wave function combined with weighted jacobian
estimates.",1008.4801v2
2013-04-25,Edge states protected by chiral symmetry in disordered photonic graphene,"We experimentally investigate the impact of uncorrelated composite and
structural disorder in photonic graphene. We find that in case of structural
disorder not only chiral symmetry, but also the vanishing of the density of
states at zero energy is preserved. This is in contrast to composite disorder,
where chiral symmetry as well as the vanishing of the density of states are
destroyed. Our observations are experimentally proven by exciting edge states
at the bearded edge in disordered photonic graphene.",1304.6911v1
2014-08-12,Non-magnetic defects in the bulk of two-dimensional topological insulators,"We found that non-magnetic defects in two-dimensional topological insulators
induce bound states of two kinds for each spin orientation: electron- and
hole-like states. Depending on the sign of the defect potential these states
can be also of two kinds with different distribution of the electron density.
The density has a maximum or minimum in the center. A surprising effect caused
by the topological order is a singular dependence of the bound-state energy on
the defect potential.",1408.2629v1
2015-01-06,Spontaneous symmetry breaking in a spin-orbit coupled $f=2$ spinor condensate,"We study the ground-state density profile of a spin-orbit coupled $f=2$
spinor condensate in a quasi-one-dimensional trap. The Hamiltonian of the
system is invariant under time reversal but not under parity. We identify
different parity- and time-reversal-symmetry-breaking states. The
time-reversal-symmetry breaking is possible for degenerate states. A phase
separation among densities of different components is possible in the domain of
time-reversal-symmetry breaking. Different types of parity- and
time-reversal-symmetry-breaking states are predicted analytically and studied
numerically. We employ numerical and approximate analytic solutions of a
mean-field model in this investigation to illustrate our findings.",1501.01164v1
2015-08-12,On quantum phase transitions in tilted 2D lattices,"We discuss the quantum phase transition from the Mott-insulator state to the
density-wave state for cold Bose atoms in a 2D square lattice as the lattice is
adiabatically tilted along one of its primary axes. It is shown that a small
misalignment of the tilt drastically changes the result of the adiabatic
passage and, instead of the density-wave state, one obtains a disordered state.
Intrinsic relation of the problem to Bloch oscillations of hard-core bosons in
a 2D lattice is illuminated.",1510.02671v1
2008-07-01,Robustness of noise-present Bell's inequality violation by entangled state,"The robustness of Bell's inequality (in CHSH form) violation by entangled
state in the simultaneous presence of colored and white noise in the system is
considered. A twophoton polarization state is modeled by twoparameter density
matrix. Setting parameter values one can vary the relative fraction of pure
entangled Bell's state as well as white and colored noise fractions. Bell's
operator-parameter dependence analysis is made. Computational results are
compared with experimental data [quant-ph/0511265] and with results computed
using a oneparameter density matrix [doi: 10.1103/PhysRevA.72.052112], which
one can get as a special case of the model considered in this work.",0807.0126v1
2009-12-23,Noise correlations of a strongly attractive spin-1/2 Fermi gas in an optical lattice,"We calculate density-density correlations of an expanding gas of strongly
attractive ultra-cold spin-1/2 fermions in an optical lattice. The phase
diagram of the tightly bound fermion pairs exhibits a Bose-Einstein condensed
state and a Mott insulating state with a single molecule per lattice site. We
study the effects of quantum fluctuations on the correlations in both phases
and show that they are especially important in the Bose-Einstein condensate
state, leading to the appearance of singular peaks. In the Mott insulating
state the correlations are characterized by sharp dips. This can be utilized in
experiments to distinguish between these two phases.",0912.4607v1
2017-11-13,Modular energy inequalities from relative entropy,"We obtain new constraints for the modular energy of general states by using
the monotonicity property of relative entropy. In some cases, modular energy
can be related to the energy density of states and these constraints lead to
interesting relations between energy and entropy. In particular, we derive new
quantum energy inequalities that improve some previous bounds for the energy
density of states in a conformal field theory. Additionally, the inequalities
derived in this manner also lead us to conclude that the entropy of the state
further restricts the possible amount of negative energy allowed by the theory.",1711.04816v1
2022-06-27,Positive-definite parametrization of mixed quantum states with deep neural networks,"We introduce the Gram-Hadamard Density Operator (GHDO), a new deep
neural-network architecture that can encode positive semi-definite density
operators of exponential rank with polynomial resources. We then show how to
embed an autoregressive structure in the GHDO to allow direct sampling of the
probability distribution. These properties are especially important when
representing and variationally optimizing the mixed quantum state of a system
interacting with an environment. Finally, we benchmark this architecture by
simulating the steady state of the dissipative transverse-field Ising model.
Estimating local observables and the R\'enyi entropy, we show significant
improvements over previous state-of-the-art variational approaches.",2206.13488v1
2019-06-03,A maximal-entropy initial state of the Universe as a microscopic description of inflation,"We propose that the initial state of the Universe was an isotropic state of
maximal entropy. Such a state can be described in terms of a state of closed,
interacting, fundamental strings in their high-temperature Hagedorn phase. The
entropy density in this state is equal to the square root of the energy density
in Planck units, while the pressure is positive and equal to the energy
density. These relations imply a maximally large entropy density and,
therefore, a state that cannot be described by a semiclassical spacetime
geometry. If one nevertheless insists on an effective semiclassical description
of this state, she can do so by ignoring the entropy. This leads to a partially
equivalent description in which the pressure appears to be negative and equal
in magnitude to the energy density, as if the energy-momentum tensor was that
of a cosmological constant. From this effective perspective, the state
describes a period of string-scale inflation. The bound state of strings
ultimately decays, possibly by a process akin to Hawking radiation, and
undergoes a transition into a phase of hot radiation. But, from the effective
perspective, the same decay corresponds to the heating of the Universe at the
end of inflation. Small quantum mechanical fluctuations in the initial state
lead to scale-invariant temperature anisotropies in the hot radiation. The
temperature anisotropies are interpreted in the effective description as
arising from quantum fluctuations of the curvature and an effective inflaton
field. The stringy microscopic description determines the parameters of the
model of inflation, as well as the cosmological observables, in terms of the
string length scale and coupling strength. Our framework is similar,
conceptually, to a recent description of black holes in terms of a maximal
entropy state of strings in the Hagedorn phase.",1906.00989v1
2003-12-19,Methods for electronic-structure calculations - an overview from a reduced-density-matrix point of view,"The methods of quantum chemistry and solid state theory to solve the
many-body problem are reviewed. We start with the definitions of reduced
density matrices, their properties (contraction sum rules, spectral
resolutions, cumulant expansion, $N$-representability), and their determining
equations (contracted Schr\""odinger equations) and we summarize recent
extensions and generalizations of the traditional quantum chemical methods, of
the density functional theory, and of the quasi-particle theory: from finite to
extended systems (incremental method), from density to density matrix (density
matrix functional theory), from weak to strong correlation (dynamical mean
field theory), from homogeneous (Kimball-Overhauser approach) to inhomogeneous
and finite systems. Measures of the correlation strength are discussed. The
cumulant two-body reduced density matrix proves to be a key quantity. Its
spectral resolution contains geminals, being possibly the solutions of an
approximate effective two-body equation, and the idea is sketched of how its
contraction sum rule can be used for a variational treatment.",0312516v1
2014-02-18,Efficient Local Density Estimation Strategy for VANETs,"Local vehicle density estimation is increasingly becoming an essential factor
of many vehicular ad-hoc network applications such as congestion control and
traffic state estimation. This estimation is used to get an approximate number
of neighbors within the transmission range since beacons do not give accurate
accuracy about neighborhood. These is due to the special characteristics of
VANETs such as high mobility, high density variation. To enhance the
performance of these applications, an accurate estimation of the local density
with minimum of overhead is needed. Most of the proposed strategies address the
global traffic density estimation without a big attention on the local density
estimation. This paper proposes an improved approach for local density
estimation in VANETs in terms of accuracy and overhead. The simulation results
showed that our strategy allows an interesting precision of estimation with
acceptable overhead.",1402.4508v1
2019-07-24,Predicting charge density distribution of materials using a local-environment-based graph convolutional network,"Electron charge density distribution of materials is one of the key
quantities in computational materials science as theoretically it determines
the ground state energy and practically it is used in many materials analyses.
However, the scaling of density functional theory calculations with number of
atoms limits the usage of charge-density-based calculations and analyses. Here
we introduce a machine learning scheme with local-environment-based graphs and
graph convolutional neural networks to predict charge density on grid-points
from crystal structure. We show the accuracy of this scheme through a
comparison of predicted charge densities as well as properties derived from the
charge density, and the scaling is O(N). More importantly, the transferability
is shown to be high with respect to different compositions and structures,
which results from the explicit encoding of geometry.",1907.10649v1
2023-09-25,Room-temperature ferroelectric nematic liquid crystal showing a large and divergent density,"The ferroelectric nematic phase (NF) is a recently discovered phase of matter
in which the orientational order of the conventional nematic liquid crystal
state is augmented with polar order. Atomistic simulations suggest that the
polar NF phase would be denser than conventional nematics owing to
contributions from polar order. Using an oscillating U-tube densitometer, we
obtain detailed temperature-dependent density values for a selection of
conventional liquid crystals with excellent agreement with earlier reports.
Having demonstrated the validity of our method, we then record density as a
function of temperature for M5, a novel room-temperature ferroelectric nematic
material. We present the first experimental density data for a NF material as
well as density data for a nematic that has not previously been reported. We
find that the room-temperature NF material shows a large (>1.3 g cm3) density
at all temperatures studied, with an increase in density at phase transitions.
The magnitude of the increase for the intermediate splay-ferroelectric nematic
(NX-NF) transition is an order of magnitude smaller than the isotropic-nematic
(I-N) transition. Present results may be typical of ferroelectric nematic
materials, potentially guiding material development, and is especially relevant
for informing ongoing studies into this emerging class of materials.",2309.14161v1
1994-11-30,Kaon Condensation in the Bound-State Approach to the Skyrme Model,"We explore kaon condensation using the bound-state approach to the Skyrme
model on a 3-sphere. The condensation occurs when the energy required to
produce a $K^-$ falls below the electron fermi level. This happens at the
baryon number density on the order of 3--4 times nuclear density.",9411430v1
2020-07-29,Pure-state density matrix that competently describes classical chaos,"We work with reference to a well-known semiclassical model, in which quantum
degrees of freedom interact with classical ones. We show that, in the classical
limit, it is possible to represent classical results (e.g., classical chaos) by
means a pure-state density matrix.",2007.14561v1
2012-01-23,Synthetic charge-flux quantum liquids,"We apply rotating optical flux lattices to spinor Bose-Einstein condensates.
Distinct quantum states emerge for fractional ratios of vortex charge density
to optical flux density. We exhibit the calculated charge-flux states and
discuss their topological structure and experimental signatures.",1201.4636v2
1997-06-24,"Is the ground state of alpha-(BEDT-TTF)2MHg(SCN)4[M=K,Rb,Tl] a charge-density wave or a spin-density wave?","The nature of the low-temperature phase of the quasi-two-dimensional
conductors $\alpha-(BEDT-TTF)_2{M}Hg(SCN)_4$[{M}=K,Rb,Tl] is considered. It is
argued that the magnetic field dependence of the phase diagram is more
consistent with a charge-density wave, rather than a spin-density wave ground
state. The phase diagram of a charge-density wave in a magnetic field is
discussed using a Ginzburg-Landau free energy derived from microscopic theory.
New experiments are proposed to test the charge-density-wave hypothesis and
detect an additional high field phase.",9706235v2
2011-03-23,Exact Density Functional for the Non-Relativistic Particle Energy in the Local External Field,"Based on the Schrodinger equation, exact expressions for the non-relativistic
particle energy in the local external field and the external field potential
are derived as inhomogeneous density functionals. On this basis, it is shown
that, when considering more than two noninteracting electrons, the energy of
such a system cannot be an inhomogeneous density functional. This means that
the Hohenberg-Kohn lemma which assert that in the ground state to each
inhomogeneous density corresponds only one potential of the external field
cannot be a justification of the existence of the universal density functional
in the general case. At the same time, statements of the density functional
theory remain valid when considering any number of noninteracting ground-state
bosons due to the Bose condensation effect.",1103.4586v1
2012-03-28,Density-functional theory for 1D harmonically trapped Bose-Fermi mixture,"We present a density-functional theory for the one dimensional harmonically
trapped Bose-Fermi mixture with repulsive contact interactions. The ground
state density distribution of each component is obtained by solving the
Kohn-Sham equations numerically based on the Local Density Approximation and
the exact solution for the homogeneous system given by Bethe ansatz method. It
is shown that for strong enough interaction, a considerable amount of fermions
are repelled out of the central region of the trap, exhibiting partial phase
separation of Bose and Fermi components. Oscillations emerge in the Bose
density curves reflecting the strong correlation with Fermions. For infinite
strong interaction, the ground state energy of the mixture and the total
density are consistent with the scenario that all atoms in the mixture are
fully fermionized.",1203.6211v1
2019-08-27,Large-time asymptotics for a matrix spin drift-diffusion model,"The large-time asymptotics of the density matrix solving a
drift-diffusion-Poisson model for the spin-polarized electron transport in
semiconductors is proved. The equations are analyzed in a bounded domain with
initial and Dirichlet boundary conditions. If the relaxation time is
sufficiently small and the boundary data is close to the equilibrium state, the
density matrix converges exponentially fast to the spinless near-equilibrium
steady state. The proof is based on a reformulation of the matrix-valued
cross-diffusion equations using spin-up and spin-down densities as well as the
perpendicular component of the spin-vector density, which removes the
cross-diffusion terms. Key elements of the proof are time-uniform positive
lower and upper bounds for the spin-up and spin-down densities, derived from
the De Giorgi-Moser iteration method, and estimates of the relative free energy
for the spin-up and spin-down densities.",1908.10096v1
2016-05-16,Novel halos in light kaonic nuclei as an indicator of nuclear equation of state at supra-normal densities,"The sensitive correlations between the low-density halo structure and the
high-density properties of the nuclear equation of state (EOS) are constructed
in light kaonic nuclei with the relativistic mean-field theory. More
specifically, the $1p_{1/2}$ halo spreads out linearly with increasing the
pressure and sound velocity square at supra-normal densities and quadratically
with decreasing the incompressibility at saturation density. These results
suggest that the novel halo in light kaonic nuclei can serve as a sensitive
indicator of the nuclear EOS of symmetric matter at supra-normal densities.",1605.04754v2
2020-05-01,Complete Density Calculations of q-State Potts and Clock Models: Reentrance of Interface Densities under Symmetry Breaking,"All local bond-state densities are calculated for q-state Potts and clock
models in three spatial dimensions, d=3. The calculations are done by an exact
renormalization group on a hierarchical lattice, including the density
recursion relations, and simultaneously are the Migdal-Kadanoff approximation
for the cubic lattice. Reentrant behavior is found in the interface densities
under symmetry breaking, in the sense that upon lowering temperature the value
of the density first increases, then decreases to its zero value at zero
temperature. For this behavior, a physical mechanism is proposed. A contrast
between the phase transition of the two models is found, and explained by
alignment and entropy, as the number of states q goes to infinity. For the
clock models, the renormalization-group flows of up to twenty energies are
used.",2005.00474v2
2020-08-10,Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice,"We study the effects of doping the Kitaev model on the honeycomb lattice
where the spins interact via the bond-directional interaction $J_K$, which is
known to have a quantum spin liquid as its exact ground state. The effect of
hole doping is studied within the $t$-$J_K$ model on a three-leg cylinder using
density-matrix renormalization group. Upon light doping, we find that the
ground state of the system has quasi-long-range charge-density-wave
correlations but short-range single-particle correlations. The dominant pairing
channel is the even-parity superconducting pair-pair correlations with
$d$-wave-like symmetry, which oscillate in sign as a function of separation
with a period equal to that of the spin-density wave and two times the
charge-density wave. Although these correlations fall rapidly (possibly
exponentially) at long distances, this is never-the-less the first example
where a pair-density wave is the strongest SC order on a bipartite lattice. Our
results may be relevant to ${\rm Na_2IrO_3}$ and $\alpha$-${\rm RuCl_3}$ upon
doping.",2008.03858v1
2022-02-11,Reversible to Irreversible Transitions for Cyclically Driven Disks on Periodic Obstacle Arrays,"We examine the collective dynamics of disks moving through a square array of
obstacles under cyclic square wave driving. Below a critical density we find
that system organizes into a reversible state in which the disks return to the
same positions at the end of every drive cycle. Above this density, the
dynamics are irreversible and the disks do not return to the same positions
after each cycle. The critical density depends strongly on the angle $\theta$
between the driving direction and a symmetry axis of the obstacle array, with
the highest critical densities appearing at commensurate angles such as
$\theta=0^\circ$ and $\theta=45^\circ$ and the lowest critical densities
falling at $\theta = \arctan(0.618)$, the inverse of the golden ratio, where
the flow is the most frustrated. As the density increases, the number of cycles
required to reach a reversible state grows as a power law with an exponent near
$\nu=1.36$, similar to what is found in periodically driven colloidal and
superconducting vortex systems.",2202.05384v1
2022-04-11,Maximum entropy optimal density control of discrete-time linear systems and Schrödinger bridges,"We consider an entropy-regularized version of optimal density control of
deterministic discrete-time linear systems. Entropy regularization, or a
maximum entropy (MaxEnt) method for optimal control has attracted much
attention especially in reinforcement learning due to its many advantages such
as a natural exploration strategy. Despite the merits, high-entropy control
policies induced by the regularization introduce probabilistic uncertainty into
systems, which severely limits the applicability of MaxEnt optimal control to
safety-critical systems. To remedy this situation, we impose a Gaussian density
constraint at a specified time on the MaxEnt optimal control to directly
control state uncertainty. Specifically, we derive the explicit form of the
MaxEnt optimal density control. In addition, we also consider the case where
density constraints are replaced by fixed point constraints. Then, we
characterize the associated state process as a pinned process, which is a
generalization of the Brownian bridge to linear systems. Finally, we reveal
that the MaxEnt optimal density control gives the so-called Schr\""odinger
bridge associated to a discrete-time linear system.",2204.05263v2
2022-10-13,Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization,"This work presents a new class of hybrid density functional theory (DFT)
approximations, incorporating nonlocal exact exchange in predefined states such
as core atomic orbitals (AOs). These projected hybrid density functionals are a
flexible generalization of range-separated hybrids. This work derives projected
hybrids using the Adiabatic Projection formalism. One projects the
electron-electron interaction operator onto the chosen predefined states,
reintroduces the projected operator into the noninteracting Kohn-Sham reference
system, and introduces a density functional approximation for the remaining
electron-electron interactions. Projected hybrids are readily implemented
existing density functional codes, requiring only a projection of the
one-electron density matrices and exchange operators entering existing
routines. This work also presents a first application: a core-projected
Perdew-Burke-Ernzerhof hybrid PBE0c70, in which the fraction of nonlocal exact
exchange is increased from 25% to 70% in core AOs. Automatic selection of the
projected AOs provides a black-box model chemistry appropriate for both core
and valence electron properties. PBE0c70 predicts core orbital energies that
accurately recover core-electron binding energies of second- and third-row
elements, without degrading PBE0's good performance for valence-electron
properties.",2210.07216v1
2023-02-10,Assessing the source of error in the Thomas-Fermi-von Weizsäcker density functional,"We investigate the source of error in the Thomas-Fermi-von Weizs\""acker (TFW)
density functional relative to Kohn-Sham density functional theory (DFT). In
particular, through numerical studies on a range of materials, for a variety of
crystal structures subject to strain and atomic displacements, we find that
while the ground state electron density in TFW orbital-free DFT is close to the
Kohn-Sham density, the corresponding energy deviates significantly from the
Kohn-Sham value. We show that these differences are a consequence of the poor
representation of the linear response within the TFW approximation for the
electronic kinetic energy, confirming conjectures in the literature. In so
doing, we find that the energy computed from a non-self-consistent Kohn-Sham
calculation using the TFW electronic ground state density is in very good
agreement with that obtained from the fully self-consistent Kohn-Sham solution.",2302.05376v2
2023-07-10,Endotaxial Stabilization of 2D Charge Density Waves with Long-range Order,"Charge density waves are emergent quantum states that spontaneously reduce
crystal symmetry, drive metal-insulator transitions, and precede
superconductivity. In low-dimensions, distinct quantum states arise, however,
thermal fluctuations and external disorder destroy long-range order. Here we
stabilize ordered two-dimensional (2D) charge density waves through endotaxial
synthesis of confined monolayers of 1T-TaS$_2$. Specifically, an ordered
incommensurate charge density wave (oIC-CDW) is realized in 2D with
dramatically enhanced amplitude and resistivity. By enhancing CDW order, the
hexatic nature of charge density waves becomes observable. Upon heating via
in-situ TEM, the CDW continuously melts in a reversible hexatic process wherein
topological defects form in the charge density wave. From these results, new
regimes of the CDW phase diagram for 1T-TaS$_2$ are derived and consistent with
the predicted emergence of vestigial quantum order.",2307.04587v1
2023-10-12,A 3D Kinetic Distribution that Yields Observed Plasma Density in the Inner Van Allen Belt,"A steady-state distribution is obtained that approximately yields the
observed plasma density profile of the inner Van Allen radiation belt. The
model assumes a collisionless, magnetized plasma with zero electric field
present. The inner Van Allen belt consists of a plasma comprising high-energy
protons and relativistic electrons. The particle trajectories are obtained from
the collisionless Lorentz Force equation for different initial distributions.
The resulting steady-state distributions obtained after particles lost to the
loss cone are eliminated and are used to generate the density profile. The
distribution's dependence on energy and magnetic moment is adjusted to make the
density profile agree with observations. For a distribution that is a function
of energy times a function of magnetic moment, the calculation leads to the
desired type of density profile. The kinetic distribution and the type of
density profile obtained are presented.",2310.08322v1
2015-12-17,Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices,"We study the conditions when mixtures of entangled pure states with maximally
mixed one-qudit reduced density matrices remain entangled. We found that the
resulting mixed state remains entangled when the number of entangled pure
states to be mixed is less than or equal to the dimension of the pure states.
For the latter case of mixing a number of pure states equal to their dimension,
we found that the mixed state is entangled provided that the entangled pure
states to be mixed are not equally weighted. We also found that one can
restrict the set of pure states that one can mix from in order to ensure that
the resulting mixed state is genuinely entangled.",1512.05539v1
2021-07-23,Mean-field interactions in evolutionary spatial games,"We introduce a mean-field term to an evolutionary spatial game model. Namely,
we consider the game of Nowak and May, based on the Prisoner's dilemma, and
augment the game rules by a self-consistent mean-field term. This way, an agent
operates based on local information from its neighbors and nonlocal information
via the mean-field coupling. We simulate the model and construct the
steady-state phase diagram, which shows significant new features due to the
mean-field term: while for the game of Nowak and May, steady states are
characterized by a constant mean density of cooperators, the mean-field game
contains steady states with a continuous dependence of the density on the
payoff parameter. Moreover, the mean-field term changes the nature of
transitions from discontinuous jumps in the steady-state density to jumps in
the first derivative. The main effects are observed for stationary steady
states, which are parametrically close to chaotic states: the mean-field
coupling drives such stationary states into spatial chaos. Our approach can be
readily generalized to a broad class of spatial evolutionary games with
deterministic and stochastic decision rules.",2107.11088v2
2020-05-06,From compact localized states to many-body scars in the random quantum comb,"In this work we investigate the effects of configurational disorder on the
eigenstates and dynamical properties of a tight-binding model on a
quasi-one-dimensional comb lattice, consisting of a backbone decorated with
linear offshoots of randomly distributed lengths. We show that all eigenstates
are exponentially localized along the backbone of the comb. Moreover, we
demonstrate the presence of an extensive number of compact localized states
with precisely zero localization length. We provide an analytical understanding
of these states and show that they survive in the presence of density-density
interactions along the backbone of the system where, for sufficiently low but
finite particle densities, they form many-body scar states. Finally, we discuss
the implications of these compact localized states on the dynamical properties
of systems with configurational disorder, and the corresponding appearance of
long-lived transient behaviour in the time evolution of physically relevant
product states.",2005.03036v3
2021-09-22,Performance of the quantum MaxEnt estimation in the presence of physical symmetries,"When an informationally complete measurement is not available, the
reconstruction of the density operator that describes the state of a quantum
system can be accomplish, in a reliable way, by adopting the maximum entropy
principle (MaxEnt principle), as an additional criterion, to obtain the least
biased estimation. In this paper, we study the performance of the MaxEnt method
for quantum state estimation when there is prior information about symmetries
of the unknown state. We explicitly describe how to work with this method in
the most general case, and present an algorithm that allows to improve the
estimation of quantum states with arbitrary symmetries. Furthermore, we
implement this algorithm to carry out numerical simulations estimating the
density matrix of several three-qubit states of particular interest for quantum
information tasks. We observed that, for most states, our approach allows to
considerably reduce the number of independent measurements needed to obtain a
sufficiently high fidelity in the reconstruction of the density matrix.
Moreover, we analyze the performance of the method in realistic scenarios,
showing that it is robust even when considering the effect of finite
statistics, and under the presence of typical experimental noise.",2109.10806v2
2007-04-27,"Wigner functions, coherent states, one-dimensional marginal probabilities and uncertainty structures of Landau levels","Following an approach based on generating function method phase space
characteristics of Landau system are studied in the autonomous framework of
deformation quantization. Coherent state property of generating functions is
established and marginal probability densities along canonical coordinate lines
are derived. Well defined analogs of inner product, Cauchy-Bunyakowsy-Schwarz
inequality and state functional have been defined in phase space and they have
been used in analyzing the uncertainty structures. The general form of the
uncertainty relation for two real-valued functions is derived and uncertainty
products are computed in states described by Wigner functions. Minimum
uncertainty state property of the standard coherent states is presented and
uncertainty structures in the case of phase space generalized coherent states
are analyzed.",0704.3699v1
2011-09-26,Steady-state solution for dark states using a three-level system in coupled quantum dots,"Quantum dots (QDs) are one of the promising candidates of interconnection
between electromagnetic field and electrons in solid-state devices. Dark states
appear as a result of coherence between the electromagnetic fields and the
discrete energy levels of the system. Here, we theoretically solve the
steady-state solutions of the density matrix equations for a thee-level double
QD system and investigate the condition of the appearance of a dark state. We
also numerically show the appearance of the dark state by time-dependent
current characteristics.",1109.5450v1
2013-09-24,Counting metastable states in a kinetically constrained model using a patch repetition analysis,"We analyse metastable states in the East model, using a recently-proposed
patch-repetition analysis based on time-averaged density profiles. The results
reveal a hierarchy of states of varying lifetimes, consistent with previous
studies in which the metastable states were identified and used to explain the
glassy dynamics of the model. We establish a mapping between these states and
configurations of systems of hard rods, which allows us to analyse both typical
and atypical metastable states. We discuss connections between the complexity
of metastable states and large-deviation functions of dynamical quantities,
both in the context of the East model and more generally in glassy systems.",1309.6247v1
2017-12-20,"Separability of 3-qubits density matrices, related to l(1) and l(2)norms and to unfolding of tensors into matrices","We treat 3-qubits states with maximally disordered subsystems, by using
Hilbert-Schmidt decompositions.By using unfolding methods, the tensors are
converted into matrices and by applying singular values decompositions to these
matrices the number 27 of the Hilbert Schmidt parameters, is reduced to 9 and
under the condition that the sum of absolute values of these parameters is not
larger than 1, we conclude that the density matrix is fully separable . In
another method we divide the 27 Hilbert Schmidt parameters into 9 triads where
for each triad we calculate the Frobenius norm of 3 Hilbert-Schmidt parameters.
If the sum of nine norms is not larger than 1 then we conclude that the density
matrix is fully separable . The condition for biseparability of maximally
disordered density matrices is obtained by the use of one qubit density matrix
multiplied by Bell entangled states of the other two qubits. If the sum of the
nine Frobenius norms for these different triads is not larger than 1, we
conclude that the density matrix is biseparable. We analyze the relations
between three qubits maximally disordered subsystems density matrices and the
method of high order singular value decomposition (HOSVD) and show that this
method may improve the sufficient condition for full separability. For three
qubits states which include multiplication with the unit matrix we find a
simple way to reduce the sum of the absolute values of the Hilbert Schmidt
parameters absolute values and get better conditions for their full
separability for special cases.",1712.07492v1
1994-12-05,Spectral Boundary of Positive Random Potential in a Strong Magnetic Field,"We consider the problem of randomly distributed positive delta-function
scatterers in a strong magnetic field and study the behavior of density of
states close to the spectral boundary at $E=\hbar\omega_{c}/2$ in both two and
three dimensions. Starting from dimensionally reduced expression of Brezin et
al. and using the semiclassical approximation we show that the density of
states in the Lifshitz tail at small energies is proportio- nal to $e^{f-2}$ in
two dimensions and to $\exp(-3.14f\ln(3.14f/\pi e)/ \sqrt(2me))$ in three
dimensions, where $e$ is the energy and $f$ is the density of scatterers in
natural units.",9412026v1
2002-09-13,Quantum states and specific heat of low-density He gas adsorbed within the carbon nanotube interstitial channels: Band structure effects and potential dependence,"We calculate the energy-band structure of a He atom trapped within the
interstitial channel between close-packed nanotubes within a bundle and its
influence on the specific heat of the adsorbed gas. A robust prediction of our
calculations is that the contribution of the low-density adsorbed gas to the
specific heat of the nanotube material shows pronounced nonmonotonic variations
with temperature. These variations are shown to be closely related to the band
gaps in the adsorbate density of states.",0209322v1
2003-07-09,Photoemission study of the spin-density wave state in thin films of Cr,"Angle-resolved photoemission (PE) was used to characterize the spin-density
wave (SDW) state in thin films of Cr grown on W(110). The PE data were analysed
using results of local spin density approximation layer-Korringa-Kohn-Rostoker
calculations. It is shown that the incommensurate SDW can be monitored and
important parameters of SDW-related interactions, such as coupling strength and
energy of collective magnetic excitations, can be determined from the
dispersion of the renormalized electronic bands close to the Fermi energy. The
developed approach can readily be applied to other SDW systems including
magnetic multilayer structures.",0307196v1
2003-07-26,Collective modes and quasiparticle interference on the local density of states of cuprate superconductors,"The energy, momentum and temperature dependence of the quasiparticle local
density of states (LDOS) of a two-dimensional $d_{x^2-y^2}$-wave superconductor
with random disorder is investigated using the first-order T-matrix
approximation. The results suggest that collective modes such as spin/charge
density waves are relevant low-energy excitations of the cuprates that
contribute to the observed LDOS modulations in recent scanning tunneling
microscopy studies of $\rm Bi_2Sr_2CaCu_2O_x$.",0307660v2
2004-02-14,First principle study on electronic structure of ferroelectric PbFe0.5Nb0.5O3,"The full potential linearized augmented plane wave (FLAPW) method was used to
study the crystal structure and electronic structure properties of
PbFe0.5Nb0.5O3 (PFN). The optimized crystal structure, density of states, band
structure and electron density distribution have been obtained to understand
the ferroelectric behavior of PFN. From the density of states analysis, it is
shown that there is a hybridization of Fe d - O p and Nb d - O p in
ferroelectric PFN. This is consistent with the calculation of electronic band
structure. This hybridization is responsible for the tendency to its
ferroelectricity.",0402380v1
2006-06-15,Interplay between phase defects and spin polarization in the specific heat of the spin density wave compound (TMTTF)_2Br in a magnetic field,"Equilibrium heat relaxation experiments provide evidence that the ground
state of the commensurate spin density wave (SDW) compound (TMTTF)$_2$Br after
the application of a sufficient magnetic field is different from the
conventional ground state. The experiments are interpreted on the basis of the
local model of strong pinning as the deconfinement of soliton-antisoliton pairs
triggered by the Zeeman coupling to spin degrees of freedom, resulting in a
magnetic field induced density wave glass for the spin carrying phase
configuration.",0606403v1
2001-11-23,Statistical spectroscopic calculation of expectation values and spin-cutoff factors,"Recently we proposed a formalism, based in nuclear statistical spectroscopy,
for efficient computation of nuclear level density, or densities of states,
through a sum of partitioned binomial functions (SUPARB). In this Letter we
extend the formalism to the calculation of locally averaged expectation values,
with specific application to spin-cutoff factors and the angular momentum
dependence of the nuclear density of states.",0111068v1
1996-04-22,Multi-mode density matrices of light via amplitude and phase control,"A new method is described for determining the quantum state of correlated
multimode radiation by interfering the modes and measuring the statistics of
the superimposed fields in four-port balanced homodyne detection. The full
information on the $N$-mode quantum state is obtained by controlling both the
relative amplitudes and the phases of the modes, which simplifies the
reconstruction of density matrices to only $N+1$ Fourier transforms. In
particular, this method yields time-correlated multimode density matrices of
optical pulses by superimposing the signal by a sequence of short
local-oscillator pulses.",9604020v1
2008-09-11,Signature of multiple glassy states in micellar nanoparticle-polymer composites,"We present results of temperature dependent measurements of dynamics of
micellar nanoparticle - polymer composites of fixed volume fraction and
variable polymer chain grafting density. For nanoparticles with lower grafting
density we observe dynamically arrested state at low temperatures corresponding
to an attractive glass while at high temperature the same system shows
relaxation typical of a repulsive glass. For higher grafting density, the low
temperature dynamics resembles more of a gel which crosses over to a repulsive
glass at high temperature. Possible reasons for such fascinating dynamical
transitions is delineated.",0809.2004v1
2011-07-05,Magnetic field and quark matter in the core,"Magnetic properties of quark matter are discussed in the light of the
observation of pulsars. Our works about spontaneous spin polarization and spin
density wave are reviewed and their implications on compact-star phenomena are
discussed. In particular, the former subject may be directly related to the
origin of strong magnetic fields. An inhomogeneous state emerges following the
chiral transition, where a kind of spin density wave develops.",1107.0807v2
2012-09-04,Electronic structure and optical properties of Graphene Monoxide,"The electronic and optical properties of graphene monoxide, a new type of
semiconductor materials, are first theoretically studied based on density
functional theory. Electronic calculations show that the band gap is 0.952 eV
which indicate that graphene monoxide is a direct band gap semiconductor. The
density of states of graphene monoxide and the partial density of states for C
and O are given to understand the electronic structure. In addition, we
calculate the optical properties of graphene monoxide including the complex
dielectric function, absorption coefficient, the complex refractive index,
loss-function, reflectivity and conductivity. These results provide a physical
basis for the potential applications in optoelectronic devices.",1209.0555v1
2010-05-10,Entangling two Bose Einstein condensates in a double cavity system,"We propose a scheme to transfer the quantum state of light fields to the
collective density excitations of a Bose Einstein condensate (BEC) in a cavity.
This scheme allows to entangle two BECs in a double cavity setup by
transferring the quantum entanglement of two light fields produced from a
nondegenerate parametric amplifier (NOPA) to the collective density excitations
of the two BECs. An EPR state of the collective density excitations can be
created by a judicious choice of the system parameters.",1005.1562v1
2016-10-12,Symmetry energy and density,"The nuclear equation-of-state is a topic of highest current interest in
nuclear structure and reactions as well as in astrophysics. In particular, the
equation-of-state of asymmetric matter and the symmetry energy representing the
difference between the energy densities of neutron matter and of symmetric
nuclear matter are not sufficiently well constrained at present. The density
dependence of the symmetry energy is conventionally expressed in the form of
the slope parameter L describing the derivative with respect to density of the
symmetry energy at saturation. Results deduced from nuclear structure and
heavy-ion reaction data are distributed around a mean value L=60 MeV.
  Recent studies have more thoroughly investigated the density range that a
particular observable is predominantly sensitive to. Two thirds of the
saturation density is a value typical for the information contained in
nuclear-structure data. Higher values exceeding saturation have been shown to
be probed with meson production and collective flows at incident energies in
the range of up to about 1 GeV/nucleon.
  From the measurement of the elliptic-flow ratio of neutrons with respect to
light charged particles in recent experiments at the GSI laboratory, a new more
stringent constraint for the symmetry energy at suprasaturation density has
been deduced. It confirms, with a considerably smaller uncertainty, the
moderately soft to linear density dependence of the symmetry energy previously
deduced from the FOPI-LAND data. Future opportunities offered by FAIR will be
discussed.",1610.03650v1
2018-05-02,Robust Particle Density Tempering for State Space Models,"Density tempering (also called density annealing) is a sequential Monte Carlo
approach to Bayesian inference for general state models; it is an alternative
to Markov chain Monte Carlo. When applied to state space models, it moves a
collection of parameters and latent states (which are called particles) through
a number of stages, with each stage having its own target distribution. The
particles are initially generated from a distribution that is easy to sample
from, e.g. the prior; the target at the final stage is the posterior
distribution. Tempering is usually carried out either in batch mode, involving
all the data at each stage, or sequentially with observations added at each
stage, which is called data tempering. Our paper proposes efficient Markov
moves for generating the parameters and states for each stage of particle based
density tempering. This allows the proposed SMC methods to increase (scale up)
the number of parameters and states that can be handled. Most of the current
literature uses a pseudo-marginal Markov move step with the states integrated
out, and the parameters generated by a random walk proposal; although this
strategy is general, it is very inefficient when the states or parameters are
high dimensional. We also build on the work of Dufays (2016) and make data
tempering more robust to outliers and structural changes for models with
intractable likelihoods by adding batch tempering at each stage. The
performance of the proposed methods is evaluated using univariate stochastic
volatility models with outliers and structural breaks and high dimensional
factor stochastic volatility models having both many parameters and many latent
states.",1805.00649v3
2014-02-21,Density of states of interacting quantum wires with impurities: a Dyson equation approach,"We calculate the density of states for an interacting quantum wire in the
presence two impurities of arbitrary potential strength. To perform this
calculation, we describe the Coulomb interactions in the wire within the
Tomonaga-Luttinger liquid theory. After establishing and solving the Dyson
equation for the fermionic retarded Green's functions, we study how the profile
of the local density of states is affected by the interactions in the entire
range of impurity potentials. Same as in the non-interacting case, when
increasing the impurity strength, the central part of the wire becomes more and
more disconnected from the semi-infinite leads, and discrete localized states
begin to form; the width of the corresponding peaks in the spectrum depends on
the interaction strength. As expected from the Luttinger liquid theory,
impurities also induce a reduction of the local density of states at small
energies. Two other important aspects are highlighted: the appearance of an
extra-modulation in the density of states at non-zero Fermi momentum when
interactions are present, and the fact that forward scattering must be taken
into account in order to recover the Coulomb blockade regime for strong
impurities.",1402.5285v2
2004-09-20,Tomographic reconstruction of quantum correlations in excited Bose-Einstein condensates,"We propose to use quantum tomography to characterize the state of a perturbed
Bose-Einstein condensate. We assume knowledge of the number of particles in the
zero-wave number mode and of density distributions in space at different times,
and we treat the condensate in the Bogoliubov approximation. For states that
can be treated with the Gross-Pitaevskii equation, we find that the
reconstructed density operator gives excellent predictions of the second
moments of the atomic creation- and annihilation operators, including the
one-body density matrix. Additional inclusion of the momentum distribution at
one point of time enables somewhat reliable predictions to be made for the
second moments for mixed states, making it possible to distinguish between
coherent and thermal perturbations of the condensate. Finally, we find that
with observation of the zero-wave number mode's anomalous second moment the
reconstructed density operator gives reliable predictions of the second moments
of locally amplitude squeezed states.",0409500v1
2002-03-16,"Groupoids, von Neumann Algebras and the Integrated Density of States","We study spectral properties of random operators in the general setting of
groupoids and von Neumann algebras. In particular, we establish an explicit
formula for the canonical trace of the von Neumann algebra of random operators
and define an abstract density of states.
  The general setting applies to many examples studied before while we lay
special emphasis on a new one: random Schr\""odinger operators on manifolds. In
this case, we show that the distribution function of the abstract density of
states coincides with the integrated density of states defined via an
exhaustion procedure.
  The presentation is as explicit as possible, yet abstract enough to cover
many examples studied so far. We extract parts of Connes' noncommutative
integration theory, present them in a self contained manner and use them in our
proofs. By reason of illustration, we parallely give more direct proofs for our
main example, whenever possible.
  (The second version contains a detailed discussion of the application of the
abstract results to Hamiltonians associated to tilings and percolation graphs.",0203026v2
2000-11-16,Extension of Kohn-Sham theory to excited states by means of an off-diagonal density array,"Early work extending the Kohn-Sham theory to excited states utilized an
ensemble average of the Hamiltonian considered as a functional of the
corresponding average density. We propose and develop an alternative that
utilizes the matrix elements of the density operator taken between any two
states of the included space. The new theory is also based on a variational
principle for the trace of the Hamiltonian over a selected space of states
viewed, however, as a functional of the associated array of matrix elements of
the density. It leads to a matrix generalization of Kohn-Sham theory. To
illustrate the formalism, we study a suitably defined weak-coupling limit and
derive from it an eigenvalue equation that has the form of the random phase
approximation. The result can be identified with a similar equation derived
directly from the time-dependent Kohn-Sham equation that has been applied
recently with considerable success to molecular excitations. We prove, within
the defined approximations, that the eigenvalues can be interpreted as true
excitation energies.",0011039v2
2004-12-03,"Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI","Wavefunctions of complex lanthanide atoms NdI, PmI and SmI, obtained via
multi-configuration Dirac-Fock method, are analyzed for density of states in
terms of partial densities, strength functions ($F_k(E)$), number of principal
components ($\xi_2(E)$) and occupancies ($\lan n_\alpha \ran^E$) of single
particle orbits using embedded Gaussian orthogonal ensemble of one plus
two-body random matrix ensembles [EGOE(1+2)]. It is seen that density of states
are in general multi-modal, $F_k(E)$'s exhibit variations as function of the
basis states energy and $\xi_2(E)$'s show structures arising from localized
states. The sources of these departures from EGOE(1+2) are investigated by
examining the partial densities, correlations between $F_k(E)$, $\xi_2(E)$ and
$\lan n_\alpha \ran^E$ and also by studying the structure of the Hamiltonian
matrices. These studies point out the operation of EGOE(1+2) but at the same
time suggest that weak admixing between well separated configurations should be
incorporated into EGOE(1+2) for more quantitative description of chaos and
localization in NdI, PmI and SmI.",0412021v2
2011-10-06,Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene,"Electronic screening strongly renormalizes the linear bands which occur near
the Dirac crossing in graphene. The single bare Dirac crossing is split into
two individual Dirac-like points, which are separated in energy but still at
zero momentum relative to the K-point. A diamond-like structure occurs in
between as a result of the formation of plasmarons. In this work we explore the
combined effect of electron-electron and electron-phonon coupling on the
renormalized energy dispersion, the spectral function and on the electronic
density of states. We find that distinct signatures of the plasmaron structure
are observable in the density of states with the split Dirac points presenting
themselves as minima with quadratic dependence on energy about such points. By
examining the slopes of both the density of states and the renormalized
dispersion near the Fermi level, we illustrate how one can separate
$k$-dependent and $\omega$-dependent renormalizations and suggest how this
might allow for the isolation of the renormalization due to the electron-phonon
interaction from that of the electron-electron interaction.",1110.1404v2
2014-09-17,Addressing spectroscopic quality of covariant density functional theory,"The spectroscopic quality of covariant density functional theory has been
accessed by analyzing the accuracy and theoretical uncertainties in the
description of spectroscopic observables. Such analysis is first presented for
the energies of the single-particle states in spherical and deformed nuclei. It
is also shown that the inclusion of particle-vibration coupling improves the
description of the energies of predominantly single-particle states in medium
and heavy-mass spherical nuclei. However, the remaining differences between
theory and experiment clearly indicate missing physics and missing terms in
covariant energy density functionals. The uncertainties in the predictions of
the position of two-neutron drip line sensitively depend on the uncertainties
in the prediction of the energies of the single-particle states. On the other
hand, many spectroscopic observables in well deformed nuclei at ground state
and finite spin only weakly depend on the choice of covariant energy density
functional.",1409.4853v1
2022-09-28,Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches,"We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations
under a stress test by applying it to a physical problem with the worst
possible sign problem: the real time evolution of a non-integrable quantum spin
chain. Benchmarks against numerical exact diagonalisation and stochastic
reweighting are presented. Both MC methods, the DoS approach and reweighting,
allow for simulations of spin chains as long as $L=40$, far beyond exact
diagonalisability, though only for short evolution times $t\lesssim 1$. We
identify discontinuities of the density of states as one of the key problems in
the MC simulations and propose to calculate some of the dominant contributions
analytically, increasing the precision of our simulations by several orders of
magnitude. Even after these improvements the density of states is found highly
non-smooth and therefore the DoS approach cannot outperform reweighting. We
prove this implication theoretically and provide numerical evidence, concluding
that the DoS approach is not well suited for quantum real time simulations with
discrete degrees of freedom.",2209.13970v2
2018-04-20,A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings,"In this paper we address the stability of resonantly forced density waves in
dense planetary rings.
  Already by Goldreich & Tremaine (1978) it has been argued that density waves
might be unstable, depending on the relationship between the ring's viscosity
and the surface mass density.
  In the recent paper Schmidt et al. (2016) we have pointed out that when -
within a fluid description of the ring dynamics - the criterion for viscous
overstability is satisfied, forced spiral density waves become unstable as
well.
  In this case, linear theory fails to describe the damping, but nonlinearity
of the underlying equations guarantees a finite amplitude and eventually a
damping of the wave.
  We apply the multiple scale formalism to derive a weakly nonlinear damping
relation from a hydrodynamical model.
  This relation describes the resonant excitation and nonlinear viscous damping
of spiral density waves in a vertically integrated fluid disk with density
dependent transport coefficients.
  The model consistently predicts density waves to be (linearly) unstable in a
ring region where the conditions for viscous overstability are met.
  Sufficiently far away from the Lindblad resonance, the surface mass density
perturbation is predicted to saturate to a constant value due to nonlinear
viscous damping.
  The wave's damping lengths of the model depend on certain input parameters,
such as the distance to the threshold for viscous overstability in parameter
space and the ground state surface mass density.",1804.07674v1
2020-06-24,Variable-density effects in incompressible non-buoyant shear-driven turbulent mixing layers,"The asymmetries that arise when a mixing layer involves two miscible fluids
of differing densities are investigated using incompressible (low-speed) direct
numerical simulations. The simulations are performed in the temporal
configuration with very large domain sizes, to allow the mixing layers to reach
prolonged states of fully-turbulent self-similar growth. Imposing a mean
density variation breaks the mean symmetry relative to the classical
single-fluid temporal mixing layer problem. Unlike prior variable-density
mixing layer simulations in which the streams are composed of the same fluids
with dissimilar thermodynamic properties, the density variations are presently
due to compositional differences between the fluid streams, leading to
different mixing dynamics. Variable-density (non-Boussinesq) effects introduce
strong asymmetries in the flow statistics that can be explained by the
strongest turbulence increasingly migrating to the lighter fluid side as free
stream density difference increases. Interface thickness growth rates also
reduce, with some thickness definitions particularly sensitive to the
corresponding changes in alignment between density and streamwise velocity
profiles. Additional asymmetries in the sense of statistical distributions of
densities at a given position within the mixing layer reveal that fine scales
of turbulence are preferentially sustained in lighter fluid, which also is
where fastest mixing occurs. These effects influence statistics involving
density fluctuations, which have important implications for mixing and more
complicated phenomena that are sensitive to the mixing dynamics, such as
combustion.",2006.13492v1
2021-12-16,Real-space density kernel method for Kohn-Sham density functional theory calculations at high temperature,"Kohn-Sham density functional theory calculations using conventional
diagonalization based methods become increasingly expensive as temperature
increases due to the need to compute increasing numbers of partially occupied
states. We present a density matrix based method for Kohn-Sham calculations at
high temperature that eliminates the need for diagonalization entirely, thus
reducing the cost of such calculations significantly. Specifically, we develop
real-space expressions for the electron density, electronic free energy,
Hellmann-Feynman forces, and Hellmann-Feynman stress tensor in terms of an
orthonormal auxiliary orbital basis and its density kernel transform, the
density kernel being the matrix representation of the density operator in the
auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we
next develop an approach akin to Clenshaw-Curtis spectral quadrature to
calculate the individual columns of the density kernel based on the Fermi
operator expansion in Chebyshev polynomials; and employ a similar approach to
evaluate band structure and entropic energy components. We implement the
proposed formulation in the SPARC electronic structure code, using which we
show systematic convergence of the aforementioned quantities to exact
diagonalization results, and obtain significant speedups relative to
conventional diagonalization based methods. Finally, we employ the new method
to compute the self-diffusion coefficient and viscosity of aluminum at 116,045
K from Kohn-Sham quantum molecular dynamics, where we find agreement with
previous more approximate orbital-free density functional methods.",2112.08639v1
2012-12-11,Kondo effect with diverging hybridization: possible realization in graphene with vacancies,"We investigate Kondo physics in a host with a strongly diverging density of
states. This study is motivated by a recent work on vacancies in the graphene
honeycomb lattice, whose density of states is enhanced at low energies due to
potential scattering. The generalized quantum impurity model describing the
vacancy is shown to support a spin-1/2 (doublet) Kondo phase. The special role
played by a diverging host density of states is examined in detail, with
distinctive signatures associated with the powerlaw Kondo effect shown to
appear in thermodynamic quantities and the scattering t matrix, with a strongly
enhanced Kondo temperature. Although the effective Kondo model supports a novel
stable phase characterized by strong renormalized particle-hole asymmetry, we
find that this phase cannot in fact be accessed in the full Anderson model. In
the more realistic case where the divergence in the host density of states is
cut off at low energies, a crossover is generated between pristine powerlaw
Kondo physics and a regular Kondo strong coupling state.",1212.2631v2
2012-09-13,Exact Density-Functionals with Initial-State Dependence and Memory,"We analytically construct the wave function that, for a given initial state,
produces a prescribed density for a quantum ring with two non-interacting
particles in a singlet state. In this case the initial state is completely
determined by the initial density, the initial time-derivative of the density
and a single integer that characterizes the (angular) momentum of the system.
We then give an exact analytic expression for the exchange-correlation
potential that relates two non-interacting systems with different initial
states. This is used to demonstrate how the Kohn-Sham procedure predicts the
density of a reference system without the need of solving the reference
system's Schr\""odinger equation. We further numerically construct the
exchange-correlation potential for an analytically solvable system of two
electrons on a quantum ring with a squared cosine two-body interaction. For the
same case we derive an explicit analytic expression for the
exchange-correlation kernel and analyze its frequency-dependence (memory) in
detail. We compare the result to simple adiabatic approximations and
investigate the single-pole approximation. These approximations fail to
describe the doubly-excited states, but perform well in describing the
singly-excited states.",1209.2949v3
2015-11-17,Gap state analysis in electric-field-induced band gap for bilayer graphene,"The origin of the low current on/off ratio at room temperature in dual-gated
bilayer graphene field-effect transistors is considered to be the variable
range hopping in gap states. However, the quantitative estimation of gap states
has not been conducted. Here, we report the systematic estimation of the energy
gap by both quantum capacitance and transport measurements and the density of
states for gap states by the conductance method. An energy gap of ~250 meV is
obtained at the maximum displacement field of ~3.1 V/nm, where the current
on/off ratio of ~3*10^3 is demonstrated at 20 K. The density of states for the
gap states are in the range from the latter half of 10^12 to 10^13 eV^-1cm^-2.
Although the large amount of gap states at the interface of high-k
oxide/bilayer graphene limits the current on/off ratio at present, our results
suggest that the reduction of gap states below ~10^11 eV^-1cm^-2 by continual
improvement of the gate stack makes bilayer graphene a promising candidate for
future nanoelectronic device applications.",1511.05231v1
2000-11-30,Separable states are more disordered globally than locally,"A remarkable feature of quantum entanglement is that an entangled state of
two parties, Alice (A) and Bob (B), may be more disordered locally than
globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is
known that satisfaction of this inequality implies that a state is
non-separable. In this paper we prove the stronger result that for separable
states the vector of eigenvalues of the density matrix of system AB is
majorized by the vector of eigenvalues of the density matrix of system A alone.
This gives a strong sense in which a separable state is more disordered
globally than locally and a new necessary condition for separability of
bipartite states in arbitrary dimensions. We also investigate the extent to
which these conditions are sufficient to characterize separability, exhibiting
examples that show separability cannot be characterized solely in terms of the
local and global spectra of a state. We apply our conditions to give a simple
proof that non-separable states exist sufficiently close to the completely
mixed state of $n$ qudits.",0011117v1
2020-08-28,Entanglement spectrum of geometric states,"The reduced density matrix of a given subsystem, denoted by $\rho_A$,
contains the information on subregion duality in a holographic theory. We may
extract the information by using the spectrum (eigenvalue) of the matrix,
called entanglement spectrum in this paper. We evaluate the density of
eigenstates, one-point and two-point correlation functions in the
microcanonical ensemble state $\rho_{A,m}$ associated with an eigenvalue
$\lambda$ for some examples, including a single interval and two intervals in
vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state
with $\lambda_0$ which can be seen as an approximate state of $\rho_A$. The
parameter $\lambda_0$ is obtained in the two examples. For a general geometric
state, the approximate microcanonical ensemble state also exists. The parameter
$\lambda_0$ is associated with the entanglement entropy of $A$ and R\'enyi
entropy in the limit $n\to \infty$. As an application of the above conclusion
we reform the equality case of the Araki-Lieb inequality of the entanglement
entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo
information. We show the constraints on the eigenstates. Finally, we point out
some unsolved problems and their significance on understanding the geometric
states.",2008.12430v2
2019-05-01,Collective Dynamics in a Monolayer of Squirmers Confined to a Boundary by Gravity,"We present a hydrodynamic study of a monolayer of squirmer model
microswimmers confined to a boundary by strong gravity using the simulation
method of multi-particle collision dynamics. The squirmers interact with each
other via their self-generated hydrodynamic flow fields and thereby form a
variety of fascinating dynamic states when density and squirmer type are
varied. Weak pushers, neutral squirmers, and pullers have an upright
orientation. With their flow fields they push neighbors away and thereby form a
hydrodynamic Wigner fluid at lower densities. Furthermore, states of
fluctuating chains and trimers, of kissing, and at large densities a global
cluster exist. Finally, pushers at all densities can tilt against the wall
normal and their in-plane velocities align to show swarming. It turns into
chaotic swarming for strong pushers at high densities. We characterize all
these states quantitatively.",1905.03348v2
2019-05-24,Strange metal behaviour from charge density fluctuations in cuprates,"Besides the mechanism responsible for high critical temperature
superconductivity, the grand unresolved issue of the cuprates is the occurrence
of a strange metallic state above the so-called pseudogap temperature $T^*$.
Even though such state has been successfully described within a
phenomenological scheme, the so-called Marginal Fermi-Liquid theory, a
microscopic explanation is still missing. However, recent resonant X-ray
scattering experiments identified a new class of charge density fluctuations
characterized by low characteristic energies and short correlation lengths,
which are related to the well-known charge density waves. These fluctuations
are present over a wide region of the temperature-vs-doping phase diagram and
extend well above $T^*$. Here we investigate the consequences of charge density
fluctuations on the electron and transport properties and find that they can
explain the strange metal phenomenology. Therefore, charge density fluctuations
are likely the long-sought microscopic mechanism underlying the peculiarities
of the metallic state of cuprates.",1905.10232v2
2022-07-26,Density-driven higher-order topological phase transitions in amorphous solids,"Amorphous topological states, which are independent of the specific spatial
distribution of microscopic constructions, have gained much attention.
Recently, higher-order topological insulators, which are a new class of
topological phases of matter, have been proposed in amorphous systems. Here, we
propose a density-driven higher-order topological phase transition in a
two-dimensional amorphous system. We demonstrate that the amorphous system
hosts a topological trivial phase at low density. With an increase in the
density of lattice sites, the topological trivial phase converts to a
higher-order topological phase characterized by a quantized quadrupole moment
and the existence of topological corner states. Furthermore, we confirm that
the density-driven higher-order topological phase transition is size dependent.
In addition, our results should be general and equally applicable to
three-dimensional amorphous systems. Our findings may greatly enrich the study
of higher-order topological states in amorphous systems.",2207.12971v2
2024-01-29,Astrophysical Equation-of-State Constraints on the Color-Superconducting Gap,"We demonstrate that astrophysical constraints on the dense-matter equation of
state place an upper bound on the color-superconducting gap in dense matter
above the transition from nuclear matter to quark matter. Pairing effects in
the color-flavor locked (CFL) quark matter phase increase the pressure at high
density, and if this effect is sufficiently large then the requirements of
causality and mechanical stability make it impossible to reach such a pressure
in a way that is consistent with what is known at lower densities. The
intermediate-density equation of state is inferred by considering extensions of
chiral effective field theory (CEFT) to neutron star densities, and
conditioning these using current astrophysical observations of neutron star
radius, maximum mass, and tidal deformability (PSR J0348+0432, PSR J1624-2230,
PSR J0740+6620, GW170817). At baryon number chemical potential $\mu =
2.6~\text{GeV}$ we find a 95% upper limit on the CFL pairing gap $\Delta$ of
$457~\text{MeV}$ using overly conservative assumptions and $216~\text{MeV}$
with more reasonable assumptions. This constraint may be strengthened by future
astrophysical measurements as well as by future advances in high density QCD
calculations.",2401.16253v1
2008-01-08,The low-energy excitation spectrum of one-dimensional dipolar quantum gases,"We determine the excitation spectrum of a bosonic dipolar quantum gas in a
one-dimensional geometry, from the dynamical density-density correlation
functions simulated by means of Reptation Quantum Monte Carlo techniques. The
excitation energy is always vanishing at the first vector of the reciprocal
lattice in the whole crossover from the liquid-like at low density to the
quasi-ordered state at high density, demonstrating the absence of a roton
minimum. Gaps at higher reciprocal lattice vectors are seen to progressively
close with increasing density, while the quantum state evolves into a
quasi-periodic structure. The simulational data together with the
uncertainty-principle inequality also provide a rigorous proof of the absence
of long-range order in such a super-strongly correlated system. Our conclusions
confirm that the dipolar gas is in a Luttinger-liquid state, significantly
affected by the dynamical correlations. The connection with ongoing experiments
is also discussed.",0801.1200v1
2000-07-26,Many-body theory of pump-probe spectra for highly excited semiconductors,"We present a unified theory for pump-probe spectra in highly excited
semiconductors, which is applicable throughout the whole density regime
including the high-density electron-hole BCS state and the low-density
excitonic Bose-Einstein condensate (BEC). The analysis is based on the BCS-like
pairing theory combined with the Bethe-Salpeter (BS) equation, which first
enables us to incorporate the state-filling effect, the band-gap
renormalization and the strong/weak electron-hole pair correlations in a
unified manner. We show that the electron-hole BCS state is distinctly
stabilized by the intense pump-light, and this result strongly suggests that
the macroscopic quantum state can be observed under the strong photoexcitation.
The calculated spectra considerably deviate from results given by the BCS-like
mean field theory and the simple BS equation without electron-hole pair
correlation especially in the intermediate density states between the
electron-hole BCS state and the excitonic BEC state. In particular, we find the
sharp stimulated emission and absorption lines which originate from the optical
transition accompanied by the collective phase fluctuation mode in the
electron-hole BCS state. From the pump-probe spectral viewpoint, we show that
this fluctuation mode changes to the exciton mode with decreasing carrier
density",0007405v1
2005-12-08,Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices,"We present an extensive numerical study of ground-state properties of
confined repulsively interacting fermions on one-dimensional optical lattices.
Detailed predictions for the atom-density profiles are obtained from parallel
Kohn-Sham density-functional calculations and quantum Monte Carlo simulations.
The density-functional calculations employ a Bethe-Ansatz-based local-density
approximation for the correlation energy, which accounts for Luttinger-liquid
and Mott-insulator physics. Semi-analytical and fully numerical formulations of
this approximation are compared with each other and with a cruder
Thomas-Fermi-like local-density approximation for the total energy. Precise
quantum Monte Carlo simulations are used to assess the reliability of the
various local-density approximations, and in conjunction with these allow to
obtain a detailed microscopic picture of the consequences of the interplay
between particle-particle interactions and confinement in one-dimensional
systems of strongly correlated fermions.",0512184v1
2003-12-16,Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector spin-orbit terms,"We extend a recent calculation of the nuclear energy density functional in
the systematic framework of chiral perturbation theory by computing the
isovector spin-orbit terms: $(\vec \nabla \rho_p- \vec \nabla \rho_n)\cdot(\vec
J_p-\vec J_n) G_{so}(k_f)+ (\vec J_p-\vec J_n)^2 G_J(k_f)$. The calculation
includes the one-pion exchange Fock diagram and the iterated one-pion exchange
Hartree and Fock diagrams. From these few leading order contributions in the
small momentum expansion one obtains already a good equation of state of
isospin-symmetric nuclear matter. We find that the parameterfree results for
the (density-dependent) strength functions $G_{so}(k_f)$ and $G_J(k_f)$ agree
fairly well with that of phenomenological Skyrme forces for densities $\rho >
\rho_0/10$. At very low densities a strong variation of the strength functions
$G_{so}(k_f)$ and $G_J(k_f)$ with density sets in. This has to do with chiral
singularities $m_\pi^{-1}$ and the presence of two competing small mass scales
$k_f$ and $m_\pi$. The novel density dependencies of $G_{so}(k_f)$ and
$G_J(k_f)$ as predicted by our parameterfree (leading order) calculation should
be examined in nuclear structure calculations.",0312059v1
2007-02-20,Application of density dependent parametrization models to asymmetric nuclear matter,"Density dependent parametrization models of the nucleon-meson effective
couplings, including the isovector scalar \delta-field, are applied to
asymmetric nuclear matter. The nuclear equation of state and the neutron star
properties are studied in an effective Lagrangian density approach, using the
relativistic mean field hadron theory. It is known that the introduction of a
\delta-meson in the constant coupling scheme leads to an increase of the
symmetry energy at high density and so to larger neutron star masses, in a pure
nucleon-lepton scheme. We use here a more microscopic density dependent model
of the nucleon-meson couplings to study the properties of neutron star matter
and to re-examine the \delta-field effects in asymmetric nuclear matter. Our
calculations show that, due to the increase of the effective \delta coupling at
high density, with density dependent couplings the neutron star masses in fact
can be even reduced.",0702064v1
2009-04-06,On the density dependence of single-proton and two-proton knockout reactions under quasifree conditions,"We consider high-energy quasifree single- and two-proton knockout reactions
induced by electrons and protons and address the question what target-nucleus
densities can be effectively probed after correcting for nuclear attenuation
(initial- and final-state interactions). Our calculations refer to ejected
proton kinetic energies of 1.5 GeV, the reactions (e,e'p), (\gamma,pp) and
(p,2p) and a carbon target. It is shown that each of the three reactions is
characterized by a distinctive sensitivity to the density of the target
nucleus. The bulk of the (\gamma,pp) strength stems from the high-density
regions in the deep nuclear interior. Despite the strong attenuation, sizable
densities can be probed by (p,2p) provided that the energy resolution allows
one to pick nucleons from s orbits. The effective mean densities that can be
probed in high-energy (e,e'p) are of the order of 30-50% of the nuclear
saturation density.",0904.0914v1
2011-02-08,Density Waves in Layered Systems with Fermionic Polar Molecules,"A layered system of two-dimensional planes containing fermionic polar
molecules can potentially realize a number of exotic quantum many-body states.
Among the predictions, are density-wave instabilities driven by the anisotropic
part of the dipole-dipole interaction in a single layer. However, in typical
multilayer setups it is reasonable to expect that the onset and properties of a
density-wave are modified by adjacent layers. Here we show that this is indeed
the case. For multiple layers the critical strength for the density-wave
instability decreases with the number of layers. The effect depends on density
and is more pronounced in the low density regime. The lowest solution of the
instability corresponds to the density waves in the different layers being
in-phase, whereas higher solutions have one or several adjancet layers that are
out of phase. The parameter regime needed to explore this instability is within
reach of current experiments.",1102.1551v3
2012-05-10,"Beyond-mean-field study of the possible ""bubble"" structure of 34Si","Recent self-consistent mean-field calculations predict a substantial
depletion of the proton density in the interior of 34Si. In the present study,
we investigate how correlations beyond the mean field modify this finding. The
framework of the calculation is a particle-number and angular-momentum
projected Generator Coordinate Method based on
Hartree-Fock-Bogoliubov+Lipkin-Nogami states with axial quadrupole deformation.
The parametrization SLy4 of the Skyrme energy density functional is used
together with a density-dependent pairing energy functional. For the first
time, the generator coordinate method is applied to the calculation of charge
and transition densities. The impact of pairing correlations, symmetry
restorations and shape mixing on the density profile is analyzed step by step.
All these effects significantly alter the radial density profile, and tend to
bring it closer to a Fermi-type density distribution.",1205.2262v1
2020-02-28,Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities,"In this paper we introduce spatiotemporal constraints for trajectories, i.e.,
restrictions that the trajectory must be in some part of the state space
(spatial constraint) at some point in time (temporal constraint).
Spatiotemporal contraints on trajectories can be used to answer a range of
important questions, including, e.g., ""where did the person that were in area A
at time t, go afterwards?"". We discuss how multiple constraints can be combined
into sets of constraints, and we then apply sets of constraints to set of
trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM)
densities. For Poisson target birth, the exact posterior density is PMBM for
both point targets and extended targets. In the paper we show that if the
unconstrained set of trajectories density is PMBM, then the constrained density
is also PMBM. Examples of constrained trajectory densities motivate and
illustrate the key results.",2002.12696v1
2023-12-18,Density Descent for Diversity Optimization,"Diversity optimization seeks to discover a set of solutions that elicit
diverse features. Prior work has proposed Novelty Search (NS), which, given a
current set of solutions, seeks to expand the set by finding points in areas of
low density in the feature space. However, to estimate density, NS relies on a
heuristic that considers the k-nearest neighbors of the search point in the
feature space, which yields a weaker stability guarantee. We propose Density
Descent Search (DDS), an algorithm that explores the feature space via gradient
descent on a continuous density estimate of the feature space that also
provides stronger stability guarantee. We experiment with DDS and two density
estimation methods: kernel density estimation (KDE) and continuous normalizing
flow (CNF). On several standard diversity optimization benchmarks, DDS
outperforms NS, the recently proposed MAP-Annealing algorithm, and other
state-of-the-art baselines. Additionally, we prove that DDS with KDE provides
stronger stability guarantees than NS, making it more suitable for adaptive
optimizers. Furthermore, we prove that NS is a special case of DDS that
descends a KDE of the feature space.",2312.11331v1
1996-05-16,Anharmonic Decay of Vibrational States in Amorphous Silicon,"Anharmonic decay rates are calculated for a realistic atomic model of
amorphous silicon. The results show that the vibrational states decay on
picosecond timescales and follow the two-mode density of states, similar to
crystalline silicon, but somewhat faster. Surprisingly little change occurs for
localized states. These results disagree with a recent experiment.",9605101v1
1993-01-19,Evolution of Pure States into Mixed States,"In the formulation of Banks, Peskin and Susskind, we show that one can
construct evolution equations for the quantum mechanical density matrix $\rho$
with operators which do not commute with hamiltonian which evolve pure states
into mixed states, preserve the normalization and positivity of $\rho$ and
conserve energy. Furthermore, it seems to be different from a quantum
mechanical system with random sources.",9301082v2
2009-01-23,Guessing Quantum Ensemble Using Laplace Principle,"For a mixed quantum state with density matrix $\rho$ there are infinitely
many ensembles of pure quantum states, which average to $\rho$. Starting from
Laplace principle of insufficient reason (not to give \emph{a priori}
preference to any particular state), we derive a `natural' distribution of pure
states averaging to $\rho$, which is `more spread' than all the others.",0901.3771v1
2013-10-22,A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane,"In this paper we construct many `new' Gibbs states of the Ising model on the
Lobachevsky plane, the millefeuilles. Unlike the usual states on the integer
lattices, our foliated states have infinitely many interfaces. The interfaces
are rigid and fill the Lobachevsky plane with positive density.",1310.5898v1
2015-01-07,Black brane steady states,"We follow the evolution of an asymptotically AdS black brane with a fixed
temperature gradient at spatial infinity until a steady state is formed. The
resulting energy density and energy flux of the steady state in the boundary
theory are compared to a conjecture on the behavior of steady states in
conformal field theories. Very good agreement is found.",1501.01627v2
2021-09-18,Tensor Network States for Vibrational Spectroscopy,"This review elaborates on the foundation, the advantages, and the prospects
of tensor network representations for quantum states in vibrational
spectroscopy. The focus is on the recently introduced matrix product state
decomposition of nuclear quantum states and its optimization by the density
matrix renormalization group algorithm.",2109.08961v1
1999-12-10,Segregation and charge-density-wave order in the spinless Falicov-Kimball model,"The spinless Falicov-Kimball model is solved exactly in the limit of
infinite-dimensions on both the hypercubic and Bethe lattices. The competition
between segregation, which is present for large U, and charge-density-wave
order, which is prevalent at moderate U, is examined in detail. We find a rich
phase diagram which displays both of these phases. The model also shows
nonanalytic behavior in the charge-density-wave transition temperature when U
is large enough to generate a correlation-induced gap in the single-particle
density of states.",9912178v1
2003-04-30,Electronic and Structural Properties of a 4d-Perovskite: Cubic Phase of SrZrO$_3$,"First-principles density functional calculations are performed within the
local density approximation to study the electronic properties of SrZrO$_3$, an
insulating 4d-perovskite, in its high-temperature cubic phase, above 1400 K, as
well as the generic 3d-perovskite SrTiO$_3$, which is also a d^0-insulator and
cubic above 105 K, for comparison reasons. The energy bands, density of states
and charge density distributions are obtained and a detailed comparison between
their band structures is presented. The results are discussed also in terms of
the existing data in the literature for both oxides.",0304703v1
1996-05-30,Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus,"We consider a very large ultra-relativistic nucleus. Assuming a simple model
of the nucleus and weak coupling we find a classical solution for the gluon
field of the nucleus and construct the two-dimensional color charge density for
McLerran-Venugopalan model out of it. We prove that the density of states
distribution, as a function of color charge density, is Gaussian, confirming
the assumption made by McLerran and Venugopalan.",9605446v2
2000-03-22,Color Superconductivity in High Density Effective Theory,"In this talk, I discuss the recent development in color superconductivity in
terms of effective field theory. By investigating the Cooper pair gap equations
at high density, we see that the effective theory simplifies the gap analysis
very much, especially in finding the ground state, the precise form of the gap,
and the critical temperature. Furthermore, the effective theory enables us to
estimate the critical density for color superconductivity, which is found to be
around $230~{\rm MeV}$ in the hard-dense-loop approximation. Finally, I briefly
mention the low-lying spectra of color superconductor at high density.",0003215v1
2005-02-04,First-Principles Method for Open Electronic Systems,"We prove the existence of the exact density-functional theory formalism for
open electronic systems, and develop subsequently an exact time-dependent
density-functional theory (TDDFT) formulation for the dynamic response. The
TDDFT formulation depends in principle only on the electron density of the
reduced system. Based on the nonequilibrium Green's function technique, it is
expressed in the form of the equation of motion for the reduced single-electron
density matrix, and this provides thus an efficient numerical approach to
calculate the dynamic properties of open electronic systems. In the
steady-state limit, the conventional first-principles nonequilibrium Green's
function formulation for the current is recovered.",0502021v1
2007-07-19,Dark Energy in Global Brane Universe,"We discuss the exact solutions of brane universes and the results indicate
the Friedmann equations on the branes are modified with a new density term.
Then, we assume the new term as the density of dark energy. Using Wetterich's
parametrization equation of state (EOS) of dark energy, we obtain the new term
varies with the red-shift z. Finally, the evolutions of the mass density
parameter $\Omega_2$, dark energy density parameter $\Omega_x$ and deceleration
parameter q_2 are studied.",0707.2825v3
2007-12-20,Non-equilibrium thermodynamics for functionals of current and density,"We study a stochastic many-body system maintained in an non-equilibrium
steady state. Probability distribution functional of the time-integrated
current and density is shown to attain a large-deviation form in the long-time
asymptotics. The corresponding Current-Density Cramer Functional (CDCF) is
explicitly derived for irreversible Langevin dynamics and discrete-space Markov
chains. We also show that the Cramer functionals of other linear functionals of
density and current, like work generated by a force, are related to CDCF in a
way reminiscent of variational relations between different thermodynamic
potentials. The general formalism is illustrated with a model example.",0712.3542v1
2008-04-01,Passive Convection of Density Fluctuations in the Local Interstellar Medium,"We have developed a time-dependent three-dimensional model of isotropic,
adiabatic, and compressible magnetohydrodynamic plasma to understand nonlinear
cascades of density fluctuations in local interstellar medium. Our simulations,
describing evolution of initial supersonic, super Alfv\'enic plasma modes,
indicate that nonlinear interactions lead to damping of plasma motion. During
the process, turbulent cascades are governed predominantly by the Alfv\'enic
modes and velocity field fluctuations evolve towards a state charachterized by
near incompressibility. Consequently, density field is advected passively by
the velocity field. Our findings thus demonstrate that the observed density
fluctuations in the interstellar medium are the structures passively convected
by the background velocity field.",0804.0045v1
2009-11-17,Non-universal lower bound for the shear viscosity to entropy density ratio,"The lower bound of the shear viscosity to entropy density ratio is examined
using an exact representation of the ratio through the density of states. It is
shown that the lower bound in a generic physical system is not universal, its
value is determined by the entropy density. Some examples of physical systems
are discussed in the paper where one can expect violation of the conformal
1/4pi value.",0911.3248v2
2011-07-21,Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential,"We propose a new approach to approximate the exchange and correlation (XC)
functional in density functional theory. The XC potential is considered as an
electrostatic potential, generated by a fictitious XC density, which is in turn
a functional of the electronic density. We apply the approach to develop a
correction scheme that fixes the asymptotic behavior of any approximated XC
potential for finite systems. Additionally, the correction procedure gives the
value of the derivative discontinuity; therefore it can directly predict the
fundamental gap as a ground-state property.",1107.4339v2
2012-05-11,Magnetic penetration depth in the presence of a spin-density wave in multiband superconductors at zero temperature,"We present a theoretical description of the London penetration depth of a
multi-band superconductor in the case when both superconducting and
spin-density wave orders coexist. We focus on clean systems and zero
temperature to emphasize the effect of the two competing orders. Our
calculation shows that the supefluid density closely follows the evolution of
the superconducting order parameter as doping is increased, saturating to a BCS
value in the pure superconducting state. Furthermore, we predict a strong
anisotropic in-pane penetration depth induced by the spin-density wave order.",1205.2564v1
2015-11-21,Stochastic Estimation of Nuclear Level Density in the Nuclear Shell Model: An Application to Parity-Dependent Level Density in $^{58}$Ni,"We introduce a novel method to obtain level densities in large-scale
shell-model calculations. Our method is a stochastic estimation of eigenvalue
count based on a shifted Krylov-subspace method, which enables us to obtain
level densities of huge Hamiltonian matrices. This framework leads to a
successful description of both low-lying spectroscopy and the experimentally
observed equilibration of $J^\pi=2^+$ and $2^-$ states in $^{58}$Ni in a
unified manner.",1511.06840v2
2010-05-26,Infinite invariant densities for anomalous diffusion in optical lattices and other logarithmic potentials,"We solve the Fokker-Planck equation for Brownian motion in a logarithmic
potential. When the diffusion constant is below a critical value the solution
approaches a non-normalizable scaling state, reminiscent of an infinite
invariant density. With this non-normalizable density we obtain the phase
diagram of anomalous diffusion for this important process. We briefly discuss
the consequence for a range of physical systems including atoms in optical
lattices and charges in vicinity of long polyelectrolytes. Our work explains in
what sense the infinite invariant density and not Boltzmann's equilibrium
describes the long time limit of these systems.",1005.4737v1
2015-12-09,Shear viscosity over entropy density ratio with extended quasi-particles,"We consider an effective field theory description of beyond-quasi-particle
excitations aiming to associate the transport properties of the system with the
spectral density of states. Tuning various properties of the many-particle
correlations, we investigate how the robust microscopic features are translated
into the macroscopic observables like shear viscosity and entropy density. The
liquid-gas crossover is analysed using several examples. A thermal constraint
on the fluidity measure, the ratio of shear viscosity to entropy density, is
discussed.",1512.03001v3
2020-08-06,"Comment on ""Resolving spatial and energetic distributions of trap states in metal halide perovskite solar cells""","Ni et al. report minimum bulk trap densities of 10^11 cm-3 and 1-4 orders
change in interfacial trap densities derived from drive-level capacitance
profiling of lead halide perovskites. From basic electrostatic arguments, we
show that such bulk trap densities cannot be resolved for a p-i-n perovskite
solar cell for the reported layer thicknesses, while the apparent interfacial
charge densities are a consequence of the geometrical capacitance and of charge
injection into the perovskite layer.",2008.02892v2
2023-07-11,Ultra Electron Density Sensitivity for Surface Plasmons,"We investigate surface plasmons from a solid-state standpoint and highlight
their ultra electron density sensitivity. When a surface plasmon is excited on
a planar gold film by an evanescent wave from 625 nm incident light, only a
minute fraction of the surface electron density, approximately one thousandth,
participates in the process. By introducing a noise-depressed surface potential
modulation, we reduce the electron density to the order of 10 um-2, enabling
electron sensitivity on the order of 0.1 e. As a practical application, we
develop a surface plasmon resonance imaging method capable of detecting single
anions in solution at a concentration of 1 aM.",2307.04982v1
2004-05-06,Density Functional Theory of Multicomponent Quantum Dots,"Quantum dots with conduction electrons or holes originating from several
bands are considered. We assume the particles are confined in a harmonic
potential and assume the electrons (or holes) belonging to different bands to
be different types of fermions with isotropic effective masses. The density
functional method with the local density approximation is used. The increased
number of internal (Kohn-Sham) states leads to a generalisation of Hund's first
rule at high densities. At low densitites the formation of Wigner molecules is
favored by the increased internal freedom.",0405107v1
2004-06-11,Electronic Structure of a Chain-like Compound: TlSe,"An ab-initio pseudopotential calculation using density functional theory
within the local density approximation has been performed to investigate the
electronic properties of TlSe which is of chain-like crystal geometry. The
energy bands and effective masses along high symmetry directions, the density
of states and valence charge density distributions cut through various planes
are presented. The results have been discussed in terms of previously existing
experimental and theoretical data, and comparisons with similar compounds have
been made.",0406287v1
2006-03-20,Non-zero entropy density in the XY chain out of equilibrium,"The von Neumann entropy density of a block of n spins is proved to be
non-zero for large n in the non-equilibrium steady state of the XY chain
constructed by coupling a finite cutout of the chain to the two infinite parts
to its left and right which act as thermal reservoirs at different
temperatures. Moreover, the non-equilibrium density is shown to be strictly
greater than the density in thermal equilibrium.",0603049v2
2012-06-26,Exact density-functional potentials for time-dependent quasiparticles,"We calculate the exact Kohn-Sham potential that describes, within
time-dependent density-functional theory, the propagation of an electron
quasiparticle wavepacket of non-zero crystal momentum added to a ground-state
model semiconductor. The potential is observed to have a highly nonlocal
functional dependence on the charge density, in both space and time, giving
rise to features entirely lacking in local or adiabatic approximations. The
dependence of the non-equilibrium part of the Kohn-Sham electric field on the
local current and charge density is identified as a key element of the correct
Kohn-Sham functional.",1206.6035v1
2018-03-08,Shear-density coupling for a compressible single-component yield-stress fluid,"Flow behavior of a single-component yield stress fluid is addressed on the
hydrodynamic level. A basic ingredient of the model is a coupling between
fluctuations of density and velocity gradient via a Herschel-Bulkley-type
constitutive model. Focusing on the limit of low shear rates and high
densities, the model approximates well---but is not limited to---gently sheared
hard sphere colloidal glasses, where solvent effects are negligible. A detailed
analysis of the linearized hydrodynamic equations for fluctuations and the
resulting cubic dispersion relation reveals the existence of a range of
densities and shear rates with growing flow heterogeneity. In this regime,
after an initial transient, the velocity and density fields monotonically reach
a spatially inhomogeneous stationary profile, where regions of high shear rate
and low density coexist with regions of low shear rate and high density. The
steady state is thus maintained by a competition between shear-induced
enhancement of density inhomogeneities and relaxation via overdamped sound
waves. An analysis of the mechanical equilibrium condition provides a criterion
for the existence of steady state solutions. The dynamical evolution of the
system is discussed in detail for various boundary conditions, imposing either
a constant velocity, shear rate, or stress at the walls.",1803.03209v2
2018-02-13,Magnetic-field Induced Pair Density Wave State in the Cuprate Vortex Halo,"When very high magnetic fields suppress the superconductivity in underdoped
cuprates, an exceptional new electronic phase appears. It supports remarkable
and unexplained quantum oscillations and exhibits an unidentified density wave
(DW) state. Although generally referred to as a ""charge"" density wave (CDW)
because of the observed charge density modulations, theory indicates that this
could actually be the far more elusive electron-pair density wave state (PDW).
To search for evidence of a field-induced PDW in cuprates, we visualize the
modulations in the density of electronic states $N(\bf{r})$ within the halo
surrounding Bi$_2$Sr$_2$CaCu$_2$O$_8$ vortex cores. This reveals multiple
signatures of a field-induced PDW, including two sets of $N(\bf{r})$
modulations occurring at wavevectors $\bf{Q}_P$ and $2\bf{Q}_P$, both having
predominantly $s$-symmetry form factors, the amplitude of the latter decaying
twice as rapidly as the former, along with induced energy-gap modulations at
$\bf{Q}_P$ . Such a microscopic phenomenology is in detailed agreement with
theory for a field-induced primary PDW that generates secondary CDWs within the
vortex halo. These data indicate that the fundamental state generated by
increasing magnetic fields from the underdoped cuprate superconducting phase is
actually a PDW with approximately eight CuO$_2$ unit-cell periodicity ($\lambda
= 8a_0$) and predominantly $d$-symmetry form factor.",1802.04673v2
2016-04-07,Quantum state tomography via reduced density matrices,"Quantum state tomography via local measurements is an efficient tool for
characterizing quantum states. However it requires that the original global
state be uniquely determined (UD) by its local reduced density matrices (RDMs).
In this work we demonstrate for the first time a class of states that are UD by
their RDMs under the assumption that the global state is pure, but fail to be
UD in the absence of that assumption. This discovery allows us to classify
quantum states according to their UD properties, with the requirement that each
class be treated distinctly in the practice of simplifying quantum state
tomography. Additionally we experimentally test the feasibility and stability
of performing quantum state tomography via the measurement of local RDMs for
each class. These theoretical and experimental results advance the project of
performing efficient and accurate quantum state tomography in practice.",1604.02046v1
2015-04-19,Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration,"We experimentally construct a novel three-qubit entangled W-superposition
($\rm W \bar{\rm W}$) state on an NMR quantum information processor. We give a
measurement-based filtration protocol for the invertible local operation (ILO)
that converts the $\rm W \bar{\rm W}$ state to the GHZ state, using a register
of three ancilla qubits. Further we implement an experimental protocol to
reconstruct full information about the three-party $\rm W \bar{\rm W}$ state
using only two-party reduced density matrices. An intriguing fact unearthed
recently is that the $\rm W \bar{\rm W}$ state which is equivalent to the GHZ
state under ILO, is in fact reconstructible from its two-party reduced density
matrices, unlike the GHZ state. We hence demonstrate that although the $\rm W
\bar{\rm W}$ state is interconvertible with the GHZ state, it stores
entanglement very differently.",1504.04856v1
1996-01-14,The ground state of the two-leg Hubbard ladder: a density--matrix renormalization group study,"We present density-matrix renormalization group results for the ground state
properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an
insulating spin-gapped system, exhibiting a crossover from a spin-liquid to a
band-insulator as a function of the interchain hopping matrix element. When the
system is doped, there is a parameter range in which the spin gap remains. In
this phase, the doped holes form singlet pairs and the pair-field and the ""$4
k_F$"" density correlations associated with pair density fluctuations decay as
power laws, while the ""$2 k_F$"" charge density wave correlations decay
exponentially. We discuss the behavior of the exponents of the pairing and
density correlations within this spin gapped phase. Additional one-band
Luttinger liquid phases which occur in the large interband hopping regime are
also discussed.",9601047v1
2003-12-23,Density of States Method at Finite Isospin Density,"The density of states method is applied for lattice QCD at a finite isospin
density. The advantage of this method is that one can easily obtain results for
various values of parameters (quark mass, coupling constant and the number of
flavors). We compare results for the chiral condensate and the quark number
density with those from the R-algorithm and find that they are in good
agreement. By calculating the chiral condensate we obtain information on the
phase structure for various quark flavors and isospin chemical potentials. We
also show results for the chiral condensate at two different quark masses and
at two different isospin densities which are not easily obtainable in the
conventional Monte Carlo method.",0312038v2
2013-04-26,Direct microscopic calculations of nuclear level densities in the shell model Monte Carlo approach,"Nuclear level densities are crucial for estimating statistical nuclear
reaction rates. The shell model Monte Carlo method is a powerful approach for
microscopic calculation of state densities in very large model spaces. However,
these state densities include the spin degeneracy of each energy level, whereas
experiments often measure level densities in which each level is counted just
once. To enable the direct comparison of theory with experiments, we introduce
a method to calculate directly the level density in the shell model Monte Carlo
approach. The method employs a projection on the minimal absolute value of the
magnetic quantum number. We apply the method to nuclei in the iron region as
well as the strongly deformed rare-earth nucleus $^{162}$Dy. We find very good
agreement with experimental data including level counting at low energies,
charged particle spectra and Oslo method at intermediate energies, neutron and
proton resonance data, and Ericson's fluctuation analysis at higher excitation
energies.",1304.7258v1
2013-12-11,Chiral density wave in nuclear matter,"Inspired by recent work on inhomogeneous chiral condensation in cold, dense
quark matter within models featuring quark degrees of freedom, we investigate
the chiral density-wave solution in nu- clear matter at zero temperature and
nonvanishing baryon number density in the framework of the so-called extended
linear sigma model (eLSM). The eLSM is an effective model for the strong
interaction based on the global chiral symmetry of quantum chromodynamics
(QCD). It contains scalar, pseudoscalar, vector, and axial-vector mesons as
well as baryons. In the latter sector, the nucleon and its chiral partner are
introduced as parity doublets in the mirror assignment. The eLSM simultaneously
provides a good description of hadrons in vacuum as well as nuclear matter
ground-state properties. We find that an inhomogeneous phase in the form of a
chiral density wave is realized, but only for densities larger than 2.4
{\rho}0, where {\rho}0 is the nuclear matter ground-state density.",1312.3244v2
1998-10-14,Stability of the maximum density droplet in quantum dots at high magnetic fields,"We have measured electron transport through a vertical quantum dot containing
a tunable number of electrons between 0 and 40. Over some region in magnetic
field the electrons are spin polarized and occupy successive angular momentum
states, i.e. the maximum density droplet (MDD) state. The stability region
where the MDD state is the ground state, decreases for increasing electron
number. The instability of the MDD is accompanied by a redistribution of charge
which increases the area of the electron droplet.",9810159v1
1999-02-19,Quasiparticle Density of States of Clean and Dirty s-Wave Superconductors in the Vortex State,"The quasiparticle density of states (DOS) in the vortex state has been probed
by specific heat measurements under magnetic fields (H) for clean and dirty
s-wave superconductors, Y(Ni1-xPtx)2B2C and Nb1-xTaxSe2. We find that the
quasiparticle DOS per vortex is appreciably H-dependent in the clean-limit
superconductors, while it is H-independent in the dirty superconductors as
expected from a conventional rigid normal electron core picture. We discuss
possible origins for our observations in terms of the shrinking of the vortex
core radius with increasing H.",9902264v1
1999-12-13,Competing Ground States of the New Class of Halogen-Bridged Metal Complexes,"Based on a symmetry argument, we study the ground-state properties of
halogen-bridged binuclear metal chain complexes. We systematically derive
commensurate density-wave solutions from a relevant two-band Peierls-Hubbard
model and numerically draw the the ground-state phase diagram as a function of
electron-electron correlations, electron-phonon interactions, and doping
concentration within the Hartree-Fock approximation. The competition between
two types of charge-density-wave states, which has recently been reported
experimentally, is indeed demonstrated.",9912212v1
2000-09-22,"spl(2,1) dynamical supersymmetry and suppression of ferromagnetism in flat band double-exchange models","The low energy spectrum of the ferromagnetic Kondo lattice model on a N-site
complete graph extended with on-site repulsion is obtained from the underlying
spl(2,1) algebra properties in the strong coupling limit. The ferromagnetic
ground state is realized for 1 and N+1 electrons only. We identify the large
density of states to be responsible for the suppression of the ferromagnetic
state and argue that a similar situation is encountered in the Kagome,
pyrochlore, and other lattices with flat bands in their one-particle density of
states.",0009358v1
2002-05-01,Field dependence of the vortex structure in chiral p-wave superconductors,"To investigate the different vortex structure between two chiral pairing p_x
+(-) i p_y, we calculate the pair potential, the internal field, the local
density of states, and free energy in the vortex lattice state based on the
quasiclassical Eilenberger theory, and analyze the magnetic field dependence.
The induced opposite chiral component of the pair potential plays an important
role in the vortex structure. It also produces H^{1/2}-behavior of the
zero-energy density of states at higher field. These results are helpful when
we understand the vortex states in Sr2RuO4.",0205012v1
2005-05-12,Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state,"We derive a relationship between the optical conductivity scattering rate
1/\tau(\omega) and the electron-boson spectral function \alpha^2F(\Omega) valid
for the case when the electronic density of states, N(\epsilon), cannot be
taken as constant in the vicinity of the Fermi level. This relationship turned
out to be useful for analyzing the experimental data in the pseudogap state of
cuprate superconductors.",0505304v2
2005-08-14,Electron self-trapping and fluctuation density-of-states tail at the critical point,"We consider electron self-trapping due to its interaction with
order-parameter fluuctuations at the second-order phase-transition or critical
point (for example, at the Curie temperature in magnetic or ferroelectric
semiconductors). Using Feynman path integral approach the autolocalization
energy and the size of the self-trapped state (fluctuon) are estimated. It is
shown that the fluctuon states are connected with the Lifshitz tail of the
electron density-of-states, the parameters of this tail being determined by the
critical exponents.",0508333v1
1999-04-30,Explicit product ensembles for separable quantum states,"We present a general method for constructing pure-product-state
representations for density operators of $N$ quantum bits. If such a
representation has nonnegative expansion coefficients, it provides an explicit
separable ensemble for the density operator. We derive the condition for
separability of a mixture of the Greenberger-Horne-Zeilinger state with the
maximally mixed state.",9904109v2
2011-08-25,SU(2) Invariants of Symmetric Qubit States,"Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is
expressed in terms of the well known Fano statistical tensor parameters.
Employing the multiaxial representation [1], wherein a spin-j density matrix is
shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the
number of invariants constructed out of these axes and scalars. These
invariants are explicitly calculated in the particular case of pure as well as
mixed spin-1 state.",1108.5105v1
2012-07-18,A higher order correlation unscented Kalman filter,"Many nonlinear extensions of the Kalman filter, e.g., the extended and the
unscented Kalman filter, reduce the state densities to Gaussian densities. This
approximation gives sufficient results in many cases. However, this filters
only estimate states that are correlated with the observation. Therefore,
sequential estimation of diffusion parameters, e.g., volatility, which are not
correlated with the observations is not possible. While other filters overcome
this problem with simulations, we extend the measurement update of the Gaussian
two-moment filters by a higher order correlation measurement update. We
explicitly state formulas for a higher order unscented Kalman filter within a
continuous-discrete state space. We demonstrate the filter in the context of
parameter estimation of an Ornstein-Uhlenbeck process.",1207.4300v1
2018-07-10,Weaker Assumptions for the Short Path Optimization Algorithm,"The short path algorithm gives a super-Grover speedup for various
optimization problems under the assumption of a unique ground state and under
an assumption on the density of low-energy states. Here, we remove the
assumption of a unique ground state; this uses the same algorithm but a
slightly different analysis and holds for arbitrary MAX-$D$-LIN-$2$ problems.
Then, specializing to the case $D=2$, we show that for certain values of the
objective function we can always achieve a super-Grover speedup (albeit a very
slight one) without any assumptions on the density of states. Finally, for
random instances, we give a heuristic treatment suggesting a more significant
improvement.",1807.03758v1
2017-09-26,Probing chiral edge states in topological superconductors through spin-polarized local density of state measurements,"We show that spin-polarized local density of states (LDOS) measurements can
uniquely determine the chiral nature of topologically protected edge states
surrounding a ferromagnetic island embedded in a conventional superconductor
with spin-orbit coupling. The spin-polarized LDOS show a strong
spin-polarization directly tied to the normal direction of the edge, with
opposite polarizations on opposite sides of the island, and with a distinct
oscillatory pattern in energy.",1709.09061v1
2020-12-14,Variational State and Parameter Estimation,"This paper considers the problem of computing Bayesian estimates of both
states and model parameters for nonlinear state-space models. Generally, this
problem does not have a tractable solution and approximations must be utilised.
In this work, a variational approach is used to provide an assumed density
which approximates the desired, intractable, distribution. The approach is
deterministic and results in an optimisation problem of a standard form. Due to
the parametrisation of the assumed density selected first- and second-order
derivatives are readily available which allows for efficient solutions. The
proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in
two numerical examples.",2012.07269v1
2019-04-08,Ab initio and nuclear inelastic scattering studies of Fe$_3$Si/GaAs heterostructures,"The structure and dynamical properties of the Fe$_3$Si/GaAs(001) interface
are investigated by density functional theory and nuclear inelastic scattering
measurements. The stability of four different atomic configurations of the
Fe$_3$Si/GaAs multilayers is analyzed by calculating the formation energies and
phonon dispersion curves. The differences in charge density, magnetization, and
electronic density of states between the configurations are examined. Our
calculations unveil that magnetic moments of the Fe atoms tend to align in a
plane parallel to the interface, along the [110] direction of the Fe$_3$Si
crystallographic unit cell. In some configurations, the spin polarization of
interface layers is larger than that of bulk Fe$_3$Si. The effect of the
interface on element-specific and layer-resolved phonon density of states is
discussed. The Fe-partial phonon density of states measured for the Fe$_3$Si
layer thickness of three monolayers is compared with theoretical results
obtained for each interface atomic configuration. The best agreement is found
for one of the configurations with a mixed Fe-Si interface layer, which
reproduces the anomalous enhancement of the phonon density of states below 10
meV",1904.04122v1
1999-02-03,Algorithm for obtaining the gradient expansion of the local density of states and the free energy of a superconductor,"We present an efficient algorithm for obtaining the gauge-invariant gradient
expansion of the local density of states and the free energy of a clean
superconductor. Our method is based on a new mapping of the semiclassical
linearized Gorkov equations onto a pseudo-Schroedinger equation for a
three-component wave-function psi(x), where one component is directly related
to the local density of states. Because psi(x) satisfies a linear equation of
motion, successive terms in the gradient expansion can be obtained by simple
linear iteration. Our method works equally well for real and complex order
parameter, and in the presence of arbitrary external fields. We confirm a
recent calculation of the fourth order correction to the free energy by
Kosztin, Kos, Stone and Leggett [Phys. Rev. B 58, 9365 (1998)], who obtained a
discrepancy with an earlier result by Tewordt [Z. Phys. 180, 385 (1964)]. We
also give the fourth order correction to the local density of states, which has
not been published before.",9902042v2
2005-06-08,Formation of clumps and patches in self-aggregation of finite size particles,"New model equations are derived for dynamics of self-aggregation of
finite-size particles. Differences from standard Debye-Huckel and Keller-Segel
models are: a) the mobility $\mu$ of particles depends on the locally-averaged
particle density and b) linear diffusion acts on that locally-averaged particle
density. The cases both with and without diffusion are considered here.
Surprisingly, these simple modifications of standard models allow progress in
the analytical description of evolution as well as the complete analysis of
stationary states. When $\mu$ remains positive, the evolution of collapsed
states in our model reduces exactly to finite-dimensional dynamics of
interacting particle clumps. Simulations show these collapsed (clumped) states
emerging from smooth initial conditions, even in one spatial dimension. If
$\mu$ vanishes for some averaged density, the evolution leads to spontaneous
formation of \emph{jammed patches} (weak solution with density having compact
support). Simulations confirm that a combination of these patches forms the
final state for the system.",0506020v1
2016-02-03,Equation of state of imbalanced cold matter from chiral perturbation theory,"We study the thermodynamic properties of matter at vanishing temperature for
non-extreme values of the isospin chemical potential and of the strange quark
chemical potential. From the leading order pressure obtained by maximizing the
static chiral Lagrangian density we derive a simple expression for the equation
of state in the pion condensed phase and in the kaon condensed phase. We find
an analytical expression for the maximum of the ratio between the energy
density and the Stefan-Boltzmann energy density as well as for the isospin
chemical potential at the peak both in good agreement with lattice simulations
of quantum chromodynamics. We speculate on the location of the crossover from
the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a
simple analysis of the thermodynamic properties of the system. For $\mu_I
\gtrsim 2 m_\pi$ the leading order chiral perturbation theory breaks down; as
an example it underestimates the energy density of the system and leads to a
wrong asymptotic behavior.",1602.01317v2
2017-03-31,Combined effects of local and nonlocal hybridization on formation and condensation of excitons in the extended Falicov-Kimball model,"We study the combined effects of local and nonlocal hybridization on the
formation and condensation of the excitonic bound states in the extended
Falicov-Kimball model by the density-matrix-renormalization-group (DMRG)
method. Analysing the resultant behaviours of the excitonic momentum
distribution $N(q)$ we found, that unlike the local hybridization $V$, which
supports the formation of the $q=0$ momentum condensate, the nonlocal
hybridization $V_n$ supports the formation of the $q=\pi$ momentum condensate.
The combined effect of local and nonlocal hybridization further enhances the
excitonic correlations in $q=0$ as well as $q=\pi$ state, especially for $V$
and $V_n$ values from the charge-density-wave (CDW) region. Strong effects of
local and nonlocal hybridization are observed also for other ground-state
quantities of the model such as the $f$-electron density, or the density of
unbound $d$-electrons, which are generally enhanced with increasing $V$ and
$V_n$. The same calculations performed for nonzero values of $f$-level energy
$E_f$ revealed that this model can yield a reasonable explanation for the
pressure-induced resistivity anomaly observed experimentally in
$TmSe_{0.45}Te_{0.55}$ compound.",1703.10911v1
2018-02-27,"Hot and Dense Homogeneous Nucleonic Matter Constrained by Observations, Experiment, and Theory","We construct a new class of phenomenological equations of state for
homogeneous matter for use in simulations of hot and dense matter in local
thermodynamic equilibrium. We construct a functional form which respects
experimental, observational and theoretical constraints on the nature of matter
in various density and temperature regimes. Our equation of state matches (i)
the virial coefficients expected from nucleon-nucleon scattering phase shifts,
(ii) experimental measurements of nuclear masses and charge radii, (iii)
observations of neutron star radii, (iv) theory results on the equation of
state of neutron matter near the saturation density, and (v) theory results on
the evolution of the EOS at finite temperatures near the saturation density.
Our analytical model allows one to compute the variation in the thermodynamic
quantities based on the uncertainties in the nature of the nucleon-nucleon
interaction. Finally, we perform a correction to ensure the equation of state
is causal at all densities, temperatures, and electron fractions.",1802.09710v1
2018-12-22,Thermal tuning of the carrier density in Dirac semimetal Cd3As2 nanoplates,"The tunable carrier density plays a key role in the investigation of novel
transport properties in three-dimensional topological semimetals. Here we
demonstrate that the carrier density as well as the mobility of Dirac semimetal
Cd3As2 nanoplates can be effectively tuned by the in-situ thermal treatment at
350 K for one hour, both showing a non-monotonic evolution with the thermal
cycling treatments. The upward shift of Fermi level relative to the Dirac nodes
blurs the surface Fermi-arc states, accompanying with an anomalous phase shift
of oscillations of bulk states due to the change of topology of electrons.
Meanwhile, the peaks of oscillations of bulk longitudinal magnetoresistivity
shift at high fields due to their coupling to the oscillations of the surface
Fermi-arc states. Our work provides a thermal control knob for manipulations of
the quantum states through the carrier density in Dirac semimetal Cd3As2 at
high temperature.",1812.09455v1
2005-07-04,Effect of density of state on isotope effect exponent of two-band superconductors,"The exact formula of Tc's equation and the isotope effect exponent of
two-band s-wave superconductors in weak-coupling limit are derived by
considering the influence of two kinds of density of state : constant and van
Hove singularity. The pairing interaction in each band consisted of 2 parts :
the electron-phonon interaction and non-electron-phonon interaction are
included in our model. We find that the interband interaction of
electron-phonon show more effect on isotope exponent than the intraband
interaction and the isotope effect exponent with constant density of state can
fit to an experimental data,MgB2, and high-Tc superconductors, better than van
Hove singularity density of state.",0507069v1
2008-06-24,Reconstruction of the Fermi surface in the pseudogap state of cuprates,"Reconstruction of the Fermi surface of high-temperature superconducting
cuprates in the pseudogap state is analyzed within nearly exactly solvable
model of the pseudogap state, induced by short-range order fluctuations of
antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave
(CDW)) order parameter, competing with superconductivity. We explicitly
demonstrate the evolution from ""Fermi arcs"" (on the ""large"" Fermi surface)
observed in ARPES experiments at relatively high temperatures (when both the
amplitude and phase of density waves fluctuate randomly) towards formation of
typical ""small"" electron and hole ""pockets"", which are apparently observed in
de Haas - van Alfen and Hall resistance oscillation experiments at low
temperatures (when only the phase of density waves fluctuate, and correlation
length of the short-range order is large enough). A qualitative criterion for
quantum oscillations in high magnetic fields to be observable in the pseudogap
state is formulated in terms of cyclotron frequency, correlation length of
fluctuations and Fermi velocity.",0806.3826v1
2011-04-29,Lifshitz tails on the Bethe lattice: a combinatorial approach,"The density of states of disordered hopping models generically exhibits an
essential singularity around the edges of its support, known as a Lifshitz
tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size
limit of random regular graphs, converging locally to the infinite regular
tree, for both diagonal and off-diagonal disorder. The exponential growth of
the volume and surface of balls on these lattices is an obstacle for the
techniques used to characterize the Lifshitz tails in the finite-dimensional
case. We circumvent this difficulty by computing bounds on the moments of the
density of states, and by deriving their implications on the behavior of the
integrated density of states.",1104.5637v2
2013-06-26,Nuclear Level Density within Extended Superfluid Model with Collective State Enhancement,"For nuclear level densities, a modification of an enhanced generalized
superfluid model with different collective state enhancement factors is
studied. An effect of collective states on forming the temperature is taken
into account. The ready-to-use tables for the asymptotic value of $a$-parameter
of level density as well as for addition shift to excitation energy are
prepared using the chi-square fit of the theoretical values of neutron
resonance spacing and cumulative number of low-energy levels to experimental
values. The systematics of these parameters as a function of mass number and
neutron excess are obtained. The collective state effect on gamma-ray spectra
and excitation functions of neutron-induced nuclear reactions is investigated
by the use of EMPIRE 3.1 code with modified enhanced generalized superfluid
model for nuclear level density.",1306.6241v1
2010-01-15,Theory of (001) surface and bulk states in Y$_{1-y}$Ca$_y$Ba$_2$Cu$_3$O$_{7-δ}$},"A self-consistent model is developed for the surface and bulk states of thin
Y_{1-y}Ca_yBa_2Cu_3O_{7-\delta} (YCBCO) films. The dispersions of the chain and
plane layers are modelled by tight-binding bands, and the electronic structure
is then calculated for a finite-thickness film. The dopant atoms are treated
within a virtual crystal approximation. Because YCBCO is a polar material,
self-consistent treatment of the long range Coulomb interaction leads to a
transfer of charge between the film surfaces, and to the formation of surface
states. The tight binding band parameters are constrained by the requirement
that the calculated band structure of surface states at CuO$_2$-terminated
surfaces be in agreement with photoemission experiments. The spectral function
and density of states are calculated and compared with experiments. Unlike the
case of Bi_2Sr_2CaCu_2O_8, where the surfaces are believed to be representative
of the bulk, the densities of states at the YCBCO surfaces are shown to be
qualitatively different from the bulk, and are sensitive to doping. The
calculated spectral function agrees closely with both bulk-sensitive and
surface-sensitive photoemission results, while the calculated density of states
for optimally-doped YCBCO agrees closely with tunneling experiments. We find
that some density of states features previously ascribed to competing order can
be understood as band structure effects.",1001.2695v1
2022-02-03,"Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride","We investigate spin and valley symmetry-broken fractional quantum Hall phases
within a formalism that naturally extends the paradigm of quantum Hall
ferromagnetism from integer to fractional quantum Hall states, allowing us to
construct detailed phase diagrams for a large class of multi-component states.
Motivated by recent experiments on Graphene aligned with a Boron Nitride
substrate, we predict a sequence of transitions realized by increasing the
magnetic field, starting from a sub-lattice polarized state to a valley
coherent Kekule charge density wave state and further to an anti-ferromagnetic
phase. Moreover for filling fractions such as $\nu=\pm 1/3$, we predict that
the system undergoes a transition at low fields, that not only differ by the
spin-valley orientation of the fractionally filled flavors but also by their
intrinsic fractional quantum Hall nature. This transition is from a
Laughlin-like state to a two component Halperin-like state both with a charge
density wave order. Moreover for $\nu=\pm 1/3,\pm 2/3$, we predict a ""canted
Kekule density phase""(CaKD) where the spinors of integer and fractionally
occupied components have different orientations in the valley Bloch sphere, in
contrast to the Kekule state for the integer quantum Hall state at neutrality
where both occupied components have the same orientation in the valley Bloch
sphere.",2202.01796v2
2002-07-24,Quasi-Particle States with Topological Quantum Numbers in the Mixed State of d-wave Superconductors,"We investigate the extended quasi-particle states in the mixed state of
d-wave superconductors on the basis of the Bogoliubov-de Gennes equation. We
prove that the quasi-particle eigen-states can be classified in terms of new
topological quantum numbers which are related to the topological nature of the
non-trivial phases of the quasi-particles. Numerical results for the
quasi-particle eigen-states reveal the crossover behavior from gapless to
gapped states as the flux density $B$ increases. In the strong field region
quantum oscillations appear in the excitation energy of the quasi-particles.",0207568v1
2013-01-10,Odd-particle number random phase approximation and extensions: Applications to particle and hole states around $^{16}$O,"The hole-state random phase approximation (hRPA) and the particle-state
random phase approximation (pRPA) for systems like odd $A$ nuclei are
discussed. These hRPA and pRPA are formulated based on the Hartree-Fock ground
state. An extension of hRPA and pRPA based on a correlated ground state is
given using time-dependent density-matrix theory. Applications to the
single-particle states around $^{16}$O are presented. It is shown that
inclusion of ground-state correlation affects appreciably the results of hRPA
and pRPA. The question of the coupling of the center of mass motion of the core
to the particle (hole) is also discussed.",1301.2026v1
2018-05-28,Resolving different pairing states in Weyl superconductors through the single-particle spectrum,"We study theoretically single-particle spectra of Weyl superconductors. Three
different superconducting pairing states are addressed, which are the BCS-type
states with the $s$-wave pairing symmetry and the $p+ip$-wave pairing symmetry,
and the FFLO pairing state. We elaborate that these three states can be
resolved well based on the bulk and surface spectral functions as well as the
local density of states. The single impurity effect is also explored, which may
help us to differentiate the BCS-type pairing states and the FFLO state
further.",1805.11013v1
2020-09-10,Distributed Density Filtering for Large-Scale Systems Using Mean-Filed Models,"This work studies distributed (probability) density estimation of large-scale
systems. Such problems are motivated by many density-based distributed control
tasks in which the real-time density of the swarm is used as feedback
information, such as sensor deployment and city traffic scheduling. This work
is built upon our previous work [1] which presented a (centralized) density
filter to estimate the dynamic density of large-scale systems through a novel
integration of mean-field models, kernel density estimation (KDE), and
infinite-dimensional Kalman filters. In this work, we further study how to
decentralize the density filter such that each agent can estimate the global
density only based on its local observation and communication with neighbors.
This is achieved by noting that the global observation constructed by KDE is an
average of the local kernels. Hence, dynamic average consensus algorithms are
used for each agent to track the global observation in a distributed way. We
present a distributed density filter which requires very little information
exchange, and study its stability and optimality using the notion of
input-to-state stability. Simulation results suggest that the distributed
filter is able to converge to the centralized filter and remain close to it.",2009.05366v2
2018-03-22,Subgap states in two dimensional spectroscopy of unconventional superconductors using graphene,"The two-dimensional nature of graphene makes it an ideal platform to explore
proximity-induced unconventional planar superconductivity and the possibility
of topological superconductivity. Using Green's functions techniques, we study
the transport properties of a finite size ballistic graphene layer placed
between a normal state electrode and a graphene lead with proximity-induced
unconventional superconductivity. Our microscopic description of such a
junction allows us to consider the effect of edge states in the graphene layer
and the imperfect coupling to the electrodes. The tunnel conductance through
the junction and the spectral density of states feature a rich interplay
between graphene's edge states, interface bound states formed at the
graphene-superconductor junction, Fabry-P\'erot resonances originated from the
finite size of the graphene layer, and the characteristic Andreev surface
states of unconventional superconductors. Within our analytical formalism, we
identify the separate contribution from each of these subgap states to the
conductance and density of states. Our results show that graphene provides an
advisable tool to determine experimentally the pairing symmetry of
proximity-induced unconventional superconductivity.",1803.08590v1
2000-03-22,Time discretization of functional integrals,"Numerical evaluation of functional integrals usually involves a finite
(L-slice) discretization of the imaginary-time axis. In the auxiliary-field
method, the L-slice approximant to the density matrix can be evaluated as a
function of inverse temperature at any finite L as
$\rho_L(\beta)=[\rho_1(\beta/L)]^L$, if the density matrix $\rho_1(\beta)$ in
the static approximation is known. We investigate the convergence of the
partition function $Z_L(\beta)=Tr\rho_L(\beta)$, the internal energy and the
density of states $g_L(E)$ (the inverse Laplace transform of $Z_L$), as
$L\to\infty$. For the simple harmonic oscillator, $g_L(E)$ is a normalized
truncated Fourier series for the exact density of states. When the
auxiliary-field approach is applied to spin systems, approximants to the
density of states and heat capacity can be negative. Approximants to the
density matrix for a spin-1/2 dimer are found in closed form for all L by
appending a self-interaction to the divergent Gaussian integral and
analytically continuing to zero self-interaction. Because of this continuation,
the coefficient of the singlet projector in the approximate density matrix can
be negative. For a spin dimer, $Z_L$ is an even function of the coupling
constant for L<3: ferromagnetic and antiferromagnetic coupling can be
distinguished only for $L\ge 3$, where a Berry phase appears in the functional
integral. At any non-zero temperature, the exact partition function is
recovered as $L\to\infty$.",0003109v1
1994-08-10,Tunneling into a Two-Dimensional Electron Liquid in a Weak Magnetic Field,"We study the spectral density function of a two-dimensional electron liquid
in a weak magnetic field, the filling factor $\nu\gg 1$. A hydrodynamic model
for low-energy excitations of the liquid is developed. It is found that even at
$\nu\gg 1$ the density of states exhibits a gap at low energies. Its width
$2E_0$ depends on the strength of interaction only logarithmically,
$2E_0=(\hbar\omega_c/\nu)\ln (\nu e^2/\varepsilon\hbar v_F)$. The effects of
temperature and disorder on the density of states are discussed.",9408033v1
2000-08-04,Spontaneous Magnetisation in a Quantum Wire,"An existence of predominant symmetrical spin configuration (spin polarised
phase) and ""diluted"" density of states (pseudo-gap) in a layer under the Fermi
level in a quantum wire is predicted. The condition of cross-over from
non-polarised phase to polarised one was derived. The transition occurs for
sufficiently low electron density in a wire and is accompanied by an acute
decrease of electron density of states near the Fermi level.It may result in a
corresponding decrease of conductance. A similar effect may exist in a
two-dimensional electron gas.",0008075v3
2000-12-07,Recent Progress in the Computational Many-Body Theory of Metal Surfaces,"In this article we describe recent progress in the computational many-body
theory of metal surfaces, and focus on current techniques beyond the
local-density approximation of density-functional theory. We overview various
applications to ground and excited states. We discuss the exchange-correlation
hole, the surface energy, and the work function of jellium surfaces, as
obtained within the random-phase approximation, a time-dependent
density-functional approach, and quantum Monte Carlo methods. We also present a
survey of recent quasiparticle calculations of unoccupied states at both
jellium and real surfaces.",0012116v1
2001-05-18,Spontaneous Magnetization of a Two-Dimensional Electron Gas,"Spontaneous magnetization of a two-dimensional electron gas (2DEG) is
discussed. It takes place for sufficiently high electron density (i.e. for a
quantum fluid state) with $r_s<10$ which is quite beyond the condition of
Wigner crystallization $(r_s>37)$ obtained by Tanatar and Ceperley. The effect
essentially depends upon screening and disorder . The energy interval under the
Fermi level where a spin polarization occurs as a function of electron density
is computed. The spontaneous magnetic moment and a decrease of electron density
of states (pseudo-gap) at the Fermi level are found.",0105361v1
2004-08-04,On the shape of the ground state eigenvalue density of a random Hill's equation,"Consider the Hill's operator $Q = - d^2/dx^2 + q(x)$ in which $q(x)$, $0 \le
x \le 1$, is a White Noise. Denote by $f(\mu)$ the probability density function
of $-\lambda_0(q)$, the negative of the ground state eigenvalue, at $\mu$. We
describe the detailed asymptotics of this density as $\mu \to +\infty$. This
result is based on a precise Laplace analysis of a functional integral
representation for $f(\mu)$ established by S. Cambronero and H.P. McKean.",0408068v2
2005-12-02,The nuclear density of states and the role of the residual interaction,"We discuss the role of mean-field and moment methods in microscopic models
for calculating the nuclear density of states (also known as the nuclear level
density). Working in a shell-model framework, we use moments of the nuclear
many-body Hamiltonian to illustrate the importance of the residual interaction
for accurate representations.",0512008v1
2008-06-02,Local Density of States for Individual Energy Levels in Finite Quantum Wires,"The local density of states (LDOS) in finite quantum wires is calculated as a
function of discrete energies and position along the wire. By using a
combination of numerical density matrix renormalization group (DMRG)
calculations and analytical bosonization techniques it is possible to obtain a
good understanding of the local spectral weights along the wire in terms of the
underlying many-body excitations.",0806.0027v2
2008-08-25,First-order quantum correction to the ground-state energy density of two-dimensional hard-sphere Bose atoms,"Divergence exponents of the first-order quantum correction of a
two-dimensional hard-sphere Bose atoms are obtained by an effective field
theory method. The first-order correction to the ground-state energy density
with respect to the zeroth-order is given by
  $\cale_1/\cale_0 \sim |D-2|^{-\al}|\ln\gamma|^{-\al'}$, where $D$ is the
spatial dimension, and $\gamma$ is the gas parameter ($\gamma=n a^D$). As $D
\to 2$, $\al =\al'=1$. We show that the first-order quantum correction of the
energy density is not perturbative in low dimensions of $D < 2.2$ regardless of
any gas parameter which is much less that 1.",0808.3288v1
2013-05-09,The density of surface states as the total time delay,"For a scattering problem of tight-binding Bloch electrons by a weak random
surface potential, a generalized Levinson theorem is put forward showing the
equality of the total density of surface states and the density of the total
time delay. The proof uses explicit formulas for the wave operators in the new
rescaled energy and interaction (REI) representation, as well as an index
theorem for adequate associated operator algebras.",1305.2187v2
2013-07-17,Density dependent magnetic field and the equation of state of hyperonic matter,"We are interested on the effects, caused by strong variable density dependent
magnetic fields, on hyperonic matter, its symmetry energy, equations of state
and mass-radius relations. The inclusion of the anomalous magnetic moment of
the particles involved in a stellar system is performed, and some results are
compared with the cases that do not take this correction under consideration.
The Lagrangian density used follows the nonlinear Walecka model plus the
leptons subjected to an external magnetic field.",1307.4805v1
2013-08-25,Determining eigenvalues of a density matrix with minimal information in a single experimental setting,"Eigenvalues of a density matrix characterize well the quantum state's
properties, such as coherence and entanglement. We propose a simple method to
determine all the eigenvalues of an unknown density matrix of a
finite-dimensional system in a single experimental setting. Without fully
reconstructing a quantum state, eigenvalues are determined with the minimal
number of parameters obtained by a measurement of a single observable.
Moreover, its implementation is illustrated in linear optical and
superconducting systems.",1308.5413v2
2020-12-17,Vibrational angular momentum level densities of linear molecules,"While linear molecules in their vibrational ground state cannot carry angular
momentum around their symmetry axis, the presence of vibrational excitations
can induce deformations away from linearity and therefore also allow angular
momentum along the molecular axis. In this work, a recurrence relation is
established for the calculation of the vibrational level densities (densities
of states) of linear molecules, specified with respect to both energy and
angular momentum. The relation is applied to the carbon clusters of sizes
$n=4,6,7$ as a case study.",2012.09380v1
2021-03-20,On a class of Fokker-Planck equations with subcritical confinement,"We study the relaxation to equilibrium for a class linear one-dimensional
Fokker-Planck equations characterized by a particular subcritical confinement
potential. An interesting feature of this class of Fokker-Planck equations is
that, for any given probability density $e(x)$, the diffusion coefficient can
be built to have $e(x)$ as steady state. This representation of the equilibrium
density can be fruitfully used to obtain one-dimensional Wirtinger-type
inequalities and to recover, for a sufficiently regular density $e(x) $, a
polynomial rate of convergence to equilibrium.Numerical results then confirm
the theoretical analysis, and allow to conjecture that convergence to
equilibrium with positive rate still holds for steady states characterized by a
very slow polynomial decay at infinity.",2103.11146v1
2022-01-06,Density-of-states similarity descriptor for unsupervised learning from materials data,"We develop a materials descriptor based on the electronic density of states
and investigate the similarity of materials based on it. As an application
example, we study the Computational 2D Materials Database that hosts thousands
of two-dimensional materials with their properties calculated by
density-functional theory. Combining our descriptor with a clustering
algorithm, we identify groups of materials with similar electronic structure.
We characterize these clusters in terms of their crystal structure, their
atomic composition, and the respective electronic configurations to rationalize
the found (dis)similarities.",2201.02187v1
2022-07-23,Mapping mechanism between density of states and ultraviolet-visible light absorption spectra,"This paper constructs the mapping relation from density of states (DOS) to
UV-vis spectra by using an ab initio perspective. Taking BiOIO3 semiconductor
photocatalyst as an example, the experimental verification was also carried
out. The optical response of the material considers the superposition benefits
of all possible transitions. Directly using the difference between valence band
maximum (VBM) and conduction band minimum (CBM) will lead to an underestimate
of the energy band gap. This paper provides a new idea of linking the density
functional theory (DFT) data with experiment phenomenon.",2207.11548v1
2023-01-24,Direct observation of magnon BEC in an out-of-plane magnetized yttrium iron garnet film,"Bose-Einstain condensation occurs at an appropriate density of bosonic
particles, depending on their mass and temperature. We were able to
experimentally observe the transition from the spin wave regime to the magnon
Bose-Einstein condensed state (mBEC) with increasing magnon density by a
microwave pumping. We used optical methods to register the spatial distribution
of the magnon density and phase. For the first time, a coherent state of
stationary magnons was demonstrated far from the region of their excitation.",2301.10725v1
2018-11-15,Histogram-Free Multicanonical Monte Carlo Sampling to Calculate the Density of States,"We report a new multicanonical Monte Carlo algorithm to obtain the density of
states for physical systems with continuous state variables in statistical
mechanics. Our algorithm is able to obtain a closed-form expression for the
density of states expressed in a chosen basis set, instead of a numerical array
of finite resolution as in previous variants of this class of MC methods such
as the multicanonical sampling and Wang-Landau sampling. This is enabled by
storing the visited states directly and avoiding the explicit collection of a
histogram. This practice also has the advantage of avoiding undesirable
artificial errors caused by the discretization and binning of continuous state
variables. Our results show that this scheme is capable of obtaining converged
results with a much reduced number of Monte Carlo steps, leading to a
significant speedup over existing algorithms.",1811.07715v1
2014-09-05,Systematic variation of the 12CO/13CO ratio as a function of star-formation rate surface density,"We show that the12CO/13CO intensity ratio in nearby galaxies varies
systematically as a function of the star formation rate surface density and gas
surface density. The same effect is observed in different transitions, and in
the 12CO/C18O ratio, while the 13CO/C18O ratio appears to remain constant as a
function of the star formation rate surface density. We discuss the cause of
these variations, considering both changes in the physical state of the gas,
and chemical changes that lead to abundance variations. We used the observed
correlations with C18O to suggest that abundance variations are unlikely to be
causing the systematic trend observed with the star formation rate surface
density, and thus that the mean gas temperature and/or velocity dispersion are
systematically higher in higher star-formation rate surface density regions. We
present the best fitting relations between the star formation rate surface
density and the 12CO/13CO and 12CO/C18O ratios, and discuss how this effect can
help us predict CO isotope emission from galaxies across the known universe.",1409.1732v1
2019-05-18,(Spin-)density-functional theory for open-shell systems: exact magnetization density functional for the half-filled Hubbard trimer,"According to the Hohenberg-Kohn theorem of density-functional theory (DFT),
all observable quantities of systems of interacting electrons can be expressed
as functionals of the ground-state density. This includes, in principle, the
spin polarization (magnetization) of open-shell systems; the explicit form of
the magnetization as a functional of the total density is, however, unknown. In
practice, open-shell systems are always treated with spin-DFT, where the basic
variables are the spin densities. Here, the relation between DFT and spin-DFT
for open-shell systems is illustrated and the exact magnetization density
functional is obtained for the half-filled Hubbard trimer. Errors arising from
spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are
analyzed and partially cured via the exact magnetization functional.",1905.07630v1
2017-04-24,U(1)$\times$SU(2) Gauge Invariance Made Simple for Density Functional Approximations,"A semi-relativistic density-functional theory that includes spin-orbit
couplings and Zeeman fields on equal footing with the electromagnetic
potentials, is an appealing framework to develop a unified first-principles
computational approach for non-collinear magnetism, spintronics, orbitronics,
and topological states. The basic variables of this theory include the
paramagnetic current and the spin-current density, besides the particle and the
spin density, and the corresponding exchange-correlation (xc) energy functional
is invariant under local U(1)$\times$SU(2) gauge transformations. The xc-energy
functional must be approximated to enable practical applications, but, contrary
to the case of the standard density functional theory, finding simple
approximations suited to deal with realistic atomistic inhomogeneities has been
a long-standing challenge. Here, we propose a way out of this impasse by
showing that approximate gauge-invariant functionals can be easily generated
from existing approximate functionals of ordinary density-functional theory by
applying a simple {\it minimal substitution} on the kinetic energy density,
which controls the short-range behavior of the exchange hole. Our proposal
opens the way to the construction of approximate, yet non-empirical
functionals, which do not assume weak inhomogeneity and should therefore have a
wide range of applicability in atomic, molecular and condensed matter physics.",1704.07304v1
2019-03-04,Reduced Density Matrix Functional Theory for Superconductors,"We present an \textit{ab initio} theory for superconductors, based on a
unique mapping between the statistical density operator at equilibrium, on the
one hand, and the corresponding one-body reduced density matrix $\gamma$ and
the anomalous density $\chi$, on the other. This new formalism for
superconductivity yields the existence of a universal functional
$\mathfrak{F}_\beta[\gamma,\chi]$ for the superconductor ground state, whose
unique properties we derive. We then prove the existence of a Kohn-Sham system
at finite temperature and derive the corresponding Bogoliubov-de Gennes-like
single particle equations. By adapting the decoupling approximation from
density functional theory for superconductors we bring these equations into a
computationally feasible form. Finally, we use the existence of the Kohn-Sham
system to extend the Sham-Schl\""uter connection and derive a first
exchange-correlation functional for our theory. This reduced density matrix
functional theory for superconductors has the potential of overcoming some of
the shortcomings and fundamental limitations of density functional theory of
superconductivity.",1903.01516v2
2021-02-05,Screening effects of superlattice doping on the mobility of GaAs two-dimensional electron system revealed by in-situ gate control,"We investigate the screening effects of excess electrons in the doped layer
on the mobility of a GaAs two-dimensional electron system (2DES) with a modern
architecture using short-period superlattice (SL) doping. By controlling the
density of excess electrons in the SL with a top gate while keeping the 2DES
density constant with a back gate, we are able to compare 2DESs with the same
density but different degrees of screening using one sample. Using a
field-penetration technique and circuit-model analysis, we determine the
density of states and excess electron density in the SL, quantities directly
linked to the screening capability. The obtained relation between mobility and
excess electron density is consistent with the theory taking into account the
screening by the excess electrons in the SL. The quantum lifetime determined
from Shubnikov-de Haas oscillations is much lower than expected from theory and
did not show a discernible change with excess electron density.",2102.03009v1
2006-03-27,Evolving momentum-projected densities in billiards with quantum states,"The classical Liouville density on the constant energy surface reveals a
number of interesting features when the initial density has no directional
preference. It has been shown (Physical Review Letters, 93 (2004) 204102) that
the eigenvalues and eigenfunctions of the momentum-projected density evolution
operator have a correspondence with the quantum Neumann energy eigenstates in
billiard systems. While the classical eigenfunctions are well approximated by
the quantum Neumann eigenfunctions, the classical eigenvalues are of the form
f(\sqrt{E_n} vt) where {E_n} are close to the quantum Neumann eigenvalues and v
is the speed of the classical particle. Despite the approximate nature of the
correspondence, we demonstrate here that the exact quantum Neumann eigenstates
can be used to expand and evolve an arbitrary classical density on the energy
surface projected on to the configuration space. For the rectangular and
stadium billiards, results are compared with the actual evolution of the
density using classical trajectories.",0603061v2
2017-04-05,Superfluidity in density imbalanced bilayers of dipolar fermions,"We study the zero temperature phase diagram of an imbalanced bilayer of
dipolar fermions. We consider perpendicularly aligned identical dipoles in two
layers and investigate the effect of population imbalance on the ground state
phase at different layer spacings and average densities. The attractive part of
the interlayer interaction could lead to the BEC-BCS crossover and the Fermi
surface mismatch between two layers results in interesting uniform and
nonuniform superfluid phases, which we have investigated here using the BCS
mean-field theory together with the superfluid-mass density criterion. The
density imbalance reduces the pairing gap. At low densities, where the system
is on the BEC side of the crossover, this reduction is quite smooth while a
dense system rapidly becomes normal at intermediate density polarizations.
Stable homogeneous superfluidity is predicted to appear on the phase diagram
when the dipolar length exceeds both the layer spacing and the average
intralayer distance between dipoles, a regime which should be readily
accessible experimentally. This homogeneous superfluid phase becomes unstable
at intermediate densities and layer spacings. We have also examined that these
uniform and inhomogeneous superfluid phases survive when the effects of
intralayer screenings are also incorporated in the formalism.",1704.01275v1
2019-10-29,Thermal state of the intergalactic medium at $z\sim2-4$,"We present a new method to infer parameters of the temperature-density
relation in the intergalactic medium in the post-reionization epoch at $z\sim
2-4$. This method is based on the analysis of the Ly$\alpha$ absorbers
distribution over column densities and Doppler parameters by the model joint
probability density function. This approach allows us to measure the power-law
index $\gamma$ of the temperature-density relation and a certain combination of
the temperature at the mean density $T_0$ and hydrogen photoionization rate
$\Gamma$. To estimate $T_0$ and $\Gamma$ separately, we employ measurements of
the Ly$\alpha$ forest effective opacity and the model gas probability density
function. We show that $\gamma$ tends to be lower than 1.6 and reaches 1.3 at
redshift $\sim3$. The inferred temperatures at the mean density are
$\sim(2\pm0.5)\times10^4$ K in the studied redshift range. Both these estimates
favour HeII reionization at $z\gtrsim3$. We find that the hydrogen
photoionization rate is $\sim0.6\times10^{-12}$ s$^{-1}$, which is consistent
with previous measurements.",1910.13184v1
2006-10-11,Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals,"The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of
quantum mechanics, and constitutes the basis for the very successful
density-functional approach to inhomogeneous interacting many-particle systems.
Here we show that in formulations of density-functional theory (DFT) that
employ more than one density variable, applied to systems with a degenerate
ground state, there is a subtle loophole in the HK theorem, as all mappings
between densities, wave functions and potentials can break down. Two weaker
theorems which we prove here, the joint-degeneracy theorem and the
internal-energy theorem, restore the internal, total and exchange-correlation
energy functionals to the extent needed in applications of DFT to atomic,
molecular and solid-state physics and quantum chemistry. The joint-degeneracy
theorem constrains the nature of possible degeneracies in general many-body
systems.",0610322v1
2009-02-18,Does hybrid density functional theory predict a non-magnetic ground state for delta-Plutonium?,"Hybrid density functionals, which replaces a fraction of density functional
theory (DFT) exchange with exact Hartree-Fock (HF) exchange, have been used to
study the structural, magnetic, and electronic properties of delta-Plutonium.
The fractions of exact Hartree-Fock exchange used were 25%, 40%, and 55%.
Compared to the pure PBE functional, the lattice constants expanded with
respect to the experimental value when the PBE-HF hybrid functionals were
applied. A non-magnetic ground state was realized for 55% HF contribution;
otherwise the ground state was anti-ferromagnetic. The 5f electrons tend to
exhibit slight delocalization or itinerancy for the pure PBE functional and
well-defined localization for the hybrid functionals, with the degree of 5f
electron localization increasing with the amount of HF exchange. Overall, the
performance of the hybrid density functionals do not seem superior to pure
density functionals for delta-Plutonium.",0902.3240v1
2014-09-01,Quantum bright solitons in the Bose-Hubbard model with site-dependent repulsive interactions,"We introduce a one-dimensional (1D) spatially inhomogeneous Bose-Hubbard
model (BHM) with the strength of the onsite repulsive interactions growing,
with the discrete coordinate $z_{j}$, as $|z_{j}|^{\alpha }$ with $\alpha >0$.
Recently, the analysis of the mean-field (MF) counterpart of this system has
demonstrated self-trapping of robust unstaggered discrete solitons, under
condition $\alpha >1$. Using the numerically implemented method of the density
matrix renormalization group (DMRG), we demonstrate that, in a certain range of
interaction, the BHM also self-traps, in the ground state, into a soliton-like
configuration, at $\alpha >1$, and remains weakly localized at $\alpha <1$. An
essential quantum feature is a residual density in the background surrounding
the soliton-like peak in the BHM ground state, while in the MF limit the
finite-density background is absent. Very strong onsite repulsion eventually
destroys soliton-like states, and, for integer densities, the system enters the
Mott phase with a spatially uniform density",1409.0335v2
2015-08-19,Hohenberg-Kohn Theorems in Electrostatic and Uniform Magnetostatic Fields,"The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar
potential and the gauge invariant nondegenerate ground state density, and the
consequent Euler variational principle for the density, are proved for
arbitrary electrostatic field and the constraint of fixed electron number. The
HK theorems are generalized for spinless electrons to the added presence of an
external uniform magnetostatic field by introducing the new constraint of fixed
canonical orbital angular momentum. Thereby a bijective relationship between
the external scalar and vector potentials, and the gauge invariant
nondegenerate ground state density and physical current density, is proved. A
corresponding Euler variational principle in terms of these densities is also
developed. These theorems are further generalized to electrons with spin by
imposing the added constraint of fixed canonical orbital and spin angular
momentum. The proofs differ from the original HK proof, and explicitly account
for the many-to-one relationship between the potentials and the nondegenerate
ground state wave function.",1508.05960v1
2017-02-09,Trapped imbalanced fermionic superfluids in one dimension: A variational approach,"We propose and analyze a variational wave function for a
population-imbalanced one-dimensional Fermi gas that allows for
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two
fermion species, while also accounting for the harmonic confining potential. In
the strongly interacting regime, we find large spatial oscillations of the
order parameter, indicative of an FFLO state. The obtained density profiles
versus imbalance are consistent with recent experimental results as well as
with theoretical calculations based on combining Bethe ansatz with the local
density approximation. Although we find no signature of the FFLO state in the
densities of the two fermion species, we show that the oscillations of the
order parameter appear in density-density correlations, both in-situ and after
free expansion. Furthermore, above a critical polarization, the value of which
depends on the interaction, we find the unpaired Fermi-gas state to be
energetically more favorable.",1702.02933v1
2008-07-18,Weak momentum scattering and the conductivity of graphene,"Electrical transport in graphene offers a fascinating parallel to spin
transport in semiconductors including the spin-Hall effect. In the weak
momentum scattering regime the steady-state density matrix contains two
contributions, one linear in the carrier number density $n$ and characteristic
scattering time $\tau$, the other independent of either. In this paper we take
the Liouville equation as our starting point and demonstrate that these two
contributions can be identified with pseudospin conservation and
non-conservation respectively, and are connected in a non-trivial manner by
scattering processes. The scattering term has a distinct form, which is
peculiar to graphene and has important consequences in transport. The
contribution linear in $\tau$ is analogous to the part of the spin density
matrix which yields a steady state spin density, while the contribution
independent of $\tau$, is analogous to the part of the spin density matrix
which yields a steady state spin current. Unlike in systems with spin-orbit
interactions, the $n$ and $\tau$-independent part of the conductivity is
reinforced in the weak momentum scattering regime by scattering between the
conserved and non-conserved pseudospin distributions.",0807.3051v2
2021-09-14,Equation of state of neutron star matter and its warm extension with an interacting hadron resonance gas,"We propose an interpolating equation of state that satisfies
phenomenologically established boundary conditions in two extreme regimes at
high temperature and low baryon density and at low temperature and high baryon
density. We confirm that the hadron resonance gas model with the
Carnahan-Starling excluded volume effect can reasonably fit the empirical
equation of state at high density up to several times the normal nuclear
density. We identify the onsets of strange particles and quantify the
strangeness contents in dense matter. We finally discuss the finite temperature
effects and estimate the thermal index $\Gamma_{\rm th}$ as a function of the
baryon density, which should be a crucial input for the core-collapse supernova
and the binary neutron star merger simulations.",2109.06799v2
2002-07-10,Description of Deconfinement at Finite Matter Density in a Generalized Nambu--Jona-Lasinio Model,"Recent years have seen extensive applications of the Nambu--Jona-Lasinio
(NJL) model in the study of matter at high density. There is a good deal of
interest in the predictions of diquark condensation and color
superconductivity, with suggested applications to the study the properties of
neutron stars. As the researchers in this field note, the NJL model does not
describe confinement, so that one is limited to the study of the deconfined
phase, which may set in at several times nuclear matter density. Recently, we
have extended the NJL model to include a covariant confinement model. In the
present work our goal is to include a phenomenological model of deconfinement
at finite matter density, using some analogy to what is known concerning
""string breaking"" and deconfinement at finite temperature. Various models may
be used, but for this work we choose a specific model for the density
dependence of the parameters of our confining interaction. We perform
relativistic random-phase-approximation (RPA) calculations of the properties of
the $\pi(138), K(495), f_0(980), a_0(980)$ and $K_0^*(1430)$ mesons and their
radial excitations. In the model chosen for this work, there are no mesonic
states beyond about $2\rho_{NM}$, where $\rho_{NM}$ is the density of nuclear
matter. This inability of the model to support hadronic excitations at large
values of the density is taken as a signal of deconfinement. In addition to the
density dependence of the confining interaction, we use the density-dependent
quark mass values obtained in either the SU(2) or SU(3)-flavor versions of the
NJL model.",0207135v1
2018-09-30,Ab-initio description of excited states of a one-dimensional nuclear matter with the Hohenberg-Kohn-theorem-inspired functional-renormalization-group method,"We demonstrate for the first time that a functional-renormalization-group
aided density-functional theory (FRG-DFT) describes well the characteristic
features of the excited states as well as the ground state of an interacting
many-body system with infinite number of particles in a unified manner. The
FRG-DFT is applied to a $(1+1)$-dimensional spinless nuclear matter. For the
excited states, the density--density spectral function is calculated at the
saturation point obtained in the framework of FRG-DFT, and it is found that our
result reproduces a notable feature of the density--density spectral function
of the non-linear Tomonaga-Luttinger liquid: The spectral function has a
singularity at the edge of its support of the lower-energy side. These findings
suggest that the FRG-DFT is a promising first-principle scheme to analyze the
excited states as well as the ground states of quantum many-body systems
starting from the inter-particle interaction.",1810.00422v2
2018-04-14,Gravitational wave asteroseismology limits from low density nuclear matter and perturbative QCD,"We investigate the fundamental mode of non-radial oscillations of
non-rotating compact stars in general relativity using a set of equations of
state (EOS) connecting state-of-the-art calculations at low and high densities.
Specifically, a low density model based on the chiral effective field theory
(EFT) and high density results based on perturbative Quantum Chromodynamics
(QCD) are matched through different interpolating polytropes fulfilling
thermodynamic stability and subluminality of the speed of sound, together with
the additional requirement that the equations of state support a two solar mass
star. We employ three representative models (EOS I, II and III) presented in
Ref. [1] such that EOS I gives the minimum stellar radius, EOS II the maximum
stellar mass, and EOS III the maximum stellar radius. Using this family of
equations of state, we find that the frequency and the damping time of the
$f$-mode are constrained within narrow quite model-independent windows. We also
analyze some proposed empirical relations that describe the $f$-mode properties
in terms of the average density and the compactness of the neutron star. We
discuss the stringency of these constrains and the possible role of physical
effects that cannot be encoded in a mere interpolation between low and high
density EOSs.",1804.05155v2
2015-09-08,Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice,"We consider an efficient scheme to simulate fermionic Hubbard models with
nonlocal density-density interactions in two dimensions, based on bond-centered
auxiliary-field quantum Monte Carlo. The simulations are shown to be
sign-problem free within a finite, restricted parameter range. Using this
approach, we first study the Hubbard model on the half-filled square lattice
bilayer, including an interlayer repulsion term in addition to the local
repulsion, and present the ground state phase diagram within the accessible
parameter region. Starting from the antiferromagnetically ordered state in the
absence of interlayer repulsion, the interlayer interactions are found to
destabilize the antiferromagnetic order, leading to a band insulator state.
Moreover, for sufficiently strong interlayer tunneling, we also observe the
emergence of a direct dimer product state of mixed D-Mott and S-Mott character
along the equal coupling line. We discuss the stability range of this state
within strong-coupling perturbation theory. Furthermore, we consider the
Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions.
Such an interaction is found to enhance both charge density and spin-current
correlations within the semimetallic region. However, inside the accessible
parameter region, they do not stabilize long-ranged charge density wave order
nor a quantum spin Hall state, and the only insulating state that we observe
exhibits long-range antiferromagnetism.",1509.02367v1
2003-09-10,Diffractive Final States and Tests of QCD Factorisation,"Measurements of hard diffractive final states performed with the H1
experiment at HERA are presented and confronted with predictions based on
diffractive parton densities.",0309037v1
2007-06-13,Compressibility and equation of state of finite nuclei,"We present a new approach for calculating the nuclear equation of state and
compressibility for finite nuclei using the density-constrained Hartree-Fock
method.",0706.1960v1
2012-06-19,Positive Quantum Brownian Evolution,"Using the independent oscillator model with an arbitrary system potential, we
derive a quantum Brownian equation assuming a correlated total initial state.
Although not of Lindblad form, the equation preserves positivity of the density
operator on a restricted set of initial states.",1206.4269v1
2021-10-04,Reducing the detection of genuine entanglement of n qubits to two qubits,"We propose a criterion for the detection of genuine entanglement of pure
multiqubit states. To this aim, we define an operator called the losing one
qubit operator, which is different from the reduced density operator. The
states obtained from a multiqubit state by applying the losing one qubit
operator are referred to as its projected states. We show that all of the
projected states of a pure product n-qubit state are pure product states
provided that it cannot be written as a product of a single qubit state and a
genuinely entangled (n-1)-qubit state. We also show that a pure n-qubit state
is genuinely entangled provided that the state has at least two genuinely
entangled (n-1)-qubit projected states. By repeating the losing process, we
reduce the detection of entanglement of pure n-qubit states to the one of pure
two-qubit states. Also we write a LISP program for the reduction process.",2110.01479v1
2001-09-03,Statistical ensembles and density of states,"We propose a definition of microcanonical and canonical statistical ensembles
based on the concept of density of states. This definition applies both to the
classical and the quantum case. For the microcanonical case this allows for a
definition of a temperature and its fluctuation, which might be useful in the
theory of mesoscopic systems. In the quantum case the concept of density of
states applies to one-particle Schroedinger operators, in particular to
operators with a periodic potential or to random Anderson type models. In the
case of periodic potentials we show that for the resulting $n$-particle system
the density of states is $[(n-1)/2]$ times differentiable, such that like for
classical microcanonical ensembles a (positive) temperature may be defined
whenever $n\geq 5$. We expect that a similar result should also hold for
Anderson type models. We also provide the first terms in asymptotic expansions
of thermodynamic quantities at large energies for the microcanonical ensemble
and at large temperatures for the canonical ensemble. A comparison shows that
then both formulations asymptotically give the same results.",0109034v2
2001-10-04,Microcanonical determination of the order parameter critical exponent,"A highly efficient Monte Carlo method for the calculation of the density of
states of classical spin systems is presented. As an application, we
investigate the density of states Omega_N(E,M) of two- and three-dimensional
Ising models with N spins as a function of energy E and magnetization M. For a
fixed energy lower than a critical value E_{c,N} the density of states exhibits
two sharp maxima at $M = \pm M_{sp}(E)$ which define the microcanonical
spontaneous magnetization. An analysis of the form $M_{sp}(E) \propto
(E_{c,\infty}-E)^{\beta_\epsilon}$ yields very good results for the critical
exponent $\beta_\epsilon$, thus demonstrating that critical exponents can be
determined by analysing directly the density of states of finite systems.",0110090v2
2003-07-03,On the effect of far impurities on the density of states of two-dimensional electron gas in a strong magnetic field,"The effect of impurities situated at different distances from a
two-dimensional electron gas on the density of states in a strong magnetic
field is analyzed. Based on the exact result of Brezin, Gross, and Itzykson, we
calculate the density of states in the whole energy range, assuming the Poisson
distribution of impurities in the bulk. It is shown that in the case of small
impurity concentration the density of states is qualitatively different from
the model case when all impurities are located in the plane of the
two-dimensional electron gas.",0307077v1
2008-09-04,Long-lived $2s$ state of muonic hydrogen: population and lifetime,"Ab initio study of the density-dependent population and lifetime of the
long-lived $(\mu p)_{2s}$ and the yield of $(\mu p)_{1s}$ atoms with kinetic
energy 0.9 keV have been performed for the first time. The direct Coulomb
$2s\to 1s$ deexcitation is proved to be the dominant quenching mechanism of the
$2s$ state at kinetic energy below $2p$ threshold and explain the lifetime of
the metastable $2s$ state and high-energy 0.9 keV component of $(\mu p)_{1S}$
observed at low densities. The cross sections of the elastic, Stark and Coulomb
deexcitation processes have been calculated in the close-coupling approach
taking into account for the first time both the closed channels and the
threshold effects due to vacuum polarization shifts of the $ns$ states. The
cross sections are used as the input data in the detailed study of the atomic
cascade kinetics. The theoretical predictions are compared with the known
experimental data at low densities. The 40% yield of the 0.9 keV$(\mu p)_{1s}$
atoms is predicted for liquid hydrogen density.",0809.0742v1
2011-12-12,Two dimensional Dirac fermions in the presence of long-range correlated disorder,"We consider 2D Dirac fermions in the presence of three types of disorder:
random scalar potential, random gauge potential and random mass with long-range
correlations decaying as a power law. Using various methods such as the
self-consistent Born approximation (SCBA), renormalization group (RG), the
matrix Green function formalism and bosonisation we calculate the density of
states and study the full counting statistics of fermionic transport at lower
energy. The SCBA and RG show that the random correlated scalar potentials
generate an algebraically small energy scale below which the density of states
saturates to a constant value. For correlated random gauge potential, RG and
bosonisation calculations provide consistent behavior of the density of states
which diverges at zero energy in an integrable way. In the case of correlated
random mass disorder the RG flow has a nontrivial infrared stable fixed point
leading to a universal power-law behavior of the density of states and also to
universal transport properties. In contrast to uncorrelated case the correlated
scalar potential and random mass disorders give rise to deviation from the
pseudodiffusive transport already to lowest order in disorder strength.",1112.2743v1
2012-02-13,An extended equation of state for core-collapse simulations,"In stellar core-collapse events matter is heated and compressed to densities
above nuclear matter saturation density. For progenitors stars with masses
above about 25 solar masses, which eventually form a black hole, the
temperatures and densities reached during the collapse are so high that a
traditional description in terms of electrons, nuclei, and nucleons is no
longer adequate. We present here an improved equation of state which contains
in addition pions and hyperons. They become abundant in the high temperature
and density regime. We study the different constraints on such an equation of
state, coming from both hyperonic data and observations of neutron star
properties. In order to test the zero-temperature versions, we perform
numerical simulations of the collapse of a neutron star with such additional
particles to a black hole. We discuss the influence of the additional particles
on the thermodynamic properties within the hot versions of the equation of
state and we show that in regimes relevant to core-collapse and black hole
formation, the effects of pions and hyperons on pressure, internal energy and
sound speed are not negligible.",1202.2679v1
2012-11-13,Tuning the electromagnetic local density of states in graphene-covered systems via strong coupling with graphene plasmons,"It is known that the near-field spectrum of the local density of states of
the electromagnetic field above a SiC/air interface displays an intense narrow
peak due to the presence of a surface polariton. It has been recently shown
that this surface wave can be strongly coupled with the sheet plasmon of
graphene in graphene-SiC heterosystems. Here, we explore the interplay between
these two phenomena and demonstrate that the spectrum of the electromagnetic
local density of states in these systems presents two peaks whose position
depends dramatically both on the distance to the interface and on the chemical
potential of graphene. This paves the way towards the active control of the
local density of states.",1211.3145v2
2015-07-19,Density of states and magnetotransport in Weyl semimetals with long-range disorder,"We study the density of states and magnetotransport properties of disordered
Weyl semimetals, focusing on the case of a strong long-range disorder. To
calculate the disorder-averaged density of states close to nodal points, we
treat exactly the long-range random potential fluctuations produced by charged
impurities, while the short-range component of disorder potential is included
systematically and controllably with the help of a diagram technique. We find
that for energies close to the degeneracy point, long-range potential
fluctuations lead to a finite density of states. In the context of transport,
we discuss that a self-consistent theory of screening in magnetic field may
conceivably lead to non-monotonic low-field magnetoresistance.",1507.05349v2
2013-08-13,Density cubes and higher-order interference theories,"Can quantum theory be seen as a special case of a more general probabilistic
theory, similarly as classical theory is a special case of the quantum one? We
study here the class of generalized probabilistic theories defined by the order
of interference they exhibit as proposed by Sorkin. A simple operational
argument shows that the theories require higher-order tensors as a
representation of physical states. For the third-order interference we derive
an explicit theory of ""density cubes"" and show that quantum theory, i.e. theory
of density matrices, is naturally embedded in it. We derive the genuine
non-quantum class of states and non-trivial dynamics for the case of
three-level system and show how one can construct the states of higher
dimensions. Additionally to genuine third-order interference, the density cubes
are shown to violate the Leggett-Garg inequality beyond the quantum Tsirelson
bound for temporal correlations.",1308.2822v2
2014-03-03,The impact of hot charge carrier mobility on photocurrent losses in polymer-based solar cells,"A typical signature of charge extraction in disordered organic systems is
dispersive transport, which implies a distribution of charge carrier mobilities
that negatively impact on device performance. Dispersive transport has been
commonly understood to originate from a time-dependent mobility of hot charge
carriers that reduces as excess energy is lost during relaxation in the density
of states. In contrast, we show via photon energy, electric field and film
thickness independence of carrier mobilities that the dispersive photocurrent
in organic solar cells originates not from the loss of excess energy during hot
carrier thermalization, but rather from the loss of carrier density to trap
states during transport. Our results emphasize that further efforts should be
directed to minimizing the density of trap states, rather than controlling
energetic relaxation of hot carriers within the density of states.",1403.0311v2
2020-12-02,Phonon density of states in lanthanide-based nanocrystals,"We report a combined inelastic neutron and X-ray scattering study of the
phonon density of states of the nano- and microcrystalline lanthanide-based
materials NaY$_{0.8}$Yb$_{0.18}$Er$_{0.02}$F$_4$ and
NaGd$_{0.8}$Yb$_{0.18}$Er$_{0.02}$F$_4$. While large (20 nm) nanocrystals
display the same vibrational spectra as their microcrystalline counterparts, we
find an enhanced phonon density of states at low energies, $E \leq
15\,\rm{meV}$, in ultra-small (5 nm) NaGd$_{0.8}$Yb$_{0.18}$Er$_{0.02}$F$_4$
nanocrystals which we assign to an increased relative spectral weight of
surface phonon modes. Based on our observations for ultra-small nanocrystals,
we rationalize that an increase of the phonon density of states in large
nanocrystals due to surface phonons is too small to be observed in the current
measurements. The experimental approach described in this report constitutes
the first step toward the rationalization of size effects on the modification
of the absolute upconversion quantum yield of upconverting nanocrystals.",2012.01056v1
2022-04-13,Impurity bands in magnetic superconductors with spin density wave,"Magnetic superconductors define a broad class of strongly correlated
materials in which superconductivity may coexist with either localized or
itinerant long-range magnetic order. In this work we consider a multiband model
of a disordered magnetic superconductor which realizes coexistence of
unconventional superconductivity and a spin-density-wave. We derive an exact
$T$-matrix and compute a single particle density of states in this system. In a
purely superconducting state the interband scattering potential leads to an
appearance of the localized Yu-Shiba-Rusinov bound states. Our main finding is
that in the fairly broad swath of the coexistence region superconductivity
remains fully gapped despite the presence of the impurity bands. We also
discuss the effects of spatial inhomogeneities on the density of states in
strongly contaminated superconductors.",2204.06565v2
2014-10-14,Fractional Quantum Hall States of Dipolar Gases in Chern Bands,"We study fermions and hardcore bosons with long range dipolar interactions at
fractional fillings in a topological checkerboard lattice with short-range
hoppings up to next-next-nearest neighbors \cite{Neupert2011}. We consider the
case that the dipoles are aligned in the perpendicular direction by an external
field without the complication of anisotropic interaction. Using exact
diagonalization, we find clear signatures of fractional quantum Hall (FQH)
states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in
the lowest Chern band with a robust spectrum gap at moderate dipolar
interaction strength. The robustness of these FQH states against long-range
interaction tail and band flatness is investigated. When the dipolar
interaction decreases, the fermionic FQH states turn into normal states, and
the bosonic 1/4-FQH state turns into a superfluid state. The bosonic 1/2-FQH
state survives even in the absence of the dipolar interaction, but vanishes
when the hard core becomes a soft core with a critical onsite repulsion. In the
thin torus limit, the static density structure factors indicates that the FQH
state turns into a commensurate charge density wave (CDW) state.",1410.3724v2
2013-08-29,Conditions for degradability of tripartite quantum states,"Alice, Bob, and Eve share a pure quantum state. We introduce the notion of
state degradability by asking whether the joint density of Alice and Eve can be
transformed to the joint density of Alice and Bob by processing Eve's part
through a quantum channel, in order words, degrading Eve. We prove necessary
and sufficient conditions for state degradability and provide an efficient
method to quickly rule out degradability for a given state. The problem of
determining degradability of states is different from that of quantum channels,
although the notion is similar. One application of state degradability is that
it can be used to test channel degradability. In particular, the degradability
of the output state of a channel obtained from the maximally entangled input
state gives information about the degradability of the channel.",1308.6359v2
2023-05-24,Topological surface states hybridized with bulk states of Bi-doped PbSb2Te4 revealed in quasiparticle interference,"Topological surface states of Bi-doped PbSb2Te4 [Pb(Bi0.20Sb0.80)2Te4] are
investigated through analyses of quasiparticle interference (QPI) patterns
observed by scanning tunneling microscopy. Interpretation of the experimental
QPI patterns in the reciprocal space is achieved by numerical QPI simulations
using two types of surface density of states produced by density functional
theory calculations or a kp surface state model. We found that the Dirac point
(DP) of the surface state appears in the bulk band gap of this material and,
with the energy being away from the DP, the isoenergy contour of the surface
state is substantially deformed or separated into segments due to hybridization
with bulk electronic states. These findings provide a more accurate picture of
topological surface states, especially at energies away from the DP, providing
valuable insight into the electronic properties of topological insulators.",2305.15198v2
2018-06-25,"Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH","We obtain multiple exact results on the entanglement of the exact excited
states of non-integrable models we introduced in arXiv:1708.05021. We first
discuss a general formalism to analytically compute the entanglement spectra of
exact excited states using Matrix Product States and Matrix Product Operators
and illustrate the method by reproducing a general result on single-mode
excitations. We then apply this technique to analytically obtain the
entanglement spectra of the infinite tower of states of the spin-$S$ AKLT
models in the zero and finite energy density limits. We show that in the zero
density limit, the entanglement spectra of the tower of states are multiple
shifted copies of the ground state entanglement spectrum in the thermodynamic
limit. We show that such a resemblance is destroyed at any non-zero energy
density. Furthermore, the entanglement entropy $\mathcal{S}$ of the states of
the tower that are in the bulk of the spectrum is sub-thermal $\mathcal{S}
\propto \log L$, as opposed to a volume-law $\mathcal{S} \propto L$, thus
indicating a violation of the strong Eigenstate Thermalization Hypothesis
(ETH). These states are examples of what are now called many-body scars.
Finally, we analytically study the finite-size effects and symmetry-protected
degeneracies in the entanglement spectra of the excited states, extending the
existing theory.",1806.09624v2
2022-06-22,Number-conserving solution for dynamical quantum backreaction in a Bose-Einstein condensate,"We provide a number-conserving approach to the backreaction problem of small
quantum fluctuations onto a classical background for the exactly soluble
dynamical evolution of a Bose-Einstein condensate, experimentally realizable in
the ultracold gas laboratory. A force density exerted on the gas particles
which is of quantum origin is uniquely identified as the deviation from the
classical Eulerian force density. The backreaction equations are then explored
for the specific example of a finite size uniform density condensate initially
at rest. By assuming that the condensate starts from a non-interacting regime,
and in its ground state, we fix a well-defined initial vacuum condition, which
is driven out-of-equilibrium by instantaneously turning on the interactions.
The assumption of this initial vacuum accounts for the ambiguity in choosing a
vacuum state for interacting condensates, which is due to phase diffusion and
the ensuing condensate collapse. As a major finding, we reveal that the time
evolution of the condensate cloud leads to condensate density corrections that
cannot in general be disentangled from the quantum depletion in measurements
probing the power spectrum of the total density. Furthermore, while the
condensate is initially at rest, quantum fluctuations give rise to a nontrivial
condensate flux, from which we demonstrate that the quantum force density
attenuates the classical Eulerian force. Finally, the knowledge of the particle
density as a function of time for a condensate at rest determines, to order
$N^0$, where $N$ is the total number of particles, the quantum force density,
thus offering a viable route for obtaining experimentally accessible quantum
backreaction effects.",2206.11317v1
2011-02-23,"Reconstructing the equation of state and density parameter for dark energy from combined analysis of recent SNe Ia, OHD and BAO data","We adopt a model independent method to reconstruct the dark energy equation
of state by analyzing 5 sets of SNe Ia data along with Baryon Acoustic
Oscillation (BAO) and Observational Hubble Data (OHD). The SNe Ia data sets
include the most recent UNION2 data and other data compilations from the year
2007 to the present. We assume a closed form parametrization of the luminosity
distance in terms of redshift and perform a $\chi^2$ analysis of the
observational data. The matter density at the present epoch $\Omega_m^0$ is
also taken to be a parameter in the analysis and its best-fit values are
obtained for each of the data sets. We found a strong dependence of dark energy
equation of state on the matter density in the present and earlier epoch. From
the analysis, we also predict the lower limit of matter density parameter at an
earlier epoch within 1$\sigma$ confidence level for a flat FRW universe. The
dark energy equation of state appears to be a slow varying function of $z$. The
variation of dark energy density parameter and the matter density parameter are
also shown along with their 1$\sigma$ variations.",1102.4726v2
2012-06-27,Time-dependent density functional theory on a lattice,"A time-dependent density functional theory (TDDFT) for a quantum many-body
system on a lattice is formulated rigorously. We prove the uniqueness of the
density-to-potential mapping and demonstrate that a given density is
$v$-representable if the initial many-body state and the density satisfy
certain well defined conditions. In particular, we show that for a system
evolving from its ground state any density with a continuous second time
derivative is $v$-representable and therefore the lattice TDDFT is guaranteed
to exist. The TDDFT existence and uniqueness theorem is valid for any connected
lattice, independently of its size, geometry and/or spatial dimensionality. The
general statements of the existence theorem are illustrated on a pedagogical
exactly solvable example which displays all details and subtleties of the proof
in a transparent form. In conclusion we briefly discuss remaining open problems
and directions for a future research.",1206.6267v1
2020-06-14,Recurrent Distillation based Crowd Counting,"In recent years, with the progress of deep learning technologies, crowd
counting has been rapidly developed. In this work, we propose a simple yet
effective crowd counting framework that is able to achieve the state-of-the-art
performance on various crowded scenes. In particular, we first introduce a
perspective-aware density map generation method that is able to produce
ground-truth density maps from point annotations to train crowd counting model
to accomplish superior performance than prior density map generation
techniques. Besides, leveraging our density map generation method, we propose
an iterative distillation algorithm to progressively enhance our model with
identical network structures, without significantly sacrificing the dimension
of the output density maps. In experiments, we demonstrate that, with our
simple convolutional neural network architecture strengthened by our proposed
training algorithm, our model is able to outperform or be comparable with the
state-of-the-art methods. Furthermore, we also evaluate our density map
generation approach and distillation algorithm in ablation studies.",2006.07755v1
2024-02-19,Image Super-resolution Inspired Electron Density Prediction,"Drawing inspiration from the domain of image super-resolution, we view the
electron density as a 3D grayscale image and use a convolutional residual
network to transform a crude and trivially generated guess of the molecular
density into an accurate ground-state quantum mechanical density. We find that
this model outperforms all prior density prediction approaches. Because the
input is itself a real-space density, the predictions are equivariant to
molecular symmetry transformations even though the model is not constructed to
be. Due to its simplicity, the model is directly applicable to unseen molecular
conformations and chemical elements. We show that fine-tuning on limited new
data provides high accuracy even in challenging cases of exotic elements and
charge states. Our work suggests new routes to learning real-space physical
quantities drawing from the established ideas of image processing.",2402.12335v1
2013-05-21,"Does a proton ""bubble"" structure exist in the low-lying states of 34Si?","The possible existence of a ""bubble"" structure in the proton density of
$^{34}$Si has recently attracted a lot of research interest. To examine the
existence of the ""bubble"" structure in low-lying states, we establish a
relativistic version of configuration mixing of both particle number and
angular momentum projected quadrupole deformed mean-field states and apply this
state-of-the-art beyond relativistic mean-field method to study the density
distribution of the low-lying states in $^{34}$Si. An excellent agreement with
the data of low-spin spectrum and electric multipole transition strengths is
achieved without introducing any parameters. We find that the central
depression in the proton density is quenched by dynamic quadrupole shape
fluctuation, but not as significantly as what has been found in a beyond
non-relativistic mean-field study. Our results suggest that the existence of
proton ""bubble"" structure in the low-lying excited $0^+_2$ and $2^+_1$ states
is very unlikely.",1305.4690v1
2018-09-05,Fast Computation of Many-Body Entanglement,"Mixed state entanglement measures can act as a versatile probes of many-body
systems. However, they are generally hard to compute, often relying on tricky
optimizations. One measure that is straightforward to compute is the
logarithmic negativity, yet done naively even this is still limited to small
system sizes. Here, we introduce a method to compute the logarithmic negativity
for arbitrary subsystems of a densely represented state, as well as block
subsystems of matrix product states. The method combines lazily evaluated,
tensor network representations of the partially transposed density matrix with
stochastic Lanczos quadrature, and is easily extendible to other quantities and
classes of many-body states. As examples, we compute the entanglement within
random pure states for density matrices of up to 30 qubits, explore scrambling
in a many-body quench, and match the results of conformal field theory in the
ground-state of the Heisenberg model for density matrices of up to 1000 spins.
An implementation of the algorithm has been made available in the open-source
library \textit{quimb}.",1809.01685v1
2014-03-31,Searching for 4$α$ linear-chain structure in excited states of $^{16}$O with a covariant density functional theory,"A study of 4$\alpha$ linear-chain structure in high-lying collective
excitation states of $^{16}$O with a covariant density functional theory is
presented. The low-spin states are obtained by configuration mixing of
particle-number and angular-momentum projected quadrupole deformed mean-field
states with generator coordinate method. The high-spin states are determined by
cranking calculations. These two calculations are based on the same energy
density functional PC-PK1. We have found a rotational band at low-spin with the
dominated intrinsic configuration considered to be the one that 4$\alpha$
clusters stay along a common axis. The strongly deformed rod shape also appears
in the high-spin region with the angular momentum $13-18\hbar$; however whether
the state is pure $4\alpha$ linear chain or not is less obvious than that in
the low-spin states.",1403.7940v2
2009-12-24,Exciton Condensate Modulation in Electron-Hole Bilayers: A Real-Space Visualization,"We study the texture of the exciton condensate at low temperatures in an
independently gated electron-hole bilayer system. A model Hamiltonian is solved
in real space within a mean-field approximation. It is found that, with
increased electron-hole density polarization, the system experiences phase
transformations from the zero center-of-mass momentum superfluid state, through
one- and two-dimensional exciton pair modulated states, into the normal state.
At weak density polarization, the modulating state resembles the
Larkin-Ovchinikov state in superconductors in the presence of an exchange field
in the weak-coupling BCS limit, and becomes stripe-like in the strong coupling
BEC limit. In the one-dimensional modulated phase, the density of states
exhibits low-energy intra-gap resonance quasiparticle states, which are
localized in the nodal region.",0912.4915v1
2018-01-09,Unidirectional spin density wave state in metallic (Sr1-xLax)2IrO4,"Materials that exhibit both strong spin orbit coupling and electron
correlation effects are predicted to host numerous new electronic states. One
prominent example is the Jeff =1/2 Mott state in Sr2IrO4, where introducing
carriers is predicted to manifest high temperature superconductivity analogous
to the S=1/2 Mott state of La2CuO4. While bulk superconductivity currently
remains elusive, anomalous quasi-particle behaviors paralleling those in the
cuprates such as pseudogap formation and the formation of a d-wave gap are
observed upon electron-doping Sr2IrO4. Here we establish a magnetic parallel
between electron-doped Sr2IrO4 and hole-doped La2CuO4 by unveiling a spin
density wave state in electron-doped Sr2IrO4. Our magnetic resonant x-ray
scattering data reveal the presence of an incommensurate magnetic state
reminiscent of the diagonal spin density wave state observed in the monolayer
cuprate (La1-xSrx)2CuO4. This link supports the conjecture that the quenched
Mott phases in electron-doped Sr2IrO4 and hole-doped La2CuO4 support common
competing electronic phases.",1801.03076v1
2017-09-23,Assessing Excited State Energy Gaps with Time-Dependent Density Functional Theory on Ru(II) Complexes,"A set of density functionals coming from different rungs on Jacob's ladder
are employed to evaluate the electronic excited states of three Ru(II)
complexes. While most studies on the performance of density functionals compare
the vertical excitation energies, in this work we focus on the energy gaps
between the electronic excited states, of the same and different multiplicity.
Excited state energy gaps are important for example to determine radiationless
transition probabilities. Besides energies, a functional should deliver the
correct state character and state ordering. Therefore, wavefunction overlaps
are introduced to systematically evaluate the effect of different functionals
on the character of the excited states. As a reference, the energies and state
characters from multi-state second-order perturbation theory complete active
space (MS-CASPT2) are used. In comparison to MS-CASPT2, it is found that while
hybrid functionals provide better vertical excitation energies, pure
functionals typically give more accurate excited state energy gaps. Pure
functionals are also found to reproduce the state character and ordering in
closer agreement to MS-CASPT2 than the hybrid functionals.",1709.08052v1
2017-03-27,Density classification performance and ergodicity of the Gacs-Kurdyumov-Levin cellular automaton model IV,"Almost four decades ago, Gacs, Kurdyumov, and Levin introduced three
different cellular automata to investigate whether one-dimensional
nonequilibrium interacting particle systems are capable of displaying phase
transitions and, as a by-product, introduced the density classification problem
(the ability to classify arrays of symbols according to their initial density)
in the cellular automata literature. Their model II became a well known model
in theoretical computer science and statistical mechanics. The other two
models, however, did not receive much attention. Here we characterize the
density classification performance of Gacs, Kurdyumov, and Levin's model IV, a
four-state cellular automaton with three absorbing states---only two of which
are attractive---, by numerical simulations. We show that model IV compares
well with its sibling model II in the density classification task: the
additional states slow down the convergence to the majority state but confer a
slight advantage in classification performance. We also show that,
unexpectedly, initial states diluted in one of the nonclassifiable states are
more easily classified. The performance of model IV under the influence of
noise was also investigated and we found signs of an ergodic-nonergodic phase
transition at some small finite positive level of noise, although the evidences
are not entirely conclusive. We set an upper bound on the critical point for
the transition, if any.",1703.09038v3
2004-11-10,The Ultimate Energy Density of Observable Cold Matter,"We demonstrate that the largest measured mass of a neutron star establishes
an upper bound to the energy density of observable cold matter. An equation of
state-independent expression satisfied by both normal neutron stars and
self-bound quark matter stars is derived for the largest energy density inside
stars as a function their masses. The largest observed mass sets the lowest
upper limit to the density. Implications from existing and future neutron star
mass measurements are discussed.",0411280v1
2007-08-24,"Ab-initio calculation of the vibrational modes of SiH4, H2SiO, Si10H16, and Si10H14O","We have studied the normal modes of hydrogenated and oxidized silicon
nanocrystals, namely SiH4 (silan), H2SiO (silanon), Si10H16 and Si10H14O. The
small clusters (SiH4 and H2SiO) have been used for convergence tests and their
bondlengths and frequencies have been compared with experimental and
theoretical reference data. For the large clusters (Si10H16 and Si10H14O) we
have investigated the vibrational density of states where we have identified
the oxygen-related spectral features. The vibrational modes have been also
analyzed with respect to the displacement patterns. The calculations have been
carried out within the density-functional and density-functional perturbation
theory using the local-density approximation.",0708.3312v1
2008-01-13,Density functional methods for polymers: a coil-globule transition case study,"We consider a free energy functional on the monomer density function that is
suitable for the study of coil-globule transition. We demonstrate, with
explicitly stated assumptions, why the entropic contribution is in the form of
the Kullback-Leibler distance, and that the energy contribution is given by
two-body and three-body terms. We then solve for the free energy analytically
on a set of trial density functions, and reproduce de Gennes' classical theory
on polymer coil-globule transition. We then discuss how our formalism can be
applied to study polymer dynamics from the perspective of dynamical density
function theory.",0801.1989v3
2008-09-23,Density-functional fidelity approach to quantum phase transitions,"We propose a new approach to quantum phase transitions in terms of the
density-functional fidelity, which measures the similarity between density
distributions of two ground states in parameter space. The key feature of the
approach, as we will show, is that the density-functional fidelity can be
measured easily in experiments. Both the validity and versatility of the
approach are checked by the Lipkin-Meshkov-Glick model and the one-dimensional
Hubbard model.",0809.3856v1
2008-12-08,Recent progress in lattice QCD at finite density,"We review recent progress in lattice QCD at finite density. The phase diagram
of QCD and the equation of state at finite temperature and density are
discussed. In particular, we focus on the critical point terminating a first
order phase transition line in the high density region. The critical point is
one of the most interesting features that may be discovered in heavy-ion
collision experiments. We summarize the current discussion on the existence of
a critical point in the QCD phase diagram and discuss some attempts to find the
critical point by numerical simulations.",0812.1534v1
2009-02-07,Density-matrix renormalization study of the frustrated fermions on the triangular lattice,"We show that the two-dimensional density-matrix renormalization analysis is
useful to detect the symmetry breaking in the fermionic model on a triangular
lattice. Under the cylindrical boundary conditions with chemical potentials on
edge sites, we find that the open edges work as perturbation to select the
strongest correlations {\it only in the presence of a long range order}. We
also demonstrate that the ordinary size scaling analysis on the charge gap as
well as that of the local charge density under this boundary condition could
determine the metal-insulator phase boundary, which scales almost perfectly
with the density of states and the exact solutions in the weak and strong
coupling region, respectively.",0902.1244v1
2010-02-23,Symmetry energy at subnuclear densities deduced from nuclear masses,"We examine how nuclear masses are related to the density dependence of the
symmetry energy. Using a macroscopic nuclear model we calculate nuclear masses
in a way dependent on the equation of state of asymmetric nuclear matter. We
find by comparison with empirical two-proton separation energies that a smaller
symmetry energy at subnuclear densities, corresponding to a larger density
symmetry coefficient L, is favored. This tendency, which is clearly seen for
nuclei that are neutron-rich, nondeformed, and light, can be understood from
the property of the surface symmetry energy in a compressible liquid-drop
picture.",1002.4325v2
2010-11-15,Time-Dependent Density Functional Theory for Driven Lattice Gas Systems with Interactions,"We present a new method to describe the kinetics of driven lattice gases with
particle-particle interactions beyond hard-core exclusions. The method is based
on the time-dependent density functional theory for lattice systems and allows
one to set up closed evolution equations for mean site occupation numbers in a
systematic manner. Application of the method to a totally asymmetric site
exclusion process with nearest-neighbor interactions yields predictions for the
current-density relation in the bulk, the phase diagram of non-equilibrium
steady states and the time evolution of density profiles that are in good
agreement with results from kinetic Monte Carlo simulations.",1011.3415v1
2012-05-08,Quantum phases of Bose-Bose mixtures on a triangular lattice,"We investigate the zero temperature quantum phases of a Bose-Bose mixture on
a triangular lattice using Bosonic Dynamical Mean Field Theory (BDMFT). We
consider the case of total filling one where geometric frustration arises for
asymmetric hopping. We map out a rich ground state phase diagram including
xy-ferromagnetic, spin-density wave, superfluid, and supersolid phases. In
particular, we identify a stripe spin-density wave phase for highly asymmetric
hopping. On top of the spin-density wave, we find that the system generically
shows weak charge (particle) density wave order.",1205.1806v2
2013-02-19,Pasta phases in neutron star studied with extended relativistic mean field models,"To explain several properties of finite nuclei, infinite matter, and neutron
stars in a unified way within the relativistic mean field models, it is
important to extend them either with higher order couplings or with
density-dependent couplings. These extensions are known to have strong impact
in the high-density regime. Here we explore their role on the equation of state
at densities lower than the saturation density of finite nuclei which govern
the phase transitions associated with pasta structures in the crust of neutron
stars.",1302.4590v1
2014-02-08,Current reversals in rapidly rotating ultra-cold Fermi gases,"We study the equilibrium current density profiles of harmonically trapped
ultra-cold Fermi gases in quantum Hall-like states that appear when the
quasi-two-dimensional trap is set in fast rotation. The density profile of the
gas (in the rotating reference frame) consists of incompressible strips of
constant quantized density separated by compressible regions in which the
density varies. Remarkably, we find that the atomic currents flow in opposite
directions in the compressible and incompressible regions -- a prediction that
should be amenable to experimental verification.",1402.1808v1
2015-11-06,Exact conditions on the temperature dependence of density functionals,"Universal exact conditions guided the construction of most ground-state
density functional approximations in use today. We derive the relation between
the entropy and Mermin free energy density functionals for thermal density
functional theory. Both the entropy and sum of kinetic and electron-electron
repulsion functionals are shown to be monotonically increasing with
temperature, while the Mermin functional is concave downwards. Analogous
relations are found for both exchange and correlation. The importance of these
conditions is illustrated in two extremes: the Hubbard dimer and the uniform
gas.",1511.02194v2
2018-04-20,Sampling the Riemann-Theta Boltzmann Machine,"We show that the visible sector probability density function of the
Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model
consisting of an infinite number of component multi-variate gaussians. The
weights of the mixture are given by a discrete multi-variate gaussian over the
hidden state space. This allows us to sample the visible sector density
function in a straight-forward manner. Furthermore, we show that the visible
sector probability density function possesses an affine transform property,
similar to the multi-variate gaussian density.",1804.07768v2
2019-05-08,Transverse Shear Viscosity to Entropy Density for the General Anisotropic Black Brane in Horava-Lifshitz Gravity,"In this paper we calculate the ratio of transverse shear viscosity to entropy
density for the general anisotropic black brane in Horava-Lifshitz gravity.
There is a well-known conjecture that states this ratio should be larger than
$\frac{1}{4\pi}$. The ratio of shear viscosity to entropy density is
proportional to the inverse square coupling of quantum thermal field
theory,$\frac{\eta }{s} \sim \frac{1}{\lambda^2 }$. Especially in QFT with
gravity dual the stronger coupling means the shear viscosity per entropy
density gets closer to the lower bound of $\frac{1}{4\pi}$. The KSS bound
preserves in the anisotropic scaling model.",1905.02932v1
2012-04-20,Spin Versus Charge Density Wave Order in Graphene-like Systems,"A variational technique is used to study sublattice symmetry breaking by
strong on-site and nearest neighbor interactions in graphene. When interactions
are strong enough to break sublattice symmetry, and with relative strengths
characteristic of graphene, a charge density wave Mott insulator is favored
over the spin density wave condensates. In the spin density wave condensate we
find that introduction of a staggered on-site energy (quasiparticle mass) leads
to a splitting of the fermi velocities and mass gaps of the quasiparticle spin
states.",1204.4531v2
2018-10-01,The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian,"We consider a large neutral atom of atomic number $Z$, modeled by a
pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably
rescaled one-particle ground state density on the Thomas--Fermi length scale
$Z^{-1/3}$. Using an observation by Fefferman and Seco (1989), we find that the
density on this scale converges to the minimizer of the Thomas--Fermi
functional of hydrogen as $Z\to\infty$ when $Z/c$ is fixed to a value not
exceeding $2/\pi$. This shows that the electron density on the Thomas--Fermi
length scale does not exhibit any relativistic effects.",1810.00632v1
2019-10-28,Charge Density Wave and Superconductivity in Transition Metal Dichalcogenides,"Competing orders in condensed matter give rise to the emergence of
fascinating, new phenomena. Here, we investigate the competition between
superconductivity and charge density wave in the context of layered-metallic
compounds, transition metal dichalcogenides, in which the superconducting state
is usually suppressed by the charge density wave. We show, using real-space
self-consistent Bogoliubov-de Gennes calculations and momentum-space
calculations involving density-functional theory and dynamical mean-field
theory, that there is a surprising reappearance of superconductivity in the
presence of non-magnetic disorder fluctuations, as observed in recent
experiments.",1910.12801v3
2020-04-30,A Triangular Network For Density Estimation,"We report a triangular neural network implementation of neural autoregressive
flow (NAF). Unlike many universal autoregressive density models, our design is
highly modular, parameter economy, computationally efficient, and applicable to
density estimation of data with high dimensions. It achieves state-of-the-art
bits-per-dimension indices on MNIST and CIFAR-10 (about 1.1 and 3.7,
respectively) in the category of general-purpose density estimators.",2004.14593v2
2016-08-20,Dynamics of expansion of the Universe in the models with non-minimally coupled dark energy,"We consider the dark energy model with barotropic equation of state, which
interacts with dark matter through gravitation and another force, causing the
energy-momentum exchange between them. Both components are described in
approximation of ideal fluids, which are parametrized by density and equation
of state parameters. Three types of interactions between dark components are
considered: the interaction independent from their densities, the one
proportional to density of dark energy and the one proportional to density of
dark matter. The equations which describe the expansion dynamics of homogeneous
and isotropic Universe and evolution of densities of both components for
different values of interaction parameter are obtained on the bases of the
general covariant conservation equations and Einstein's ones. For three kinds
of interactions we show the existence of the range of values of parameters of
dark energy for which the densities of dark components and their sum are
negative. We find the conditions of positivity of density of dark energy and
dark matter. The constraints on the value of parameter of interaction are
derived. The dynamics of expansion of the Universe with these interactions of
dark energy and dark matter is analysed.",1608.06553v1
2020-06-30,Vibrational Spectrum of Granular Packings With Random Matrices,"The vibrational spectrum of granular packings can be used as a signature of
the jamming transition, with the density of states at zero frequency becoming
non-zero at the transition. It has been proposed previously that the
vibrational spectrum of granular packings can be approximately obtained from
random matrix theory. Here we show that although the density of states
predicted by random matrix theory does not agree with certain aspects of
dynamical numerical simulations, the correlations of the density of states,
which---in contrast to the density of states---are expected to be universal, do
show good agreement between dynamical numerical simulations of bead packs near
the jamming point and the analytic predictions of the Laguerre orthogonal
ensemble of random matrices. At the same time, there is clear disagreement with
the Gaussian orthogonal ensemble. These findings establish that the Laguerre
ensemble correctly reproduces the universal statistical properties of jammed
granular matter and exclude the Gaussian orthogonal ensemble. We also present a
random lattice model which is a physically motivated variant of the random
matrix ensemble. Numerical calculations reveal that this model reproduces the
known features of the vibrational density of states of granular matter, while
also retaining the correlation structure seen in the Laguerre random matrix
theory. We propose that the random lattice model can therefore be applied the
understand not only the spectrum but more general properties of the vibration
of bead packs including the spatial structure of modes both at the jamming
point and far from it.",2006.16497v1
2010-09-23,Equilibration of integer quantum Hall edge states,"We study equilibration of quantum Hall edge states at integer filling
factors, motivated by experiments involving point contacts at finite bias.
Idealising the experimental situation and extending the notion of a quantum
quench, we consider time evolution from an initial non-equilibrium state in a
translationally invariant system. We show that electron interactions bring the
system into a steady state at long times. Strikingly, this state is not a
thermal one: its properties depend on the full functional form of the initial
electron distribution, and not simply on the initial energy density. Further,
we demonstrate that measurements of the tunneling density of states at long
times can yield either an over-estimate or an under-estimate of the energy
density, depending on details of the analysis, and discuss this finding in
connection with an apparent energy loss observed experimentally. More
specifically, we treat several separate cases: for filling factor \nu=1 we
discuss relaxation due to finite-range or Coulomb interactions between
electrons in the same channel, and for filling factor \nu=2 we examine
relaxation due to contact interactions between electrons in different channels.
In both instances we calculate analytically the long-time asymptotics of the
single-particle correlation function. These results are supported by an exact
solution at arbitrary time for the problem of relaxation at \nu=2 from an
initial state in which the two channels have electron distributions that are
both thermal but with unequal temperatures, for which we also examine the
tunneling density of states.",1009.4555v2
2013-09-23,"A cosmological model describing the early inflation, the intermediate decelerating expansion, and the late accelerating expansion by a quadratic equation of state","We develop a cosmological model based on a quadratic equation of state
p/c^2=-(\alpha+1){\rho^2}/{\rho_P}+\alpha\rho-(\alpha+1)\rho_{\Lambda} (where
\rho_P is the Planck density and \rho_{\Lambda} the cosmological density)
""unifying"" vacuum energy and dark energy in the spirit of a generalized
Chaplygin gas model. For $\rho\rightarrow \rho_P$, it reduces to p=-\rho c^2
leading to a phase of early accelerated expansion (early inflation) with a
constant density equal to the Planck density \rho_P (vacuum energy). For
$\rho_{\Lambda}\ll\rho\ll \rho_P$, we recover the standard linear equation of
state p=\alpha \rho c^2 describing radiation (\alpha=1/3) or pressureless
matter (\alpha=0) and leading to an intermediate phase of decelerating
expansion. For $\rho\rightarrow \rho_{\Lambda}$, we get p=-\rho c^2 leading to
a phase of late accelerated expansion (late inflation) with a constant density
equal to the cosmological density \rho_{\Lambda} (dark energy). We show a nice
symmetry between the early universe (vacuum energy + \alpha-fluid) and the late
universe (\alpha-fluid + dark energy). In our model, they are described by two
polytropic equations of state with index n=+1 and n=-1 respectively.
Furthermore, the Planck density \rho_P in the early universe plays a role
similar to the cosmological density \rho_{\Lambda} in the late universe. They
represent fundamental upper and lower density bounds differing by 122 orders of
magnitude. This quadratic equation of state leads to a fully analytical model
describing the evolution of the universe from the early inflation (Planck era)
to the late accelerated expansion (de Sitter era). These two phases are bridged
by a decelerating algebraic expansion (\alpha-era). This model does not present
any singularity at t=0 and exists eternally in the past. It admits a scalar
field interpretation based on a quintessence field or a tachyon field.",1309.5784v2
2003-02-19,Orientational field-dependence of low-lying excitations in mixed state of unconventional superconductors,"Orientational field-dependence of the zero energy density of states (ZEDOS)
is calculated for superconductors with the polar state (line node), axial state
(point node) and 3D d-wave state. Depending on the gap topology and relative
field direction the field dependencies of ZEDOS sensitively differ, providing
us a useful and practical method to identify the gap topology. It is also
demonstrated that for d-wave state the field rotation in the basal plane shows
a sizable oscillation ~3% of ZEDOS. This is directly measurable in low-T
specific heat experiment in the mixed state.",0302374v1
2000-07-17,"Reconstruction of SU(1,1) States","We show how group symmetries can be used to reconstruct quantum states. In
our scheme for SU(1,1) states, the input field passes through a non-degenerate
parametric amplifier and one measures the probability of finding the output
state with a certain number (usually zero) of photons in each mode. The density
matrix in the Fock basis is retrieved from the measured data by least squares
method after singular value decomposition of the design matrix. Several
illustrative examples involving the reconstruction of a pair coherent state, a
Perelomov coherent state, and a coherent superposition of pair coherent states
are considered.",0007049v1
2005-02-25,Optimal Unambiguous State Discrimination of two density matrices and its link with the Fidelity,"Recently the problem of Unambiguous State Discrimination (USD) of mixed
quantum states has attracted much attention. So far, bounds on the optimum
success probability have been derived [1]. For two mixed states they are given
in terms of the fidelity. Here we give tighter bounds as well as necessary and
sufficient conditions for two mixed states to reach these bounds. Moreover we
construct the corresponding optimal measurement strategies. With this result,
we provide analytical solutions for unambiguous discrimination of a class of
generic mixed states. This goes beyond known results which are all reducible to
some pure state case. Additionally, we show that examples exist where the
bounds cannot be reached.",0502165v1
1997-11-20,The Cooperon and the Random Matrix Model for Type-II Superconductors,"We derive the connection between the Cooperon problem in weak localization
theory and the random matrix description of type-II superconductors. As
magnetic field and disorder increase, an extreme type-II superconductor crosses
over from a state in which the low energy quasiparticles are primarily
localized and the density of states is determined by the electronic structure
of individual vortices, to a `chaotic' state, in which quasiparticles are
primarily extended and the density of states is determined by the random matrix
description.",9711200v1
2000-12-07,Ground State of a trapped Bose-Einstein Condensate in Two Dimensions; Beyond the Mean-field Approximation,"We consider the ground state of a trapped Bose-Einstein condensate in two
dimensions. In the mean-field approximation, the ground state density profile
satisfies the Gross-Pitaevskii equation. We compute the leading quantum
corrections to the density profile to second order in an expansion around the
Thomas-Fermi limit. By summing the ladder diagrams, we are generalizing
Schick's result for the ground state energy of a homogeneouns Bose gas to the
case of a trapped Bose gas.",0012101v1
2005-02-25,Double-Exchange Model: Phase Diagram at Zero-Temperature,"The analytical zero-temperature phase diagram of the double exchange model
for classical background spins as a function of the carrier density and Hund's
coupling in the entire range of these parameters is presented. By constructing
a continuum field theory we explore the possibility of a continuous phase
transition from ferromagnetic state to a gently varying textured state. We find
such a transition in and below two dimensions and show that the emerging stable
state is a spin-spiral which survives the tendency towards phase separation
into commonly considered phases, and is also energetically favored to the
canted state, for low carrier density.",0502621v1
2005-06-24,Polarized resonant inelastic x-ray scattering as an ultra-fine probe of excited states in La2CuO4,"X-ray absorption is the standard method to probe the unoccupied density of
states at a given edge. Here we show that polarized Resonant Inelastic X-Ray
Scattering in La2CuO4 at the Cu K-edge is extremely sensitive to the
environment of the Cu atom and the fine structure in the Cu 4p density of
states. Combined ab initio and many-body cluster calculations, used for the
first time in such a context, show remarkable agreement with experiment. In
particular we identify a non-local effect namely a transition to off-site Cu 3d
states.",0506650v1
2005-11-16,Calculating state-to-state transition probabilities within TDDFT,"The determination of the elements of the S-matrix within the framework of
time-dependent density-functional theory (TDDFT) has remained a widely open
question. We explore two different methods to calculate state-to-state
transition probabilities. The first method closely follows the extraction of
the S-matrix from the time-dependent Hartree-Fock approximation. This method
suffers from cross-channel correlations resulting in oscillating transition
probabilities in the asymptotic channels. An alternative method is proposed
which corresponds to an implicit functional in the time-dependent density. It
gives rise to stable and accurate transition probabilities. An exactly solvable
two-electron system serves as benchmark for a quantitative test.",0511167v1
2011-01-13,Canonical ensemble of an interacting Bose gas: stochastic matter fields and their coherence,"We present a novel quantum stochastic evolution equation for a matter field
describing the canonical state of a weakly interacting ultracold Bose gas. In
the ideal gas limit our approach is exact. This numerically very stable
equation suppresses high-energy fluctuations exponentially, which enables us to
describe condensed and thermal atoms within the same formalism. We present
applications to ground state occupation and fluctuations, density profile of
ground state and thermal cloud, and ground state number statistics. Our main
aim are spatial coherence properties which we investigate through the
determination of interference contrast and spatial density correlations.
Parameters are taken from actual experiments [1].
  [1] S. Hofferberth et al., Nature Physics 4, 489 (2008).",1101.2617v1
2012-07-30,Half-metallic magnetization plateaux,"We propose a novel interaction-based route to half-metal state for
interacting electrons on two-dimensional lattices. Magnetic field applied
parallel to the lattice is used to tune one of the spin densities to a
particular commensurate with the lattice value in which the system
spontaneously `locks in' via van Hove enhanced density wave state. Electrons of
opposite spin polarization retain their metallic character and provide for the
half-metal state which, in addition, supports magnetization plateau in a finite
interval of external magnetic field. Similar half-metal state is realized in
the finite-U Hubbard model on a triangular lattice at 1/3 of the maximum
magnetization.",1207.7124v1
2018-11-29,Pekar's Ansatz and the Ground-State Symmetry of a Bound Polaron,"We consider a Fr\""ohlich polaron bound in a symmetric Mexican hat-type
potential. The ground state is unique and therefore invariant under rotations.
However, we show that the minimizers of the corresponding Pekar problem are
nonradial. Assuming these nonradial minimizers are unique up to rotation, we
prove in the strong-coupling limit that the ground-state electron density
converges in a weak sense to a rotational average of the densities of the
minimizers.",1811.12347v2
2022-01-25,A Kernel Learning Method for Backward SDE Filter,"In this paper, we develop a kernel learning backward SDE filter method to
estimate the state of a stochastic dynamical system based on its partial noisy
observations. A system of forward backward stochastic differential equations is
used to propagate the state of the target dynamical model, and Bayesian
inference is applied to incorporate the observational information. To
characterize the dynamical model in the entire state space, we introduce a
kernel learning method to learn a continuous global approximation for the
conditional probability density function of the target state by using discrete
approximated density values as training data. Numerical experiments demonstrate
that the kernel learning backward SDE is highly effective and highly efficient.",2201.10600v1
2023-01-13,Topological superconductivity in helical crystals,"We study superconductivity and surface Andreev bound states in helical
crystals. We consider the interlayer pairings along the helical hopping and
investigate the surface local density of states on the (001) and zigzag
surfaces for all the possible irreducible representations. There are three and
four irreducible representations exhibiting the zero energy peaks in the local
density of states at the (001) and zigzag surfaces of helical lattices,
respectively. By calculating the one dimensional winging number, we show that
these appearances of the zero energy peaks stem from the surface Andreev bound
states.",2301.05340v2
2001-02-10,Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors,"We evaluate analytically some ground state properties of two-dimensional
harmonically confined Fermi vapors with isotropy and for an arbitrary number of
closed shells. We first derive a differential form of the virial theorem and an
expression for the kinetic energy density in terms of the fermion particle
density and its low-order derivatives. These results allow an explicit
differential equation to be obtained for the particle density. The equation is
third-order, linear and homogeneous. We also obtain a relation between the
turning points of kinetic energy and particle densities, and an expression of
the non-local kinetic energy density functional.",0102186v1
2001-09-13,Local Casimir Energy For Solitons,"Direct calculation of the one-loop contributions to the energy density of
bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode
regularization. Requiring the mode density in the kink and the trivial sectors
to be equal at each point in space yields the anomalous part of the energy
density. (2) Phase space factorization. A striking position-momentum
factorization for reflectionless potentials gives the non-anomalous energy
density a simple relation to that for the bound state. For the supersymmetric
kink, our expression for the energy density (both the anomalous and
non-anomalous parts) agrees with the published central charge density, whose
anomalous part we also compute directly by point-splitting regularization.
Finally we show that, for a scalar field with arbitrary scalar background
potential in one space dimension, point-splitting regularization implies local
mode regularization of the Casimir energy density.",0109110v3
2006-11-15,Optimal rates for plug-in estimators of density level sets,"In the context of density level set estimation, we study the convergence of
general plug-in methods under two main assumptions on the density for a given
level $\lambda$. More precisely, it is assumed that the density (i) is smooth
in a neighborhood of $\lambda$ and (ii) has $\gamma$-exponent at level
$\lambda$. Condition (i) ensures that the density can be estimated at a
standard nonparametric rate and condition (ii) is similar to Tsybakov's margin
assumption which is stated for the classification framework. Under these
assumptions, we derive optimal rates of convergence for plug-in estimators.
Explicit convergence rates are given for plug-in estimators based on kernel
density estimators when the underlying measure is the Lebesgue measure. Lower
bounds proving optimality of the rates in a minimax sense when the density is
H\""older smooth are also provided.",0611473v4
2017-08-03,Neutron matter within QCD sum rules,"Equation of state (EOS) of pure neutron matter (PNM) is studied in QCD sum
rules (QCDSR). It is found that the QCDSR results on EOS of PNM are in good
agreement with predictions by current advanced microscopic many-body theories.
Moreover, the higher-order density terms in quark condensates are shown to be
important to describe the empirical EOS of PNM in the density region around and
above nuclear saturation density although they play minor role at subsaturation
densities. The chiral condensates in PNM are also studied, and our results
indicate that the higher-order density terms in quark condensates, which are
introduced to reasonably describe the empirical EOS of PNM at suprasaturation
densities, tend to hinder the appearance of chiral symmetry restoration in PNM
at high densities.",1708.01010v2
2021-07-28,Self-interaction corrected Kohn-Sham effective potentials using the density-consistent effective potential method,"Density functional theory (DFT) and beyond-DFT methods are often used in
combination with photoelectron spectroscopy to obtain physical insights into
the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are
not electron removal energies except for the highest occupied orbital. The
eigenvalues of the highest occupied molecular orbitals often underestimate the
electron removal or ionization energies due to the self-interaction (SI) errors
in approximate density functionals. In this work, we adapt and implement the
density-consistent effective potential(DCEP) method of Kohut, Ryabinkin, and
Staroverov to obtain SI corrected local effective potentials from the SI
corrected Fermi-L\""owdin orbitals and density in the FLOSIC scheme. The
implementation is used to obtain the density of states (photoelectron spectra)
and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with
experimental values is obtained compared to a range of SI uncorrected density
functional approximations.",2107.13631v1
2022-06-22,Neural Inverse Transform Sampler,"Any explicit functional representation $f$ of a density is hampered by two
main obstacles when we wish to use it as a generative model: designing $f$ so
that sampling is fast, and estimating $Z = \int f$ so that $Z^{-1}f$ integrates
to 1. This becomes increasingly complicated as $f$ itself becomes complicated.
In this paper, we show that when modeling one-dimensional conditional densities
with a neural network, $Z$ can be exactly and efficiently computed by letting
the network represent the cumulative distribution function of a target density,
and applying a generalized fundamental theorem of calculus. We also derive a
fast algorithm for sampling from the resulting representation by the inverse
transform method. By extending these principles to higher dimensions, we
introduce the \textbf{Neural Inverse Transform Sampler (NITS)}, a novel deep
learning framework for modeling and sampling from general, multidimensional,
compactly-supported probability densities. NITS is a highly expressive density
estimator that boasts end-to-end differentiability, fast sampling, and exact
and cheap likelihood evaluation. We demonstrate the applicability of NITS by
applying it to realistic, high-dimensional density estimation tasks:
likelihood-based generative modeling on the CIFAR-10 dataset, and density
estimation on the UCI suite of benchmark datasets, where NITS produces
compelling results rivaling or surpassing the state of the art.",2206.11172v1
2022-11-22,Non-conservation of the valley density and its implications for the observation of the valley Hall effect,"We show that the conservation of the valley density in multi-valley and
time-reversal-invariant insulators is broken in an unexpected way by the
electric field that drives the valley Hall effect. This implies that
fully-gapped insulators can support a valley Hall current in the bulk and yet
show no valley density accumulation on the edges. Thus, the valley Hall effect
cannot be observed in such systems. If the system is not fully gapped then
valley density accumulation at the edges is possible and can result in a net
generation of valley density. The accumulation has no contribution from
undergap states and can be expressed as a Fermi surface average, for which we
derive an explicit formula. We demonstrate the theory by calculating the valley
density accumulations in an archetypical valley-Hall insulator: a gapped
graphene nanoribbon. Surprisingly, we discover that a net valley density
polarization is dynamically generated for some types of edge terminations.",2211.12428v3
2023-09-08,Strong Electron Correlation from Partition Density Functional Theory,"Standard approximations for the exchange-correlation (XC) functional in
Kohn-Sham density functional theory (KS-DFT) typically lead to unacceptably
large errors when applied to strongly-correlated electronic systems.
Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the
ground-state density and energy of a system are obtained through
self-consistent calculations on isolated fragments, with a partition energy
representing the \textit{inter}-fragment interactions. Here we show how typical
errors of the local density approximation (LDA) in KS-DFT can be largely
suppressed through a simple approximation, the generalized overlap
approximation (GOA), for the partition energy in PDFT. Our method is
illustrated on simple models of one-dimensional strongly-correlated linear
hydrogen chains. The GOA, when used in combination with the LDA for the
fragments, improves the LDA dissociation curves of hydrogen chains and produces
results that are comparable to those of spin-unrestricted LDA, but without
breaking the spin symmetry. GOA also induces a correction to the LDA electron
density that partially captures the correct density dimerization in
strongly-correlated hydrogen chains. Moreover, with an additional correction to
the partition energy, the approximation is shown to produce dissociation
energies in quantitative agreement to calculations based on the Density Matrix
Renormalization Group method.",2309.04571v1
2024-04-04,Correlation and Spectral Density Functions in Mode-Stirred Reverberation -- III. Measurements,"Experimental auto- and cross-correlation functions and their corresponding
spectral density functions are extracted from measured sweep data of
mode-stirred fields. These are compared with theoretical models derived in part
I, using estimated spectral moments from part II. The second-order Pad\'{e}
approximant based model accounts for the main features of the spectral density
function, including its slope near stir DC, corner frequency, stir
DC-to-Nyquist level drop, and asymptotic spectral density. Ensemble averaging
across secondary tune states offers a reduction of spectral bias and RMS
spectral fluctuation, compared to spectral densities for individual stir sweeps
or their concatenation. Periodogram- and correlation-based methods produce
near-identical results. Distinctive theoretical features between power-based
vs. field-based spectral densities are experimentally verified. Interchanging
the roles of stirrer and tuner demonstrates the effect of stir efficiency on
correlation and spectral density. The spectral characterization allows for
stirrer diagnostics, which is demonstrated through detection and identification
of EMI caused by mains power harmonics in the measured stir spectrum at low
frequencies.",2404.03497v1
2003-05-28,Density of states of a binary Lennard-Jones Glass,"We calculate the density of states of a binary Lennard-Jones glass using a
recently proposed Monte Carlo algorithm. Unlike traditional molecular
simulation approaches, the algorithm samples distinct configurations according
to self-consistent estimates of the density of states, thereby giving rise to
uniform internal-energy histograms. The method is applied to simulate the
equilibrium, low-temperature thermodynamic properties of a widely studied glass
former consisting of a binary mixture of Lennard-Jones particles. We show how a
density-of-states algorithm can be combined with particle identity swaps and
configurational bias techniques to study that system. Results are presented for
the energy and entropy below the mode coupling temperature.",0305666v1
2005-05-30,Cooper pairing and superconductivity on a spherical surface,"Electrons in a multielectron bubble in helium form a spherical,
two-dimensional system coupled to the ripplons at the bubble surface. The
electron-ripplon coupling, known to lead to polaronic effects, is shown to give
rise also to Cooper pairing. A Bardeen-Cooper-Schrieffer (BCS) Hamiltonian
arises from the analysis of the electron-ripplon interaction in the bubble, and
values of the coupling strength are obtained for different bubble
configurations. The BCS Hamiltonian on the sphere is analysed using the
Richardson method. We find that although the typical ripplon energies are
smaller than the splitting between electronic levels, a redistribution of the
electron density over the electronic levels is energetically favourable as
pairing correlations can be enhanced. The density of states of the system with
pairing correlations is derived. No gap is present, but the density of states
reveals a strong step-like increase at the pair-breaking energy. This feature
of the density of states should enable the unambiguous detection of the
proposed state with pairing correlations in the bubble, through either
capacitance spectroscopy or tunneling experiments, and allow to map out the
phase diagram of the electronic system in the bubble.",0505721v1
2017-06-07,Partial local density of states from scanning gate microscopy,"Scanning gate microscopy images from measurements made in the vicinity of
quantum point contacts were originally interpreted in terms of current flow.
Some recent work has analytically connected the local density of states to
conductance changes in cases of perfect transmission, and at least
qualitatively for a broader range of circumstances. In the present paper, we
show analytically that in any time-reversal invariant system there are
important deviations that are highly sensitive to imperfect transmission.
Nevertheless, the unperturbed partial local density of states can be extracted
from a weakly invasive scanning gate microscopy experiment, provided the
quantum point contact is tuned anywhere on a conductance plateau. A
perturbative treatment in the reflection coefficient shows just how sensitive
this correspondence is to the departure from the quantized conductance value
and reveals the necessity of local averaging over the tip position. It is also
shown that the quality of the extracted partial local density of states
decreases with increasing tip radius.",1706.02220v2
2023-12-15,Three-state active lattice gas: a discrete Vicseklike model with excluded volume,"We study a discrete-space model of active matter with excluded volume.
Particles are restricted to the sites of a triangular lattice, and can assume
one of three orientations. Varying the density and noise intensity, Monte Carlo
simulations reveal a variety of spatial patterns. Ordered states occur in the
form of condensed structures, which (away from the full occupancy limit)
coexist with a low-density vapor. The condensed structures feature low particle
mobility, particularly those that wrap the system via the periodic boundaries.
As the noise intensity is increased, dense structures give way to a disordered
phase. We characterize the parameter values associated with the condensed
phases and perform a detailed study of the order-disorder transition at (1)
full occupation and (2) at a density of 0.1. In the former case, the model
possesses the same symmetry as the three-state Potts model and exhibits a
continuous phase transition, as expected, with critical exponents consistent
with those of the associated Potts model. In the low-density case, the
transition is clearly discontinuous, with strong dependence of the final state
upon the initial configuration, hysteresis,and nonmonotonic dependence of the
Binder cumulant upon noise intensity.",2312.09492v1
1996-05-07,Local Density of States in a Dirty Normal Metal connected to a Superconductor,"A superconductor in contact with a normal metal not only induces
superconducting correlations, known as proximity effect, but also modifies the
density of states at some distance from the interface. These modifications can
be resolved experimentally in microstructured systems. We, therefore, study the
local density of states $N(E,x)$ of a superconductor - normal metal
heterostructure. We find a suppression of $N(E,x)$ at small energies, which
persists to large distances. If the normal metal forms a thin layer of
thickness $L_n$, a minigap in the density of states appears which is of the
order of the Thouless energy $\sim \hbar D/L_n^2$. A magnetic field suppresses
the features. We find good agreement with recent experiments of Gu\'eron {\it
et al.}",9605039v2
2002-02-19,Band structure calculations for Ba$_{6}$Ge$_{25}$ and Ba$_{4}$Na$_{2}$Ge$_{25}$ clathrates,"Electronic band structures for Ba$_{6}$Ge$_{25}$ and
Ba$_{4}$Na$_{2}$Ge$_{25}$ clathrates are calculated using linear muffin-tin
orbital method within the local density approximation. It is found that barium
states strongly contribute to the density of states at the Fermi level and thus
can influence the transport properties of the compounds. A sharp peak of the
density of states is found just at the Fermi level. It is also shown that the
shifting of barium atoms toward experimentally deduced split positions in
Ba$_{6}$Ge$_{25}$ produces a splitting of this peak which may therefore be
interpreted as a band Jahn-Teller effect. If the locking of the barium atoms at
the observed structural phase transition is assumed, this reduction of the
density of states at the Fermi level can qualitatively account for the
experimentally observed decrease of the magnetic susceptibility and electrical
resistivity at the phase transition.",0202318v2
2019-05-03,Application of the random matrix theory to the boson peak in glasses,"The density of vibrational states $g(\omega)$ of an amorphous system is
studied by using the random-matrix theory. Taking into account the most
important correlations between elements of the random matrix of the system,
equations for the density of vibrational states $g(\omega)$ are obtained. The
analysis of these equations shows that in the low-frequency region the
vibrational density of states has the Debye behavior $g(\omega) \sim \omega^2$.
In the higher frequency region, there is the boson peak as an additional
contribution to the density of states. The obtained equations are in a good
agreement with the numerical results and allow us to find an exact shape of the
boson peak.",1905.01114v1
2019-02-03,Scarring in open chaotic systems: The local density of states,"Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles
in the apparent randomness of their spectra and wavefunction statistics.
Deviations form RMT also do occur, however, due to system-specific properties,
or as quantum signatures of classical chaos. Scarring, for instance, is the
enhancement of wavefunction intensity near classical periodic orbits, and it
can be characterized by a local density of states (or local spectrum) that
clearly deviates from RMT expectations, by exhibiting a peaked envelope, which
has been described semiclassically. Here, the system is connected to an
opening, the local density of states is introduced for the resulting
non-Hermitian chaotic Hamiltonian, and estimated a priori in terms of the
Green's function of the closed system and the open channels. The predictions
obtained are tested on quantum maps coupled both to a single-channel opening
and to a Fresnel-type continuous opening. The main outcome is that strong
coupling to the opening gradually suppresses the energy dependence of the local
density of states due to scarring, and restores RMT behavior.",1902.00879v2
2019-06-05,Existence and nonexistence of HOMO-LUMO excitations in Kohn-Sham density functional theory,"In numerical computations of response properties of electronic systems, the
standard model is Kohn-Sham density functional theory (KS-DFT). Here we
investigate the mathematical status of the simplest class of excitations in
KS-DFT, HOMO-LUMO excitations. We show using concentration-compactness
arguments that such excitations, i.e. excited states of the Kohn-Sham
Hamiltonian, exist for $Z>N$, where $Z$ is the total nuclear charge and $N$ is
the number of electrons. The result applies under realistic assumptions on the
exchange-correlation functional, which we verify explicitly for the widely used
PZ81 and PW92 functionals. By contrast, and somewhat surprisingly, we find
using a method of Glaser, Martin, Grosse, and Thirring \cite{glaser1976} that
in case of the hydrogen and helium atoms, excited states do not exist in the
neutral case $Z=N$ when the self-consistent KS ground state density is replaced
by a realistic but easier to analyze approximation (in case of hydrogen, the
true Schr\""{o}dinger ground state density). Implications for interpreting minus
the HOMO eigenvalue as an approximation to the ionization potential are
indicated.",1907.00064v1
2022-11-15,Time-dependent theory of optical electro- and magnetostriction,"Electrostriction, the deformation of dielectric materials under the influence
of an electric field, is of continuous interest in optics. The classic
experiment by Hakim and Higham [Proc. Phys. Soc. 80, 190 (1962)] for a
stationary field supports a different formula of the electrostrictive force
density than the recent experiment by Astrath et al. [Light Sci. Appl. 11, 103
(2022)] for an optical field. In this work, we study the origin of this
difference by developing a time-dependent covariant theory of optical force
densities in photonic materials. When a light pulse propagates in a bulk
dielectric, the field-induced force density consists of two parts: (i) The
optical wave momentum force density carries the wave momentum of light and
drives forward a mass density wave of the covariant coupled field-material
state of light. (ii) The optostrictive force density arises from the atomic
density dependence of the electric and magnetic field energy densities. It
represents an optical Lorentz-force-law-based generalization of the electro-
and magnetostrictive force densities well known for static electromagnetic
fields and derived from the principle of virtual work. Since the work done by
the optostrictive force density is not equal to the change of the field energy
density during the contraction of the material, we have to describe this
difference by optostriction-related dissipation terms to fulfill the energy
conservation. The detailed physical model of the dissipation is left for
further works. The optostrictive force density can be understood in terms of
field-induced pair interactions inside the material. Because of the related
action and reaction effects, this force density cannot contribute to the net
momentum transfer of the optical field. We also use the theory to simulate the
propagation of a Gaussian light pulse through a dielectric material.",2211.08040v2
2001-01-30,Effect of nearest- and next-nearest neighbor interactions on the spin-wave velocity of one-dimensional quarter-filled spin-density-wave conductors,"We study spin fluctuations in quarter-filled one-dimensional
spin-density-wave systems in presence of short-range Coulomb interactions. By
applying a path integral method, the spin-wave velocity is calculated as a
function of on-site (U), nearest (V) and next-nearest (V_2) neighbor-site
interactions. With increasing V or V_2, the pure spin-density-wave state
evolves into a state with coexisting spin- and charge-density waves. The
spin-wave velocity is reduced when several density waves coexist in the ground
state, and may even vanish at large V. The effect of dimerization along the
chain is also considered.",0101450v2
2012-03-29,Implied Filtering Densities on Volatility's Hidden State,"We formulate and analyze an inverse problem using derivatives prices to
obtain an implied filtering density on volatility's hidden state. Stochastic
volatility is the unobserved state in a hidden Markov model (HMM) and can be
tracked using Bayesian filtering. However, derivative data can be considered as
conditional expectations that are already observed in the market, and which can
be used as input to an inverse problem whose solution is an implied conditional
density on volatility. Our analysis relies on a specification of the martingale
change of measure, which we refer to as \textit{separability}. This
specification has a multiplicative component that behaves like a risk premium
on volatility uncertainty in the market. When applied to SPX options data, the
estimated model and implied densities produce variance-swap rates that are
consistent with the VIX volatility index. The implied densities are relatively
stable over time and pick up some of the monthly effects that occur due to the
options' expiration, indicating that the volatility-uncertainty premium could
experience cyclic effects due to the maturity date of the options.",1203.6631v5
2020-05-18,Level-density parameters in superheavy nuclei,"We systematically study the nuclear level densities of superheavy nuclei,
including odd systems, using the single-particle energies obtained with the
Woods-Saxon potential diagonalization. Minimization over many deformation
parameters for the global minima - ground states and the ""imaginary water flow""
technique on many deformation energy grids for the saddle points, including
nonaxial shapes has been applied. The level density parameters are calculated
by fitting the obtained results with the standard Fermi gas expression. The
total potential energy and shell correction dependencies of the level-density
parameter are analyzed and compared at the ground state and saddle point. These
parameters are compared with the results of the phenomenological expression. As
shown, this expression should be modified for the saddle points, especially for
small excitation energy. The ratio of the level-density parameter at the saddle
point to that at the ground state is shown to be crucial for the survival
probability of the heavy nucleus.",2005.08685v1
2020-05-19,Density fitting in periodic systems: application to TDHF in diamond and oxides,"A robust density fitting method for calculating Coulomb matrix elements over
Bloch functions based on calculation of two- and three-center matrix elements
of the Ewald potential is described and implemented in a Gaussian orbital basis
in the Exciton code. The method is tested by comparing Coulomb and exchange
energies from density fitting to corresponding energies from SCF HF
calculations for diamond, magnesium oxide and bulk Ne. Density fitting
coefficients from the robust method are compared to coefficients from a
variational method applied to wave function orbital products in bulk Ne. Four
center Coulomb matrix elements from density fitting are applied to time
dependent Hartree-Fock (TDHF) calculations in diamond, magnesium oxide and
anatase and rutile polytypes of titanium dioxide. Shifting virtual states
downwards uniformly relative to occupied states and scaling the electron-hole
attraction term in the TDHF Hamiltonian by 0.4 yields good agreement with
either experiment and/or Bethe-Salpeter equation calculations. This approach
mirrors similar 'scissors' adjustments of occupied and virtual states and
introduction of a scaled electron-hole attraction term in some time dependent
DFT calculations.",2005.09291v1
2024-03-14,Solving deep-learning density functional theory via variational autoencoders,"In recent years, machine learning models, chiefly deep neural networks, have
revealed suited to learn accurate energy-density functionals from data.
However, problematic instabilities have been shown to occur in the search of
ground-state density profiles via energy minimization. Indeed, any small noise
can lead astray from realistic profiles, causing the failure of the learned
functional and, hence, strong violations of the variational property. In this
article, we employ variational autoencoders to build a compressed, flexible,
and regular representation of the ground-state density profiles of various
quantum models. Performing energy minimization in this compressed space allows
us to avoid both numerical instabilities and variational biases due to
excessive constraints. Our tests are performed on one-dimensional
single-particle models from the literature in the field and, notably, on a
three-dimensional disordered potential. In all cases, the ground-state energies
are estimated with errors below the chemical accuracy and the density profiles
are accurately reproduced without numerical artifacts.",2403.09788v1
2021-08-24,Formal Aspects of Quantum Decay,"The Fock-Krylov formalism for the calculation of survival probabilities of
unstable states is revisited paying particular attention to the mathematical
constraints on the density of states, the Fourier transform of which gives the
survival amplitude. We show that it is not possible to construct a density of
states corresponding to a purely exponential survival amplitude. he survival
probability $P(t)$ and the autocorrelation function of the density of states
are shown to form a pair of cosine Fourier transforms. This result is a
particular case of the Wiener Khinchin theorem and forces $P(t)$ to be an even
function of time which in turn forces the density of states to contain a form
factor which vanishes at large energies. Subtle features of the transition
regions from the non-exponential to the exponential at small times and the
exponential to the power law decay at large times are discussed by expressing
$P(t)$ as a function of the number of oscillations, $n$, performed by it. The
transition at short times is shown to occur when the survival probability has
completed one oscillation. The number of oscillations depend on the properties
of the resonant state and a complete description of the evolution of the
unstable state is provided by determining the limits on the number of
oscillations in each region.",2108.10957v1
2004-09-28,Correlations in Hot Asymmetric Nuclear Matter,"The single-particle spectral functions in asymmetric nuclear matter are
computed using the ladder approximation within the theory of finite temperature
Green's functions. The internal energy and the momentum distributions of
protons and neutrons are studied as a function of the density and the asymmetry
of the system. The proton states are more strongly depleted when the asymmetry
increases while the occupation of the neutron states is enhanced as compared to
the symmetric case. The self-consistent Green's function approach leads to
slightly smaller energies as compared to the Brueckner Hartree Fock approach.
This effect increases with density and thereby modifies the saturation density
and leads to smaller symmetry energies.",0409067v1
2013-08-08,Lifshitz asymptotics for percolation Hamiltonians,"We study a discrete Laplace operator $\Delta$ on percolation subgraphs of an
infinite graph. The ball volume is assumed to grow at most polynomially. We are
interested in the behavior of the integrated density of states near the lower
spectral edge. If the graph is a Cayley graph we prove that it exhibits
Lifshitz tails. If we merely assume that the graph has an exhausting sequence
with positive $\delta$-dimensional density, we obtain an upper bound on the
integrated density of states of Lifshitz type.",1308.1842v2
2014-06-11,Variational occupation numbers to a Müller-type pair-density,"Based on a parametric point-wise decomposition, a kind of isospectral
deformation, of the exact one-particle probability density of an externally
confined, analytically solvable interacting two-particle model system we
introduce the associated parametric ($p$) one-matrix and apply it in the
conventional M\""uller-type partitioning of the pair-density. Using the
Schr\""odinger Hamiltonian of the correlated system, the corresponding
approximate ground-state energy $E_p$ is then calculated. The
optimization-search performed on $E_p$ with such restricted informations has a
robust performance and results in the exact ($ex$) ground-state energy for the
correlated model system $E_p=E_{ex}$.",1406.2809v1
2018-09-30,Existence of densities for multi-type CBI processes,"Let X be a multi-type continuous-state branching process with immigration
(CBI process) on state space $\mathbb{R}^d$. Denote by $g_t$, $t \geq 0$, the
law of $X_{t}$. We provide sufficient conditions under which $g_t$ has, for
each $t > 0$, a density with respect to the Lebesgue measure. Such density has,
by construction, some anisotropic Besov regularity. Our approach neither relies
on the use of Malliavin calculus nor on the study of corresponding Laplace
transform.",1810.00400v1
1997-01-05,Novel universal correlations in invariant random-matrix models,"We show that eigenvalue correlations in unitary-invariant ensembles of large
random matrices adhere to novel universal laws that only depend on a
multicriticality of the bulk density of states near the soft edge of the
spectrum. Our consideration is based on the previously unknown observation that
genuine density of states and n-point correlation function are completely
determined by the Dyson's density analytically continued onto the whole real
axis.",9701006v1
1999-01-26,AC-Conductivity of Pinned Charge Density Wave Fluctuations in Quasi One-Dimensional Conductors,"Quasi one-dimensional conductors which undergo a Peierls transition to a
charge density wave state at a temperature T_P show a region of one-dimensional
fluctuations above T_P. The Ginzburg-Landau-Langevin theory for the frequency
dependent collective conductivity from conductive fluctuations into the charge
density wave state is developed. By inclusion of a phase breaking term the
effect of local pinning due to random impurities is simulated. It is found that
the spectral weight of unpinned fluctuations is partly redistributed into a
pinned mode around a pinning frequency in the far infrared region. In addition,
selection rule breaking by the imputities makes the fluctuating amplitude mode
visible in the optical response.",9901281v1
1999-03-12,Pseudogap Formation in an Electronic System with d-wave Attraction at Low-density,"On the basis of an electronic model with separable attractive interaction,
the precursors at high temperature and strong coupling of the d-wave
superconducting state are investigated in the one-particle spectral function
$A({\bf k},\omega)$ and the total density of states $\rho(\omega)$, with the
use of the self-consistent $t$-matrix approximation. In the low-density region,
it is found that a gap-like structure at the Fermi level appears in $A({\bf
k},\omega)$ and $\rho(\omega)$ above the superconducting transition
temperature. It is shown that the pseudogap energy scale is determined by the
binding energy of the Cooper-pair.",9903208v1
2000-04-14,Magnetoresistance of a two-dimensional electron gas in a parallel magnetic field,"The conductivity of a two-dimensional electron gas in a parallel magnetic
field is calculated. We take into account the magnetic field induced
spin-splitting, which changes the density of states, the Fermi momentum and the
screening behavior of the electron gas. For impurity scattering we predict a
positive magnetoresistance for low electron density and a negative
magnetoresistance for high electron density. The theory is in qualitative
agreement with recent experimental results found for Si inversion layers and Si
quantum wells.",0004234v1
2006-01-12,Negative linear compressibility in confined dilatating systems,"The role of a matrix response to a fluid insertion is analyzed in terms of a
perturbation theory and Monte Carlo simulations applied to a hard sphere fluid
in a slit of fluctuating density-dependent width.
  It is demonstrated that a coupling of the fluid-slit repulsion, spatial
confinement and the matrix dilatation acts as an effective fluid-fluid
attraction, inducing a pseudo-critical state with divergent linear
compressibility and non-critical density fluctuations. An appropriate
combination of the dilatation rate, fluid density and the slit size leads to
the fluid states with negative linear compressibility. It is shown that the
switching from positive to negative compressibility is accompanied by an abrupt
change in the packing mechanism.",0601258v1
2006-11-18,Shape of the ground state energy density of Hill's equation with nice Gaussian potential,"Consider Hill's operator Q = -D^2 + q(x) in which the potential q(x) is an
almost surely continuous and rotation invariant Gaussian process on the circle
of perimeter one. Viewing the classical Riccati map as a change of measure, we
establish functional integral formulas for the probability density function of
the ground state energy and also determine the density's shape.",0611555v2
1996-10-24,Effects of state dependent correlations on nucleon density and momentum distributions,"The proton momentum and density distributions of closed shell nuclei are
calculated within a model treating short--range correlations up to first order
in the cluster expansion. The validity of the model is verified by comparing
the results obtained with purely scalar correlations with those produced by
finite nuclei Fermi Hypernetted Chain calculations. State dependent
correlations are used to calculate momentum and density distributions of 12C,
16O, 40Ca, and 48Ca, and the effects of their tensor components are studied.",9610036v1
2004-05-26,Relation between the density-matrix theory and the pairing theory,"The time-dependent density-matrix theory (TDDM) gives a correlated ground
state as a stationary solution of the time-dependent equations for one-body and
two-body density matrices. The small amplitude limit of TDDM (STDDM) is a
version of extended RPA theories which include the effects of ground state
correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov
theory and the quasi-particle RPA satisfy the TDDM and STDDM equations,
respectively, when only pairing-type correlations are taken into account in
TDDM and STDDM.",0405070v1
2003-09-08,Measuring the Density Matrix by Local Addressing,"We introduce a procedure to measure the density matrix of a material system.
The density matrix is addressed locally in this scheme by applying a sequence
of delayed light pulses. The procedure is based on the stimulated Raman
adiabatic passage (STIRAP) technique. It is shown that a series of population
measurements on the target state of the population transfer process yields
unambiguous information about the populations and coherences of the addressed
states, which therefore can be determined.",0309067v1
2009-09-30,Recursive Method for the Density of States in One Dimension,"We derive a powerful yet simple method for analyzing the local density of
states in gapless one dimensional fermionic systems, including extensions such
as momentum dependent interaction parameters and hard-wall boundaries. We study
the crossover of the local DOS from individual density waves to the well-known
asymptotic powerlaws and identify characteristic signs of spin charge
separation in possible STM experiments. For semi-infinite systems a closed
analytic expression is found in terms of hypergeometric functions.",0910.0003v2
2010-08-06,Density Functional of a Two-Dimensional Gas of Dipolar Atoms: Thomas-Fermi-Dirac Treatment,"We derive the density functional for the ground-state energy of a
two-dimensional, spin-polarized gas of neutral fermionic atoms with
magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many
atoms in a harmonic trap, we give analytical solutions for the single-particle
spatial density and the ground-state energy, in dependence on the interaction
strength, and we discuss the weak-interaction limit that is relevant for
experiments. We then lift the restriction of full spin polarization and account
for a time-independent inhomogeneous external magnetic field. The field
strength necessary to ensure full spin polarization is derived.",1008.1163v2
2010-11-25,Average Density of States for Hermitian Wigner Matrices,"We consider ensembles of $N \times N$ Hermitian Wigner matrices, whose
entries are (up to the symmetry constraints) independent and identically
distributed random variables. Assuming sufficient regularity for the
probability density function of the entries, we show that the expectation of
the density of states on {\it arbitrarily} small intervals converges to the
semicircle law, as $N$ tends to infinity.",1011.5594v2
2011-05-13,Equation of state of hard oblate ellipsoids by replica exchange Monte Carlo,"We implemented the replica exchange Monte Carlo technique to produce the
equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density
range. For this purpose, we considered the analytical approximation of the
overlap distance given by Bern and Pechukas and the exact numerical solution
given by Perram and Wertheim. For both cases we capture the expected
isotropic-nematic transition at low densities and a nematic-crystal transition
at larger densities. For the exact case, these transitions occur at the volume
fraction 0.341, and in the interval $0.584-0.605$, respectively.",1105.2789v3
2013-10-30,Towards a density of states approach for dense matter systems,"The density-of-states method (Phys.Rev.Lett. 109 (2012) 111601) features an
exponential error suppression and is not restricted to theories with positive
probabilistic weight. It is applied to the SU(2) gauge theory at finite
densities of heavy quarks. The key ingredient here is the Polyakov line
probability distribution, which is obtained of over 80 orders of magnitude. We
briefly address whether the exponential error suppression could be sufficient
to simulate theories with a strong sign problem.",1310.8231v1
2013-11-01,Lattice dynamics and electronic structure of energetic solids LiN3 and NaN3: A first principles study,"We report density functional theory calculations on the crystal structure,
elastic, lattice dynamics and electronic properties of iso-structural layered
monoclinic alkali azides, LiN3 and NaN3. The effect of van der Waals
interactions on the ground- state structural properties is studied by using
various dispersion corrected density functionals. Based on the equilibrium
crystal structure, the elastic constants, phonon dispersion and phonon density
of states of the compounds are calculated. The accurate energy band gaps are
obtained by using the recently developed Tran Blaha-modified Becke Johnson
(TB-mBJ) functional and found that both the azides are direct band gap
insulators.",1311.0145v1
2016-11-01,Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium,"We study the density-density correlation function of the 1D Lieb-Liniger
model and obtain an exact expression for the small momentum limit of the static
correlator in the thermodynamic limit. We achieve this by summing exactly over
the relevant form factors of the density operator in the small momentum limit.
The result is valid for any eigenstate, including thermal and non-thermal
states. We also show that the small momentum limit of the dynamic structure
factors obeys a generalized detailed balance relation valid for any equilibrium
state.",1611.00194v3
2012-01-26,Liouville coherent states,"For a certain class of open quantum systems there exists a dynamical symmetry
which connects different time-evolved density matrices. We show how to use this
symmetry for dynamics in the Liouville space with time-dependent parameters.
This allows us to introduce a concept of generalized coherent states (e.g.
density matrices) in the Liouville space. Dynamics of this class of density
matrices is characterized by robustness with respect to any time-dependent
perturbations of the couplings. We study their dynamical context while focusing
on common physical situations corresponding to compact and non-compact
symmetries.",1201.5661v2
2020-12-05,Higher-order uncertainty bounds for mixed states,"Uncertainty lower bounds for parameter estimations associated with a unitary
family of mixed-state density matrices are obtained by embedding the space of
density matrices in the Hilbert space of square-root density matrices. In the
Hilbert-space setup the measure of uncertainty is given by the skew information
of the second kind, while the uncertainty lower bound is given by the
Wigner-Yanase skew information associated with the conjugate observable.
Higher-order corrections to the uncertainty lower bound are determined by
higher-order quantum skew moments; expressions for these moments are worked out
in closed form.",2012.02965v1
2021-07-06,Properties of Skyrme force as a residual interaction in beyond mean-field theories,"In an effort to find an effective interaction which can consistently be used
for both the mean-field part and the residual part in beyond mean-field
theories, properties of the Skyrme interactions as a residual interaction are
investigated. The time-dependent density-matrix theory (TDDM) is used as a
beyond mean-field theory and the ground states of $^{16}$O and $^{40}$Ca are
calculated using the five standard parametrizations of the Skyrme interaction
which differs in density and momentum dependence. It is found that the Skyrme
interaction which has strong density dependence and weak momentum dependence
induces substantial ground-state correlations comparable to the results of
other theoretical calculations.",2107.02332v1
2022-09-17,Gaussian dynamics equation in normal product form,"In this paper, we discuss the normal product form of the density operator of
multimode Gaussian states, and obtain the correlation equation between the
kernel matrix R of the Gaussian density operator in the normal product form and
its kernel matrix G in the standard quadratic form. Further, we explore the
time evolution mechanism of R and obtain the Gaussian dynamical equation under
the normal product R=i(RJH-HJR). Our work is devoted to searching for another
mechanism for Gaussian dynamics. By exploring the description of the normal
ordered density matrix under the coherent state representation, we find that
our mechanism is feasible and easy to operate.",2209.08250v1
2023-06-30,Stability of a one-dimensional full viscous quantum hydrodynamic system,"A full viscous quantum hydrodynamic system for particle density, current
density, energy density and electrostatic potential coupled with a Poisson
equation in one dimensional bounded intervals is studied. First, the existence
and uniqueness of a steady-state solution to the quantum hydrodynamic system is
established. Then, utilizing the fact that the third order perturbation term
has an appropriate sign, the local-in-time existence of the solution is
investigated by introducing a fourth order viscous regularization and using the
entropy dissipation method. In the end, the exponential stability of the
steady-state solution is shown by constructing a uniform a-priori estimate.",2306.17495v1
2006-07-27,Phenomenological Theory of Multiple Spin Density Waves in fcc Transition Metals,"The relative stability among the multiple spin density wave (MSDW) states in
fcc transition metals has been investigated on the basis of a Ginzburg-Landau
type of free energy with terms up to the fourth order in magnetic moments.
Obtained magnetic phase diagrams in the space of expansion coefficients
indicate the possibility of various 3Q MSDW states in fcc transition metals:
the commensurate 3Q state, the incommensurate linear 3Q state, and the
incommensurate helical 3Q state. It is shown that these 3Q states are always
stabilized, when they are compared with the corresponding 2Q and 1Q states, and
their magnetic moment amplitudes are the largest among those of the three
states. The results are compared with previous results of the ground-state
calculations, and possible scenarios to explain the experimental data of fcc-Fe
are proposed.",0607710v1
2013-03-07,Mapping Image Potential States on Graphene Quantum Dots,"Free electron like image potential states are observed in scanning tunneling
spectroscopy on graphene quantum dots on Ir(111) acting as potential wells. The
spectrum strongly depends on the size of the nanostructure as well as on the
spatial position on top, indicating lateral confinement. Analysis of the
substructure of the first state by spatial mapping of constant energy local
density of states reveals characteristic patterns of confined states. The most
pronounced state is not the ground state, but an excited state with a favorable
combination of local density of states and parallel momentum transfer in the
tunneling process. Chemical gating tunes the confining potential by changing
the local workfunction. Our experimental determination of this workfunction
allows to deduce the associated shift of the Dirac point.",1303.1800v2
2006-02-06,On the analysis of the vibrational Boson peak and low-energy excitations in glasses,"Implications of reduction procedures applied to the low energy part of the
vibrational density of states in glasses and supercooled liquids are considered
by advancing a detailed comparison between the excess - over the Debye limit -
vibrational density of states g(w) and the frequency-reduced representation
g(w)/w^2 usually referred to as the Boson peak. Analyzing representative
experimental data from inelastic neutron and Raman scattering we show that
reduction procedures distort to a great extent the otherwise symmetric excess
density of states. The frequency of the maximum and the intensity of the excess
experience dramatic changes; the former is reduced while the latter increases.
The frequency and the intensity of the Boson peak are also sensitive to the
distribution of the excess. In the light of the critical appraisal between the
two forms of the density of states (i.e. the excess and the frequency-reduced
one) we discuss changes of the Boson peak spectral features that are induced
under the presence of external stimuli such as temperature (quenching rate,
annealing), pressure, and irradiation. The majority of the Boson peak changes
induced by the presence of those stimuli can be reasonably traced back to
simple and expected modifications of the excess density of states and can be
quite satisfactorily accounted for the Euclidean random matrix theory.
Parallels to the heat capacity Boson peak are also briefly discussed.",0602148v1
2015-01-28,Fluctuation effects in rotating Bose-Einstein condensates with broken $\mathrm{SU}(2)$ and $\mathrm{U}(1)\times \mathrm{U}(1)$ symmetries in the presence of intercomponent density-density interactions,"Thermal fluctuations and melting transitions for rotating single-component
superfluids have been intensively studied and are well understood. In contrast,
the thermal effects on vortex states for two-component superfluids with
density-density interaction, which have a much richer variety of vortex ground
states, have been much less studied. Here, we investigate the thermal effects
on vortex matter in superfluids with $\mathrm{U(1)}\times \mathrm{U(1)}$ broken
symmetries and intercomponent density-density interactions, as well as the case
with a larger $\mathrm{SU(2)}$ broken symmetry obtainable from the
$\mathrm{U(1)}\times \mathrm{U(1)}$-symmetric case by tuning scattering
lengths. In the former case we find that, in addition to first-order melting
transitions, the system exhibits thermally driven phase transitions between
square and hexagonal lattices. Our main result, however, concerns the case
where the condensate exhibits $\mathrm{SU(2)}$-symmetry, and where vortices are
not topological. At finite temperature, the system exhibits effects which do
not have a counter-part in single component systems. Namely, it has a state
where thermally averaged quantities show no regular vortex lattice, yet the
system retains superfluid coherence along the axis of rotation. In such a
state, the thermal fluctuations result in transitions between different
(nearly)-degenerate vortex states without undergoing a melting transition. Our
results apply to multi-component Bose-Einstein condensates, and we suggest how
to experimentally detect some of these unusual effects in such systems.",1501.07278v1
2013-12-19,Electronic Structure of $\textrm{Fe}\textrm{Se}_{1-x}\textrm{Te}_x$ Studied by X-ray Spectroscopy and Density Functional Theory,"We study the electronic properties of the
$\textrm{Fe}\textrm{Se}_{1-x}\textrm{Te}_x$ system ($x=0$, 0.25, 0.5, 0.75, and
1) from the perspective of X-ray spectroscopy and density functional theory
(DFT). The analysis performed on the density of states reveals marked
differences in the distribution of the $5p$ states of Te for $x>0$. We think
that this finding can be associated with the fact that superconductivity is
suppressed in FeTe. Moreover, using resonant inelastic X-ray scattering, we
estimate the spin state of our system which can be correlated to the magnetic
order. We find that the spin state of the
$\textrm{Fe}\textrm{Se}_{1-x}\textrm{Te}_x$ system fluctuates, as a function of
$x$, between $S=0$ and $S=2$ with Fe in FeSe in the highest spin state.
Finally, our DFT calculations nicely reproduce the X-ray emission spectra
performed at the Fe $L$-edge (which probe the occupied states) and suggest that
the $\textrm{Fe}\textrm{Se}_{1-x}\textrm{Te}_x$ system can be considered at
most as a moderately correlated system.",1312.5405v2
2017-01-31,Local incompressibility estimates for the Laughlin phase,"We prove sharp density upper bounds on optimal length-scales for the ground
states of classical 2D Coulomb systems and generalizations thereof. Our method
is new, based on an auxiliary Thomas-Fermi-like variational model. Moreover, we
deduce density upper bounds for the related low-temperature Gibbs states. Our
motivation comes from fractional quantum Hall physics, more precisely, the
perturbation of the Laughlin state by external potentials or impurities. These
give rise to a class of many-body wave-functions that have the form of a
product of the Laughlin state and an analytic function of many variables. This
class is related via Laughlin's plasma analogy to Gibbs states of the
generalized classical Coulomb systems we consider. Our main result shows that
the perturbation of the Laughlin state cannot increase the particle density
anywhere, with implications for the response of FQHE systems to external
perturbations.",1701.09064v3
2014-06-27,Separability and entanglement of spin $1$ particle,"We define the separability and entanglement notion for particle with spin
$s=1$. We consider two cases. In the first the particle is composed of two
fermions with $s_1=1/2$ and $s_2=1/2$. In the second case the state is the
qutrit state which is not composed system. The notion of negativity and
concurrence is defined for the qutrit state. The concurrence and negativity of
entangled and separable qutrit states determined by the parameters of the
density matrix are explicitly calculated. The maximum entanglement of the
qutrit state is observed for maximum values of non diagonal matrix elements of
the density matrix. New entropic inequalities for the density matrix of the
qutrit state are obtained.",1406.7118v2
2008-09-25,N-Qubit W States are Determined by their Bipartite Marginals,"We prove that the most general W class of N-qubit states are uniquely
determined among arbitrary states (pure or mixed) by just their bipartite
reduced density matrices. Moreover, if we consider only pure states, then (N-1)
of them are shown to be sufficient.",0809.4394v2
2014-09-28,Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry,"Noncentrosymmetric superconductors with strong spin-orbit coupling and the B
phase of ${}^3$He are possible realizations of topological superconductors with
time-reversal symmetry. The nontrivial topology of these time- reversal
invariant superconductors manifests itself at the material surface in the form
of helical Majorana modes. In this paper, using extensive numerical
simulations, we investigate the stability and properties of these Majorana
states under strong surface disorder, which influences both bulk and surface
states. To characterize the effects of strong disorder, we compute the level
spacing statistics and the local density of states of both two- and
three-dimensional topological superconductors. The Majorana surface states,
which are located in the outermost layers of the superconductor, are protected
against weak disorder, due to their topological characteristic. Sufficiently
strong disorder, on the other hand, partially localizes the surface layers,
with a more pronounced effect on states with energies close to the gap than on
those with energies close to zero. In particular, we observe that for all
disorder strengths and configurations there always exist two extended states at
zero-energy that can carry thermal current. At the crossover from weak to
strong disorder the surface state wave functions and the local density of
states show signs of critical delocalization. We find that at this crossover
the edge density of states of two-dimensional topological superconductors
exhibits a zero-energy divergence, reminiscent of the Dyson singularity of
quasi-one-dimensional dirty superconductors.",1409.7893v2
2000-06-30,The Size and Shape of Voids in Three-Dimensional Galaxy Surveys,"The sizes and shapes of voids in a galaxy survey depend not only on the
physics of structure formation, but also on the sampling density of the survey
and on the algorithm used to define voids. Using an N-body simulation with a
CDM power spectrum, we study the properties of voids in samples with different
number densities of galaxies, both in redshift space and in real space. When
voids are defined as regions totally empty of galaxies, their characteristic
volume is strongly dependent on sampling density; when they are defined as
regions whose density is 0.2 times the mean galaxy density, the dependence is
less strong. We compare two void-finding algorithms, one in which voids are
nonoverlapping spheres, and one, based on the algorithm of Aikio and Mahonen,
which does not predefine the shape of a void. Regardless of the algorithm
chosen, the characteristic void size is larger in redshift space than in real
space, and is larger for low sampling densities than for high sampling
densities. We define an elongation statistic Q which measures the tendency of
voids to be stretched or squashed along the line of sight. Using this
statistic, we find that at sufficiently high sampling densities (comparable to
the number densities of galaxies brighter than L_*), large voids tend to be
slightly elongated along the line of sight in redshift space.",0006452v1
2016-02-27,Voids in cosmological simulations over cosmic time,"We study evolution of voids in cosmological simulations using a new method
for tracing voids over cosmic time. The method is based on tracking watershed
basins (contiguous regions around density minima) of well developed voids at
low redshift, on a regular grid of density field. It enables us to construct a
robust and continuous mapping between voids at different redshifts, from
initial conditions to the present time. We discuss how the new approach
eliminates strong spurious effects of numerical origin when voids evolution is
traced by matching voids between successive snapshots (by analogy to halo
merger trees). We apply the new method to a cosmological simulation of a
standard LambdaCDM cosmological model and study evolution of basic properties
of typical voids (with effective radii between 6Mpc/h and 20Mpc/h at redshift
z=0) such as volumes, shapes, matter density distributions and relative
alignments. The final voids at low redshifts appear to retain a significant
part of the configuration acquired in initial conditions. Shapes of voids
evolve in a collective way which barely modifies the overall distribution of
the axial ratios. The evolution appears to have a weak impact on mutual
alignments of voids implying that the present state is in large part set up by
the primordial density field. We present evolution of dark matter density
profiles computed on iso-density surfaces which comply with the actual shapes
of voids. Unlike spherical density profiles, this approach enables us to
demonstrate development of theoretically predicted bucket-like shape of the
final density profiles indicating a wide flat core and a sharp transition to
high-density void walls.",1602.08541v2
2018-03-02,Building a Telescope to Look Into High-Dimensional Image Spaces,"An image pattern can be represented by a probability distribution whose
density is concentrated on different low-dimensional subspaces in the
high-dimensional image space. Such probability densities have an astronomical
number of local modes corresponding to typical pattern appearances. Related
groups of modes can join to form macroscopic image basins that represent
pattern concepts. Recent works use neural networks that capture high-order
image statistics to learn Gibbs models capable of synthesizing realistic images
of many patterns. However, characterizing a learned probability density to
uncover the Hopfield memories of the model, encoded by the structure of the
local modes, remains an open challenge. In this work, we present novel
computational experiments that map and visualize the local mode structure of
Gibbs densities. Efficient mapping requires identifying the global basins
without enumerating the countless modes. Inspired by Grenander's jump-diffusion
method, we propose a new MCMC tool called Attraction-Diffusion (AD) that can
capture the macroscopic structure of highly non-convex densities by measuring
metastability of local modes. AD involves altering the target density with a
magnetization potential penalizing distance from a known mode and running an
MCMC sample of the altered density to measure the stability of the initial
chain state. Using a low-dimensional generator network to facilitate
exploration, we map image spaces with up to 12,288 dimensions (64 $\times$ 64
pixels in RGB). Our work shows: (1) AD can efficiently map highly non-convex
probability densities, (2) metastable regions of pattern probability densities
contain coherent groups of images, and (3) the perceptibility of differences
between training images influences the metastability of image basins.",1803.01043v1
2022-12-17,Unrolling SVT to obtain computationally efficient SVT for n-qubit quantum state tomography,"Quantum state tomography aims to estimate the state of a quantum mechanical
system which is described by a trace one, Hermitian positive semidefinite
complex matrix, given a set of measurements of the state. Existing works focus
on estimating the density matrix that represents the state, using a compressive
sensing approach, with only fewer measurements than that required for a
tomographically complete set, with the assumption that the true state has a low
rank. One very popular method to estimate the state is the use of the Singular
Value Thresholding (SVT) algorithm. In this work, we present a machine learning
approach to estimate the quantum state of n-qubit systems by unrolling the
iterations of SVT which we call Learned Quantum State Tomography (LQST). As
merely unrolling SVT may not ensure that the output of the network meets the
constraints required for a quantum state, we design and train a custom neural
network whose architecture is inspired from the iterations of SVT with
additional layers to meet the required constraints. We show that our proposed
LQST with very few layers reconstructs the density matrix with much better
fidelity than the SVT algorithm which takes many hundreds of iterations to
converge. We also demonstrate the reconstruction of the quantum Bell state from
an informationally incomplete set of noisy measurements.",2212.08852v1
2005-01-17,Hamiltotian Formalism of Game Theory,"A new representation of Game Theory is developed in this paper. State of
players is represented by a density matrix, and payoff function is a set of
hermitian operators, which when applied onto the density matrix give the payoff
of players. By this formulism, a new way to find the equilibria of games is
given by generalizing the thermodynamical evolutionary process leading to
equilibrium in Statistical Mechanics. And in this formulism, when quantum
objects instead of classical objects are used as the objects in the game, it's
naturally leads to the so-called Quantum Game Theory, but with a slight
difference in the definition of strategy state of players: the probability
distribution is replaced with a density matrix. Further more, both games of
correlated and independent players can be reached in this single framework,
while traditionally, they are treated separately by Non-cooperative Game Theory
and Coalitional Game Theory. Because of the density matrix is used as state of
players, besides classical correlated strategy, quantum entangled states can
also be used as strategies, which is an entanglement of strategies between
players, and it is different with the entanglement of objects' states as in the
so-called Quantum Game Theory. At last, in the form of density matrix, a class
of quantum games, where the payoff matrixes are commutative, can be reduced
into classical games. In this sense, it will put the classical game as a
special case of our quantum game.",0501088v4
2022-07-27,Understanding density driven errors for reaction barrier heights,"Delocalization errors, such as charge-transfer and some self-interaction
errors, plague computationally-efficient and otherwise-accurate density
functional approximations (DFAs). Evaluating a semi-local DFA
non-self-consistently on the Hartree-Fock (HF) density is often recommended as
a computationally cheap remedy for delocalization errors. For sophisticated
meta-GGAs like SCAN, this approach can achieve remarkable accuracy. When this
HF-DFT (or DFA@HF) significantly improves over the DFA, it is often presumed
that the HF density is more accurate than the self-consistent DFA density. By
applying the metrics of density-corrected density functional theory (DFT), we
show that HF-DFT works for barrier heights by making a localizing charge
transfer error or density over-correction, thereby producing a
somewhat-reliable cancellation of density- and functional-driven errors for the
energy. A quantitative analysis of the charge transfer errors in a few
transition states confirms this trend. We do not have the exact functional and
exact densities that are needed to evaluate the exact density- and
functional-driven errors for the large BH76 database of barrier heights.
Instead, we have identified and used three non-local proxy functionals (the
SCAN 50% global hybrid, the range-separated hybrid LC-$\omega$PBE, and
SCAN-FLOSIC) and their self-consistent densities. These functionals yield
reasonably accurate self-consistent barrier heights, and their self-consistent
total energies are nearly piecewise linear in fractional electron number - two
important points of similarity to the exact functional. We argue that
density-driven errors of the energy in a self-consistent density functional
calculation are second-order in the density error, and that large
density-driven errors arise primarily from incorrect electron transfers over
length scales larger than the diameter of an atom.",2207.13509v3
2003-04-02,Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems,"It is shown that for a given bipartite density matrix and by choosing a
suitable separable set (instead of product set) on the separable-entangled
boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via
optimization for a generic entangled density matrix. Based on this, We obtain
optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and
$2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters
basis, iso-concurrence decomposable states, states obtained from BD states via
one parameter and three parameters local operations and classical
communications (LOCC), $d\otimes d$ Werner and isotropic states, and a one
parameter $3\otimes 3$ state. We also obtain the optimal decomposition for
multi partite isotropic state. It is shown that in all $2\otimes 2$ systems
considered here the average concurrence of the decomposition is equal to the
concurrence. We also show that for some $2\otimes 3$ Bell decomposable states
the average concurrence of the decomposition is equal to the lower bound of the
concurrence of state presented recently in [Buchleitner et al,
quant-ph/0302144], so an exact expression for concurrence of these states is
obtained. It is also shown that for $d\otimes d$ isotropic state where
decomposition leads to a separable and an entangled pure state, the average
I-concurrence of the decomposition is equal to the I-concurrence of the state.
  Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition,
Concurrence, Bell decomposable states, LOCC}
  PACS Index: 03.65.Ud",0304019v1
2015-02-09,Density matrix of black hole radiation,"Hawking's model of black hole evaporation is not unitary and leads to a mixed
density matrix for the emitted radiation, while the Page model describes a
unitary evaporation process in which the density matrix evolves from an almost
thermal state to a pure state. We compare a recently proposed model of
semiclassical black hole evaporation to the two established models. In
particular, we study the density matrix of the outgoing radiation and determine
how the magnitude of the off-diagonal corrections differs for the three
frameworks. For Hawking's model, we find power-law corrections to the two-point
functions that induce exponentially suppressed corrections to the off-diagonal
elements of the full density matrix. This verifies that the Hawking result is
correct to all orders in perturbation theory and also allows one to express the
full density matrix in terms of the single-particle density matrix. We then
consider the semiclassical theory for which the corrections, being
non-perturbative from an effective field-theory perspective, are much less
suppressed and grow monotonically in time. In this case, the R\'enyi entropy
for the outgoing radiation is shown to grow linearly at early times; but this
growth slows down and the entropy eventually starts to decrease at the Page
time. In addition to comparing models, we emphasize the distinction between the
state of the radiation emitted from a black hole, which is highly quantum, and
that of the radiation emitted from a typical classical black body at the same
temperature.",1502.02687v2
1999-10-12,"Novel coexisting density wave ground state in strongly correlated, two-dimensional electronic materials","Two-dimensional (2D) strongly correlated electron systems underlie many of
the most important phenomena in contemporary condensed matter physics,
including the Quantum Hall Effect (QHE), ``high T_c'' superconductivity, and
possible exotic conducting states in silicon MOSFETs. We demonstrate the
existence of yet another exotic ground state in strongly correlated, 2D
electronic materials: a novel, insulating bond-order/charge density wave state
(BCDW) in the commensurate 1/4-filled band that persists for all anisotropies
within the 2D lattice, in contradiction to the non-interacting electron
prediction of the vanishing of density waves in 2D for non-1/2-filled bands.
The persistence of the BCDW in the 2D lattice is a consequence of strong
electron-electron (e-e) interaction and the resultant ``confinement,'' a
concept recently widely debated. Our results have implications for experiments
in the organic charge transfer solids (CTS), where they explain the observation
of a ``mysterious'' coexistence of density waves, clarify the optical
conductivity of the ``metallic'', and suggest an approach to the observed
organic superconductivity.",9910164v1
2001-10-08,Structural and Electronic Instabilities in Polyacenes: Density Matrix Renormalization Group Study of a Long--Range Interacting Model,"We have carried out Density Matrix Renormalization Group (DMRG) calculations
on the ground state of long polyacene oligomers within a Pariser-Parr-Pople
(PPP) Hamiltonian. The PPP model includes long-range electron correlations
which are required for physically realistic modeling of conjugated polymers. We
have obtained the ground state energy as a function of the dimerization
$\delta$ and various correlation functions and structure factors for
$\delta=0$. From energetics, we find that while the nature of the Peierls'
instabilityin polyacene is conditional and strong electron correlations enhance
the dimerization. The {\it cis} form of the distortion is favoured over the
{\it trans} form. However, from the analysis of correlation functions and
associated structure factors, we find that polyacene is not susceptible to the
formation of a bond order wave (BOW), spin density wave (SDW) or a charge
density wave (CDW) in the ground state.",0110136v1
2006-01-04,Prospect for room temperature tunneling anisotropic magnetoresistance effect: density of states anisotropies in CoPt systems,"Tunneling anisotropic magnetoresistance (TAMR) effect, discovered recently in
(Ga,Mn)As ferromagnetic semiconductors, arises from spin-orbit coupling and
reflects the dependence of the tunneling density of states in a ferromagnetic
layer on orientation of the magnetic moment. Based on ab initio relativistic
calculations of the anisotropy in the density of states we predict sizable TAMR
effects in room-temperature metallic ferromagnets. This opens prospect for new
spintronic devices with a simpler geometry as these do not require
antiferromagnetically coupled contacts on either side of the tunnel junction.
We focus on several model systems ranging from simple hcp-Co to more complex
ferromagnetic structures with enhanced spin-orbit coupling, namely bulk and
thin film L1$_0$-CoPt ordered alloys and a monatomic-Co chain at a Pt surface
step edge. Reliability of the predicted density of states anisotropies is
confirmed by comparing quantitatively our ab initio results for the
magnetocrystalline anisotropies in these systems with experimental data.",0601071v1
2007-05-03,A Family of Equations of State Based on Lattice QCD: Impact on Flow in Ultrarelativistic Heavy-Ion Collisions,"We construct a family of equations of state within a quasiparticle model by
relating pressure, energy density, baryon density and susceptibilities adjusted
to first-principles lattice QCD calculations. The relation between pressure and
energy density from lattice QCD is surprisingly insensitive to details of the
simulations. Effects from different lattice actions, quark masses and lattice
spacings used in the simulations show up mostly in the quark-hadron phase
transition region which we bridge over by a set of interpolations to a hadron
resonance gas equation of state. Within our optimized quasiparticle model we
then examine the equation of state along isentropic expansion trajectories at
small net baryon densities, as relevant for experiments and hydrodynamic
simulations at RHIC and LHC energies. We illustrate its impact on azimuthal
flow anisotropies and transverse momentum spectra of various hadron species.",0705.0397v2
2013-05-17,Accurate densities of states for disordered systems from free probability: Live Free or Diagonalize,"We investigate how free probability allows us to approximate the density of
states in tight binding models of disordered electronic systems. Extending our
previous studies of the Anderson model in neighbor interactions [J. Chen et
al., Phys. Rev. Lett. 109, 036403 (2012)], we find that free probability
continues to provide accurate approximations for systems with constant
interactions on two- and three-dimensional lattices or with
next-nearest-neighbor interactions, with the results being visually
indistinguishable from the numerically exact solution. For systems with
disordered interactions, we observe a small but visible degradation of the
approximation. To explain this behavior of the free approximation, we develop
and apply an asymptotic error analysis scheme to show that the approximation is
accurate to the eighth moment in the density of states for systems with
constant interactions, but is only accurate to sixth order for systems with
disordered interactions. The error analysis also allows us to calculate
asymptotic corrections to the density of states, allowing for systematically
improvable approximations as well as insight into the sources of error without
requiring a direct comparison to an exact solution.",1305.3968v1
2019-01-24,Abelian oil and water dynamics does not have an absorbing-state phase transition,"The oil and water model is an interacting particle system with two types of
particles and a dynamics that conserves the number of particles, which belongs
to the so-called class of Abelian networks. Widely studied processes in this
class are sandpiles models and activated random walks, which are known (at
least for some choice of the underlying graph) to undergo an absorbing-state
phase transition. This phase transition characterizes the existence of two
regimes, depending on the particle density: a regime of fixation at low
densities, where the dynamics converges towards an absorbing state and each
particle jumps only finitely many times, and a regime of activity at large
densities, where particles jump infinitely often and activity is sustained
indefinitely. In this work we show that the oil and water model is
substantially different than sandpiles models and activated random walks, in
the sense that it does not undergo an absorbing-state phase transition and is
in the regime of fixation at all densities. Our result works in great
generality: for any graph that is vertex transitive and for a large class of
initial configurations.",1901.08425v1
2018-10-17,Strain induced superconducting pair-density-wave states in graphene,"Graphene is known to be non-superconducting. However, surprising
superconductivity is recently discovered in a flat-band in a twisted bi-layer
graphene. Here we show that superconductivity can be more easily realized in
topological flat-bands induced by strain in graphene through periodic ripples.
Specifically, it is shown that by including correlation effects, the chiral
d-wave superconductivity can be stabilized under strain even for slightly doped
graphene. The chiral d-wave superconductivity generally coexists with charge
density waves (CDW) and pair density waves (PDW) of the same period.
Remarkably, a pure PDW state with doubled period that coexists with the CDW
state is found to emerge at a finite temperature region under reasonable strain
strength. The emergent PDW state is shown to be superconducting with
non-vanishing superfluid density, and it realizes the long searched
superconducting states with non-vanishing center of mass momentum for Cooper
pairs.",1810.07515v1
2023-10-30,Efficient learning of arbitrary single-copy quantum states,"Quantum state tomography is the problem of estimating a given quantum state.
Usually, it is required to run the quantum experiment - state preparation,
state evolution, measurement - several times to be able to estimate the output
quantum state of the experiment, because an exponentially high number of copies
of the state is required. In this work, we present an efficient algorithm to
estimate with a small but non-zero probability of error the output state of the
experiment using a single copy of the state, without knowing the evolution
dynamics of the state. It also does not destroy the original state, which can
be recovered easily for any further quantum processing. As an example, it is
usually required to repeat a quantum image processing experiment many times,
since many copies of the state of the output image are needed to extract the
information from all its pixels. The information from $\mathcal{N}$ pixels of
the image can be inferred from a single run of the image processing experiment
in our algorithm, to efficiently estimate the density matrix of the image
state.",2310.19748v2
2004-08-31,Mixed phase and bound states in the phase diagram of the extended Hubbard model,"The paper examines part of the ground state diagram of the extended Hubbard
model, with the on-site attraction U<0 and intersite repulsion W>0 in the
presence of charge density waves, superconducting and $\eta$-superconducting
order parameters. We show the possibility of the stabilization of the mixed
state, with all three nonzero order parameters, in the model with nearest
neighbor interactions. The other result of the paper is application of the
exact solution of the Schrodinger equation for the two electron bound state, as
an additional bound for the phase diagram of the model, resulting in the
partial suppression of the superconducting state of the s-wave symmetry, in
favor of the normal state phase.",0408692v1
2022-08-07,Bubble nuclei: single-particle versus Coulomb interaction effects,"The detailed investigation of microscopic mechanisms leading to the formation
of bubble structures in the nuclei has been performed in the framework of
covariant density functional theory. The main emphasis of this study is on the
role of single-particle degrees of freedom and Coulomb interaction. In general,
the formation of bubbles lowers the Coulomb energy. However, in nuclei this
trend is counteracted by the quantum nature of the single-particle states: only
specific single-particle states with specific density profiles can be occupied
with increasing proton and neutron numbers. A significant role of central
classically forbidden region at the bottom of the wine bottle potentials in the
formation of nuclear bubbles (via primarily the reduction of the densities of
the $s$ states at $r=0$) has been revealed for the first time. Their formation
also depends on the availability of low-$l$ single-particle states for
occupation since single-particle densities represent the basic building blocks
of total densities. Nucleonic potentials disfavor the occupation of such states
in hyperheavy nuclei and this contributes to the formation of bubbles in such
nuclei. Additivity rule for densities has been proposed for the first time. It
was shown that the differences in the densities of bubble and flat density
nuclei follow this rule in the $A\approx 40$ mass region and in superheavy
nuclei with comparable accuracy. This strongly suggests the same mechanism of
the formation of central depression in bubble nuclei of these two mass regions.
Nuclear saturation mechanisms and self-consistency effects also affect the
formation of bubble structures. The detailed analysis of different aspects of
bubble physics strongly suggests that the formation of bubble structures in
superheavy nuclei is dominated by single-particle effects.",2208.03833v1
2004-09-07,Density profiles for atomic quantum Hall states,"We analyze density profiles for atomic quantum Hall states, which are
expected to form in systems of rotating cold atoms in the high-rotation limit.
For a two-dimensional (single-layer) system we predict a density landscape
showing plateaus at quantized densities, signaling the formation of
incompressible groundstates. For a set-up with parallel, coupled layers, we
predict (i) at intermediate values of the inter-layer tunneling: a continuously
varying density profile $\rho(z)$ across the layers, showing cusps at specific
positions, (ii) at small values for the tunneling, quantum Hall-Mott phases,
with individual layers at sharply quantized particle number, and plateaus in
the density profile $\rho(z)$.",0409146v1
2009-09-01,Quantum state depression in semiconductor quantum well,"In this study, the quantum state depression (QSD) in semiconductor quantum
well (QW) is investigated. The QSD emerge from the ridged geometry of the QW
boundary. Ridges impose additional boundary conditions on the electron wave
function and some quantum states become forbidden. State density reduces in all
energy bands, including conduction band (CB). Hence, electrons, rejected from
the filled bands, must occupy quantum states in the empty bands due to Pauli
Exclusion principle. Both the electron concentration in CB and Fermi energy
increases as in the case of donor doping. Since quantum state density is
reduced, the ridged quantum well (RQW) exhibits quantum properties at widths
approaching 200 nm. Wide RQW can be used to improve photon confinement in
QW-based optoelectronics devices. Reduction in the state density increases the
carrier mobility and makes the ballistic transport regime more pronounced in
the semiconductor QW devices. Furthermore, the QSD doping does not introduce
scattering centers and can be used for power electronics.",0909.0154v1
1998-02-23,Density-Induced Breaking of Pairs in the Attractive Hubbard Model,"A conserving T-matrix approximation is applied to the two-dimensional
attractive Hubbard model in the low-density regime. A set of self-consistent
equations is solved in the real-frequency domain to avoid the analytic
continuation procedure. By tuning the chemical potential the particle density
was varied in the limits 0.01 < n < 0.18. For the value of the attractive
potential U=8t the binding energy of pairs monotonically decreases with
increasing n, from its zero-density limit 2.3t and vanishes at a critical
density n=0.19. A pairing-induced pseudogap in the single-particle density of
states is found at low densities and temperatures.",9802239v1
2019-11-22,Crowd Density Forecasting by Modeling Patch-based Dynamics,"Forecasting human activities observed in videos is a long-standing challenge
in computer vision, which leads to various real-world applications such as
mobile robots, autonomous driving, and assistive systems. In this work, we
present a new visual forecasting task called crowd density forecasting. Given a
video of a crowd captured by a surveillance camera, our goal is to predict how
that crowd will move in future frames. To address this task, we have developed
the patch-based density forecasting network (PDFN), which enables forecasting
over a sequence of crowd density maps describing how crowded each location is
in each video frame. PDFN represents a crowd density map based on spatially
overlapping patches and learns density dynamics patch-wise in a compact latent
space. This enables us to model diverse and complex crowd density dynamics
efficiently, even when the input video involves a variable number of crowds
that each move independently. Experimental results with several public datasets
demonstrate the effectiveness of our approach compared with state-of-the-art
forecasting methods.",1911.09814v1
2022-01-13,Reconstruction of dark energy density by non-parametric approaches,"The evolution of dark energy density is a crucial quantity in understanding
the nature of dark energy. Often, the quantity is described by the so-called
equation of state, that is the ratio of dark energy pressure to its density. In
this scenario, the dark energy density is always positive throughout cosmic
history and a negative value is not allowed. Assuming a homogeneous and
isotropic universe, we reconstruct the dark energy density directly from
observational data and investigate its evolution through cosmic history. We
consider the latest SNIa, BAO and cosmic chronometer data and reconstruct the
dark energy density in both flat and non-flat universes up to redshift $z\sim
3$. The results are well in agreement with the $\Lambda$CDM up to redshift
$z\sim 1.5$, whereas all data and methods, in our analysis, provide a negative
dark energy density at high redshifts.",2201.04993v1
2023-08-17,Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction,"Safety-critical applications such as autonomous vehicles and social robots
require fast computation and accurate probability density estimation on
trajectory prediction. To address both requirements, this paper presents a new
normalizing flow-based trajectory prediction model named FlowChain. FlowChain
is a stack of conditional continuously-indexed flows (CIFs) that are expressive
and allow analytical probability density computation. This analytical
computation is faster than the generative models that need additional
approximations such as kernel density estimation. Moreover, FlowChain is more
accurate than the Gaussian mixture-based models due to fewer assumptions on the
estimated density. FlowChain also allows a rapid update of estimated
probability densities. This update is achieved by adopting the \textit{newest
observed position} and reusing the flow transformations and its
log-det-jacobians that represent the \textit{motion trend}. This update is
completed in less than one millisecond because this reuse greatly omits the
computational cost. Experimental results showed our FlowChain achieved
state-of-the-art trajectory prediction accuracy compared to previous methods.
Furthermore, our FlowChain demonstrated superiority in the accuracy and speed
of density estimation. Our code is available at
\url{https://github.com/meaten/FlowChain-ICCV2023}",2308.08824v1
2011-03-28,General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States,"We consider (2+1)-dimensional topological quantum states which possess edge
states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT),
such as e.g. a general quantum Hall state. We demonstrate that for such states
the reduced density matrix of a finite spatial region of the gapped topological
state is a thermal density matrix of the chiral edge state CFT which would
appear at the spatial boundary of that region. We obtain this result by
applying a physical instantaneous cut to the gapped system, and by viewing the
cutting process as a sudden ""quantum quench"" into a CFT, using the tools of
boundary conformal field theory. We thus provide a demonstration of the
observation made by Li and Haldane about the relationship between the
entanglement spectrum and the spectrum of a physical edge state.",1103.5437v1
2020-11-17,C-Learning: Learning to Achieve Goals via Recursive Classification,"We study the problem of predicting and controlling the future state
distribution of an autonomous agent. This problem, which can be viewed as a
reframing of goal-conditioned reinforcement learning (RL), is centered around
learning a conditional probability density function over future states. Instead
of directly estimating this density function, we indirectly estimate this
density function by training a classifier to predict whether an observation
comes from the future. Via Bayes' rule, predictions from our classifier can be
transformed into predictions over future states. Importantly, an off-policy
variant of our algorithm allows us to predict the future state distribution of
a new policy, without collecting new experience. This variant allows us to
optimize functionals of a policy's future state distribution, such as the
density of reaching a particular goal state. While conceptually similar to
Q-learning, our work lays a principled foundation for goal-conditioned RL as
density estimation, providing justification for goal-conditioned methods used
in prior work. This foundation makes hypotheses about Q-learning, including the
optimal goal-sampling ratio, which we confirm experimentally. Moreover, our
proposed method is competitive with prior goal-conditioned RL methods.",2011.08909v2
2022-11-08,Spin-state Gaps and Self-Interaction-Corrected Density Functional Approximations: Octahedral Fe(II) Complexes as Case Study,"Accurate prediction of spin-state energy difference is crucial for
understanding the spin crossover (SCO) phenomena and is very challenging for
the density functional approximations, especially for the local and semi-local
approximations, due to delocalization errors. Here, we investigate the effect
of self-interaction error removal from the local spin density approximation
(LSDA) and PBE generalized gradient approximation (GGA) on the spin-state gaps
of Fe(II) complexes with various ligands using recently developed locally
scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151,
214108 (2019)]. The LSIC method is exact for one-electron density, which
recovers uniform electron gas limit of underlying functional and approaches the
well-known Perdew-Zunger self-interaction correction [Phys. Rev. B, 23, 5048
(1981)] (PZSIC) as a special case when the scaling factor is constant. Our
results, when compared with reference diffusion Monte Carlo (DMC) results, show
that the PZSIC method significantly overestimates spin-state gaps favoring low
spin states for all ligands and does not improve upon DFAs. The perturbative
LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean
absolute error of 0.51 eV but slightly overcorrects for the stronger CO
ligands. The quasi-self-consistent LSIC-LSDA, like CCSD(T), gives a correct
sign of spin-state gaps for all ligands with MAE of 0.56 eV, comparable to that
of CCSD(T) (0.49 eV).",2211.03935v1
2006-06-16,Orbitally quantized density-wave states perturbed from equilibrium,"We consider the effect that a change in the magnetic induction B has in
causing an orbitally quantized field-induced spin- or charge density wave
(FISDW or FICDW) state to depart from thermodynamic equilibrium. The
competition between elastic forces of the density wave (DW) and pinning leads
to the realization of a critical state that is in many ways analogous to that
realized within the vortex state of type II superconductors. Such a critical
state has been verified experimentally in charge-transfer salts of the
composition alpha-(BEDT-TTF)MHg(SCN)4, but should be a generic property of all
orbitally quantized DW phases. The metastable state consists of a balance
between the DW pinning force and the Lorentz force on extended currents
associated with drifting cyclotron orbits, resulting in the establishment of
persistent currents throughout the bulk and to the possibly of a
three-dimensional `chiral metal' that extends deep into the interior of a
crystal.",0606460v1
2005-06-20,Microcanonical distributions for quantum systems,"The standard assumption for the equilibrium microcanonical state in quantum
mechanics, that the system must be in one of the energy eigenstates, is
weakened so as to allow superpositions of states. The weakened form of the
microcanonical postulate thus asserts that all quantum states giving rise to
the same energy expectation value must be realised with equal probability. The
consequences that follow from this assertion are investigated. In particular, a
closed-form expression for the density of states associated with any system
having a nondegenerate energy spectrum is obtained. The result is applied to a
variety of examples, for which the behaviour of the state density, as well as
the relation between energy and temperature, are determined. Numerical studies
indicate that the density of states converges to a distribution when the number
of energy levels approaches infinity.",0506163v1
2007-10-30,RNA Secondary Structures: Complex Statics and Glassy Dynamics,"Models for RNA secondary structures (the topology of folded RNA) without
pseudo knots are disordered systems with a complex state-space below a critical
temperature. Hence, a complex dynamical (glassy) behavior can be expected, when
performing Monte Carlo simulation. Interestingly, in contrast to most other
complex systems, the ground states and the density of states can be computed in
polynomial time exactly using transfer matrix methods. Hence, RNA secondary
structure is an ideal model to study the relation between static/thermodynamic
properties and dynamics of algorithms. Also they constitute an ideal benchmark
system for new Monte Carlo methods.
  Here we considered three different recent Monte Carlo approaches: entropic
sampling using flat histograms, optimized-weights ensembles, and ParQ, which
estimates the density of states from transition matrices.
  These methods were examined by comparing the obtained density of states with
the exact results. We relate the complexity seen in the dynamics of the Monte
Carlo algorithms to static properties of the phase space by studying the
correlations between tunneling times, sampling errors, amount of meta-stable
states and degree of ultrametricity at finite temperature.",0710.5716v2
2018-12-11,Bath engineering of a fluorescing artificial atom with a photonic crystal,"We demonstrate how the dissipative interaction between a superconducting
qubit and a microwave photonic crystal can be used for quantum bath
engineering. The photonic crystal is created with a step-impedance transmission
line which suppresses and enhances the quantum spectral density of states,
influencing decay transitions of a transmon circuit. The qubit interacts with
the transmission line indirectly via dispersive coupling to a cavity. We
characterize the photonic crystal density of states from both the unitary and
dissipative dynamics of the qubit. When the qubit is driven, it dissipates into
the frequency dependent density of states of the photonic crystal. Our result
is the deterministic preparation of qubit superposition states as the
steady-state of coherent driving and dissipation near by the photonic crystal
band edge, which we characterize with quantum state tomography. Our results
highlight how the multimode environment from the photonic crystal forms a
resource for quantum control.",1812.04205v3
2023-10-12,Selective Wigner phase space tomography and its application for studying quantum chaos,"The quasiprobability distribution of the discrete Wigner function provides a
complete description of a quantum state and is, therefore, a useful alternative
to the usual density matrix description. Moreover, the experimental quantum
state tomography in discrete Wigner phase space can also be implemented. We
observe that for a certain class of states, such as harmonic states, the Wigner
matrix is far more sparse compared to the density matrix in the computational
basis. Additionally, reading only a small part of the Wigner matrix may suffice
to infer certain behavior of quantum dynamics. In such cases, selective Wigner
phase space tomography (SWPST) can be more efficient than the usual density
matrix tomography (DMT). Employing nuclear magnetic resonance methods on a
three-qubit nuclear spin register, we experimentally estimate Wigner matrices
of various two-qubit quantum states. As a specific example application of
SWPST, we study the evolution of spin coherent states under the quantum chaotic
kicked top model and extract signatures of quantum-classical correspondence in
the Wigner phase space.",2310.08307v1
2003-11-06,Extended RPA with ground-state correlations,"We propose a time-independent method for finding a correlated ground state of
an extended time-dependent Hartree-Fock theory, known as the time-dependent
density-matrix theory (TDDM). The correlated ground state is used to formulate
the small amplitude limit of TDDM (STDDM) which is a version of extended RPA
theories with ground-state correlations. To demonstrate the feasibility of the
method, we calculate the ground state of 22O and study the first 2+ state and
its two-phonon states using STDDM.",0311016v1
2003-01-06,Requirements for compatibility between local and multipartite quantum states,"We consider a partial trace transformation which maps a multipartite quantum
state to collection of local density matrices. We call this collection a mean
field state. The necessary and sufficient conditions under which a mean field
state is compatible with at least one multipartite pure state are found for the
system of $n$ qubits and for the tripartite system with the Hilbert space of
dimension 2x2x4. Compatibility of mean field states with more general classes
of multipartite quantum states is discussed.",0301014v2
2008-09-18,Undetermined states: how to find them and their applications,"We investigate the undetermined sets consisting of two-level, multi-partite
pure quantum states, whose reduced density matrices give absolutely no
information of their original states. Two approached of finding these quantum
states are proposed. One is to establish the relation between codewords of the
stabilizer quantum error correction codes (SQECCs) and the undetermined states.
The other is to study the local complementation rules of the graph states. As
an application, the undetermined states can be exploited in the quantum secret
sharing scheme. The security is guaranteed by their undetermineness.",0809.3081v2
2023-04-12,Entanglement distillation in terms of Schmidt rank and matrix rank,"Entanglement distillation is a key task in quantum-information processing. In
this paper, we distill non-positive-partial-transpose (NPT) bipartite states of
some given Schmidt rank and matrix rank. We show that all bipartite states of
Schmidt rank two are locally equivalent to classical-classical states, and all
bipartite states of Schmidt rank three are 1-undistillable. Subsequently, we
show that low-rank B-irreducible NPT states are distillable for large-rank
reduced density operators by proving low-rank B-irreducible NPT state whose
range contains a product vector is distillable. Eventually, we present an
equivalent condition to distill $M\times N$ bipartite states of rank
$\max\{M,N\}+1$.",2304.05563v2
2008-09-10,Quantum Density Fluctuations in Classical Liquids,"We discuss the density fluctuations of a fluid due to zero point motion.
These can be regarded as density fluctuations in the phonon vacuum state. We
assume a linear dispersion relation with a fixed speed of sound and calculate
the density correlation function. We note that this function has the same form
as the correlation function for the time derivative of a relativistic massless
scalar field, but with the speed of light replaced by the speed of sound. As a
result, the study of density fluctuations in a fluid can be a useful analog
model for better understanding fluctuations in relativistic quantum field
theory. We next calculate the differential cross section for light scattering
by the zero point density fluctuations, and find a result proportional to the
fifth power of the light frequency. This can be understood as the product of
fourth power dependence of the usual Rayleigh cross section with the linear
frequency dependence of the spectrum of zero point density fluctuations. We
give some estimates of the relative magnitude of this effect compared to the
scattering by thermal density fluctuations, and find that it can be of order
0.5% for water at room temperature and optical frequencies. This relative
magnitude is proportional to frequency and inversely proportional to
temperature. Although the scattering by zero point density fluctuation is
small, it may be observable.",0809.1851v1
2009-08-10,Taming Density Functional Theory by Coarse-Graining,"The standard (``fine-grained'') interpretation of quantum density functional
theory, in which densities are specified with infinitely-fine spatial
resolution, is mathematically unruly. Here, a coarse-grained version of DFT,
featuring limited spatial resolution, and its relation to the fine-grained
theory in the $L^1\cap L^3$ formulation of Lieb, is studied, with the object of
showing it to be not only mathematically well-behaved, but consonant with the
spirit of DFT, practically (computationally) adequate and sufficiently close to
the standard interpretation as to accurately reflect its non-pathological
properties. The coarse-grained interpretation is shown to be a good model of
formal DFT in the sense that: all densities are (ensemble)-V-representable; the
intrinsic energy functional $F$ is a continuous function of the density and the
representing external potential is the (directional) functional derivative of
the intrinsic energy. Also, the representing potential $v[\rho]$ is
quasi-continuous, in that $v[\rho]\rho$ is continuous as a function of $\rho$.
The limit of coarse-graining scale going to zero is studied to see if
convergence to the non-pathological aspects of the fine-grained theory is
adequate to justify regarding coarse-graining as a good approximation. Suitable
limiting behaviors or intrinsic energy, densities and representing potentials
are found. Intrinsic energy converges monotonically, coarse-grained densities
converge uniformly strongly to their low-intrinsic-energy fine-grainings, and
$L^{3/2}+L^\infty$ representability of a density is equivalent to the existence
of a convergent sequence of coarse-grained potential/ground-state density
pairs.",0908.1263v3
2001-07-12,P-wave pairing and ferromagnetism in the metal-insulator transition in two dimensions,"Based on recent experimental evidence for a spin polarized ground state in
the insulating phase of the two-dimensional electron system, we propose that
ferromagnetic spin fluctuations lead to an attractive interaction in the
triplet channel and cause p-wave pairing in the conducting phase. We use the
Landau Fermi liquid phenomenology to explain how the enhanced spin
susceptibility near the critical density yields an attractive potential, in a
similar mechanism to superfluidity in $^3$He. As the density is decreased, the
p-wave order parameter undergoes a transition from a unitary to a nonunitary
state, in which it coexists with ferromagnetism for a range of densities. As
the density is further reduced, the pairing amplitude vanishes and the system
is described by a ferromagnetic insulator. Thus, we find two quantum critical
points as a function of density associated with the polarization of the paired
state and ferromagnetism. We explain the magnetotransport measurements in
parallel and perpendicular magnetic fields and propose a shot noise experiment
to measure the pair charge.",0107271v1
2007-05-11,A lower bound for the density of states of the lattice Anderson model,"We consider the Anderson model on the multi-dimensional cubic lattice and
prove a positive lower bound on the density of states under certain conditions.
For example, if the random variables are independently and identically
distributed and the probability measure has a bounded Lebesgue density with
compact support, and if this density is essentially bounded away from zero on
its support, then we prove that the density of states is strictly positive for
Lebesgue-almost every energy in the deterministic spectrum.",0705.1707v2
2015-12-13,Emergence of Metallic Quantum Solid Phase in a Rydberg-Dressed Fermi Gases,"We examine possible low-temperature phases of a repulsively Rydberg-dressed
Fermi gas in a three-dimensional free space. It is shown that the collective
density excitations develop a roton minimum, which is softened at a wavevector
smaller than the Fermi wavevector when the particle density is above a critical
value. The mean field calculation shows that unlike the insulating charge
density waves states often observed in conventional condensed matters, a
self-assembled metallic density wave state emerges at low temperatures. In
particular, the density wave state supports a Fermi surface and a
body-center-cubic crystal order at the same time with the estimated critical
temperature being about one-tenth of the non-interacting Fermi energy. Our
results suggest the emergency of a fermionic quantum solid that should be
observable in current experimental setup.",1512.04079v2
2022-02-09,Connection between a degenerate particle flow model and a free boundary problem,"In this paper a strongly degenerate parabolic equation derived from a density
dependent particle flow model is studied. Furthermore, a free boundary problem
and its connection to the strongly degenerate parabolic equation is
investigated. First, it is shown that the strongly degenerate parabolic
equation has a unique global bounded weak solution that converges towards a
steady state for large time horizons. Two scenarios might occur: When the
average density $\rho_{\infty}$ is larger than a certain critical density
$\rho_{cr}$, the steady state coincides with $\rho_{\infty}$ and the
convergence rate is exponential in the $L^2$ norm; while in the opposite case
$\rho_{\infty}<\rho_{cr}$, the steady state is unknown and the convergence is
algebraic in a negative Sobolev seminorm. Further investigations show that for
radially symmetric and decreasing initial data, the solution of the strongly
degenerate parabolic equation can be constructed by using the solution of a
corresponding free boundary problem. Moreover, the global existence of weak
solutions to the latter problem is proved. Finally, numerical experiments in
two space dimensions are presented, which show that segregation phenomena can
appear when the initial average density is smaller than the critical density.",2202.04416v3
2016-04-27,Coexistence curves and molecule number densities of AdS black holes in the reduced parameter space,"In this paper, we investigate the coexistence curves and molecule number
densities of $f(R)$ AdS black holes and Gauss-Bonnet AdS black holes.
Specifically, we work with the reduced parameter space and derive the analytic
expressions of the universal coexistence curves that are independent of theory
parameters. Moreover, we obtain the explicit expressions of the physical
quantity describing the difference of the number densities of black hole
molecules between the small and large black hole. It is found that both the
coexistence curve and the difference of the molecule number densities of $f(R)$
AdS black holes coincide with those of RN-AdS black holes. It may be attributed
to the same equation of state they share in the reduced parameter space. The
difference of the molecule number densities between the small and large
Gauss-Bonnet AdS black hole exhibits different behavior. This may be attributed
to the fact that the charge of RN-AdS black hole is non-trivial. Our research
will not only deepen the understanding of both the physics along the
coexistence curve and the underlying microscopic freedom of AdS black holes,
but also highlight the importance of the law of corresponding states.",1604.07931v1
2021-02-24,Density of Quasi-localized Modes in Glasses: where are the Two-Level Systems?,"The existence of a constant density of two-level systems (TLS) was proposed
as the basis of some intriguing universal aspects of glasses at ultra-low
temperatures. Here we ask whether their existence is necessary for explaining
the universal density of states quasi-localized modes (QLM) in glasses at
ultra-low temperatures. A careful examination of the QLM that exist in a
generic atomistic model of a glass former reveals at least two types of them,
each exhibiting a different density of states, one depending on the frequency
as $\omega^3$ and the other as $\omega^4$. The properties of the glassy energy
landscape that is responsible for the two types of modes is examined here,
explaining the analytic feature responsible for the creations of (at least) two
families of QLM's. Although adjacent wells certainly exist in the complex
energy landscape of glasses, doubt is cast on the relevance of TLS for the
universal density of QLM's.",2102.12368v2
2010-06-18,Sensitivity of the Moment of Inertia of Neutron Stars to the Equation of State of Neutron-Rich Matter,"The sensitivity of the stellar moment of inertia to the neutron-star matter
equation of state is examined using accurately-calibrated relativistic
mean-field models. We probe this sensitivity by tuning both the density
dependence of the symmetry energy and the high density component of the
equation of state, properties that are at present poorly constrained by
existing laboratory data. Particularly attractive is the study of the fraction
of the moment of inertia contained in the solid crust. Analytic treatments of
the crustal moment of inertia reveal a high sensitivity to the transition
pressure at the core-crust interface. This may suggest the existence of a
strong correlation between the density dependence of the symmetry energy and
the crustal moment of inertia. However, no correlation was found. We conclude
that constraining the density dependence of the symmetry energy - through, for
example, the measurement of the neutron skin thickness in 208Pb - will place no
significant bound on either the transition pressure or the crustal moment of
inertia.",1006.3758v1
2012-12-21,Fluctuations and Symmetry Energy in Nuclear Fragmentation Dynamics,"Within a dynamical description of nuclear fragmentation, based on the
liquid-gas phase transition scenario, we explore the relation between
neutron-proton density fluctuations and nuclear symmetry energy. We show that,
along the fragmentation path, isovector fluctuations follow the evolution of
the local density and approach an equilibrium value connected to the local
symmetry energy. Higher density regions are characterized by smaller average
asymmetry and narrower isotopic distributions. This dynamical analysis points
out that fragment final state isospin fluctuations can probe the symmetry
energy of the density domains from which fragments originate.",1212.5364v2
2015-05-20,Cracking in charged relativistic spheres,"Using the concept of cracking, we have explored the influence of density
fluctuations on isotropic and anisotropic charged matter configurations in
General Relativity with ""barotropic"" equations of state, $P = P(\rho)$ and
$P_{\perp}= P_{\perp}(\rho)$ and a mass-charge relation $Q=Q(\rho)$. We have
refined the idea that density fluctuations affect physical variables and their
gradients, i.e. the radial pressure and charge density gradients. It is found
that not only anisotropic charged models could present cracking (or
overturning), but also isotropic charged matter configurations could be
affected by density fluctuations.",1505.05550v1
1995-04-05,Evidence for a superfluid density in t--J ladders,"Applying three independent techniques, we give numerical evidence for a
finite superfluid density in isotropic hole-doped t--J ladders: We show the
existence of anomalous flux quantization, emphasising the contrasting behaviour
to that found in the `Luttinger liquid' regime stabilised at low electron
densities; We consider the nature of the low-lying excitation modes, finding
the 1-D analog of the superconducting state; And using a density matrix
renormalization group approach, we find long range pairing correlations and
exponentially decaying spin-spin correlations.",9504018v1
1999-04-06,Quantum dots in magnetic fields: Phase diagram and broken symmetry of the Chamon-Wen edge,"Quantum dots in magnetic fields are studied within the current spin density
functional formalism avoiding any spatial symmetry restrictions of the
solutions. We find that the maximum density droplet reconstructs into states
with broken internal symmetry: The Chamon-Wen edge co-exists with a modulation
of the charge density along the edge. The phase boundaries between the
polarization transition, the maximum density droplet and its reconstruction are
in agreement with recent experimental results.",9904067v1
2008-03-04,LaFeAsO$_{1-x}$F$_x$: A low carrier density superconductor near itinerant magnetism,"Density functional studies of 26K superconducting LaFeAs(O,F) are reported.
We find a low carrier density, high density of states, $N(E_F)$ and modest
phonon frequencies relative to $T_c$. The high $N(E_F)$ leads to proximity to
itinerant magnetism, with competing ferromagnetic and antiferromagnetic
fluctuations and the balance between these controlled by doping level. Thus
LaFeAs(O,F) is in a unique class of high $T_c$ superconductors: high $N(E_F)$
ionic metals near magnetism.",0803.0429v2
2008-08-30,Correlation density matrix: an unbiased analysis of exact diagonalizations,"Given the ground state wavefunction for an interacting lattice model, we
define a ""correlation density matrix""(CDM) for two disjoint, separated clusters
$A$ and $B$, to be the density matrix of their union, minus the direct product
of their respective density matrices. The CDM can be decomposed systematically
by a numerical singular value decomposition, to provide a systematic and
unbiased way to identify the operator(s) dominating the correlations, even
unexpected ones.",0809.0075v1
2008-12-18,Density Matrix Functional Theory for the Lipkin model,"A Density Matrix Functional theory is constructed semi-empirically for the
two-level Lipkin model. This theory, based on natural orbitals and occupation
numbers, is shown to provide a good description for the ground state energy of
the system as the two-body interaction and particle number vary. The
application of Density Matrix Functional theory to the Lipkin model illustrates
that it could be a valuable tool for systems presenting a shape
phase-transition such as nuclei. The improvement of one-body observables
description as well as the interest for Energy Density Functional theory are
discussed.",0812.3604v1
2010-12-28,Photonic spectral density of coupled microwave cavities,"We study a pair of anharmonic microwave cavities that is connected by an
optical fiber. The photonic spectral density characterizes the evolution of the
coupled cavities after the system has been prepared in a Fock or N00N state. We
evaluate the photonic spectral density within the recursive projection method
and find that the anharmonicity has no substantial effect on the spectral
properties. In all cases the photonic spectral density has a Gaussian envelope
for large photon numbers.",1012.5848v1
2014-01-09,Spin-isospin Response in Finite Nuclei from an Extended Skyrme Interaction,"The magnetic dipole (M1) and the Gamow-Teller (GT) excitations of finite
nuclei have been studied in a fully self-consistent Hartree-Fock (HF) plus
random phase approximation (RPA) approach by using a Skyrme energy density
functional with spin and spin-isospin densities. To this end, we adopt the
extended SLy5st interaction which includes spin-density dependent terms and
stabilize nuclear matter with respect to spin instabilities. The effect of the
spin-density dependent terms is examined in both the mean field and the
spin-flip excited state calculations. The numerical results show that those
terms give appreciable repulsive contributions to the M1 and GT response
functions of finite nuclei.",1401.1981v1
2014-09-19,The role of electron localization in density functionals,"We introduce a new functional for simulating ground-state and time-dependent
electronic systems within density-functional theory. The functional combines an
expression for the exact Kohn-Sham (KS) potential in the limit of complete
electron localization with a measure of the actual localization. We find
accurate self-consistent charge densities, even for systems where the exact
exchange-correlation potential exhibits non-local dependence on the density,
such as potential steps. We compare our results to the exact KS potential for
each system. The self-interaction correction is accurately described, avoiding
the need for orbital-dependent potentials.",1409.5666v1
2014-11-19,"Existence of isoperimetric sets with densities ""converging from below"" in $\mathbb{R}^N$","In this paper, we consider the isoperimetric problem in the space
$\mathbb{R}^N$ with density. Our result states that, if the density f is l.s.c.
and converges to a positive limit at infinity, being smaller than this limit
far from the origin, then isoperimetric sets exist for all volumes. Several
known results or counterexamples show that the present result is essentially
sharp. The special case of our result for radial and increasing densities
positively answers a conjecture made in [10].",1411.5208v1
2016-07-14,On the Ribosomal Density that Maximizes Protein Translation Rate,"During mRNA translation, several ribosomes attach to the same mRNA molecule
simultaneously translating it into a protein. This pipelining increases the
protein production rate. A natural and important question is what ribosomal
density maximizes the protein production rate. Using mathematical models of
ribosome flow along both a linear and a circular mRNA molecule we prove that
typically the steady-state production rate is maximized when the ribosomal
density is one half of the maximal possible density. We discuss the
implications of our results to endogenous genes under natural cellular
conditions and also to synthetic biology.",1607.04064v1
2018-07-01,Holographic Magnetized Chiral Density Wave,"We explore the end point of the helical instability in finite density, finite
magnetic field background discussed by Kharzeev and Yee [1]. The nonlinear
solution is obtained and identified with the (magnetized) chiral density wave
phase in literature. We find there are two branches of solutions, which match
with the two unstable modes in [1]. At large chemical potential and magnetic
field, the magnetized chiral density wave can be thermodynamically preferred
over chirally symmetric phase and chiral symmetry breaking phase.
Interestingly, we find an exotic state with vanishing chemical potential at
large magnetic field. We also attempt to clarify the role of anomalous charge
in holographic model.",1807.00330v1
2013-08-28,"Nonequilibrium ""melting"" of a charge density wave insulator via an ultrafast laser pulse","We employ an exact solution of the simplest model for pump-probe
time-resolved photoemission spectroscopy in charge-density-wave systems to show
how, in nonequilibrium the gap in the density of states disappears while the
charge density remains modulated, and then the gap reforms after the pulse has
passed. This nonequilibrium scenario qualitatively describes the common
short-time experimental features in TaS2 and TbTe3 indicating a
quasiuniversality for nonequilibrium ""melting"" with qualitative features that
can be easily understood within a simple picture.",1308.6066v1
2016-12-13,Holographic Pair and Charge Density Waves,"We examine a holographic model in which a U(1) symmetry and translational
invariance are broken spontaneously at the same time. Our construction provides
an example of a system with pair-density wave order, in which the
superconducting order parameter is spatially modulated but has a zero average.
In addition, the charge density oscillates at twice the frequency of the scalar
condensate. Depending on the choice of parameters, the model also admits a
state with co-existing superconducting and charge density wave orders, in which
the scalar condensate has a uniform component.",1612.04385v1
2020-10-19,Imitation with Neural Density Models,"We propose a new framework for Imitation Learning (IL) via density estimation
of the expert's occupancy measure followed by Maximum Occupancy Entropy
Reinforcement Learning (RL) using the density as a reward. Our approach
maximizes a non-adversarial model-free RL objective that provably lower bounds
reverse Kullback-Leibler divergence between occupancy measures of the expert
and imitator. We present a practical IL algorithm, Neural Density Imitation
(NDI), which obtains state-of-the-art demonstration efficiency on benchmark
control tasks.",2010.09808v1
2021-11-17,Freiheitssatz and phase transition for the density model of random groups,"Magnus' Freiheitssatz states that if a group is defined by a presentation
with $m$ generators and a single relator containing the last generating letter,
then the first $m-1$ letters freely generate a free subgroup. We study an
analogue of this theorem in the Gromov density model of random groups, showing
a phase transition phenomenon at density $d_r = \min\{\frac{1}{2},
1-\log_{2m-1}(2r-1)\}$ with $1\leq r\leq m-1$: we prove that for a random group
with $m$ generators at density $d$, if $d < d_r$ then the first $r$ letters
freely generate a free subgroup; whereas if $d > d_r$ then the first $r$
letters generate the whole group.",2111.08958v2
2023-10-14,Reduced probability densities of long-lived metastable states as those of distributed thermal systems: possible experimental implications for supercooled fluids,"When liquids are cooled sufficiently rapidly below their melting temperature,
they may bypass crystalization and, instead, enter a long-lived metastable
supercooled state that has long been the focus of intense research. Although
they exhibit strikingly different properties, both the (i) long-lived
supercooled liquid state and (ii) truly equilibrated (i.e., conventional
equilibrium fluid or crystalline) phases of the same material share an
identical Hamiltonian. This suggests a mapping between dynamical and other
observables in these two different arenas. We formalize these notions via a
simple theorem and illustrate that given a Hamiltonian defining the dynamics:
(1) the reduced probability densities of all possible stationary states are
linear combinations of reduced probability densities associated with thermal
equilibria at different temperatures, chemical potentials, etc. (2) Excusing
special cases, amongst all of these stationary states, a clustering of
correlations is only consistent with conventional thermal equilibrium states
(associated with a sharp distribution of the above state variables). (3) Other
stationary states may be modified so as to have local correlations. These
deformations concomitantly lead to metastable (yet possibly very long-lived)
states. Since the lifetime of the supercooled state is exceptionally long
relative to the natural microscopic time scales, their reduced probability
densities may be close to those that we find for exact stationary states (i.e.,
a weighted average of equilibrium probability densities at different state
variables). This form suggests several new predictions such as the existence of
dynamical heterogeneity stronger than probed for thus far and a relation
between the specific heat peak and viscosities. Our theorem may further place
constraints on the putative ""ideal glass"" phase.",2310.09641v5
2022-04-25,Ab-initio QCD calculations impact the inference of the neutron-star-matter equation of state,"We demonstrate that ab-initio calculations in QCD at high densities offer
significant and nontrivial information about the equation of state of matter in
the cores of neutron stars, going beyond that which is obtainable from current
astrophysical observations. We do so by extrapolating the equation of state to
neutron-star densities using a Gaussian process and conditioning it
sequentially with astrophysical observations and QCD input. Using our recent
work, imposing the latter does not require an extrapolation to asymptotically
high density. We find the QCD input to be complementary to the astrophysical
observations, offering strong additional constraints at the highest densities
reached in the cores of neutron stars; with the QCD input, the equation of
state is no longer prior dominated at any density. The QCD input reduces the
pressure and speed of sound at high densities, and it predicts that binary
collisions of equal-mass neutron stars will produce a black hole with greater
than $95\%$ ($68\%$) credence for masses $M \geq 1.38 M_\odot$ ($M \geq 1.25
M_\odot$). We provide a Python implementation of the QCD likelihood function so
that it can be conveniently used within other inference setups.",2204.11877v2
2011-05-31,Realizing vector meson dominance with transverse charge densities,"The transverse charge density in a fast-moving nucleon is represented as a
dispersion integral of the imaginary part of the Dirac form factor in the
timelike region (spectral function). At a given transverse distance b the
integration effectively extends over energies in a range sqrt{t} ~< 1/b, with
exponential suppression of larger values. The transverse charge density at
peripheral distances thus acts as a low-pass filter for the spectral function
and allows one to select energy regions dominated by specific t-channel states,
corresponding to definite exchange mechanisms in the spacelike form factor. We
show that distances b ~ 0.5 - 1.5 fm in the isovector density are maximally
sensitive to the rho meson region, with only a ~10% contribution from
higher-mass states. Soft-pion exchange governed by chiral dynamics becomes
relevant only at larger distances. In the isoscalar density higher-mass states
beyond the omega are comparatively more important. The dispersion approach
suggests that the positive transverse charge density in the neutron at b ~ 1
fm, found previously in a Fourier analysis of spacelike form factor data, could
serve as a sensitive test of the the isoscalar strength in the ~1 GeV mass
region. In terms of partonic structure, the transverse densities in the vector
meson region b ~ 1 fm support an approximate mean-field picture of the motion
of valence quarks in the nucleon.",1105.6364v1
2013-02-10,Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm,"We investigate tree tensor network states for quantum chemistry. Tree tensor
network states represent one of the simplest generalizations of matrix product
states and the density matrix renormalization group. While matrix product
states encode a one-dimensional entanglement structure, tree tensor network
states encode a tree entanglement structure, allowing for a more flexible
description of general molecules. We describe an optimal tree tensor network
state algorithm for quantum chemistry. We introduce the concept of
half-renormalization which greatly improves the efficiency of the calculations.
Using our efficient formulation we demonstrate the strengths and weaknesses of
tree tensor network states versus matrix product states. We carry out benchmark
calculations both on tree systems (hydrogen trees and \pi-conjugated
dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and
chromium dimer). In general, tree tensor network states require much fewer
renormalized states to achieve the same accuracy as matrix product states. In
non-tree molecules, whether this translates into a computational savings is
system dependent, due to the higher prefactor and computational scaling
associated with tree algorithms. In tree like molecules, tree network states
are easily superior to matrix product states. As an ilustration, our largest
dendrimer calculation with tree tensor network states correlates 110 electrons
in 110 active orbitals.",1302.2298v2
2001-07-12,Superconducting proximity effect in clean ferromagnetic layers,"We investigate superconducting proximity effect in clean ferromagnetic layers
with rough boundaries. The subgap density of states is formed by Andreev bound
states at energies which depend on trajectory length and the ferromagnetic
exchange field. At energies above the gap, the spectrum is governed by resonant
scattering states. The resulting density of states, measurable by tunneling
spectroscopy, exhibits a rich structure, which allows to connect the
theoretical parameters from experiments.",0107252v1
2006-10-04,Existence of Density Functionals for Excited States and Resonances,"We show how every bound state of a finite system of identical fermions,
whether a ground state or an excited one, defines a density functional.
Degeneracies created by a symmetry group can be trivially lifted by a
pseudo-Zeeman effect. When complex scaling can be used to regularize a
resonance into a square integrable state, a DF also exists.",0610108v1
2005-02-26,Undoing static correlation: Long-range charge transfer in time-dependent density functional theory,"Long-range charge transfer excited states are notoriously badly
underestimated in time-dependent density functional theory (TDDFT). We resolve
how {\it exact} TDDFT captures charge transfer between open-shell species: in
particular the role of the step in the ground-state potential, and the severe
frequency-dependence of the exchange-correlation kernel. An expression for the
latter is derived, that becomes exact in the limit that the charge-transfer
excitations are well-separated from other excitations. The exchange-correlation
kernel has the task of undoing the static correlation in the ground state
introduced by the step, in order to accurately recover the physical
charge-transfer states.",0502147v1
2010-02-16,Polarized Superfluidity in the imbalanced attractive Hubbard model,"We investigate the attractive Hubbard model in infinite spatial dimensions by
means of dynamical mean-field theory. Using a continuous-time Monte Carlo
algorithm in the Nambu formalism as an impurity solver, we directly deal with
the superfluid phase in the population imbalanced system. By calculating the
superfluid order parameter, the magnetization, and the density of states, we
discuss how the polarized superfluid state is realized in the attractive
Hubbard model at quarter filling. We find that a drastic change in the density
of states is induced by spin imbalanced populations in the superfluid state.",1002.2958v1
2010-08-23,Vortex states in hole-doped iron-pnictide superconductors,"Based on a phenomenological model with competing spin-density-wave (SDW) and
extended $s-$wave superconductivity, the vortex states in
Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ are investigated by solving Bogoliubov-de
Gennes equations. Our result for the optimally doped compound without induced
SDW is in qualitative agreement with recent scanning tunneling microscopy
experiment. We also propose that the main effect of the SDW on the vortex
states is to reduce the intensity of the in-gap peak in the local density of
states and transfer the spectral weight to form additional peaks outside the
gap.",1008.3885v1
2020-02-24,Using dark states to charge and stabilise open quantum batteries,"We introduce an open quantum battery protocol using dark states to achieve
both superextensive capacity and power density, with non-interacting spins
coupled to a reservoir. Further, our power density actually scales with the of
number of spins $N$ in the battery. We show that the enhanced capacity and
power is correlated with entanglement. Whilst connected to the charger, the
charged state of the battery is a steady state, stabilized through quantum
interference in the open system.",2002.10044v2
2022-11-17,Curing the Divergence in Time-Dependent Density Functional Quadratic Response Theory,"The adiabatic approximation in time-dependent density functional theory
(TDDFT) is known to give an incorrect pole structure in the quadratic response
function, leading to unphysical divergences in excited state-to-state
transition probabilities and hyperpolarizabilties. We find the form of the
exact quadratic response kernel and derive a practical and accurate
approximation that cures the divergence. We demonstrate our results on excited
state-to-state transition probabilities of a model system and of the LiH
molecule.",2211.09885v3
1995-08-14,Density-dependent phonoriton states in highly excited semiconductors,"The dynamical aspects of the phonoriton state in highly-photoexcited
semiconductors is studied theoretically. The effect of the exciton-exciton
interaction and nonbosonic character of high-density excitons are taken into
account. Using Green's function method and within the Random Phase
Approximation it is shown that the phonoriton dispersion and damping are very
sensitive to the exciton density, characterizing the excitation degree of
semiconductors.",9508046v1
2004-06-01,Luttinger liquid versus charge density wave behaviour in the one-dimensional spinless fermion Holstein model,"We discuss the nature of the different ground states of the half-filled
Holstein model of spinless fermions in 1D. In the metallic regime we determine
the renormalised effective coupling constant and the velocity of the charge
excitations by a density-matrix renormalisation group (DMRG) finite-size
scaling approach. At low (high) phonon frequencies the Luttinger liquid is
characterised by an attractive (repulsive) effective interaction. In the
charge-density wave Peierls-distorted state the charge structure factor scales
to a finite value indicating long-range order.",0406023v1
2004-06-24,Conductance through Quantum Dots Studied by Finite Temperature DMRG,"With the Finite temperature Density Matrix Renormalization Group method
(FT-DMRG), we depeloped a method to calculate thermo-dynamical quantities and
the conductance of a quantum dot system. Conductance is written by the local
density of states on the dot. The density of states is calculated with the
numerical analytic continuation from the thermal Green's function which is
obtained directly from the FT-DMRG. Typical Kondo behaviors in the quantum dot
system are observed conveniently by comparing the conductance with the magnetic
and charge susceptibilities: Coulomb oscillation peaks and the unitarity limit.
We discuss advantage of this method compared with others.",0406594v1
2004-07-29,Field-induced spin density wave in (TMTSF)$_2$NO$_3$,"Interlayer magnetoresistance of the Bechgaard salt (TMTSF)$_2$NO$_3$ is
investigated up to 50 teslas under pressures of a few kilobars. This compound,
the Fermi surface of which is quasi two-dimensional at low temperature, is a
semi metal under pressure. Nevertheless, a field-induced spin density wave is
evidenced at 8.5 kbar above $\sim$ 20 T. This state is characterized by a
drastically different spectrum of the quantum oscillations compared to the low
pressure spin density wave state.",0407764v2
2005-10-11,Origin of the anomalous heat current in collisional granular fluids,"We present a heuristic explanation for the anomalous
(density-gradient-dependent) heat current in collisional granular fluids.
Inelastic grain collisions lead to highly non-equilibrium states which are
characterized by large spatial gradients and/or temporal variations in the
granular temperature. It is argued that the heat current in such
non-equilibrium states is driven by the temperature gradient averaged over the
typical collision time and/or mean free path. Due to the density dependence of
the inelastic energy loss, the nonlocal averaging of the temperature gradient
leads to an effective dependence of the heat current upon the density gradient.",0510295v1
2005-10-25,Field-induced Berezinskii-Kosterlitz-Thouless transition and string-density plateau in the anisotropic triangular antiferromagnetic Ising model,"The field-induced Berezinskii-Kosterlitz-Thouless (BKT) transition in the
ground state of the triangular antiferromagnetic Ising model is studied by the
level-spectroscopy method. We analyze dimensions of operators around the BKT
line, and estimate the BKT point $H_{\rm c}\simeq0.5229\pm0.001$, which is
followed by a level-consistency check to demonstrate the accuracy of our
estimate. Further we investigate the anisotropic case to clarify the stability
of the field-induced string-density plateau against an incommensurate liquid
state by the density-matrix renormalization-group method.",0510653v2
2006-06-20,A new challenge for time-dependent density-functional theory,"Time-dependent density functional theory is thought to work well for the test
cases of He and Be atoms. We perform a quantum defect analysis of the s, p, and
d Rydberg states of Be with accurate ground state Kohn-Sham potentials. The s-
and p-quantum defects are well described by the ALDA, but fails badly for the
d-quantum defect. The same failure is observed in case of He. This provides a
new challenge for functional development in time-dependent density functional
theory.",0606534v1
2007-03-28,Density dependence of the forbidden lines in Ni-like tungsten,"The magnetic-octupole (M3) and electric-quadrupole (E2) transitions between
the ground state $3d^{10} ^1S_0$ and the lowest excited $3d^94s$ $(5/2,1/2)$ J
= 3 and J = 2 states in the Ni-like tungsten are shown to exhibit a strong
dependence on electron density $N_e$ in the range of values typical for tokamak
plasmas. Remarkably, the total intensity of these overlapping lines remains
almost constant, which may explain the strong emission in the 7.93 \AA line
observed in tokamak experiments (Neu R et al. 1997 J Phys B {\bf 30} 5057).
Utilization of the M3 and E2 line ratios for density diagnostics in
high-spectral-resolution experiments is discussed as well.",0703263v2
2007-10-16,Friedel oscillations of Density of States in a one-dimensional Mott insulator and Incommensurate Charge Density Wave/Superconductor,"Oscillations of local density of states generated by a single scalar impurity
potential are calculated for one-dimensional systems with dynamically generated
charge or spin gap. At zero temperature the oscillations develop at finite wave
vector ($\pi$ for the Mott insulator and $2k_F$ for ICDW/SC) and at frequencies
larger than the soliton spectral gap $m$. Their amplitude has a broad maximum
at $\omega \approx 3m$, where $m$ is the gap magnitude.",0710.3131v2
2008-11-06,Quantum measuring processes for trapped ultracold bosonic gases,"The standard experimental techniques usually adopted in the study of the
behaviour of ultracold atoms in optical lattices involve extracting the atom
density profile from absorption images of the atomic sample after trap release.
Quantum mechanically this procedure is described by a generalized measure
(POVM); interference patterns found in absorption images suggest a generalized
measure based on fixed-phase, coherent-like states. We show that this leads to
an average atomic density which differs from the usually adopted one, obtained
as the expectation value of the atom density operator in the many-body state.",0811.0925v1
2010-08-23,Closed virial equation-of-state for the hard-disk fluid,"A closed virial equation-of-state for the low density fluid phase of hard
disks is obtained from the known virial coefficients. The equation exhibits
6-figure accuracy for the thermodynamic (MD) pressure up to the reduced number
density ~ 0.4 Interpolation of the discrepancy at higher densities indicates a
higher-order thermodynamic phase transition at the extensive-intensive
free-volume percolation transition previously located by Hoover et al. (JCP 70
1837 1979)",1008.3872v1
2012-11-15,Spin-Droplet State of an Interacting 2D Electron System,"We report thermodynamic magnetization measurements of two-dimensional
electrons in several high mobility Si metal-oxide-semiconductor field-effect
transistors. We provide evidence for an easily polarizable electron state in a
wide density range from insulating to deep into the metallic phase. The
temperature and magnetic field dependence of the magnetization is consistent
with the formation of large-spin droplets in the insulating phase. These
droplets melt in the metallic phase with increasing density and temperature,
although they survive up to large densities.",1211.3536v1
2018-08-30,Nuclear magnetic moments in covariant density functional theory,"The nuclear magnetic moment is an important physical observable and serves as
a useful tool for the stringent test of nuclear models. For the past decades,
the covariant density functional theory and its extension have been proved to
be successful in describing the nuclear ground-states and excited states
properties. However, a long-standing problem is its failure to predict magnetic
moments. This article reviews the recent progress in the description of the
nuclear magnetic moments within the covariant density functional theory. In
particular, the magnetic moments of spherical odd-A nuclei with doubly closed
shell core plus or minus one nucleon and deformed odd-A nuclei.",1808.10124v1
2008-07-07,Density matrix of the superposition of excitation on coherent states with thermal light and its statistical properties,"A beam's density matrix that is described by the superposition of excitation
on coherent states with thermal noise (SECST) is presented, and its matrix
elements in Fock space are calculated. The maximum information transmitted by
the SECST beam is derived. It is more than that by coherent light beam and
increases as the excitation photon number increases. In addition, the
nonclassicality of density matrix is demonstrated by calculating its Wigner
function.",0807.1028v1
2013-09-12,Thermal Density Functional Theory in Context,"This chapter introduces thermal density functional theory, starting from the
ground-state theory and assuming a background in quantum mechanics and
statistical mechanics. We review the foundations of density functional theory
(DFT) by illustrating some of its key reformulations. The basics of DFT for
thermal ensembles are explained in this context, as are tools useful for
analysis and development of approximations. We close by discussing some key
ideas relating thermal DFT and the ground state. This review emphasizes thermal
DFT's strengths as a consistent and general framework.",1309.3043v1
2020-11-11,Phase transitions in the one-dimensional ionic Hubbard model,"We study quantum phase transitions by measuring the bond energy, the number
density, and the half-chain entanglement entropy in the one-dimensional ionic
Hubbard model. By performing the infinite density matrix renormalization group
with matrix product operator, we obtain ground states as the canonical form of
matrix product states. Depending on the chemical potential and the staggered
potential, the number density and the half-chain entanglement entropy shows
clear signatures of the Mott transition. Our results confirm the success of the
matrix product operator method for investigation of itinerant fermion systems.",2011.05592v1
2022-03-16,Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow,"Tuning of measurement models is challenging in real-world applications of
sequential Monte Carlo methods. Recent advances in differentiable particle
filters have led to various efforts to learn measurement models through neural
networks. But existing approaches in the differentiable particle filter
framework do not admit valid probability densities in constructing measurement
models, leading to incorrect quantification of the measurement uncertainty
given state information. We propose to learn expressive and valid probability
densities in measurement models through conditional normalizing flows, to
capture the complex likelihood of measurements given states. We show that the
proposed approach leads to improved estimation performance and faster training
convergence in a visual tracking experiment.",2203.08617v1
2005-07-21,Ferromagnetic semiconductor single wall carbon nanotube,"Possibility of a ferromagnetic semiconductor single wall carbon nanotube
(SWCNT), where ferromagnetism is due to coupling between doped magnetic
impurity on a zigzag SWCNT and electrons spin, is investigate. We found, in the
weak impurity-spin couplings, at low impurity concentrations the spin up
electrons density of states remain semiconductor while the spin down electrons
density of states shows a metallic behavior. By increasing impurity
concentrations the semiconducting gap of spin up electrons in the density of
states is closed, hence a semiconductor to metallic phase transition is take
place. In contrast, for the case of strong coupling, spin up electrons density
of states remain semiconductor and spin down electron has metallic behavior.
Also by increasing impurity spin magnitude, the semiconducting gap of spin up
electrons is increased.",0507503v1
2002-06-19,Equation of state of quark-nuclear matter,"Quark-nuclear matter (QNM) is a many-body system containing hadrons and
deconfined quarks. Starting from a microscopic quark-meson coupling (QMC)
Hamiltonian with a density dependent quark-quark interaction, an effective
quark-hadron Hamiltonian is constructed via a mapping procedure. The mapping is
implemented with a unitary operator such that composites are redescribed by
elementary-particle field operators that satisfy canonical commutation
relations in an extended Fock space. Application of the unitary operator to the
microscopic Hamiltonian leads to effective, hermitian operators that have a
clear physical interpretation. At sufficiently high densities, the effective
Hamiltonian contains interactions that lead to quark deconfinement. The
equation of state of QNM is obtained using standard many-body techniques with
the effective quark-hadron Hamiltonian. At low densities, the model is
equivalent to a QMC model with confined quarks. Beyond a critical density, when
quarks start to deconfine, the equation of state predicted for QNM is softer
than the QMC equation of state with confined quarks.",0206047v1
2015-07-14,Density of States for Warped Energy Bands,"An angular effective mass formalism previously introduced is used to study
the density of states in warped and non-warped energy bands. Band warping may
or may not increase the density-of-states effective mass. Band ""corrugation,""
referring to energy dispersions that deviate ""more severely"" from being
twice-differentiable at isolated critical points, may also vary independently
of density-of-states effective masses and band warping parameters. We
demonstrate these effects and the superiority of an angular effective mass
treatment for valence band energy dispersions in cubic materials. We also
provide some two-dimensional physical and mathematical examples that may be
relevant to studies of band warping in heterostructures and surfaces. These
examples may also be useful in clarifying the interplay between possible band
warping and band non-parabolicity for non-degenerate conduction band minima in
thermoelectric materials of corresponding interest.",1507.04031v1
2017-08-31,Extreme plasma states in laser-governed vacuum breakdown,"Triggering vacuum breakdown at the upcoming laser facilities can provide
rapid electron-positron pair production for studies in laboratory astrophysics
and fundamental physics. However, the density of the emerging plasma should
seemingly stop rising at the relativistic critical density, when the plasma
becomes opaque. Here we identify the opportunity of breaking this limit using
optimal beam configuration of petawatt-class lasers. Tightly focused laser
fields allow plasma generation in a small focal volume much less than
${\lambda}^3$, and creating extreme plasma states in terms of density and
produced currents. These states can be regarded as a new object of nonlinear
plasma physics. Using 3D QED-PIC simulations we demonstrate the possibility of
reaching densities of more than $10^{25}$ cm$^{-3}$, which is an order of
magnitude higher than previously expected. Controlling the process via the
initial target parameters gives the opportunity to reach the discovered plasma
states at the upcoming laser facilities.",1708.09636v1
2016-12-01,Particle Model Predictive Control: Tractable Stochastic Nonlinear Output-Feedback MPC,"We combine conditional state density construction with an extension of the
Scenario Approach for stochastic Model Predictive Control to nonlinear systems
to yield a novel particle-based formulation of stochastic nonlinear
output-feedback Model Predictive Control. Conditional densities given noisy
measurement data are propagated via the Particle Filter as an approximate
implementation of the Bayesian Filter. This enables a particle-based
representation of the conditional state density, or information state, which
naturally merges with scenario generation from the current system state. This
approach attempts to address the computational tractability questions of
general nonlinear stochastic optimal control. The Particle Filter and the
Scenario Approach are shown to be fully compatible and -- based on the time-
and measurement-update stages of the Particle Filter -- incorporated into the
optimization over future control sequences. A numerical example is presented
and examined for the dependence of solution and computational burden on the
sampling configurations of the densities, scenario generation and the
optimization horizon.",1612.00505v2
2019-07-17,Density of states measurements for heavy subband of holes in HgTe quantum wells,"Valence band in narrow HgTe quantum wells contains well-conductive Dirac-like
light holes at the $\Gamma$ point and poorly conductive heavy hole subband
located in the local valleys. Here we propose and employ two methods to measure
the density of states for these heavy holes. The first method uses a
gate-recharging technique to measure thermodynamical entropy per particle. As
the Fermi level is tuned with gate voltage from light to heavy subband, the
entropy increases dramatically, and the value of this increase gives an
estimate for the density of states. The second method determines the density of
states for heavy holes indirectly from the gate voltage dependence of the
period of the Shubnikov-de Haas oscillations for light holes. The results
obtained by both methods are in the reasonable agreement with each other. Our
approaches can be applied to measure large effective carrier masses in other
two-dimensional gated systems.",1907.07731v2
2020-01-28,"Comments on ""Total and fractional densities of states from caloric relations"" by S. F. Chekmarev and S. V. Krivov, Phys. Rev. E 57 2445 (1998)","We showed that the equations (3), (4), (5) and (6), used in the paper Total
and fractional densities of states from caloric relations by S. F. Chekmarev
and S. V. Krivov, Phys. Rev. E 57 2445 (1998), are incorrect, the data,
presented in the paper by lines on Figs. 1, (3a) and (3b), are not correct, the
data presented by the symbols on Figs. 3(a) and 3(b) in the paper are made
manually (false), all conclusions made in the paper have no sense, the
assertion in the paper that the molecular dynamics simulations sample the
potential energy surface not uniformly, but according to the fractional
densities of state for the isomers is incorrect. We showed also that the total
and fractional densities of states obtained in the paper from caloric relations
are not equal to that of microcanonical ensemble of clusters, the ensemble of
clusters used in the paper does not represent the microcanonical ensemble of
clusters.",2001.10166v1
2021-08-11,Charge density waves in multiple-$Q$ spin states,"Coupling between spin and charge degrees of freedom in electrons is a source
of various electronic and magnetic properties of solids. We theoretically study
charge density waves induced by the spin-charge coupling in the presence of
magnetic orderings in itinerant magnets. By performing a perturbative
calculation in the weak-coupling limit of the Kondo lattice model, we derive a
useful formula for the relationship between charge and spin density waves,
which can be applied to any magnetic orderings, including noncollinear and
noncoplanar ones composed of multiple spin density waves called multiple-$Q$
magnetic orderings. We demonstrate the predictive power for single-$Q$ and
double-$Q$ states including skyrmion and meron-antimeron crystals on a square
lattice, in comparison with the numerical calculations. Moreover, we show that
the charge density waves contain richer information than the spin density
waves, and are indeed useful in distinguishing the spin textures with similar
spin structure factors. We discuss the relation to bond modulation in terms of
the kinetic bond energy and the vector spin chirality. We also perform
numerical calculations beyond the perturbative regime and find that the charge
density waves can be enhanced when the electron filling is commensurate.
Furthermore, we investigate the effect of the spin-orbit coupling, which can
lead to additional charge density waves owing to effective anisotropic magnetic
interactions in momentum space. Our result will provide a way to identify
complex magnetic orderings and their origins from the charge modulations.",2108.04997v2
1998-06-18,Recovering the Primordial Density Fluctuations: A comparison of methods,"We present a comparative study of six different methods for reversing the
gravitational evolution of a cosmological density field to recover the
primordial fluctuations: linear theory, the Gaussianization mapping scheme, two
different quasi-linear dynamical schemes based on the Zel'dovich approximation,
a Hybrid dynamical-Gaussianization method and the Path Interchange Zel'dovich
Approximation (PIZA). The final evolved density field from an N-body simulation
constitutes our test case. We use a variety of statistical measures to compare
the initial density field recovered from it to the true initial density field,
using each of the six different schemes. These include point-by-point
comparisons of the density fields in real space, the individual modes in
Fourier space, as well as global statistical properties such as the genus, the
PDF of the density, and the distribution of peak heights and their shapes. We
find linear theory to be the most inaccurate of all the schemes. The
Gaussianization scheme is the least accurate after linear theory. The two
quasi-linear dynamical schemes are more accurate than Gaussianization, although
they break down quite drastically when used outside their range of validity -
the quasi-linear regime. The complementary beneficial aspects of the dynamical
and the Gaussianization schemes are combined in the Hybrid method. We find this
Hybrid scheme to be more accurate and robust than either Gaussianization or the
dynamical method alone. The PIZA scheme performs substantially better than the
others in all point-by-point comparisons. However, it produces an oversmoothed
initial density field, with a smaller number of peaks than expected, but
recovers the PDF of the initial density with impressive accuracy on scales as
small as 3Mpc/h.",9806255v1
2024-03-11,Towards the Uncharted: Density-Descending Feature Perturbation for Semi-supervised Semantic Segmentation,"Semi-supervised semantic segmentation allows model to mine effective
supervision from unlabeled data to complement label-guided training. Recent
research has primarily focused on consistency regularization techniques,
exploring perturbation-invariant training at both the image and feature levels.
In this work, we proposed a novel feature-level consistency learning framework
named Density-Descending Feature Perturbation (DDFP). Inspired by the
low-density separation assumption in semi-supervised learning, our key insight
is that feature density can shed a light on the most promising direction for
the segmentation classifier to explore, which is the regions with lower
density. We propose to shift features with confident predictions towards
lower-density regions by perturbation injection. The perturbed features are
then supervised by the predictions on the original features, thereby compelling
the classifier to explore less dense regions to effectively regularize the
decision boundary. Central to our method is the estimation of feature density.
To this end, we introduce a lightweight density estimator based on normalizing
flow, allowing for efficient capture of the feature density distribution in an
online manner. By extracting gradients from the density estimator, we can
determine the direction towards less dense regions for each feature. The
proposed DDFP outperforms other designs on feature-level perturbations and
shows state of the art performances on both Pascal VOC and Cityscapes dataset
under various partition protocols. The project is available at
https://github.com/Gavinwxy/DDFP.",2403.06462v2
2021-09-29,Finite-State Mutual Dimension,"In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the
finite-state dimension (a finite-state version of algorithmic dimension) of a
sequence $S \in \Sigma^\infty$ and, in 2018, Case and Lutz defined and
investigated the mutual (algorithmic) dimension between two sequences $S \in
\Sigma^\infty$ and $T \in \Sigma^\infty$. In this paper, we propose a
definition for the lower and upper finite-state mutual dimensions
$mdim_{FS}(S:T)$ and $Mdim_{FS}(S:T)$ between two sequences $S \in
\Sigma^\infty$ and $T \in \Sigma^\infty$ over an alphabet $\Sigma$.
Intuitively, the finite-state dimension of a sequence $S \in \Sigma^\infty$
represents the density of finite-state information contained within $S$, while
the finite-state mutual dimension between two sequences $S \in \Sigma^\infty$
and $T \in \Sigma^\infty$ represents the density of finite-state information
shared by $S$ and $T$. Thus ``finite-state mutual dimension'' can be viewed as
a ``finite-state'' version of mutual dimension and as a ``mutual'' version of
finite-state dimension.
  The main results of this investigation are as follows. First, we show that
finite-state mutual dimension, defined using information-lossless finite-state
compressors, has all of the properties expected of a measure of mutual
information. Next, we prove that finite-state mutual dimension may be
characterized in terms of block mutual information rates. Finally, we provide
necessary and sufficient conditions for two normal sequences to achieve
$mdim_{FS}(S:T) = Mdim_{FS}(S:T) = 0$.",2109.14574v1
2016-09-12,Observation of electronic bound states in charge-ordered YBa$_2$Cu$_3$O$_y$,"Observing how electronic states in solids react to a local symmetry breaking
provides insight into their microscopic nature. A striking example is the
formation of bound states when quasiparticles are scattered off defects. This
is known to occur, under specific circumstances, in some metals and
superconductors but not, in general, in the charge-density-wave (CDW) state.
Here, we report the unforeseen observation of bound states when a magnetic
field quenches superconductivity and induces long-range CDW order in
YBa$_2$Cu$_3$O$_y$. Bound states indeed produce an inhomogeneous pattern of the
local density of states $N(E_F)$ that leads to a skewed distribution of Knight
shifts which is detected here through an asymmetric profile of $^{17}$O NMR
lines. We argue that the effect arises most likely from scattering off defects
in the CDW state, which provides a novel case of disorder-induced bound states
in a condensed-matter system and an insightful window into charge ordering in
the cuprates.",1609.03539v1
2006-10-03,"Crossover, Fluctuations and Anderson Transition in Quark Matter Formation","We argue that there is a unique transition state of moderate density between
the nuclear matter and superconducting quark matter alternatives. The
distinguishing features of this state are discussed.",0610031v1
1999-11-12,Construction of quantum states with bound entanglement,"We present a new family of bound-entangled quantum states in 3x3 dimensions.
Their density matrix depends on 7 independent parameters and has 4 different
non-vanishing eigenvalues.",9911056v1
2008-02-02,Quantization of bosonic fields with two mass and spin states,"We investigate bosonic fields possessing two mass and spin states. The
density matrix in the first order formalism is obtained. The quantization of
fields in the first order formulation is performed and propagators are found.",0802.0256v1
2017-10-27,Large-scale pedestrian flow experiments under high-density conditions,"Despite the vast amount of studies on pedestrian flow, the data concerning
high densities are still very inadequate. We organize one large-scale
pedestrian flow experiment on a ring corridor. With 278 participants, the
density as high as 9 m^(-2) is reached. In the uni-directional flow, four
different states are observed, including the free flow, congested state,
over-congested state and hyper-congested state. The features of the
hyper-congested state are similar to the ""crowd turbulence"" reported in the
empirical data of Helbing et al., and the transition between the stopped state
and the moving state can be found. The flow rates in the over-congested state
are nearly constant, due to the downstream propagation of pedestrian clusters.
In the bi-directional flow, three different types of lane formations are
observed in the experiment: (1) three lanes are directly formed ; (2) two lanes
are directly formed; (3) firstly three lanes are formed, and then they transit
into two lanes. After the lane formation, some interesting phenomena have been
observed, including the inhomogeneous distribution of pedestrians across the
lanes, and the formation and dissipation of localized crowd. Our study is
expected to help for better understanding and modeling the dynamics of high
density pedestrian flow.",1710.10263v1
2021-10-11,"Charge, bond, and pair density wave orders in a strongly correlated system","The coexistence of multiple quasi-degenerate orders is the hallmark of the
strongly correlated materials. Experiments often reveal several spatially
modulated orders in the underdoped cuprates. This has come to the forefront
with the possible detection of the pair density wave states. However,
microscopic calculations often struggle to stabilize such spatially modulating
orders as the ground state in the strong correlation limit. This work uses the
$t-t^\prime-J$-model with an additional nearest-neighbor repulsion to stabilize
spatially oscillating charge, bond, and pairing orders in the underdoped
regime. We employ the standard Gutzwiller approach while treating the
inhomogeneity for the spatial orders using the self-consistent
Hartree-Fock-Bogoliubov methodology. Our calculations reveal that
unidirectional bond density states coexisting with charge and pairing
modulations can have lower energy than the uniform superconducting state over
an extensive doping range. These modulating states vanish monotonically as the
modulation wavevector becomes shorter with increased dopings. The finite
momentum orders melt upon increasing doping to a vestigial nematic state which
breaks the rotational symmetry of the system. The spatial features of the
ground state at each doping reveal multiple wavevectors, which potentially
drives the incommensuration of charge orders. Interestingly, the spatially
modulating states are absent when the strong correlations criteria are relaxed,
suggesting that the removal of double occupancy aids the stabilization of
density wave orders.",2110.05620v2
2001-06-30,Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram,"We describe an efficient Monte Carlo algorithm using a random walk in energy
space to obtain a very accurate estimate of the density of states for classical
statistical models. The density of states is modified at each step when the
energy level is visited to produce a flat histogram. By carefully controlling
the modification factor, we allow the density of states to converge to the true
value very quickly, even for large systems. This algorithm is especially useful
for complex systems with a rough landscape since all possible energy levels are
visited with the same probability. In this paper, we apply our algorithm to
both 1st and 2nd order phase transitions to demonstrate its efficiency and
accuracy. We obtained direct simulational estimates for the density of states
for two-dimensional ten-state Potts models on lattices up to $200 \times 200 $
and Ising models on lattices up to $256 \times 256$. Applying this approach to
a 3D $\pm J$ spin glass model we estimate the internal energy and entropy at
zero temperature; and, using a two-dimensional random walk in energy and
order-parameter space, we obtain the (rough) canonical distribution and energy
landscape in order-parameter space. Preliminary data suggest that the glass
transition temperature is about 1.2 and that better estimates can be obtained
with more extensive application of the method.",0107006v1
2024-01-14,Spatial distribution of ultracold neutron probability density in the gravitational field of the earth above a mirror,"We propose a theoretical analysis of the experimental data by Ichikawa et al.
(Phys. Rev. Lett. 112, 071101 (2014)) on a spatial distribution of ultracold
neutrons in the gravitational field of the Earth above a mirror, projected onto
a pixelated detector by scattering by a cylindrical mirror. We calculate a
theoretical spatial distribution of a probability density of quantum
gravitational states of ultracold neutrons and analyse a spatial distribution
of quantum gravitational states in term of the Wigner function. We cannot
confirm that the experimental data by Ichikawa et al. (Phys. Rev. Lett. 112,
071101 (2014)) correspond to a spatial distribution of quantum gravitational
states of ultracold neutrons.",2401.07377v1
2011-06-25,Spectral densities and diagrams of states of one-dimensional ionic Pauli conductor,"We focus on the features of spectra and diagrams of states obtained via exact
diagonalization technique for finite ionic conductor chain in periodic boundary
conditions. One dimensional ionic conductor is described with the lattice model
where ions are treated within the framework of ""mixed"" Pauli statistics. The
ion transfer and nearest-neighbour interaction between ions are taken into
account. The spectral densities and diagrams of states for various temperatures
and values of interaction are obtained. The conditions of transition from
uniform (Mott insulator) to the modulated (charge density wave state) through
the superfluid-like state (similar to the state with the Bose-Einstein
condensation observed in hard-core boson models) are analyzed.",1106.5136v1
2016-09-22,Fractional quantum Hall states of bosons on cones,"Motivated by a recent experiment which synthesizes Landau levels for photons
on cones [Schine {\em et al.}, Nature 534, 671 (2016)], and more generally the
interest in understanding gravitational responses of quantum Hall states, we
study fractional quantum Hall states of bosons on cones. A variety of trial
wave functions for conical systems are constructed and compared with exact
diagonalization results. The tip of a cone is a localized geometrical defect
with singular curvature which can modify the density profiles of quantum Hall
states. The density profiles on cones can be used to extract some universal
information about quantum Hall states. The values of certain quantities are
computed numerically using the density profiles of some quantum Hall states and
they agree with analytical predictions.",1609.07123v5
2017-08-13,The Minimum Distance of PPT Bound Entangled States from the Maximally Mixed State,"Using a geometric measure of entanglement quantification based on Euclidean
distance of the Hermitian matrices, we obtain the minimum distance between a
bipartite bound entangled $n$- qudit density matrix and the maximally mixed
state.This minimum distance for which entangled density matrices necessarily
have positive partial transpose (PPT) is obtained as
$\frac{1}{\sqrt{\sqrt{d^n(d^n-1)}+1}}$, which is also a lower limit for the
existence of 1-distillable entangled states. The separable states necessarily
lie within a minimum distance of $\frac{R}{1+d^{n-1}}$ from the Identity,where
R is the radius of the closed ball homeomorphic to the set of density matrices,
which is lesser than the limit for the limit for PPT bound entangled states.
Furthermore an alternate proof on the non-emptiness of the PPT bound entangled
states has also been given.",1708.03885v2
2023-11-25,A Replica-BCS theory for dirty superconductors,"Motivated by the discovery of the anomalous metal state in superconductor
thin films, we revisit in this paper the problem of dirty superconductors using
a replica-symmetric BCS (RS-BCS) theory for dirty metals with net attractive
interactions. Within the RS-BCS mean field theory, we show that the (dirty)
superconductor transits to a Cooper-pair-glass state beyond a critical strength
of disorder. The single particle tunneling density of states and the superfluid
density are computed within the RS-BCS theory for different strengths of
disorder. We find that the single-particle spectral gap is strongly enhanced by
disorder and the superfluid density reduces rapidly from the corresponding
clean superconducting limit with increasing strength of disorder but remains
finite in the Cooper-pair-glass state. The nature of the Cooper-pair-glass
state and relevance of our result to the anomalous metal state are briefly
discussed.",2311.14914v2
2014-09-30,"General Relativistic Evolution Equations for Density Perturbations in Closed, Flat and Open FLRW Universes","It is shown that the decomposition theorems of York, Stewart and Walker for
symmetric spatial second-rank tensors, such as the perturbed metric tensor and
perturbed Ricci tensor, and the spatial fluid velocity vector imply that, for
open, flat or closed Friedmann-Lemaitre-Robertson-Walker universes, there are
exactly two, unique, independent gauge-invariant quantities which describe the
true, physical perturbations to the energy density and particle number density.
Using these two new quantities, evolution equations for cosmological density
perturbations and for entropy perturbations, adapted to non-barotropic
equations of state for the pressure, are derived. Density perturbations evolve
adiabatically if and only if the particle number density does not contribute to
the pressure. Local density perturbations do not affect the global expansion of
the universe. The new perturbation theory has an exact non-relativistic limit
in a non-static universe. The gauge problem of cosmology has thus been solved.",1410.0211v4
2021-05-06,Random density matrices: Analytical results for mean root fidelity and mean square Bures distance,"Bures distance holds a special place among various distance measures due to
its several distinguished features and finds applications in diverse problems
in quantum information theory. It is related to fidelity and, among other
things, it serves as a bona fide measure for quantifying the separability of
quantum states. In this work, we calculate exact analytical results for the
mean root fidelity and mean square Bures distance between a fixed density
matrix and a random density matrix, and also between two random density
matrices. In the course of derivation, we also obtain spectral density for
product of above pairs of density matrices. We corroborate our analytical
results using Monte Carlo simulations. Moreover, we compare these results with
the mean square Bures distance between reduced density matrices generated using
coupled kicked tops and find very good agreement.",2105.02743v2
2021-12-12,Isovector density and isospin impurity in $^{40} \mathrm{Ca}$,"We study isoscalar (IS) and isovector (IV) densities in ${}^{40} \mathrm{Ca}$
in comparison with theoretical densities calculated by Skyrme Hartree-Fock (HF)
models. The charge symmetry breaking and the charge independence breaking
forces are introduced to study the effect on the IV density. The effect of
isospin mixing in the ground-state density is examined by using the
particle-vibration coupling model taking into account the collective IV giant
monopole excitation. We show a clear correlations in the IV density and isospin
impurity of ${}^{40} \mathrm{Ca}$ within the HF and the particle-vibration
coupling model. We extract for the first time the experimental information of
isospin impurity from the magnitude of IV density.",2112.06169v4
2022-10-10,Charge distribution and spin textures in magic-angle twisted bilayer graphene,"We examine the coexisting spin and charge density waves as a possible ground
state of the magic-angle twisted bilayer graphene. When interactions are not
included, the spectrum of the material has 4 (8 if spin is taken into account)
almost flat almost degenerate bands. Interactions break down the degeneracy
forming an order parameter which is usually assumed to be a spin density wave
with a preset spin structure. Here we take into account a possible charge
density wave contribution to the order parameter, that is, inhomogeneous
distribution of the charge density within a twisted graphene supercell. We also
calculate self-consistently the spin structure of the order parameter. We find
that the density wave order is stable in the whole doping range from $-4$ to
$+4$ extra electrons per supercell. The spin texture changes from collinear at
zero doping to almost coplanar at finite doping. The density wave order shows
nematic distortion when we dope the system. We demonstrate that the local spin
magnetization is much stronger than the charge density variation, unless the
doping exceeds $3$ extra electrons or holes per supercell.",2210.04670v1
2014-09-08,Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor,"We experimentally demonstrate the freezing of evolution of quantum states in
one- and two-dimensional subspaces of two qubits, on an NMR quantum information
processor. State evolution was frozen and leakage of the state from its
subspace to an orthogonal subspace was successfully prevented using super-Zeno
sequences, comprising of a set of inverting radio frequency (rf) pulses
punctuated by pre-selected time intervals. We demonstrate the efficacy of the
scheme by preserving different types of states, including separable and
maximally entangled states in one- and two-dimensional subspaces of two qubits.
The change in the experimental density matrices was tracked by carrying out
full state tomography at several time points. We use the fidelity measure for
the one-dimensional case and the leakage (fraction) into the orthogonal
subspace for the two-dimensional case, as qualitative indicators to estimate
the resemblance of the density matrix at a later time to the initially prepared
density matrix. For the case of entangled states, we additionally compute an
entanglement parameter to indicate the presence of entanglement in the state at
different times. We experimentally demonstrate that the super-Zeno scheme is
able to successfully confine state evolution to the one- or two-dimensional
subspace being protected.",1409.2419v2
2011-05-10,Local density of states of two-dimensional electron systems under strong in-plane electric and perpendicular magnetic fields,"We calculate the local density of states of a two-dimensional electron system
under strong crossed magnetic and electric fields. We assume a strong
perpendicular magnetic field which, in the absence of in-plane electric fields
and collision broadening effects, leads to Landau quantization and the
well-known singular Landau density of states. Unidirectional in-plane electric
fields lead to a broadening of the delta-function-singularities of the Landau
density of states. This results in position-dependent peaks of finite height
and width, which can be expressed in terms of the energy eigenfunctions. These
peaks become wider with increasing strength of the electric field and may
eventually overlap, which indicates the onset of inter-Landau-level scattering,
if electron-impurity scattering is considered. We present analytical results
for two simple models and discuss their possible relevance for the breakdown of
the integer quantized Hall effect. In addition, we consider a more realistic
model for an incompressible stripe separating two compressible regions, in
which nearly perfect screening pins adjacent Landau levels to the
electrochemical potential. We also discuss the effect of an imposed current on
the local density of states in the stripe region.",1105.2026v1
2018-12-19,Maximum disorder model for dense steady-state flow of granular materials,"A flow model is developed for dense shear-driven granular flow. As described
in the geomechanics literature, a critical state condition is reached after
sufficient shearing beyond an initial static packing. During further shearing
at the critical state, the stress, fabric, and density remain nearly constant,
even as particles are being continually rearranged. The paper proposes a
predictive framework for critical state flow, viewing it as a condition of
maximum disorder at the micro-scale. The flow model is constructed in a
two-dimensional setting from the probability density of the motions, forces,
and orientations of inter-particle contacts. Constraints are applied to this
probability density: constant mean stress, constant volume, consistency of the
contact dissipation rate with the stress work, and the fraction of sliding
contacts. The differential form of Shannon entropy, a measure of disorder, is
applied to the density, and the Jaynes formalism is used to find the density of
maximum disorder in the underlying phase space. The resulting distributions of
contact force, movement, and orientation are compared with two-dimensional DEM
simulations of biaxial compression. The model favorably predicts anisotropies
of the contact orientations, contact forces, contact movements, and the
orientations of those contacts undergoing slip. The model also predicts the
relationships between contact force magnitude and contact motion. The model is
an alternative to affine-field descriptions of granular flow.",1812.07753v1
2018-12-18,Mask-aware networks for crowd counting,"Crowd counting problem aims to count the number of objects within an image or
a frame in the videos and is usually solved by estimating the density map
generated from the object location annotations. The values in the density map,
by nature, take two possible states: zero indicating no object around, a
non-zero value indicating the existence of objects and the value denoting the
local object density. In contrast to traditional methods which do not
differentiate the density prediction of these two states, we propose to use a
dedicated network branch to predict the object/non-object mask and then combine
its prediction with the input image to produce the density map. Our rationale
is that the mask prediction could be better modeled as a binary segmentation
problem and the difficulty of estimating the density could be reduced if the
mask is known. A key to the proposed scheme is the strategy of incorporating
the mask prediction into the density map estimator. To this end, we study five
possible solutions, and via analysis and experimental validation we identify
the most effective one. Through extensive experiments on five public datasets,
we demonstrate the superior performance of the proposed approach over the
baselines and show that our network could achieve the state-of-the-art
performance.",1901.00039v2
2022-07-08,Accurate Kohn-Sham auxiliary system from the ground state density of solids,"The Kohn-Sham (KS) system is an auxiliary system whose effective potential is
unknown in most cases. It is in principle determined by the ground state
density, and it has been found numerically for some low-dimensional systems by
inverting the KS equations starting from a given accurate density. For solids,
only approximate results are available. In this work, we determine accurate
exchange correlation (xc) potentials for Si and NaCl using the ground state
densities obtained from Auxiliary Field Quantum Monte Carlo calculations. We
show that these xc potentials can be rationalized as an ensemble of
environment-adapted functions of the local density. The KS band structure can
be obtained with high accuracy. The true KS band gap turns out to be larger
than the prediction of the local density approximation, but significantly
smaller than the measurable photoemission gap, which confirms previous
estimates. Finally, our findings show that the conjecture that very different
xc potentials can lead to very similar densities and other KS observables is
true also in solids, which questions the meaning of details of the potentials
and, at the same time, confirms the stability of the KS system.",2207.03919v2
2000-12-15,Super-Eddington Atmospheres that Don't Blow Away,"We show that magnetized, radiation dominated atmospheres can support steady
state patterns of density inhomogeneity that enable them to radiate at far
above the Eddington limit, without suffering mass loss. The inhomogeneities
consist of periodic shock fronts bounding narrow, high-density regions,
interspersed with much broader regions of low density. The radiation flux
avoids the regions of high density, which are therefore weighed down by
gravity, while gas in the low-density regions is slammed upward into the shock
fronts by radiation force. As the wave pattern moves through the atmosphere,
each parcel of matter alternately experiences upward and downward forces, which
balance on average. Magnetic tension shares the competing forces between
regions of different densities, preventing the atmosphere from blowing apart.
We calculate the density structure and phase speed of the wave pattern, and
relate these to the wavelength, the density contrast, and the factor by which
the net radiation flux exceeds the Eddington limit. In principle, this factor
can be as large as the ratio of magnetic pressure to mean gas pressure, or the
ratio of radiation pressure to gas pressure, whichever is smaller. Although the
magnetic pressure must be large compared to the mean gas pressure in order to
support a large density contrast, it need not be large compared to the
radiation pressure. These highly inhomogeneous flows could represent the
nonlinear development of the ""photon bubble"" instability discovered by Gammie.
We briefly discuss the applicability of these solutions to astrophysical
systems.",0012360v1
2016-07-19,Functional theories of thermoelectric phenomena,"We review the progress that has been recently made in the application of
time-dependent density functional theory to thermoelectric phenomena. As the
field is very young, we emphasize open problems and fundamental issues. We
begin by introducing the formal structure of \emph{thermal density functional
theory}, a density functional theory with two basic variables -- the density
and the energy density -- and two conjugate fields -- the ordinary scalar
potential and Luttinger's thermomechanical potential. The static version of
this theory is contrasted with the familiar finite-temperature density
functional theory, in which only the density is a variable. We then proceed to
constructing the full time-dependent non equilibrium theory, including the
practically important Kohn-Sham equations that go with it. The theory is shown
to recover standard results of the Landauer theory for thermal transport in the
steady state, while showing greater flexibility by allowing a description of
fast thermal response, temperature oscillations and related phenomena. Several
results are presented here for the first time, i.e., the proof of invertibility
of the thermal response function in the linear regime, the full expression of
the thermal currents in the presence of Luttinger's thermomechanical potential,
an explicit prescription for the evaluation of the Kohn-Sham potentials in the
adiabatic local density approximation, a detailed discussion of the leading
dissipative corrections to the adiabatic local density approximation and the
thermal corrections to the resistivity that follow from it.",1607.05464v1
2019-04-09,Electron transport through self-assembled monolayers of tripeptides,"We report how the electron transport through a solid-state metal/Gly-Gly-His
tripeptide (GGH) monolayer/metal junction and the metal/GGH work function are
modified by the GGH complexation with Cu2+ ions. Conducting AFM is used to
measure the current-voltage histograms. The work function is characterized by
combining macroscopic Kelvin probe and Kelvin probe force microscopy at the
nanoscale. We observe that the Cu2+ ions complexation with the GGH monolayer is
highly dependent on the molecular surface density and results in opposite
trends. In the case of a high density monolayer the conformational changes are
hindered by the proximity of the neighboring peptides, hence forming an
insulating layer in response to copper-complexation. Whereas the slightly lower
density monolayers allow for the conformational change to a looped peptide
wrapping the Cu-ion, which results in a more conductive monolayer. Copper-ion
complexation to the high- and low-density monolayers systematically induces an
increase of the work functions. Copper-ion complexation to the low-density
monolayer induces an increase of electron transport efficiency, while the
copper-ion complexation to the high-density monolayer results in a slight
decrease of electron transport. Both of the observed trends are in agreement
with first-principle calculations. Complexed copper to low density
GGH-monolayer induces a new gap state slightly above the Au Fermi energy that
is absent in the high density monolayer.",1904.04887v1
1999-11-17,Instabilities Toward Charge Density Wave and Paired Quantum Hall State of Half-Filled Landau Levels,"We study the stability of spin-resolved Landau levels at electron filling
factor $\nu=n+1/2$, where n is a positive integer. Representing the half-filled
topmost Landau level by fermions and the n filled inner Landau levels by n
bosons, coupled to the Chern-Simons gauge fields, we show that the ground
states exhibit charge density wave order for $n(n+1/2)>15.54 \pi(a_B^*)^2 n_e$,
where $n_e$ is the 2D carrier density and $a_B^*$ is the effective Bohr radius.
We find that the pairing interaction mediated by the fluctuating gauge field is
enhanced near the charge density wave instability such that p-wave pairing of
the Chern-Simons fermions prevails for
$3.49(\pi{\ab}^2)n_e<n^2(n+1/2)<20.22\pi(a_B^*)^2 n_e$. The competition between
charge density wave order and paired quantum Hall state is discussed in
connection to recent experiments.",9911265v1
2002-05-27,Combinatorial Level Densities from a Microscopic Relativistic Structure Model,"A new model for calculating nuclear level densities is investigated. The
single-nucleon spectra are calculated in a relativistic mean-field model with
energy-dependent effective mass, which yields a realistic density of
single-particle states at the Fermi energy. These microscopic single-nucleon
states are used in a fast combinatorial algorithm for calculating the
non-collective excitations of nuclei. The method, when applied to magic and
semi-magic nuclei, such as $^{60}$Ni, $^{114}$Sn and $^{208}$Pb, reproduces the
cumulative number of experimental states at low excitation energy, as well as
the s-wave neutron resonance spacing at the neutron binding energy.
Experimental level densities above 10 MeV are reproduced by multiplying the
non-collective level densities by a simple vibrational enhancement factor.
Problems to be solved in the extension to open-shell nuclei are discussed",0205068v2
2012-04-02,Spin Transition in the ν=8/3 Fractional Quantum Hall Effect,"We present here the results from a density dependent study of the activation
energy gaps of the fractional quantum Hall effect states at Landau level
fillings \nu=8/3 and 7/3 in a series of high quality quantum wells. In the
density range from 0.5 x 10^{11} to 3 x 10^{11} cm^{-2}, the 7/3 energy gap
increases monotonically with increasing density, supporting its ground state
being spin polarized. For the 8/3 state, however, its energy gap first
decreases with increasing density, almost vanishes at n ~ 0.8 x 10^{11}
cm^{-2}, and then turns around and increases with increasing density, clearly
demonstrating a spin transition.",1204.0557v1
2014-05-05,Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains,"We obtain the exact Kohn-Sham potentials $V_{\mathrm{KS}}$ of time-dependent
density-functional theory for 1D Hubbard chains, driven by a d.c.\ external
field, using the time-dependent electron density and current density obtained
from exact many-body time-evolution. The exact $V_{\mathrm{xc}}$ is compared to
the adiabatically-exact $V_{\mathrm{xc}}^{\mathrm{ad}}$ and the ""instantaneous
ground state"" $V_{\mathrm{xc}}^{\mathrm{igs}}$. The latter is shown to work
effectively in some cases when the former fails. Approximations for the
exchange-correlation potential $V_{\mathrm{xc}}$ and its gradient, based on the
local density and on the local current density, are also considered and both
physical quantities are observed to be far outside the reach of any possible
local approximation. Insight into the respective roles of ground-state and
excited-state correlation in the time-dependent system, as reflected in the
potentials, is provided by the pair correlation function.",1405.0885v1
2022-06-21,Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Control,"Learned models and policies can generalize effectively when evaluated within
the distribution of the training data, but can produce unpredictable and
erroneous outputs on out-of-distribution inputs. In order to avoid distribution
shift when deploying learning-based control algorithms, we seek a mechanism to
constrain the agent to states and actions that resemble those that it was
trained on. In control theory, Lyapunov stability and control-invariant sets
allow us to make guarantees about controllers that stabilize the system around
specific states, while in machine learning, density models allow us to estimate
the training data distribution. Can we combine these two concepts, producing
learning-based control algorithms that constrain the system to in-distribution
states using only in-distribution actions? In this work, we propose to do this
by combining concepts from Lyapunov stability and density estimation,
introducing Lyapunov density models: a generalization of control Lyapunov
functions and density models that provides guarantees on an agent's ability to
stay in-distribution over its entire trajectory.",2206.10524v1
1997-07-16,Averaged Green function and density of states for electrons in a high magnetic field and random potential,"We consider a model for 2D electrons in a very strong magnetic field (i.e.
projected onto a single Landau level) and a random potential $V$. The
computation of the averaged Green function for this system reduces to
calculating the averaged density of states. We have constructed a computer
algebra program which automatically generates a perturbation expansion in $V$
for these quantities. This is equivalent to computing moments of the density of
states. When $V$ is a sum of Gaussians from Poisson distributed impurities,
each term in the perturbation expansion can be evaluated automatically. We have
done so up to 12th order. The resulting information can be used to reconstruct
the density of states to good precision.",9707159v1
2003-03-07,Surface Induced Anomalous Superconductivity,"The Ginzburg-Landau (GL) theory is recast using a Hamiltonian involving the
complete kinetic energy density which requires that the surface energy must
contain a term \nabla |\psi|^2 to support superconducting (SC) states. The GL
equations contain two temperature, t, dependent parameters \alpha(t) and
\beta(t), which are respectively the coefficients of the SC pair density
\propto |\psi|^2, and the pair interaction term \propto |\psi|^4 in the free
energy density. The sign of these parameters, which define distinct solution
classes, and the ratio s(t) = \sqrt{|\alpha|/|\beta|} are governed by the
characteristics of the surface energy density. In addition to the conventional
bulk superconducting states with (\alpha < 0, \beta > 0), anomalous
superconducting states exist for all other sign combinations, including cases
with \beta < 0 which may exist only when surface pair interactions are
significant. All possible solutions of our generalized nonlinear, one
dimensional GL equations are found analytically and applied to a thin
superconducting slab which manifests the possibility of states exhibiting
enhanced, diminished, and pre-wetting superconductivity. Critical currents are
determined as functions of s(t) and surface parameters. The results are applied
to critical current experiments on SNS systems.",0303121v1
2007-12-20,Density of state and non-magnetic impurity effects in electron-doped cuprates,"We analyze the density of state (DOS) and a non-magnetic impurity effect in
electron-doped cuprates starting from two different scenarios: the
$d_{x^{2}-y^{2}}$-wave superconductivity coexisting with antiferromagnetic spin
density wave (SDW) order versus $d_{x^{2}-y^{2}}$-wave superconductivity with a
higher harmonic. We find that in both cases the local density of state (LDOS)
exhibits two impurity-induced resonance states at low energies. We also find
that for the intermediate value of the SDW gap, the DOS looks similar to that
obtained from the scenario of the $d_{x^{2}-y^{2}}$-wave gap with a higher
harmonic, suggesting the presence of a non-monotonic $d_{x^{2}-y^{2}}$-wave
gap. However, if the SDW gap is sufficiently large the DOS looks more
conventional s-wave like. This obvious difference from the DOS resulted from
the $d_{x^{2}-y^{2}}$-wave gap with a higher harmonic model, could
differentiate the two above scenarios and is needed to be proved in the further
doping dependence of tunneling spectrum measurement.",0712.3307v4
2015-06-12,"Ab initio study of structural, electronic, and thermal properties of Ir$_{1-x}$Rh$_{x}$ alloys","The structural, electronic, mechanical and thermal properties of
Ir$_{1-x}$Rh$_{x}$ alloys were studied systematically using ab initio density
functional theory at different concentrations (x = 0.00, 0.25, 0.50, 0.75,
1.00). A Special Quasirandom Structure method was used to make alloys having
FCC structure with four atoms per unit cell. The ground state properties such
as lattice constant and bulk modulus were calculated to find the equilibrium
atomic position for stable alloys. The calculated ground state properties are
in good agreement with the experimental and previously presented other
theoretical data. The electronic band structure and density of states were
calculated to study the electronic properties for these alloys at different
concentrations. The electronic properties substantiate the metallic behavior of
alloys. The first principle density functional perturbation theory as
implemented in quasiharmonic approximation was used for the calculation of
thermal properties. We have calculated the thermal properties such as Debye
temperatures, vibration energy, entropy, constant-volume specific heat and
internal energy. The ab initio linear-response method was used to calculate
phonon densities of states.",1506.03966v1
2017-05-12,Mixed state dynamical quantum phase transition and emergent topology,"Preparing an integrable system in a mixed state described by a thermal
density matrix , we subject it to a sudden quench and explore the subsequent
unitary dynamics. Defining a version of the generalised Loschmidt overlap
amplitude (GLOA) through the purifications of the time evolved density matrix,
we claim that non-analyiticies in the corresponding ""dynamical free energy
density"" persist and is referred to as mixed state dynamical quantum phase
transitions (MSDQPTs). Furthermore, these MSDQPTs are uniquely characterised by
a topological index constructed by the application of the Pancharatnam geometry
on the purifications of the thermal density matrix; the quantization of this
index however persists up to a critical temperature. These claims are
corroborated analysing the non-equilibrium dynamics of a transverse Ising chain
initially prepared in a thermal state and subjected to a sudden quench of the
transverse field.",1705.04555v1
2020-03-03,Two-Qubit Bloch Sphere,"Three unit spheres were used to represent the two-qubit pure states. The
three spheres are named the base sphere, entanglement sphere, and fiber sphere.
The base sphere and entanglement sphere represent the reduced density matrix of
the base qubit and the non-local entanglement measure, concurrence, while the
fiber sphere represents the fiber qubit via a simple rotation under a local
single-qubit unitary operation; however, in an entangled bipartite state, the
fiber sphere has no information on the reduced density matrix of the fiber
qubit. When the bipartite state becomes separable, the base and fiber spheres
seamlessly become the single-qubit Bloch spheres of each qubit. Since either
qubit can be chosen as the base qubit, two alternative sets of these three
spheres are available, where each set fully represents the bipartite pure
state, and each set has information of the reduced density matrix of its base
qubit. Comparing this model to the two Bloch balls representing the reduced
density matrices of the two qubits, each Bloch ball corresponds to two unit
spheres in our model, namely, the base and entanglement spheres. The
concurrence-coherence complementarity is explicitly shown on the entanglement
sphere via a single angle.",2003.01699v2
2023-02-13,Ground state of Tonks-Girardeau gas under density-dependent gauge potential in a one dimensional harmonic potential,"In the present paper we investigate the ground state of Tonks-Girardeau gas
under density-dependent gauge potential. With Bose-Fermi mapping method we
obtain the exact ground state wavefunction for the system confined in a
harmonic potential. Based on the ground state wavefunction, the reduced one
body density matrix (ROBDM), natural orbitals and their occupations, and the
momentum distributions are obtained. Compared with the case without gauge
potential, the present wavefunction and ROBDM have additional phase factors
induced by gauge potential. The momentum distribution is the convolution of
that without gauge potential to the Fourier transformation of definite integral
of gauge potential. It is shown that because of the density-dependent gauge
potential the peak of momentum distributions deviate from zero momentum and the
Bose gas take finite total momentum. In particular the momentum distribution is
no longer symmetric although the total momentum can become zero by adding a
constant to the gauge potential.",2302.06106v1
2023-02-21,Many-body correlations in one-dimensional optical lattices with alkaline-earth(-like) atoms,"We explore the rich nature of correlations in the ground state of ultracold
atoms trapped in state-dependent optical lattices. In particular, we consider
interacting fermionic ytterbium or strontium atoms, realizing a two-orbital
Hubbard model with two spin components. We analyze the model in one-dimensional
setting with the experimentally relevant hierarchy of tunneling and interaction
amplitudes by means of exact diagonalization and matrix product states
approaches, and study the correlation functions in density, spin, and orbital
sectors as functions of variable densities of atoms in the ground and
metastable excited states. We show that in certain ranges of densities these
atomic systems demonstrate strong density-wave, ferro- and antiferromagnetic,
as well as antiferroorbital correlations.",2302.10854v3
1996-02-14,Exact and Semiclassical Density Matrix of a Particle Moving in a Barrier Potential with Bound States,"We present a barrier potential with bound states that is exactly solvable and
determine the eigenfunctions and eigenvalues of the Hamiltonian. The
equilibrium density matrix of a particle moving at temperature T in this
nonlinear barrier potential field is determined. The exact density matrix is
compared with the result of the path integral approach in the semiclassical
approximation. For opaque barriers the simple semiclassical approximation is
found to be sufficient at high temperatures while at low temperatures the
fluctuation paths may have a caustic depending on temperature and endpoints.
Near the caustics the divergence of the simple semiclassical approximation of
the density matrix is removed by a nonlinear fluctuation potential. For opaque
barriers the improved semiclassical approximation is again in agreement with
the exact result. In particular, bound states and the form of resonance states
are described accurately by the semiclassical approach.",9602002v1
2011-09-12,Macroscopic limits and phase transition in a system of self-propelled particles,"We investigate systems of self-propelled particles with alignment
interaction. Compared to previous work, the force acting on the particles is
not normalized and this modification gives rise to phase transitions from
disordered states at low density to aligned states at high densities. This
model is the space inhomogeneous extension of a previous work by Frouvelle and
Liu in which the existence and stability of the equilibrium states were
investigated. When the density is lower than a threshold value, the dynamics is
described by a non-linear diffusion equation. By contrast, when the density is
larger than this threshold value, the dynamics is described by a hydrodynamic
model for self-alignment interactions previously derived in Degond and Motsch.
However, the modified normalization of the force gives rise to different
convection speeds and the resulting model may lose its hyperbolicity in some
regions of the state space.",1109.2404v1
2016-02-16,Effective bias and potentials in steady-state quantum transport: A NEGF reverse-engineering study,"Using non-equilibrium Green's functions combined with many-body perturbation
theory, we have calculated steady-state densities and currents through short
interacting chains subject to a finite electric bias. By using a steady-state
reverse-engineering procedure, the effective potential and bias which reproduce
such densities and currents in a non-interacting system have been determined.
The role of the effective bias is characterised with the aid of the so-called
exchange-correlation bias, recently introduced in a steady-state
density-functional-theory formulation for partitioned systems. We find that the
effective bias (or, equivalently, the exchange-correlation bias) depends
strongly on the interaction strength and the length of the central (chain)
region. Moreover, it is rather sensitive to the level of many-body
approximation used. Our study shows the importance of the
effective/exchange-correlation bias out of equilibrium, thereby offering hints
on how to improve the description of density-functional-theory based approaches
to quantum transport.",1602.05235v1
2021-05-04,Odd integer quantum Hall states with interlayer coherence in twisted bilayer graphene,"We report on the quantum Hall effect in two stacked graphene layers rotated
by 2 degree. The tunneling strength among the layers can be varied from very
weak to strong via the mechanism of magnetic breakdown when tuning the density.
Odd-integer quantum Hall physics is not anticipated in the regime of suppressed
tunneling for balanced layer densities, yet it is observed. We interpret this
as a signature of Coulomb interaction induced interlayer coherence and Bose
Einstein condensation of excitons that form at half filling of each layer. A
density imbalance gives rise to reentrant behavior due to a phase transition
from the interlayer coherent state to incompressible behavior caused by
simultaneous condensation of both layers in different quantum Hall states. With
increasing overall density, magnetic breakdown gains the upper hand. As a
consequence of the enhanced interlayer tunneling, the interlayer coherent state
and the phase transition vanish.",2105.01314v2
2024-03-13,Quantum fluctuating theory for one-dimensional shock waves,"We study the formation and the subsequent dynamics of shock waves in
repulsive one-dimensional Bose gases during the free expansion of a density
hump. By building coherent Fermi states for interacting Bethe fermions, we
define a quantum fluctuating initial state expressed in terms of universal
quantities, namely the density and the Luttinger parameter. In the integrable
case, this fluctuating state is then evolved by generalized hydrodynamics (GHD)
and, differently from non-fluctuating initial states, it develops density
ripples on top of the hydrodynamic mean value. Our analysis gives a general
theory of quantum ripples and wave breaking in integrable and quasi-integrable
one-dimensional liquids and clarifies the role of the interaction strength. In
particular, for strongly/intermediately interacting bosons, we find quantum
ripples originating from low-energy modes at the Fermi surface interfering when
transported by GHD. In the low coupling limit, near the quasicondensate regime,
we find instead that density ripples have a semi-classical nature, and their
description requires information on the curvature of the Fermi surface.",2403.08875v2
2002-08-14,High order correlations of generic pure states of finite-dimensional quantum systems are determined by lower order correlations,"We show that almost every pure state of multi-party quantum systems (each of
whose local Hilbert space has the same dimension) is completely determined by
the state's reduced density matrices of a fraction of the parties; this
fraction is less than about two-thirds of the parties for states of large
numbers of parties. In other words once the reduced states of this fraction of
the parties have been specified, there is no further freedom in the state.",0208093v1
2011-04-26,Landscape encodings enhance optimization,"Hard combinatorial optimization problems deal with the search for the minimum
cost solutions (ground states) of discrete systems under strong constraints. A
transformation of state variables may enhance computational tractability. It
has been argued that these state encodings are to be chosen invertible to
retain the original size of the state space. Here we show how redundant
non-invertible encodings enhance optimization by enriching the density of
low-energy states. In addition, smooth landscapes may be established on encoded
state spaces to guide local search dynamics towards the ground state.",1104.5024v2
2011-07-29,Metastable states of hydrogen: their geometric phases and flux densities,"We discuss the geometric phases and flux densities for the metastable states
of hydrogen with principal quantum number n=2 being subjected to adiabatically
varying external electric and magnetic fields. Convenient representations of
the flux densities as complex integrals are derived. Both, parity conserving
(PC) and parity violating (PV) flux densities and phases are identified.
General expressions for the flux densities following from rotational invariance
are derived. Specific cases of external fields are discussed. In a pure
magnetic field the phases are given by the geometry of the path in magnetic
field space. But for electric fields in presence of a constant magnetic field
and for electric plus magnetic fields the geometric phases carry information on
the atomic parameters, in particular, on the PV atomic interaction. We show
that for our metastable states also the decay rates can be influenced by the
geometric phases and we give a concrete example for this effect. Finally we
emphasise that the general relations derived here for geometric phases and flux
densities are also valid for other atomic systems having stable or metastable
states, for instance, for He with n=2. Thus, a measurement of geometric phases
may give important experimental information on the mass matrix and the electric
and magnetic dipole matrices for such systems. This could be used as a check of
corresponding theoretical calculations of wave functions and matrix elements.",1107.6006v2
2019-02-11,Multi-faceted machine learning of competing orders in disordered interacting systems,"While the non-perturbative interaction effects in the fractional quantum Hall
regime can be readily simulated through exact diagonalization, it has been
challenging to establish a suitable diagnostic that can label different phases
in the presence of competing interactions and disorder. Here we introduce a
multi-faceted framework using a simple artificial neural network (ANN) to
detect defining features of a fractional quantum Hall state, a charge density
wave state and a localized state using the entanglement spectra and charge
density as independent input. We consider the competing effects of a perturbing
interaction ($l = 1$ pseudopotential $\Delta V_1$), a disorder potential $W$,
and the Coulomb interaction to the system at filling fraction ${\nu} = 1/3$.
Our phase diagram benchmarks well against previous estimates of the phase
boundary using conventional measures along the $\Delta V_1 = 0$ and $W = 0$
axes, the only regions where conventional approaches have been explored.
Moreover, exploring the entire two-dimensional phase diagram for the first
time, we establish the robustness of the fractional quantum Hall state and map
out the charge density wave micro-emulsion phase wherein droplets of charge
density wave region appear before the charge density wave is completely
disordered. Hence we establish that the ANN can access and learn the defining
traits of topological as well as broken symmetry phases using multi-faceted
inputs of entanglement spectra and charge density.",1902.04079v1
2022-09-16,Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning,"Density of the reachable states can help understand the risk of
safety-critical systems, especially in situations when worst-case reachability
is too conservative. Recent work provides a data-driven approach to compute the
density distribution of autonomous systems' forward reachable states online. In
this paper, we study the use of such approach in combination with model
predictive control for verifiable safe path planning under uncertainties. We
first use the learned density distribution to compute the risk of collision
online. If such risk exceeds the acceptable threshold, our method will plan for
a new path around the previous trajectory, with the risk of collision below the
threshold. Our method is well-suited to handle systems with uncertainties and
complicated dynamics as our data-driven approach does not need an analytical
form of the systems' dynamics and can estimate forward state density with an
arbitrary initial distribution of uncertainties. We design two challenging
scenarios (autonomous driving and hovercraft control) for safe motion planning
in environments with obstacles under system uncertainties. We first show that
our density estimation approach can reach a similar accuracy as the
Monte-Carlo-based method while using only 0.01X training samples. By leveraging
the estimated risk, our algorithm achieves the highest success rate in goal
reaching when enforcing the safety rate above 0.99.",2209.08073v1
2011-01-19,Density of states of a dissipative quantum dot coupled to a quantum wire,"We examine the local density of states of an impurity level or a quantum dot
coupled to a fractional quantum Hall edge, or to the end of a single
one-dimensional Luttinger-liquid lead. Effects of an Ohmic dissipative bath are
also taken into account. Using both analytical and numerical techniques we show
that, in general, the density of states exhibits power-law frequency dependence
near the Fermi energy. In a substantial region of the parameter space it simply
reflects the behavior of the tunneling density of states at the end of a
Luttinger-liquid, and is insensitive either to the value of the dot-lead
interaction or to the strength of dissipation; otherwise it depends on these
couplings too. This behavior should be contrasted with the thermodynamic
properties of the level, in particular, its occupancy, which were previously
shown to depend on the various interactions in the system only through the
corresponding Fermi edge singularity exponent, and thus cannot display any
Luttinger-liquid specific power-law. Hence, we can construct different models,
some with and some without interactions in the wire (but with equal Fermi edge
singularity exponents), which would have very different level densities of
states, although they all result in the same level population vs. energy
curves.",1101.3731v1
2011-04-21,Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states,"We study the influence of different edge types on the electronic density of
states of graphene nanostructures. To this end we develop an exact expansion
for the single particle Green's function of ballistic graphene structures in
terms of multiple reflections from the system boundary, that allows for a
natural treatment of edge effects. We first apply this formalism to calculate
the average density of states of graphene billiards. While the leading term in
the corresponding Weyl expansion is proportional to the billiard area, we find
that the contribution that usually scales with the total length of the system
boundary differs significantly from what one finds in semiconductor-based,
Schr\""odinger type billiards: The latter term vanishes for armchair and
infinite mass edges and is proportional to the zigzag edge length, highlighting
the prominent role of zigzag edges in graphene. We then compute analytical
expressions for the density of states oscillations and energy levels within a
trajectory based semiclassical approach. We derive a Dirac version of
Gutzwiller's trace formula for classically chaotic graphene billiards and
further obtain semiclassical trace formulae for the density of states
oscillations in regular graphene cavities. We find that edge dependent
interference of pseudospins in graphene crucially affects the quantum spectrum.",1104.4292v2
2023-11-05,One- and two-parameter equation of state parametrizations with continuous sound speed for neutron star simulations,"We describe two fitting schemes that aim to represent the high-density part
of realistic equations of state for numerical simulations such as neutron star
oscillations. The low-density part of the equation of state is represented by
an arbitrary polytropic crust, and we propose a generic procedure to stitch any
desired crust to the high-density fit, which is performed on the internal
energy, pressure and sound speed of barotropic equations of state that describe
cold neutron stars in $\beta$-equilibrium. An extension of the fitting schemes
to equations of state with an additional compositional parameter is proposed.
In particular we develop a formalism that ensures the existence of a
$\beta$-equilibrium at low densities. An additional feature of this low-density
model is that it can be, in principle, applied to any parametrization. The
performance of the fits is checked on mass, radius and tidal deformability as
well as on the dynamical radial oscillation frequencies. To that end, we use a
pseudospectral isolated neutron star evolution code based on a non-conservative
form of the hydrodynamical equations. A comparison to existing parametrizations
is proposed, as far as possible, and to published radial frequency values in
the literature. The static and dynamic quantities are well reproduced by the
fitting schemes. Our results suggest that, even though the radius is very
sensitive to the choice of the crust, this choice has little influence on the
oscillation frequencies of a neutron star.",2311.02653v1
2006-11-12,Unambiguous State Discrimination of two density matrices in Quantum Information Theory,"In this thesis we study the problem of unambiguously discriminating two mixed
quantum states. We first present reduction theorems for optimal unambiguous
discrimination of two generic density matrices. We show that this problem can
be reduced to that of two density matrices that have the same rank $r$ in a
2$r$-dimensional Hilbert space. These reduction theorems also allow us to
reduce USD problems to simpler ones for which the solution might be known. As
an application, we consider the unambiguous comparison of $n$ linearly
independent pure states with a simple symmetry. Moreover, lower bounds on the
optimal failure probability have been derived. For two mixed states they are
given in terms of the fidelity. Here we give tighter bounds as well as
necessary and sufficient conditions for two mixed states to reach these bounds.
We also construct the corresponding optimal measurement. With this result, we
provide analytical solutions for unambiguously discriminating a class of
generic mixed states. This goes beyond known results which are all reducible to
some pure state case. We however show that examples exist where the bounds
cannot be reached. Next, we derive properties on the rank and the spectrum of
an optimal USD measurement. This finally leads to a second class of exact
solutions. Indeed we present the optimal failure probability as well as the
optimal measurement for unambiguously discriminating any pair of geometrically
uniform mixed states in four dimensions. This class of problems includes for
example the discrimination of both the basis and the bit value mixed states in
the BB84 QKD protocol with coherent states.",0611133v1
2020-10-26,"Analysis of a simple equation for the ground state of the Bose gas II: Monotonicity, Convexity and Condensate Fraction","In a recent paper we studied an equation (called the ""simple equation"")
introduced by one of us in 1963 for an approximate correlation function
associated to the ground state of an interacting Bose gas. Solving the equation
yields a relation between the density $\rho$ of the gas and the energy per
particle. Our construction of solutions gave a well-defined function $\rho(e)$
for the density as a function of the energy $e$. We had conjectured that
$\rho(e)$ is a strictly monotone increasing function, so that it can be
inverted to yield the strictly monotone increasing function $e(\rho)$. We had
also conjectured that $\rho e(\rho)$ is convex as a function of $\rho$. We
prove both conjectures here for small densities, the context in which they have
the most physical relevance, and the monotonicity also for large densities.
Both conjectures are grounded in the underlying physics, and their proof
provides further mathematical evidence for the validity of the assumptions
underlying the derivation of the simple equation, at least for low or high
densities, if not intermediate densities, although the equation gives
surprisingly good predictions for all densities $\rho$. Another problem left
open in our previous paper was whether the simple equation could be used to
compute accurate predictions of observables other than the energy. Here, we
provide a recipe for computing predictions for any one- or two-particle
observables for the ground state of the Bose gas. We focus on the condensate
fraction and the momentum distribution, and show that they have the same low
density asymptotic behavior as that predicted for the Bose gas. Along with the
computation of the low density energy of the simple equation in our previous
paper, this shows that the simple equation reproduces the known and conjectured
properties of the Bose gas at low densities.",2010.13882v3
2000-03-24,Does localization occur in a hierarchical random-matrix model for many-body states?,"We use random-matrix theory and supersymmetry techniques to work out the
two-point correlation function between states in a hierarchical model which
employs Feshbach's chaining hypothesis: Classes of many-body states are
introduced. Only states within the same or neighboring classes are coupled. We
assume that the density of states per class grows monotonically with class
index. The problem is mapped onto a one-dimensional non-linear sigma model. In
the limit of a large number of states in each class we derive the critical
exponent for the growth of the level density with class index for which
delocalization sets in. From a realistic modelling of the class-dependence of
the level density, we conclude that the model does not predict Fock-space
localization in nuclei.",0003053v1
2014-07-07,Multiqubit symmetric states with maximally mixed one-qubit reductions,"We present a comprehensive study of maximally entangled symmetric states of
arbitrary numbers of qubits in the sense of the maximal mixedness of the
one-qubit reduced density operator. A general criterion is provided to easily
identify whether given symmetric states are maximally entangled in that respect
or not. We show that these maximally entangled symmetric (MES) states are the
only symmetric states for which the expectation value of the associated
collective spin of the system vanishes, as well as in corollary the dipole
moment of the Husimi function. We establish the link between this kind of
maximal entanglement, the anticoherence properties of spin states, and the
degree of polarization of light fields. We analyze the relationship between the
MES states and the classes of states equivalent through stochastic local
operations with classical communication (SLOCC). We provide a nonexistence
criterion of MES states within SLOCC classes of qubit states and show in
particular that the symmetric Dicke state SLOCC classes never contain such MES
states, with the only exception of the balanced Dicke state class for even
numbers of qubits. The 4-qubit system is analyzed exhaustively and all MES
states of this system are identified and characterized. Finally the
entanglement content of MES states is analyzed with respect to the geometric
and barycentric measures of entanglement, as well as to the generalized
N-tangle. We show that the geometric entanglement of MES states is ensured to
be larger than or equal to 1/2, but also that MES states are not in general the
symmetric states that maximize the investigated entanglement measures.",1407.1738v2
2007-04-03,Density dependence of the symmetry energy and the nuclear equation of state: A Dynamical and Statistical model perspective,"The density dependence of the symmetry energy in the equation of state of
isospin asymmetric nuclear matter is of significant importance for studying the
structure of systems as diverse as the neutron-rich nuclei and the neutron
stars. A number of reactions using the dynamical and the statistical models of
multifragmentation, and the experimental isoscaling observable, is studied to
extract information on the density dependence of the symmetry energy. It is
observed that the dynamical and the statistical model calculations give
consistent results assuming the sequential decay effect in dynamical model to
be small. A comparison with several other independent studies is also made to
obtain important constraint on the form of the density dependence of the
symmetry energy. The comparison rules out an extremely "" stiff "" and "" soft ""
form of the density dependence of the symmetry energy with important
implications for astrophysical and nuclear physics studies.",0704.0471v1
2015-06-22,Neutron star structure in an in-medium modified chiral soliton model,"We study the internal structure of a static and spherically symmetric neutron
star in the framework of an in-medium modified chiral soliton model. The
Equations of State describing an infinite and asymmetric nuclear matter are
obtained introducing the density dependent functions into the low energy free
space Lagrangian of the model starting from the phenomenology of pionic atoms.
The parametrizations of density dependent functions are related to the
properties of isospin asymmetric nuclear systems at saturation density of
symmetric nuclear matter $\rho_0\simeq 0.16$~fm$^{-3}$. Our results,
corresponding to the compressibility of symmetric nuclear matter in the range
$250\,\mbox{MeV}\le K_0\le 270\,\mbox{MeV}$ and the slop parameter value of
symmetry energy in the range $30\,\mbox{MeV}\le L_S\le 50\,\mbox{MeV}$, are
consistent with the results from other approaches and with the experimental
indications. Using the modified Equations of State, near the saturation density
of symmetric nuclear matter $\rho_0$, the extrapolations to the high density
and highly isospin asymmetric regions have been performed. The calculations
showed that the properties of $\sim 1.4M_\odot$ and $\sim 2M_\odot$ neutron
stars can be well reproduced in the framework of present approach.",1506.06481v1
2022-09-14,Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties,"The spectral and localization properties of heterogeneous random graphs are
determined by the resolvent distributional equations, which have so far
resisted an analytic treatment. We solve analytically the resolvent equations
of random graphs with an arbitrary degree distribution in the high-connectivity
limit, from which we perform a thorough analysis of the impact of degree
fluctuations on the spectral density, the inverse participation ratio, and the
distribution of the local density of states. We show that all eigenvectors are
extended and that the spectral density exhibits a logarithmic or a power-law
divergence when the variance of the degree distribution is large enough. We
elucidate this singular behaviour by showing that the distribution of the local
density of states at the center of the spectrum displays a power-law tail
determined by the variance of the degree distribution. In the regime of weak
degree fluctuations the spectral density has a finite support, which promotes
the stability of large complex systems on random graphs.",2209.06805v1
2015-04-29,Randomized estimation of spectral densities of large matrices made accurate,"For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the
case that the only affordable operation is matrix-vector multiplication. In
such case, randomized method is a powerful way to estimate the spectral density
(or density of states) of $A$. However, randomized methods developed so far for
estimating spectral densities only extract information from different random
vectors independently, and the accuracy is therefore inherently limited to
$\mathcal{O}(1/\sqrt{N_{v}})$ where $N_{v}$ is the number of random vectors. In
this paper we demonstrate that the ""$\mathcal{O}(1/\sqrt{N_{v}})$ barrier"" can
be overcome by taking advantage of the correlated information of random vectors
when properly filtered by polynomials of $A$. Our method uses the fact that the
estimation of the spectral density essentially requires the computation of the
trace of a series of matrix functions that are numerically low rank. By
repeatedly applying $A$ to the same set of random vectors and taking different
linear combination of the results, we can sweep through the entire spectrum of
$A$ by building such low rank decomposition at different parts of the spectrum.
Under some assumptions, we demonstrate that a robust and efficient
implementation of such spectrum sweeping method can compute the spectral
density accurately with $\mathcal{O}(N^2)$ computational cost and
$\mathcal{O}(N)$ memory cost. Numerical results indicate that the new method
can significantly outperform existing randomized methods in terms of accuracy.
As an application, we demonstrate a way to accurately compute a trace of a
smooth matrix function, by carefully balancing the smoothness of the integrand
and the regularized density of states using a deconvolution procedure.",1504.07690v2
2000-05-16,Regimes Of Helium Burning,"The burning regimes encountered by laminar deflagrations and ZND detonations
propagating through helium-rich compositions in the presence of buoyancy-driven
turbulence are analyzed. Particular attention is given to models of X-ray
bursts which start with a thermonuclear runaway on the surface of a neutron
star, and the thin shell helium instability of intermediate-mass stars. In the
X-ray burst case, turbulent deflagrations propagating in the lateral or radial
directions encounter a transition from the distributed regime to the flamlet
regime at a density of 10^8 g cm^{-3}. In the radial direction, the purely
laminar deflagration width is larger than the pressure scale height for
densities smaller than 10^6 g cm^{-3}. Self-sustained laminar deflagrations
travelling in the radial direction cannot exist below this density. Similarily,
the planar ZND detonation width becomes larger than the pressure scale height
at 10^7 g cm^{-3}, suggesting that a steady-state, self-sustained detonations
cannot come into existance in the radial direction. In the thin helium shell
case, turbulent deflagrations travelling in the lateral or radial directions
encounter the distributed regime at densities below 10^7 g cm^{-3}, and the
flamelet regime at larger densities. In the radial direction, the purely
laminar deflagration width is larger than the pressure scale height for
densities smaller than 10^4 g cm^{-3}, indicating that steady-state laminar
deflagrations cannot form below this density. The planar ZND detonation width
becomes larger than the pressure scale height at 5 10^4 g cm^{-3}, suggesting
that steady-state, self-sustained detonations cannot come into existance in the
radial direction.",0005339v1
2009-07-09,Effects of Vacuum Fluctuation Suppression on Atomic Decay Rates,"The use of atomic decay rates as a probe of sub-vacuum phenomena will be
studied. Because electromagnetic vacuum fluctuations are essential for
radiative decay of excited atomic states, decay rates can serve as a measure of
the suppression of vacuum fluctuation in non-classical states, such as squeezed
vacuum states. In such states the renormalized expectation value of the square
of the electric field or the energy density can be periodically negative,
representing suppression of vacuum fluctuations. We explore the extent to which
atomic decays can be used to measure the mean squared electric field or energy
density. We consider a scheme in which atoms in an excited state transit a
closed cavity whose lowest mode contains photons in a non-classical state. The
change in the decay probability of the atom in the cavity due to the
non-classical state can, under certain circumstances, serve as a measure of the
mean squared electric field or energy density in the cavity. We derive a
quantum inequality bound on the decrease in this probability. We also show that
the decrease in decay rate can sometimes be a measure of negative energy
density or negative squared electric field. We make some estimates of the
magnitude of this effect, which indicate that an experimental test might be
possible.",0907.1638v1
2018-03-15,Metallic state in bosonic systems with continuously degenerate minima,"In systems above one dimension a continuously degenerate minimum of the
single particle dispersion is realized due to one or a combination of
system-parameters such as lattice structure, isotropic spin-orbit coupling, and
interactions. A unit codimension of the dispersion-minima leads to a divergent
density of states which enhances the effects of interactions, and may lead to
novel states of matter as exemplified by Luttinger liquids in one dimensional
bosonic systems. Here we show that in dilute, homogeneous bosonic systems above
one dimension, weak, spin-independent, inter-particle interactions stabilize a
metallic state at zero temperature in the presence of a curved manifold of
dispersion minima. In this metallic phase the system possesses a quasi
long-range order with non-universal scaling exponents. At a fixed positive
curvature of the manifold, increasing either the dilution or the interaction
strength destabilizes the metallic state towards charge density wave states
that break one or more symmetries. The magnitude of the wave vector of the
dominant charge density wave state is controlled by the product of the mean
density of bosons and the curvature of the manifold. We obtain the zero
temperature phase diagram, and identify the phase boundary.",1803.05839v2
1995-07-31,Density-Dependent Squeezing of Excitons in Highly Excited Semiconductors,"The time evolution from coherent states to squeezed states of high density
excitons is studied theoretically based on the boson formalism and within the
Random Phase Approximation. Both the mutual interaction between excitons and
the anharmonic exciton-photon interaction due to phase-space filling of
excitons are included in consideration. It is shown that the exciton squeezing
depends strongly on the exciton density in semiconductors and becomes smaller
with increasing the latter.",9507140v1
2001-03-26,The Droplet State and the Compressibility Anomaly in Dilute 2D Electron Systems,"We investigate the space distribution of carrier density and the
compressibility of two-dimensional (2D) electron systems by using the local
density approximation. The strong correlation is simulated by the local
exchange and correlation energies. A slowly varied disorder potential is
applied to simulate the disorder effect. We show that the compressibility
anomaly observed in 2D systems which accompanies the metal-insulator transition
can be attributed to the formation of the droplet state due to disorder effect
at low carrier densities.",0103541v1
2001-09-04,Phase Diagram of One-Dimensional Extended Hubbard Model at Half Filling,"We reexamine the ground-state phase diagram of the one-dimensional
half-filled Hubbard model with on-site and nearest-neighbor repulsive
interactions. We calculate second-order corrections to coupling constants in
the g-ology to show that the bond-charge-density-wave (BCDW) phase exists for
weak couplings in between the charge density wave (CDW) and spin density wave
(SDW) phases. We find that the umklapp scattering of parallel-spin electrons
destabilizes the BCDW state and gives rise to a bicritical point where the
CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW
first-order transition line.",0109051v1
2003-05-29,Eigenstates of the time-dependent density-matrix theory,"An extended time-dependent Hartree-Fock theory, known as the time-dependent
density-matrix theory (TDDM), is solved as a time-independent eigenvalue
problem for low-lying $2^+$ states in $^{24}$O to understand the foundation of
the rather successful time-dependent approach. It is found that the calculated
strength distribution of the $2^+$ states has physically reasonable behavior
and that the strength function is practically positive definite though the
non-hermitian hamiltonian matrix obtained from TDDM does not guarantee it. A
relation to an extended RPA theory with hermiticity is also investigated. It is
found that the density-matrix formalism is a good approximation to the
hermitian extended RPA theory.",0305088v1
2008-01-31,Virial Equation-of-State for Hard Spheres,"Recent values for virial coefficients up to B12, when expressed in powers of
density relative to maximum close packing,lead to a closed equation-of-state
for the equilibrium fluid. The series obtained converges for all densities;it
becomes negative and diverges to a negative pole at maximum packing. MD data
for 64000 spheres in the metastable region shows the virial pressure begins to
deviate at the fluid freezing density.",0801.4846v3
2008-04-04,Virial equation-of-state for the hard-disk fluid,"Virial coefficients for the two-dimensional hard-disk fluid, when expressed
in powers of density relative to maximum close packing, lead to an accurate
closed equation-of-state for the equilibrium fluid, analogous to that recently
found for hard spheres. The 2D series also converges for all densities up to a
negative pole at close packing density. The virial pressure begins to deviate
from the thermodynamic fluid in the approach to the ordering transition.",0804.0679v2
2012-08-23,Reduced density matrix functional theory at finite temperature. II. Application to the electron gas: Exchange only,"Using the newly introduced theory of finite-temperature reduced density
matrix functional theory, we apply the first-order approximation to the
homogeneous electron gas. We consider both collinear spin states as well as
symmetry broken states describing planar spin spirals and investigate the
magnetic phase diagram as well as the temperature-dependence of the single
particle spectra.",1208.4705v1
2013-12-19,Charge-density-wave states in double-layer graphene structures in a high magnetic field,"We study the phases of correlated charge-density waves that form at a high
magnetic field in two parallel graphene flakes separated by a thin insulator.
The predicted phases include the square and hexagonal charge-density-wave
bubbles, and a quasi-one-dimensional stripe phase. We find that the transition
temperature for such phases is within the experimentally accessible range and
that formation of interlayer-correlated states produces a negative
compressibility contribution to the differential capacitance of this system.",1312.5475v3
2014-04-09,"Electron-Phonon Spectral Density of MgB2 from Optical Data, through Maximum Entropy","We use maximum entropy techniques to extract an electron-phonon density from
optical data in the normal state at T = 45 K in MgB2. Limiting the analysis to
a range of phonon energies below 110 meV which is sufficient to capture all
phonon structures we find a spectral function which is in good agreement with
that calculated for the quasi two-dimensional sigma-band. Extending the
analysis to higher energies up to 160 meV we find no evidence for any
additional contributions to the fluctuation spectrum but find that the data can
only be understood if the density of states is taken to decrease with
increasing energy.",1404.2494v1
2015-05-04,Metallic State of Low Mobility Silicon at High Carrier density induced by an Ionic Liquid,"High mobility and dilute two-dimensional electron systems exhibit metallic
behavior down to the lowest experimental temperatures. In studies of ionic
liquid gated insulating silicon, we have observed transitions to a metallic
state in low mobility samples at much higher areal carrier densities than found
for samples of high mobility. We have also observed a mobility peak in metallic
samples as the carrier density was increased beyond $10^{13} \text{cm}^{-2}$.",1505.00656v2
2016-01-12,The density of states approach at finite chemical potential: a numerical study of the Bose gas,"Recently, a novel algorithm for computing the density of states in
statistical systems and quantum field theories has been proposed. The same
method can be applied to theories at finite density affected by the notorious
sign problem, reducing a high-dimensional oscillating integral to a more
tractable one-dimensional one. As an example we applied the method to the
relativistic Bose gas.",1601.02929v1
2016-02-12,Density matrix embedding theory for interacting electron-phonon systems,"We describe the extension of the density matrix embedding theory (DMET)
framework to coupled interacting fermion-boson systems. This provides a
frequency-independent, entanglement embedding formalism to treat bulk
fermion-boson problems. We illustrate the concepts within the context of the
one-dimensional Hubbard-Holstein model, where the phonon bath states are
obtained from the Schmidt decomposition of a self-consistently adjusted
coherent state. We benchmark our results against accurate density matrix
renormalization group calculations.",1602.04195v1
2018-01-12,Metrics for two electron random potential systems,"Metrics have been used to investigate the relationship between wavefunction
distances and density distances for families of specific systems. We extend
this research to look at random potentials for time-dependent single electron
systems, and for ground-state two electron systems. We find that Fourier series
are a good basis for generating random potentials. These random potentials also
yield quasi-linear relationships between the distances of ground-state
densities and wavefunctions, providing a framework in which Density Functional
Theory can be explored.",1801.04132v2
2023-03-22,Superconductivity in lightly doped Hubbard model on honeycomb lattice,"We have performed large-scale density-matrix renormalization group studies of
the lightly doped Hubbard model on the honeycomb lattice on long three and
four-leg cylinders. We find that the ground state of the system upon lightly
doping is consistent with that of a superconducting state with coexisting
quasi-long-range superconducting and charge density wave orders. Both the
superconducting and charge density wave correlations decay as a power law at
long distances with corresponding exponents $K_{sc}<2$ and $K_c<2$. On the
contrary, the spin-spin and single-particle correlations decay exponentially,
although with relatively long correlation lengths.",2303.12348v1
2007-03-01,Ground-state structure and stability of dipolar condensates in anisotropic traps,"We study the Hartree ground state of a dipolar condensate of atoms or
molecules in an three-dimensional anisotropic geometry and at T=0. We determine
the stability of the condensate as a function of the aspect ratios of the trap
frequencies and of the dipolar strength. We find numerically a rich phase space
structure characterized by various structures of the ground-state density
profile.",0703044v1
2013-08-16,Constraints on the Skyrme Equations of State from Properties of Doubly Magic Nuclei,"I use properties of doubly-magic nuclei to constrain nuclear matter and
neutron matter equations of state. I conclude that the data determined the
value of the neutron equation of state and the symmetry energy near a density
of $\rho_{on}$ = 0.10 nucleons/fm$^{3}$. The slope at that point is constrained
by the value of the neutron skin.",1308.3664v1
2003-05-09,Spontaneous Magnetization and Electron Momentum Density in 3D Quantum Dots,"We discuss an exactly solvable model Hamiltonian for describing the
interacting electron gas in a quantum dot. Results for a spherical square well
confining potential are presented. The ground state is found to exhibit
striking oscillations in spin polarization with dot radius at a fixed electron
density. These oscillations are shown to induce characteristic signatures in
the momentum density of the electron gas, providing a novel route for direct
experimental observation of the dot magnetization via spectroscopies sensitive
to the electron momentum density.",0305222v1
2006-06-30,A variational coupled-cluster study of magnon-density-wave excitations in quantum antiferromagnets,"We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum antiferromagnetic bipartite lattices. We reproduce
the spin-wave excitations (i.e., magnons with spin $\pm 1$). In addition, we
obtain a new, spin-zero excitation (magnon-density waves) which has been
missing in all existing spin-wave theories. Within our approximation, this
magnon-density-wave excitation has a nonzero energy gap in a cubic lattice and
is gapless in a square lattice, similar to those charge-density-wave
excitations (plasmons) in quantum electron gases.",0606813v2
1999-02-24,Calculation of exciton densities in SMMC,"We develop a shell-model Monte Carlo (SMMC) method to calculate densities of
states with varying exciton (particle-hole) number. We then apply this method
to the doubly closed-shell nucleus 40Ca in a full 0s-1d-0f-1p shell-model space
and compare our results to those found using approximate analytic expressions
for the partial densities. We find that the effective one-body level density is
reduced by approximately 22% when a residual two-body interaction is included
in the shell model calculation.",9902067v1
1999-10-08,Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen,"A new variational principle for optimizing thermal density matrices is
introduced. As a first application, the variational many body density matrix is
written as a determinant of one body density matrices, which are approximated
by Gaussians with the mean, width and amplitude as variational parameters. The
method is illustrated for the particle in an external field problem, the
hydrogen molecule and dense hydrogen where the molecular, the dissociated and
the plasma regime are described. Structural and thermodynamic properties
(energy, equation of state and shock Hugoniot) are presented.",9910009v1
2006-12-15,Attosecond time-scale multi-electron collisions in the Coulomb four-body problem: traces in classical probability densities,"In the triple ionization of the Li ground state by single photon absorption
the three electrons escape to the continuum mainly through two collision
sequences with individual collisions separated by time intervals on the
attosecond scale. We investigate the traces of these two collision sequences in
the classical probability densities. We show that each collision sequence has
characteristic phase space properties which distinguish it from the other.
Classical probability densities are the closest analog to quantum mechanical
densities allowing our results to be directly compared to quantum mechanical
results.",0612151v1
2009-02-13,All-electron density functional theory and time-dependent density functional theory with high-order finite elements,"We present for static density functional theory and time-dependent density
functional theory calculations an all-electron method which employs high-order
hierarchical finite element bases. Our mesh generation scheme, in which
structured atomic meshes are merged to an unstructured molecular mesh, allows a
highly nonuniform discretization of the space. Thus it is possible to represent
the core and valence states using the same discretization scheme, i.e., no
pseudopotentials or similar treatments are required. The nonuniform
discretization also allows the use of large simulation cells, and therefore
avoids any boundary effects.",0902.2306v2
1992-08-27,Electronic and structural properties of GaN by the full-potential LMTO method : the role of the $d$ electrons,"The structural and electronic properties of cubic GaN are studied within the
local density approximation by the full-potential linear muffin-tin orbitals
method. The Ga $3d$ electrons are treated as band states, and no shape
approximation is made to the potential and charge density. The influence of $d$
electrons on the band structure, charge density, and bonding properties is
analyzed. It is found that due to the energy resonance of the Ga 3$d$ states
with nitrogen 2$s$ states, the cation $d$ bands are not inert, and features
unusual for a III-V compound are found in the lower part of the valence band
and in the valence charge density and density of states. To clarify the
influence of the Ga $d$ states on the cohesive properties, additional full and
frozen--overlapped-core calculations were performed for GaN, cubic ZnS, GaAs,
and Si. The results show, in addition to the known importance of non-linear
core-valence exchange-correlation corrections, that an explicit description of
closed-shell repulsion effects is necessary to obtain accurate results for GaN
and similar systems. In summary, GaN appears to be somewhat exceptional among
the III-V compounds and reminiscent of II-VI materials, in that its band
structure and cohesive properties are sensitive to a proper treatment of the
cation $d$ bands, as a result of the presence of the latter in the valence band
range.",9208022v1
1998-06-05,The Density of States of hole-doped Manganites: A Scanning Tunneling Microscopy/Spectroscopy study,"Variable temperature scanning tunneling microscopy/spectroscopy studies on
single crystals and epitaxial thin films of hole-doped manganites, which show
colossal magnetoresistance, have been done. We have investigated the variation
of the density of states, at and near the Fermi energy ($E_f$), as a function
of temperature. Simple calculations have been carried out, to find out the
effect of temperature on the tunneling spectra and extract the variation of
density of states with temperature, from the observed data. We also report
here, atomic resolution images, on the single crystals and larger range images
showing the growth patterns on thin films. Our investigation shows
unambiguously that there is a rapid variation in density of states for
temperatures near the Curie temperature ($T_c$). While for temperatures below
$T_c$, a finite DOS is observed at $E_f$, for temperatures near $T_c$ a hard
gap opens up in the density of states near $E_f$. For temperatures much higher
than $T_c$, this gap most likely gives way to a soft gap. The observed hard gap
for temperatures near $T_c$, is somewhat higher than the transport gap for all
the materials. For different materials, we find that the magnitude of the hard
gap decreases as the $T_c$ of the material increases and eventually, for
materials with a $T_c$ close to 400 K, the value of the gap approaches zero.",9806084v1
2001-05-30,The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials,"The object of the present study is the integrated density of states of a
quantum particle in multi-dimensional Euclidean space which is characterized by
a Schr{\""o}dinger operator with magnetic field and a random potential which may
be unbounded from above and below. In case that the magnetic field is constant
and the random potential is ergodic and admits a so-called one-parameter
decomposition, we prove the absolute continuity of the integrated density of
states and provide explicit upper bounds on its derivative, the density of
states. This local Lipschitz continuity of the integrated density of states is
derived by establishing a Wegner estimate for finite-volume Schr\""odinger
operators which holds for rather general magnetic fields and different boundary
conditions. Examples of random potentials to which the results apply are
certain alloy-type and Gaussian random potentials. Besides we show a
diamagnetic inequality for Schr\""odinger operators with Neumann boundary
conditions.",0105046v2
2013-02-08,High density matter,"The microscopic composition and properties of matter at super-saturation
densities have been the subject of intense investigation for decades. The
scarcity of experimental and observational data has lead to the necessary
reliance on theoretical models. However, there remains great uncertainty in
these models, which, of necessity, have to go beyond the over-simple assumption
that high density matter consists only of nucleons and leptons. Heavy strange
baryons, mesons and quark matter in different forms and phases have to be
included to fulfil basic requirements of fundamental laws of physics. In this
review the latest developments in construction of the Equation of State (EoS)
of high-density matter at zero and finite temperature assuming different
composition of the matter are surveyed. Critical comparison of model EoS with
available observational data on neutron stars, including gravitational masses,
radii and cooling patterns is presented. The effect of changing rotational
frequency on the composition of neutron stars during their lifetime is
demonstrated. Compatibility of EoS of high-density, low temperature compact
objects and low density, high temperature matter created in heavy-ion
collisions is discussed.",1302.1928v2
2003-02-05,"A low density finite temperature apparent ""insulating"" phase in 2D systems","We propose that the observed low density ``insulating'' phase of a 2D
semiconductor system, with the carrier density being just below ($n < n_c$) the
so-called critical density where the derivative of resistivity changes sign at
low temperatures (i.e. resistivity $\rho(T)$ increases with increasing $T$ for
$n > n_c$ whereas it decreases with increasing $T$ for $n < n_c$), is in fact a
``high-temperature'' crossover version of the same effective metallic phase
seen at higher densities ($n>n_c$). This low density ($n<n_c$) finite
temperature crossover 2D effective insulating phase is characterized by
$\rho(T)$ with power law temperature dependence in contrast to the truly
insulating state (occurring at still lower densities) whose resistivity
increases exponentially with decreasing temperature.",0302112v1
2018-12-21,Improvement of functionals in density functional theory by the inverse Kohn--Sham method and density functional perturbation theory,"We propose a way to improve energy density functionals (EDFs) in the density
functional theory based on the combination of the inverse Kohn--Sham method and
the density functional perturbation theory. Difference between the known EDF
and the exact one is treated as the first-order perturbation. As benchmark
calculations, we reproduce the theoretical exchange and correlation functionals
in the local density approximation. Systems of noble-gas atoms are used for
benchmark calculations, and the ground-state energies and densities, as well as
the functionals, are reproduced with good accuracies.",1812.09285v3
2019-12-06,Traffic flow on star graph: Nonlinear diffusion,"We study the urban-scale macroscopic traffic flow in city networks. Star
graph is considered as traffic network. Star graphs with controlled traffic
flow are transformed to various cell-transmission graphs by using the cell
transmission method. The dynamic equations of vehicular densities on all nodes
(roads) are presented on cell-transmission graphs by using the speed-matching
model. The density equations are given by nonlinear-diffusion equations. The
traffic flow on star graph is mapped to the nonlinear diffusion process on the
cell-transmission graphs. At low mean density, the dynamic equations of
densities can be approximated by the conventional diffusion equations. At low
and high mean densities, the analytical solutions of densities on all nodes
(roads) are obtained on cell-transmission complete, cycle and star graphs. By
solving the dynamic equations numerically, the densities on all roads are
derived at a steady state. The urban-scale macroscopic fundamental diagrams are
obtained numerically on the cell-transmission graphs. The analytical solutions
agree with the numerical solutions.",1912.03380v1
2021-07-20,The Stefan-Boltzmann constant re-visited for photons thermally generated within matter,"The Stefan-Boltzmann constant arose from photon densities inside a cavity,
but inside matter photon mode densities are material specific. Photon speeds
are governed by the mode they occupy, so mode densities can be expressed in
terms of speed. Cavity intensities at temperature \(T_{K}\) combined
\(\left[\frac {8\pi k^4}{c^3h^3}\right] T_{K }^4\) with \(({\pi^4}/{15})\). A
material dependent number from summation of internal photon spectral energy
densities replaces \(\frac {\pi^4}{15}\). Spectral densities are presented for
water, germanium and silver. Output intensity combines revised hemispherical
emittance \(\epsilon_{Q,H}\) based on these densities, with universal factor
\(\left[\frac {8\pi k^4}{c^3h^3}\right] T_{K }^4\). Emitted radiance after
interface internal reflectance of directionally invariant internal radiance
elements defines \(\epsilon_{Q,H}\). Predicted internal densities are
verifiable using measured external spectral intensities, provided refraction
upon exit is accounted for in emissivity, which the Kirchhoff rule neglects.
Virtual bound state photon resonances are predicted in dielectrics and
observed.",2107.09455v1
2000-06-11,CPA density of states and conductivity in a double-exchange system containing impurities,"We study density of states and conductivity of the doped double-exchange
system, treating interaction of charge carriers both with the localized spins
and with the impurities in the coherent potential approximation. It is shown
that under appropriate conditions there is a gap between the conduction band
and the impurity band in paramagnetic phase, while the density of states is
gapless in ferromagnetic phase. This can explain metal-insulator transition
frequently observed in manganites and magnetic semiconductors. Activated
conductivity in the insulator phase is numerically calculated.",0006184v2
2001-11-16,1/f Noise in Electron Glasses,"We show that 1/f noise is produced in a 3D electron glass by charge
fluctuations due to electrons hopping between isolated sites and a percolating
network at low temperatures. The low frequency noise spectrum goes as
\omega^{-\alpha} with \alpha slightly larger than 1. This result together with
the temperature dependence of \alpha and the noise amplitude are in good
agreement with the recent experiments. These results hold true both with a
flat, noninteracting density of states and with a density of states that
includes Coulomb interactions. In the latter case, the density of states has a
Coulomb gap that fills in with increasing temperature. For a large Coulomb gap
width, this density of states gives a dc conductivity with a hopping exponent
of approximately 0.75 which has been observed in recent experiments. For a
small Coulomb gap width, the hopping exponent approximately 0.5.",0111302v4
2005-08-25,Atomic density of an harmonically trapped ideal gas near Bose-Einstein transition temperature,"We have studied the atomic density of a cloud confined in an isotropic
harmonic trap at the vicinity of the Bose-Einstein transition temperature. We
show that, for a non-interacting gas and near this temperature, the
ground-state density has the same order of magnitude as the excited states
density at the centre of the trap. This holds in a range of temperatures where
the ground-state population is negligible compared to the total atom number. We
compare the exact calculations, available in a harmonic trap, to semi-classical
approximations. We show that these latter should include the ground-state
contribution to be accurate..",0508186v2
2008-12-09,Occupation times via Bessel functions,"This study of occupation time densities for continuous-time Markov processes
was inspired by the work of E.Nir et al (2006) in the field of Single Molecule
FRET spectroscopy. There, a single molecule fluctuates between two or more
states, and the experimental observable depends on the state's occupation time
distribution. To mathematically describe the observable there was a need to
calculate a single state occupation time distribution.
  In this paper, we consider a Markov process with countably many states. In
order to find a one-stete occupation time density, we use a combination of
Fourier and Laplace transforms in the way that allows for inversion of the
Fourier transform. We derive an explicit expression for an occupation time
density in the case of a simple continuous time random walk on Z. Also we
examine the spectral measures in Karlin-McGregor diagonalization in an attempt
to represent occupation time densities via modified Bessel functions.",0812.1775v1
2016-07-08,Uniqueness of density-to-potential mapping for fermionic lattice systems,"We demonstrate that, for a fermionic lattice system, the ground-state
particle density uniquely determines the external potential except for the
sites corresponding to nodes of the wave function, and the limiting case where
the Pauli exclusion principle completely determines the occupation of all
sites. Our fundamental finding completes, for this general class of systems,
the one-to-one correspondence between ground states, their densities, and the
external potential at the base of the Hohenberg-Kohn theorem. Moreover we
demonstrate that the mapping from wave function to potential is unique not just
for the ground state, but also for excited states. To illustrate our findings,
we develop a practical inversion scheme to determine the external potential
from a given density. Our results hold for a general class of lattice models,
which includes the Hubbard model.",1607.02308v1
2018-12-06,Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation,"Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is the
DFT analog of state-averaged wavefunction-based (SA-WF) methods. In GOK-DFT,
the state-averaged (so-called ensemble) exchange-correlation (xc) energy is
described by a single functional of the density which, for a fixed density,
depends on the weights assigned to each state in the ensemble. We show that, if
a many-weight-dependent xc functional is employed, then it becomes possible to
extract, in principle exactly, all individual energy levels from a single
GOK-DFT calculation, exactly like in a SA-WF calculation. More precisely,
starting from the Kohn-Sham energies, a global Levy-Zahariev-type shift as well
as a state-specific (ensemble-based) xc derivative correction must be applied
in order to reach the energy level of interest. We illustrate with the
asymmetric Hubbard dimer the importance and substantial weight dependence of
both corrections. A comparison with more standard extraction procedures, which
rely on a sequence of ensemble calculations, is made at the ensemble exact
exchange level of approximation.",1812.02461v3
2008-07-14,"Mechanism of phase transitions and the electronic density of states in (La,Sm)FeAsO$_{1-x}$F$_x$ from ab initio calculations","The structure and electronic density of states in layered
LnFeAsO$_{1-x}$F$_x$ (Ln=La,Sm; $x$=0.0, 0.125, 0.25) are investigated using
density functional theory. For the $x$=0.0 system we predict a complex
potential energy surface, formed by close-lying single-well and double-well
potentials, which gives rise to the tetragonal-to-orthorhombic structural
transition, appearance of the magnetic order, and an anomaly in the specific
heat capacity observed experimentally at temperatures below $\sim$140--160 K.
We propose a mechanism for these transitions and suggest that these phenomena
are generic to all compounds containing FeAs layers. For $x>$0.0 we demonstrate
that transition temperatures to the superconducting state and their dependence
on $x$ correlate well with the calculated magnitude of the electronic density
of states at the Fermi energy.",0807.2213v1
2019-03-12,"Entanglement in disordered superfluids: the impact of density, interaction and harmonic confinement on the Superconductor-Insulator transition","We investigate the influence of density, interaction and harmonic confinement
on the superfluid to insulator transition (SIT) in disordered fermionic
superfluids described by the one-dimensional Hubbard model. We quantify the
ground-state single-site entanglement via density-functional theory
calculations of the linear entropy. We analyze the critical concentration $C_C$
at which the fully-localized state $-$ a special type of localization, with
null entanglement $-$ emerges. We find that $C_C$ is independent on the
interaction, but demands a minimum disorder strength to occur. We then derive
analytical relations for $C_C$ as a function of the average particle density
for attractive and repulsive disorder. Our results reveal that weak harmonic
confinement does not impact the properties of the fully-localized state, which
occurs at the same $C_C$, but stronger confinements may lead the system from
the fully-localized state to the ordinary localization.",1903.04680v1
2019-03-22,Yu-Shiba-Rusinov states in the charge-density modulated superconductor NbSe2,"NbSe$_2$ is a remarkable superconductor in which charge-density order
coexists with pairing correlations at low temperatures. Here, we study the
interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states
with the charge density order. Exploiting the incommensurate nature of the
charge-density wave (CDW), our measurements provide a thorough picture of how
the CDW affects both the energies and the wavefunctions of the YSR states. Key
features of the dependence of the YSR states on adsorption site relative to the
CDW are explained by model calculations. Several properties make NbSe$_2$ a
promising substrate for realizing topological nanostructures. Our results will
be important in designing such systems.",1903.09663v2
2009-10-06,Modeling a striped pseudogap state,"We study the electronic structure within a system of phase-decoupled
one-dimensional superconductors coexisting with stripe spin and charge density
wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a
hole pocket and an antinodal pseudogap. The spectral function in the antinodes
is approximately particle-hole symmetric contrary to the gapped regions just
outside the pocket. We find that states at the Fermi energy are extended
whereas states near the pseudogap energy have localization lengths as short as
the inter-stripe spacing. We consider pairing which has either local d-wave or
s-wave symmetry and find similar results in both cases, consistent with the
pseudogap being an effect of local pair correlations. We suggest that this
state is a stripe ordered caricature of the pseudogap phase in underdoped
cuprates with coexisting spin-, charge-, and pair-density wave correlations.
Lastly, we also model a superconducting state which 1) evolves smoothly from
the pseudogap state, 2) has a signature subgap peak in the density of states,
and 3) has the coherent pair density concentrated to the nodal region.",0910.0981v3
2006-02-20,"Exact stripe, checkerboard, and droplet ground states in two dimensions","Exact static nondegenerate stripe and checkerboard ground states are obtained
in a two-dimensional generalized periodic Anderson model, for a broad
concentration range below quarter filling. The random droplet states, also
present in the degenerate ground state, are eliminated by extending the
Hamiltonian with terms of different physical origin such as dimerization,
periodic charge displacements, density waves, or distorsion lines.",0602456v1
2023-03-06,Theory for charge density wave and orbital-flux state in antiferromagnetic kagome metal FeGe,"In this work, we theoretically study the charge order and orbital magnetic
properties of a new type of antiferromagnetic kagome metal FeGe. Based on first
principles density functional theory (DFT) calculations, we have studied the
electronic structures, Fermi-surface quantum fluctuations, as well as phonon
properties of the antiferromagnetic kagome metal FeGe. We find that charge
density wave emerges in such a system due to a subtle cooperation between
electron-electron ($e$-$e$) interactions and electron-phonon couplings, which
gives rise to an unusual scenario of interaction-triggered phonon
instabilities, and eventually yields a charge density wave (CDW) state. We
further show that, in the CDW phase, the ground-state current density
distribution exhibits an intriguing star-of-David pattern, leading to flux
density modulation. The orbital fluxes (or current loops) in this system
emerges as a result of the subtle interplay between magnetism, lattice
geometries, charge order, and spin-orbit coupling (SOC), which can be described
by a simple, yet universal, tight-binding theory including a Kane-Mele type SOC
term and a magnetic exchange interaction. We further study the origin of the
peculiar step-edge states in FeGe, which shed light on the topological
properties and correlation effects in this new type of kagome antiferromagnetic
material.",2303.02824v1
2023-04-08,Predicting Polymer Brush Behavior in Solvents using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework,"The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is
utilized to study the effects of temperature on polymer brushes. The brushes
are represented by a discrete energy spectrum and energy degeneracies obtained
through the Replica-Exchange Wang-Landau algorithm. The SEAQT equation of
motion is applied to the density of states to establish a unique kinetic path
from an initial thermodynamic state to a stable equilibrium state. The kinetic
path describes the brush's evolution in state space as it interacts with a
thermal reservoir. The predicted occupation probabilities along the kinetic
path are used to determine expected thermodynamic and structural properties.
The polymer density profile of a polystyrene brush in cyclohexane solvent is
predicted using the equation of motion, and it agrees qualitatively with
experimental density profiles. The Flory-Huggins parameter chosen to describe
brush-solvent interactions affects the solvent distribution in the brush but
has minimal impact on the polymer density profile. Three types of
non-equilibrium kinetic paths with differing amounts of entropy production are
considered: a heating path, a cooling path, and a heating-cooling path.
Properties such as tortuosity, radius of gyration, brush density, solvent
density, and brush chain conformations are calculated for each path.",2304.04105v2
2004-08-11,Checkerboard patterns in the t-J model,"Using the density matrix renormalization group, we study the possibility of
real space checkerboard patterns arising as the ground states of the t-J model.
We find that checkerboards with a commensurate (pi,pi) background are not low
energy states and can only be stabilized with large external potentials.
However, we find that striped states with charge density waves along the
stripes can form approximate checkerboard patterns. These states can be
stabilized with a very weak external field aligning and pinning the CDWs on
different stripes.",0408249v2
2007-07-20,Stratificational and antipodean properties of boundary states for N x N density matrices,"We investigate the space of N x N dimensional density matrices. We show that
there exist strata such that boundary states \rho_{p} with p zero eigenvalues
lie on or outside the spheres with radii r_{p}=\sqrt{p/N(N-p)}. Moreover, we
show that if in a certain direction there is a boundary state with q=N-p equal
eigenvalues, then in the opposite (antipodean) direction exists a boundary
state with p=N-q equal eigenvalues.",0707.3094v1
2020-07-14,Charge density waves in Weyl semimetals,"We present a theory of charge density wave (CDW) states in Weyl semimetals
and their interplay with the chiral anomaly. In particular, we demonstrate a
special nature of the shortest-period CDW state, which is obtained when the
separation between the Weyl nodes equals exactly half a primitive reciprocal
lattice vector. Its topological properties are shown to be distinct from all
other Weyl CDW states. We make a connection between this observation and the
three-dimensional fractional quantum Hall state, which was recently proposed to
exist in magnetic Weyl semimetals.",2007.07256v3
2012-04-09,Low temperature properties of the fermionic mixtures with mass imbalance in optical lattice,"We study the attractive Hubbard model with mass imbalance to clarify low
temperature properties of the fermionic mixtures in the optical lattice. By
combining dynamical mean-field theory with the continuous-time quantum Monte
Carlo simulation, we discuss the competition between the superfluid and density
wave states at half filling. By calculating the energy and the order parameter
for each state, we clarify that the coexisting (supersolid) state, where the
density wave and superfluid states are degenerate, is realized in the system.
We then determine the phase diagram at finite temperatures.",1204.1783v1
2021-05-10,Self-Bound Quantum Droplet with Internal Stripe Structure in 1D Spin-Orbit-Coupled Bose Gas,"We study the quantum-droplet state in a 3-dimensional (3D) Bose gas in the
presence of 1D spin-orbit-coupling and Raman coupling, especially the stripe
phase with density modulation, by numerically computing the ground state energy
including the mean-field energy and Lee-HuangYang correction. In this droplet
state, the stripe can exist in a wider range of Raman coupling, compared with
the BEC-gas state. More intriguingly, both spin-orbit-coupling and Raman
coupling strengths can be used to tune the droplet density.",2105.04172v1
2022-06-14,"Unification of Perdew-Zunger Self-Interaction Correction, DFT+U, and Rung 3.5 Density Functionals","We unify the Perdew-Zunger self-interaction correction (PZSIC) to approximate
density functional theory (DFT), the Hubbard correction DFT+U, and Rung 3.5
functionals within the Adiabatic Projection formalism. We modify the Kohn-Sham
reference system, introducing electron self-interaction in selected states.
Choosing those states as localized orbitals, localized atomic states, or states
at each point in space recovers PZSIC, DFT+U, and Rung 3.5. Typical Hubbard U
parameters approximate scaled-down PZSIC. A Rung 3.5 variant of DFT+U opens a
band gap in the homogeneous electron gas.",2206.07118v1
2013-07-31,"A multi-phase, multi-component critical equation of state","Realistic equations of state valid in the whole state space of a
multi-component mixture should satisfy at least three important constraints:
(i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial
equation of state with the correct multi-component structure. (iii) Close to
critical points, plait points, and consolute points, the correct universality
and scaling behavior is guaranteed.
  This paper discusses semiempirical equations of state for mixtures that
express the pressure as an explicit function of temperature and the chemical
potentials. In the first part, expressions are derived for the most important
thermodynamic quantities. The main result of the second part is the
construction of a large family of equations of state with the properties
(i)--(iii).",1307.8391v1
2010-03-24,Geometric measures of entanglement and the Schmidt decomposition,"In the standard geometric approach, the entanglement of a pure state is
$\sin^2\theta$, where $\theta$ is the angle between the entangled state and the
closest separable state of products of normalised qubit states. We consider
here a generalisation of this notion by considering separable states that
consist of products of unnormalised states of different dimension. The distance
between the target entangled state and the closest unnormalised product state
can be interpreted as a measure of the entanglement of the target state. The
components of the closest product state and its norm have an interpretation in
terms of, respectively, the eigenvectors and eigenvalues of the reduced density
matrices arising in the Schmidt decomposition of the state vector. For several
cases where the target state has a large degree of symmetry, we solve the
system of equations analytically, and look specifically at the limit where the
number of qubits is large.",1003.4755v1
2005-08-27,Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix,"We clarify different definitions of the density matrix by proposing the use
of different names, the full density matrix for a single-closed quantum system,
the compressed density matrix for the averaged single molecule state from an
ensemble of molecules, and the reduced density matrix for a part of an
entangled quantum system, respectively. We show that ensembles with the same
compressed density matrix can be physically distinguished by observing
fluctuations of various observables. This is in contrast to a general belief
that ensembles with the same compressed density matrix are identical. Explicit
expression for the fluctuation of an observable in a specified ensemble is
given. We have discussed the nature of nuclear magnetic resonance quantum
computing. We show that the conclusion that there is no quantum entanglement in
the current nuclear magnetic resonance quantum computing experiment is based on
the unjustified belief that ensembles having the same compressed density matrix
are identical physically. Related issues in quantum communication are also
discussed.",0508207v2
2014-08-21,Continuous dependence on the density for stratified steady water waves,"There are two distinct regimes commonly used to model traveling waves in
stratified water: continuous stratification, where the density is smooth
throughout the fluid, and layer-wise continuous stratification, where the fluid
consists of multiple immiscible strata. The former is the more physically
accurate description, but the latter is frequently more amenable to analysis
and computation. By the conservation of mass, the density is constant along the
streamlines of the flow; the stratification can therefore be specified by
prescribing the value of the density on each streamline. We call this the
streamline density function.
  Our main result states that, for every smoothly stratified periodic traveling
wave in a certain small-amplitude regime, there is an $L^\infty$ neighborhood
of its streamline density function such that, for any piecewise smooth
streamline density function in that neighborhood, there is a corresponding
traveling wave solution. Moreover, the mapping from streamline density function
to wave is Lipschitz continuous in a certain function space framework. As this
neighborhood includes piecewise smooth densities with arbitrarily many jump
discontinues, this theorem provides a rigorous justification for the ubiquitous
practice of approximating a smoothly stratified wave by a layered one. We also
discuss some applications of this result to the study of the qualitative
features of such waves.",1408.5030v1
2014-11-21,Smallest state spaces for which bipartite entangled quantum states are separable,"According to usual definitions, entangled states cannot be given a separable
decomposition in terms of products of local density operators. If we relax the
requirement that the local density operators be positive, then an entangled
quantum state may admit a separable decomposition in terms of more general sets
of single-system operators. This form of separability can be used to construct
classical models and simulation methods when only restricted set of
measurements are available. With such motivations in mind, we ask what are the
smallest such sets of local operators such that a pure bipartite entangled
quantum state becomes separable? We find that in the case of maximally
entangled states there are many inequivalent solutions, including for example
the sets of phase point operators that arise in the study of discrete Wigner
functions. We therefore provide a new way of interpreting these operators, and
more generally, provide an alternative method for constructing local hidden
variable models for entangled quantum states under subsets of quantum
measurements.",1411.5907v2
2008-02-08,Renormalization algorithm with graph enhancement,"We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.",0802.1211v1
2005-05-17,Shell structure in the density profile of a rotating gas of spin-polarized fermions,"We present analytical expressions and numerical illustrations for the
ground-state density distribution of an ideal gas of spin-polarized fermions
moving in two dimensions and driven to rotate in a harmonic well of circular or
elliptical shape. We show that with suitable choices of the strength of the
Lorentz force for charged fermions, or of the rotational frequency for neutral
fermions, the density of states can be tuned as a function of the angular
momentum so as to display a prominent shell structure in the spatial density
profile of the gas. We also show how this feature of the density profile is
revealed in the static structure factor determining the elastic light
scattering spectrum of the gas.",0505416v1
2005-05-10,Density Dependence of the Symmetry energy and the Equation of State of Isospin Asymmetric Nuclear Matter,"The density dependence of the symmetry energy in the equation of state of
isospin asymmetric nuclear matter is studied using the isoscaling of the
fragment yields and the antisymmetrized molecular dynamic calculation. It is
observed that the experimental data at low densities are consistent with the
form of symmetry energy,E$_{sym}$ $\approx$ 31.6 ($\rho/\rho_{\circ})^{0.69}$,
in close agreement with those predicted by the results of variational many-body
calculation. A comparison of the present result with those reported recently
using the NSCL-MSU data suggests that the heavy ion studies favor a dependence
of the form, E$_{sym}$ $\approx$ 31.6 ($\rho/\rho_{\circ})^{\gamma}$, where
$\gamma$ = 0.6 - 1.05. This constraints the form of the density dependence of
the symmetry energy at higher densities, ruling out an extremely "" stiff "" and
"" soft "" dependences.",0505011v3
2008-12-16,The Study of Relatively Low Density Stellar Matter in Presence of Strong Quantizing Magnetic Field,"The effect of strong quantizing magnetic field on the equation of state of
matter at the outer crust region of magnetars is studied. The density of such
matter is low enough compared to the matter density at the inner crust or outer
core region. Based on the relativistic version of semi-classical
Thomas-Fermi-Dirac model in presence of strong quantizing magnetic field a
formalism is developed to investigate this specific problem. The equation of
state of such low density crustal matter is obtained by replacing the
compressed atoms/ions by Wigner-Seitz cells with nonuniform electron density.
The results are compared with other possible scenarios. The appearance of
Thomas-Fermi induced electric charge within each Wigner-Seitz cell is also
discussed.",0812.3004v1
2022-09-03,Effects of a phase transition on two-pion interferometry in heavy-ion collisions at $\sqrt{s_\mathrm{NN}}=2.4-7.7$ GeV,"Hanbury-Brown-Twiss (HBT) correlations for charged pions in central Au+Au
collisions at $\sqrt{s_\mathrm{NN}}=2.4 - 7.7~\text{GeV}$ (corresponding to
beam kinetic energies in the fixed target frame from
$E_{\rm{lab}}=1.23~\text{to}~30~\text{GeV/nucleon}$) are calculated using the
UrQMD model with different equations of state. The effects of a phase
transition at high baryon densities are clearly observed in the HBT parameters
that are explored. It is found that the available data on the HBT radii,
$R_{O}/R_{S}$ and $R^{2}_{O}-R^{2}_{S}$, in the investigated energy region
favors a relatively stiff equation of state at low beam energies which then
turns into a soft equation of state at high collision energies consistent with
astrophysical constraints on the high density equation of state of QCD. The
specific effects of two different phase transition scenarios on the
$R_{O}/R_{S}$ and $R^{2}_{O}-R^{2}_{S}$ are investigated. It is found that a
phase transition with a significant softening of the equation of state below 4
times nuclear saturation density can be excluded using HBT data. Our results
highlight that the pion's $R_{O}/R_{S}$ and $R^{2}_{O}-R^{2}_{S}$ are sensitive
to the stiffness of the equation of state, and can be used to constrain and
understand the QCD equation of state in the high baryon density region.",2209.01413v1
1999-10-27,Band structure of the Jahn-Teller polaron from Quantum Monte Carlo,"A path-integral representation is constructed for the Jahn-Teller polaron
(JTP). It leads to a perturbation series that can be summed exactly by the
diagrammatic Quantum Monte Carlo technique. The ground-state energy, effective
mass, spectrum and density of states of the three-dimensional JTP are
calculated with no systematic errors. The band structure of JTP interacting
with dispersionless phonons, is found to be similar to that of the Holstein
polaron. The mass of JTP increases exponentially with the coupling constant. At
small phonon frequencies, the spectrum of JTP is flat at large momenta, which
leads to a strongly distorted density of states with a massive peak at the top
of the band.",9910436v1
2005-11-14,Combinatorial Identities and Quantum State Densities of Supersymmetric Sigma Models on N-Folds,"There is a remarkable connection between the number of quantum states of
conformal theories and the sequence of dimensions of Lie algebras. In this
paper, we explore this connection by computing the asymptotic expansion of the
elliptic genus and the microscopic entropy of black holes associated with
(supersymmetric) sigma models. The new features of these results are the
appearance of correct prefactors in the state density expansion and in the
coefficient of the logarithmic correction to the entropy.",0511143v1
2006-11-08,Inconsistencies in the MIT bag model of hadrons,"It is shown that what is commonly referred to as the MIT `bag' model of
hadrons is thermodynamically wrong: The adiabatic conditions between pressure
and temperature, and between pressure and volume imply the third, an adiabatic
relation between temperature and volume. Consequently, the bag model is
destitute of any predictive power since it reduces to a single adiabatic state.
The virial theorems proposed by the MIT group are shown to be the result of the
normal power density of states of a non-degenerate gas and not the exponential
density of states of the Hagedorn mass spectrum. A number of other elementary
misconceptions and inaccuracies are also pointed out.",0611089v1
2003-05-30,Quantum states of hierarchic systems,"The density matrix formalism which is widely used in the theory of
measurements, quantum computing, quantum description of chemical and biological
systems always imply the averaging over the states of the environment. In
practice this is impossible because the environment $U\setminusS$ of the system
$S$ is the complement of this system to the whole Universe and contains
infinitely many degrees of freedom. A novel method of construction density
matrix which implies the averaging only over the direct environment is
proposed. The Hilbert space of state vectors for the hierarchic quantum systems
is constructed.",0305194v3
2010-04-25,Husimi coordinates of multipartite separable states,"A parametrization of multipartite separable states in a finite-dimensional
Hilbert space is suggested. It is proved to be a diffeomorphism between the set
of zero-trace operators and the interior of the set of separable density
operators. The result is applicable to any tensor product decomposition of the
state space. An analytical criterion for separability of density operators is
established in terms of the boundedness of a sequence of operators.",1004.4370v1
2013-10-07,High posterior density ellipsoids of quantum states,"Regions of quantum states generalize the classical notion of error bars. High
posterior density (HPD) credible regions are the most powerful of region
estimators. However, they are intractably hard to construct in general. This
paper reports on a numerical approximation to HPD regions for the purpose of
testing a much more computationally and conceptually convenient class of
regions: posterior covariance ellipsoids (PCEs). The PCEs are defined via the
covariance matrix of the posterior probability distribution of states. Here it
is shown that PCEs are near optimal for the example of Pauli measurements on
multiple qubits. Moreover, the algorithm is capable of producing accurate PCE
regions even when there is uncertainty in the model.",1310.1903v1
2014-09-03,Tensor Representation of Spin States,"We propose a generalization of the Bloch sphere representation for arbitrary
spin states. It provides a compact and elegant representation of spin density
matrices in terms of tensors that share the most important properties of Bloch
vectors. Our representation, based on covariant matrices introduced by Weinberg
in the context of quantum field theory, allows for a simple parametrization of
coherent spin states, and a straightforward transformation of density matrices
under local unitary and partial tracing operations. It enables us to provide a
criterion for anticoherence, relevant in a broader context such as quantum
polarization of light.",1409.1106v2
2014-03-15,"The vortex state (A-phase) of helimagnets Fe0.5Co0.5Si, MnSi, FeGe, as a continuous distribution of the dislocation density in the magnetic sublattice","In this paper we propose to describe the deformed state of a helimagnet in
the magnetic field (A-phase) with a pair of variables: the order parameter
which characterizes the magnetic density and the tensor of distortion. Such
description corresponds to discontinuities in the magnetic sublattice of the
helimagnet accompanied by appearance of dislocations. It is shown that the
phase diagram we found for the helimagnet is analogous to the phase diagram of
the superconductors of second kind in the magnetic field, where the A-phase is
a counterpart of the superconducting mixed state with the Abrikosov vortices.",1403.3774v1
2022-09-07,Thin He-4 films on alkali substrates: where do He-3 atoms bind?,"The possible occurrence of bound states of He-3 atoms in the vicinity of a
weakly attractive substrate coated with a thin superfluid He-4film is
investigated by first principle computer simulations. No evidence is seen of
such bound states, even in the case of the weakest substrate, i.e., Cs; a
single He-3 atom always binds to the free He-4 surface, regardless of the
thickness of the He-4 film. A comparison of He-4 density profiles computed in
this work with those yielded by the Density Functional approach that led to the
prediction of He-3 bound states near the substrate, shows that the latter may
not have afforded a sufficiently accurate structural description of the
adsorbed He-4 film.",2209.03412v1
2017-07-08,Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling,"Motivated by a recent experiment [L. F. Livi, et al., Phys. Rev. Lett. 117,
220401(2016)], we study the ground-state properties of interacting fermions in
a one-dimensional optical lattice clock with spin-orbit coupling. As the
electronic and the hyperfine-spin states in the clock-state manifolds can be
treated as effective sites along distinct synthetic dimensions, the system can
be considered as multiple two-leg ladders with uniform magnetic flux
penetrating the plaquettes of each ladder. As the inter-orbital spin-exchange
interactions in the clock-state manifolds couple individual ladders together,
we show that exotic interaction-induced vortex states emerge in the
coupled-ladder system, which compete with existing phases of decoupled ladders
and lead to a rich phase diagram. Adopting the density matrix renormalization
group approach, we map out the phase diagram, and investigate in detail the
currents and the density-density correlations of the various phases. Our
results reveal the impact of interactions on spin-orbit coupled systems, and
are particularly relevant to the on-going exploration of spin-orbit coupled
optical lattice clocks.",1707.02379v2
2020-03-22,Thermoelectric probe of defect state induced by ionic liquid gating in vanadium dioxide,"Thermoelectric measurements detect the asymmetry between the density of
states above and below the chemical potential in a material. It provides
insights into small variations in the density of states near the chemical
potential, complementing electron transport measurements. Here, combined
resistance and thermoelectric power measurements are performed on vanadium
dioxide (VO2), a prototypical correlated electron material, under ionic-liquid
(IL) gating. With IL gating, charge transport below the
metal-to-insulator-transition (MIT) temperature remains in the thermally
activated regime, while the Seebeck coefficient exhibits an apparent transition
from semiconducting to metallic behavior. The contrasting behavior indicates
changes in electronic structure upon IL gating, due to the formation of oxygen
defect states. The experimental results are corroborated by numerical
simulations based on a model density of states incorporating a gating induced
defect band. This study reveals thermoelectric measurements to be a convenient
and sensitive probe for the role of defect states induced by IL gating in
suppressing the MIT in VO2, which remains benign in charge transport
measurements, and possibly for studying defect sates in other materials.",2003.09840v1
2002-12-24,Density-of-states picture and stability of ferromagnetism in the highly-correlated Hubbard model,"The problem of stability of saturated and non-saturated ferromagnetism in the
Hubbard model is considered in terms of the one-particle Green's functions.
Approximations by Edwards and Hertz and some versions of the self-consistent
approximations based on the 1/z-expansion are considered. The account of
longitudinal fluctuations turns out to be essential for description of the
non-saturated state. The corresponding pictures of density of states are
obtained. ""Kondo"" density-of-states singularities owing to spin-flip processes
are analyzed. The critical electron concentrations for instabilities of
saturated ferromagnetism and paramagnetic state are calculated for various
lattices. Drawbacks of various approximations are discussed. A comparison with
the results of previous works is performed.",0212586v2
2003-01-16,Charge density and electric charge in quantum electrodynamics,"The convergence of integrals over charge densities is discussed in relation
with the problem of electric charge and (non-local) charged states in Quantum
Electrodynamics (QED). Delicate, but physically relevant, mathematical points
like the domain dependence of local charges as quadratic forms and the time
smearing needed for strong convergence of integrals of charge densities are
analyzed. The results are applied to QED and the choice of time smearing is
shown to be crucial for the removal of vacuum polarization effects responible
for the time dependence of the charge (Swieca phenomenon). The possibility of
constructing physical charged states in the Feynman-Gupta-Bleuler gauge as
limits of local states vectors is discussed, compatibly with the vanishing of
the Gauss charge on local states. A modification by a gauge term of the Dirac
exponential factor which yields the physical Coulomb fields from the
Feynman-Gupta-Bleuler fields is shown to remove the infrared divergence of
scalar products of local and physical charged states, allowing for a
construction of physical charged fields with well defined correlation functions
with local fields.",0301111v1
2010-06-23,Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers,"We study the strong localization of atomic matter waves in a disordered
potential created by atoms pinned at the nodes of a lattice, for both
three-dimensional (3D) and two-dimensional (2D) systems. The localization
length of the matter wave, the density of localized states, and the occurrence
of energy mobility edges (for the 3D system), are numerically investigated as a
function of the effective scattering length between the atomic matter wave and
the pinned atoms. Both positive and negative matter wave energies are explored.
Interesting features of the density of states are discovered at negative
energies, where maxima in the density of bound states for the system can be
interpreted in terms of bound states of a matter wave atom with a few pinned
atomic scatterers. In 3D we found evidence of up to three mobility edges, one
at positive energies, and two at negative energies, the latter corresponding to
transitions between extended and localized bound states. In 2D, no mobility
edge is found, and a rapid exponential-like increase of the localization length
is observed at high energy.",1006.4429v2
2001-12-03,Flat Histogram Method of Wang-Landau and N-fold Way,"We present a method for estimating the density of states of a classical
statistical model. The algorithm successfully combines the Wang-Landau flat
histogram method with the N-fold way in order to improve efficiency of the
original single spin flip version. We test our implementation of the
Wang-Landau method with the two-dimensional nearest neighbor Ising model for
which we determine the tunneling time and the density of states. Furthermore,
we show that our new algorithm performs correctly at right edges of an energy
interval over which the density of states is computed. This removes a
disadvantage of the original single spin flip Wang-Landau method where results
showed systematically higher errors in the density of states at right
boundaries. We compare our data with the detailed numerical tests presented in
a study by Wang and Swendsen where the original Wang-Landau method was tested
against various other methods. Finally, we apply our method to a thin Ising
film of size $32\times 32\times 6$ with antisymmetric surface fields. With the
density of states obtained from the simulations we calculate canonical averages
related to the energy such as internal energy, Gibbs free energy and entropy,
but we also sample microcanonical averages during simulations in order to
determine canonical averages of the susceptibility, the order parameter and its
fourth order cumulant. We compare our results with simulational data obtained
from a conventional MC algorithm.",0112037v2
2019-10-22,Solitons in the Einstein universe,"We show that equations of Newtonian hydrodynamics and gravity with Einstein's
cosmological constant included admit gravitostatic wave solutions propagating
in the background of Einstein's static Universe. In the zero pressure limit
these waves exist at an average matter density exceeding that of Einstein's
Universe. They have the form of a lattice of integrable density singularities
localized at the maxima of the gravitational potential. These singularities are
steady-state counterparts of the so-called Zeldovich pancakes (ZP), interim
wall-like structures appearing at nonlinear stages of development of
gravitational instability. As the average matter density decreases, the period
of the ZP lattice increases diverging at the density of Einstein's Universe.
Solitary wave solutions are found at exactly the density of Einstein's
Universe, and at a slightly larger density the wave may be viewed as a lattice
of well-separated ZP solitons.",1910.10216v2
2019-01-28,"Comments On the heat capacity of liquids at high temperatures, S.M. Stishov, Physica A 478 (2017) 205","It is shown that the isochoric heat capacity of dense gas, fluid and liquid
decreases with increasing temperature at arbitrary values of a density for many
pair interaction potentials, including bonded potentials; that a decrease of
the isochoric heat capacity of the liquid with increasing temperature is
related to a decrease of the interaction between the particles with increasing
temperature; that a radial distribution function for nonideal dilute gas, which
is independent of density, can describe a temperature dependence of the
isochoric heat capacity of liquid argon; that a radial distribution function
dependent on the density and temperature describes a temperature dependence of
the isochoric heat capacity of liquid and dense fluid; that the
Carnahan-Starling equation of state for soft spheres gives a good quantitative
description of the isochoric heat capacity of argon; that the fluctuations of
the kinetic energy increases with temperature faster than that of the potential
energy; and finally, that a liquid state can be considered as a state of dense
gas. The explicit expressions to define the Frenkel line on the (temperature,
density) plane are derived.",1901.09528v1
2015-10-26,"Neutron Star Radii, Universal Relations, and the Role of Prior Distributions","We investigate constraints on neutron star structure arising from the
assumptions that neutron stars have crusts, that recent calculations of pure
neutron matter limit the equation of state of neutron star matter near the
nuclear saturation density, that the high-density equation of state is limited
by causality and the largest high-accuracy neutron star mass measurement, and
that general relativity is the correct theory of gravity. We explore the role
of prior assumptions by considering two classes of equation of state models. In
a first, the intermediate- and high-density behavior of the equation of state
is parameterized by piecewise polytropes. In the second class, the high-density
behavior of the equation of state is parameterized by piecewise continuous line
segments. The smallest density at which high-density matter appears is varied
in order to allow for strong phase transitions above the nuclear saturation
density. We critically examine correlations among the pressure of matter,
radii, maximum masses, the binding energy, the moment of inertia, and the tidal
deformability, paying special attention to the sensitivity of these
correlations to prior assumptions about the equation of state. It is possible
to constrain the radii of $1.4~\mathrm{M}_{\odot}$ neutron stars to a be larger
than 10 km, even without consideration of additional astrophysical
observations, for example, those from photospheric radius expansion bursts or
quiescent low-mass X-ray binaries. We are able to improve the accuracy of known
correlations between the moment of inertia and compactness as well as the
binding energy and compactness. We also demonstrate the existence of a
correlation between the neutron star binding energy and the moment of inertia.",1510.07515v1
2019-03-15,Vortices in low-density neutron matter and cold Fermi gases,"Cold gas experiments can be tuned to achieve strongly-interacting regimes
such as that of low-density neutron matter found in neutron-stars' crusts. We
report $T$=0 diffusion Monte Carlo results (i) for the ground state of both
spin-1/2 fermions with short-range interactions and low-density neutron matter
in a cylindrical container, and (ii) properties of these systems with a vortex
line excitation. We calculate the equation of state for cold atoms and
low-density neutron matter in the bulk systems, and we contrast it to our
results in the cylindrical container. We compute the vortex line excitation
energy for different interaction strengths, and we find agreement between cold
gases and neutron matter for very low densities. We also calculate density
profiles, which allow us to determine the density depletion at the vortex core,
which depends strongly on the short-ranged interaction in cold atomic gases,
but it is of $\approx$ 25% for neutron matter in the density regimes studied in
this work. Our results can be used to constrain neutron matter properties by
using measurements from cold Fermi gases experiments.",1903.06724v2
2001-10-08,Exact stationary state of a staggered stochastic hopping model,"We determine the $N$-particle stationary states of a staggered stochastic
hopping model with reflective boundaries. It is shown that the stationary
states are in fact so-called optimum ground states. Recursion relations in the
particle number for any $l$-point density correlation function will be derived.
Furthermore, the connection between reflective boundaries and the occurrence of
optimum ground states is examined. An explicit counterexample shows that
reflective boundaries do not enforce the stationary state to be an optimum
ground state.",0110142v1
2004-04-21,Photoluminescence of p-doped quantum wells with strong spin splitting,"The spectroscopic properties of a spin polarized two-dimensional hole gas are
studied in modulation doped (Cd,Mn)Te quantum wells. The giant Zeeman effect
induces a significant spin splitting even at very small values of the applied
field. Several methods of measuring the carrier density (Hall effect, filling
factors of the Landau levels at high field, various manifestations of
Moss-Burstein shifts) are described and calibrated. The value of the spin
splitting needed to fully polarize the hole gas, evidences a strong enhancement
of the spin susceptibility of the hole gas due to carrier-carrier interaction.
At small values of the spin splitting, whatever the carrier density (non zero)
is, photoluminescence lines are due to the formation of charged excitons in the
singlet state. Spectral shifts in photoluminescence and in transmission
(including an ""excitonic Moss-Bustein shift"") are observed and discussed in
terms of excitations of the partially or fully polarized hole gas. At large
spin splitting, and without changing the carrier density, the singlet state of
the charged exciton is destabilized in favour of a triplet state configuration
of holes. The binding energy of the singlet state is thus measured and found to
be independent of the carrier density (in contrast with the splitting between
the charged exciton and the neutral exciton lines). The state stable at large
spin splitting is close to the neutral exciton at low carrier density, and
close to an uncorrelated electron-hole pair at the largest values of the
carrier density achieved. The triplet state gives rise to a characteristic
double-line structure with an indirect transition to the ground state (with a
strong phonon replica) and a direct transition to an excited state of the hole
gas.",0404490v1
2017-07-17,From hadrons to quarks in neutron stars: a review,"We review the equation of state of matter in neutron stars from the solid
crust through the liquid nuclear matter interior to the quark regime at higher
densities. We focus in detail on the question of how quark matter appears in
neutron stars, and how it affects the equation of state. After discussing the
crust and liquid nuclear matter in the core we briefly review aspects of
microscopic quark physics relevant to neutron stars, and quark models of dense
matter based on the Nambu--Jona-Lasinio framework, in which gluonic processes
are replaced by effective quark interactions. We turn then to describing
equations of state useful for interpretation of both electromagnetic and
gravitational observations, reviewing the emerging picture of hadron-quark
continuity in which hadronic matter turns relatively smoothly, with at most
only a weak first order transition, into quark matter with increasing density.
We review construction of unified equations of state that interpolate between
the reasonably well understood nuclear matter regime at low densities and the
quark matter regime at higher densities. The utility of such interpolations is
driven by the present inability to calculate the dense matter equation of state
in QCD from first principles. As we review, the parameters of effective quark
models -- which have direct relevance to the more general structure of the QCD
phase diagram of dense and hot matter -- are constrained by neutron star mass
and radii measurements, in particular favoring large repulsive density-density
and attractive diquark pairing interactions. We describe the structure of
neutron stars constructed from the unified equations of states with crossover.
Lastly we present the current equations of state -- called ""QHC18"" for
quark-hadron crossover -- in a parametrized form practical for neutron star
modeling.",1707.04966v3
1999-01-13,Condensates Break Chiral Symmetry,"In the physical vacuum of QCD, the energy density of light-quark fields
strongly coupled to slowly varying gluon fields can be negative. The states
that drive this energy density lowest are condensates of pairs of quarks and
antiquarks of nearly opposite momenta. These quark-antiquark condensates break
chiral symmetry. They may also affect other features of hadronic physics, such
as the range of the strong force and the confinement of color.",9901285v1
2003-03-05,Density Matrix Kinetic Equation Describing a Passage of Fast Atomic Systems Through Matter,"The quantum-mechanical consideration of a passage of fast dimesoatoms through
matter is given. A set of quantum-kinetic equations for the density matrix
elements describing their internal state evolution is derived. It is shown that
probabilistic description of internal dynamics of hydrogen-like atoms is
impossible even at sufficiently low energies because of the ``accidental''
degeneracy of their energy levels.",0303040v1
2020-06-15,Continuity equations for entanglement,"We introduce a complex purity density and its associated current for pure
states of continuous variable systems. The scheme is constructed by analogy
with the notions of probability density and probability current. Taking
advantage of the formal continuity equations obtained this way we can introduce
an entanglement subdynamics. We suggest the use of the dimensionality of this
subdynamics as a potential measure of the complexity of entanglement. The
scheme also provides insights into the relation between the global and local
aspects of quantum correlations.",2006.08377v1
2001-09-21,Dark Matter Properties and Halo Central Densities,"Using an analytic model calibrated against numerical simulations, we
calculate the central densities of dark matter halos in a ``conventional'' cold
dark matter model with a cosmological constant (LCDM) and in a ``tilted'' model
(TLCDM) with slightly modified parameters motivated by recent analyses of
Ly-alpha forest data. We also calculate how warm dark matter (WDM) would modify
these predicted densities by delaying halo formation and imposing phase space
constraints. As a measure of central density, we adopt the quantity D_{V/2},
the density within the radius R_{V/2} at which the halo rotation curve falls to
half of its maximum value, in units of the critical density. We compare the
theoretical predictions to values of D_{V/2} estimated from the rotation curves
of dark matter dominated disk galaxies. Assuming that dark halos are described
by NFW profiles, our results suggest that the conventional LCDM model predicts
excessively high dark matter densities, unless there is some selection bias in
the data toward the low-concentration tail of the halo distribution. A WDM
model with particle mass 0.5-1 keV provides a better match to the observational
data. However, the modified cold dark matter model, TLCDM, fits the data
equally well, suggesting that the solution to the ``halo cores'' problem might
lie in moderate changes to cosmological parameters rather than radical changes
to the properties of dark matter. If CDM halos have the steeper density
profiles found by Moore et al., then neither conventional LCDM nor TLCDM can
reproduce the observed central densities.",0109392v1
2014-12-22,"Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory","In this work we review the mapping from densities to potentials in quantum
mechanics, which is the basic building block of time-dependent
density-functional theory and the Kohn-Sham construction. We first present
detailed conditions such that a mapping from potentials to densities is defined
by solving the time-dependent Schr\""odinger equation. We specifically discuss
intricacies connected with the unboundedness of the Hamiltonian and derive the
local-force equation. This equation is then used to set up an iterative
sequence that determines a potential that generates a specified density via
time propagation of an initial state. This fixed-point procedure needs the
invertibility of a certain Sturm-Liouville problem, which we discuss for
different situations. Based on these considerations we then present a
discussion of the famous Runge-Gross theorem which provides a density-potential
mapping for time-analytic potentials. Further we give conditions such that the
general fixed-point approach is well-defined and converges under certain
assumptions. Then the application of such a fixed-point procedure to lattice
Hamiltonians is discussed and the numerical realization of the
density-potential mapping is shown. We conclude by presenting an extension of
the density-potential mapping to include vector-potentials and photons.",1412.7052v2
2018-10-08,Hierarchical clustering that takes advantage of both density-peak and density-connectivity,"This paper focuses on density-based clustering, particularly the Density Peak
(DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a
new method which takes advantage of the individual strengths of these two
methods to yield a density-based hierarchical clustering algorithm. Our
investigation begins with formally defining the types of clusters DP and DBSCAN
are designed to detect; and then identifies the kinds of distributions that DP
and DBSCAN individually fail to detect all clusters in a dataset. These
identified weaknesses inspire us to formally define a new kind of clusters and
propose a new method called DC-HDP to overcome these weaknesses to identify
clusters with arbitrary shapes and varied densities. In addition, the new
method produces a richer clustering result in terms of hierarchy or dendrogram
for better cluster structures understanding. Our empirical evaluation results
show that DC-HDP produces the best clustering results on 14 datasets in
comparison with 7 state-of-the-art clustering algorithms.",1810.03393v2
2023-05-11,Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Buser,"Spectral clustering is one of the most popular clustering algorithms that has
stood the test of time. It is simple to describe, can be implemented using
standard linear algebra, and often finds better clusters than traditional
clustering algorithms like $k$-means and $k$-centers. The foundational
algorithm for two-way spectral clustering, by Shi and Malik, creates a
geometric graph from data and finds a spectral cut of the graph.
  In modern machine learning, many data sets are modeled as a large number of
points drawn from a probability density function. Little is known about when
spectral clustering works in this setting -- and when it doesn't. Past
researchers justified spectral clustering by appealing to the graph Cheeger
inequality (which states that the spectral cut of a graph approximates the
``Normalized Cut''), but this justification is known to break down on large
data sets.
  We provide theoretically-informed intuition about spectral clustering on
large data sets drawn from probability densities, by proving when a continuous
form of spectral clustering considered by past researchers (the unweighted
spectral cut of a probability density) finds good clusters of the underlying
density itself. Our work suggests that Shi-Malik spectral clustering works well
on data drawn from mixtures of Laplace distributions, and works poorly on data
drawn from certain other densities, such as a density we call the `square-root
trough'.
  Our core theorem proves that weighted spectral cuts have low weighted
isoperimetry for all probability densities. Our key tool is a new Cheeger-Buser
inequality for all probability densities, including discontinuous ones.",2305.06541v1
2007-03-12,Local density of states at zigzag edge of carbon nanotubes and graphene,"The electron-phonon matrix element for edge states of carbon nanotubes and
graphene at zigzag edges is calculated for obtaining renormalized energy
dispersion of the edge states. Self-energy correction by electron-phonon
interaction contributes to the energy dispersion of edge states whose energy
bandwidth is similar to phonon energy. Since the energy-uncertainty of the edge
state is larger than temperature, we conclude that the single-particle picture
of the edge state in not appropriate when the electron-phonon interaction is
taken into account. The longitudinal acoustic phonon mode contributes to the
matrix element through the on-site deformation potential because the
wavefunction of the edge state has an amplitude only on one of the two
sublattices. The on-site deformation potentials for the longitudinal and
in-plane tangential optical phonon modes are enhanced at the boundary. The
results of local density of states are compared with the recent experimental
data of scanning tunneling spectroscopy.",0703318v2
2018-04-13,Triangle geometry for qutrit states in the probability representation,"We express the matrix elements of the density matrix of the qutrit state in
terms of probabilities associated with artificial qubit states. We show that
the quantum statistics of qubit states and observables is formally equivalent
to the statistics of classical systems with three random vector variables and
three classical probability distributions obeying special constrains found in
this study. The Bloch spheres geometry of qubit states is mapped onto triangle
geometry of qubits. We investigate the triada of Malevich's squares describing
the qubit states in quantum suprematism picture and the inequalities for the
areas of the squares for qutrit (spin-1 system). We expressed quantum channels
for qutrit states in terms of a linear transform of the probabilities
determining the qutrit-state density matrix.",1804.04886v1
2023-01-22,Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits,"In this paper we study the entanglement in symmetric $N$-quDit systems. In
particular we use generalizations to $U(D)$ of spin $U(2)$ coherent states and
their projections on definite parity $\mathbb{C}\in\mathbb{Z}_2^{D-1}$
(multicomponent Schr\""odinger cat) states and we analyse their reduced density
matrices when tracing out $M<N$ quDits. The eigenvalues (or Schmidt
coefficients) of these reduced density matrices are completely characterized,
allowing to proof a theorem for the decomposition of a $N$-quDit Schr\""odinger
cat state with a given parity $\mathbb{C}$ into a sum over all possible
parities of tensor products of Schr\""odinger cat states of $N-M$ and $M$
particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied
and, in particular, for the (rescaled) double thermodynamic limit
($N,M\rightarrow\infty,\,M/N$ fixed), we reproduce and generalize to quDits
known results for photon loss of parity adapted coherent states of the harmonic
oscillator, thus providing an unified Schmidt decomposition for both
multi-quDits and (multi-mode) photons. These results allow to determine the
entanglement properties of these states and also their decoherence properties
under quDit loss, where we demonstrate the robustness of these states.",2301.09193v1
2019-04-09,Pseudogap and weak multifractality in disordered Mott charge-density-wave insulator,"The competition, coexistence and cooperation of various orders in
low-dimensional materials like spin, charge, topological orders and
charge-density-wave has been one of the most intriguing issues in condensed
matter physics. In particular, layered transition metal dichalcogenides provide
an ideal platform for studying such an interplay with a notable case of
1${T}$-TaS$_{2}$ featuring Mott-insulating ground state, charge-density-wave,
spin frustration and emerging superconductivity together. We investigated local
electronic states of Se-substituted 1${T}$-TaS$_{2}$ by scanning tunneling
microscopy/spectroscopy (STM/STS), where superconductivity emerges from the
unique Mott-CDW state. Spatially resolved STS measurements reveal that an
apparent V-shape pseudogap forms at the Fermi Level (E$_{F}$), with the origin
of the electronic states splitting and transformation from the Mott states, and
the CDW gaps are largely preserved. The formation of the pseudogap has little
correlation to the variation of local Se concentration, but appears to be a
global characteristics. Furthermore, the correlation length of local density of
states (LDOS) diverges at the Fermi energy and decays rapidly at high energies.
The spatial correlation shows a power-law decay close to the Fermi energy. Our
statistics analysis of the LDOS indicates that our system exhibits weak
multifractal behavior of the wave functions. These findings strongly support a
correlated metallic state induced by disorder in our system, which provides an
new insight into the novel mechanism of emerging superconductivity in the
two-dimensional correlated electronic systems.",1904.04508v1
2020-07-15,Excitation Energies from Thermally-Assisted-Occupation Density Functional Theory: Theory and Computational Implementation,"The time-dependent density functional theory (TDDFT) has been broadly used to
investigate the excited-state properties of various molecular systems. However,
the current TDDFT heavily relies on outcomes from the corresponding
ground-state density functional theory (DFT) calculations which may be prone to
errors due to the lack of proper treatment in the non-dynamical correlation
effects. Recently, thermally-assisted-occupation density functional theory
(TAO-DFT) [J.-D. Chai, \textit{J. Chem. Phys.} \textbf{136}, 154104 (2012)], a
DFT with fractional orbital occupations, was proposed, explicitly incorporating
the non-dynamical correlation effects in the ground-state calculations with low
computational complexity. In this work, we develop time-dependent (TD) TAO-DFT,
which is a time-dependent, linear-response theory for excited states within the
framework of TAO-DFT. With tests on the excited states of H$_{2}$, the first
triplet excited state ($1^3\Sigma_u^+$) was described well, with non-imaginary
excitation energies. TDTAO-DFT also yields zero singlet-triplet gap in the
dissociation limit, for the ground singlet ($1^1\Sigma_g^+$) and the first
triplet state ($1^3\Sigma_u^+$). In addition, as compared to traditional TDDFT,
the overall excited-state potential energy surfaces obtained from TDTAO-DFT are
generally improved and better agree with results from the equation-of-motion
coupled-cluster singles and doubles (EOM-CCSD).",2007.07590v2
2011-02-02,"Comments on ""Band gap and band parameters of InN and GaN from quasiparticle energy calculations based on exact-exchange density-functional theory"" [Appl. Phys. Lett. 89, 161919 (2006)]","An oversight of some previous density functional calculations of the band
gaps of wurtzite and cubic InN and of wurtzite GaN by Rinke et al. [Appl. Phys.
Lett. 89,161919, 2006] led to an inaccurate and misleading statement relative
to limitations of density functional theory (DFT) for the description of
electronic properties of these materials. These comments address this
statement. In particular, they show that some local density approximation (LDA)
calculations have correctly described or predicted electronic and related
properties of these systems [Phys. Rev. B 60, 1563, 1999; J. Appl. Phys. 96,
4297, 2004, and 97, 123708, 2005]. These successful calculations solved
self-consistently the system of equations defining LDA, i.e., the Kohn-Sham
equation and the equation giving the ground state charge density in terms of
the wave functions of the occupied states.",1102.0498v1
2014-11-03,Equation of state of nuclear matter from empirical constraints,"From empirically determined values of some of the characteristic constants
associated with homogeneous nuclear matter at saturation and sub-saturation
densities, within the framework of a Skyrme-inspired energy density functional,
we construct an equation of state (EoS) of nuclear matter.This EoS is then used
to predict values of density slope parameters of symmetry energy $L(\rho)$,
isoscalar incompressibility $K(\rho)$ and a few related quantities. The close
consonance of our predicted values with the currently available ones for the
density dependence of symmetry energy and incompressibility gleaned from
diverse approaches offers the possibility that our method may help in settling
their values in tighter bounds. Extrapolation of our EoS at supranormal
densities shows that it is in good harmony with the one extracted from
experimental data.",1411.0404v1
2015-02-05,Relativistic density functional theory for finite nuclei and neutron stars,"The main goal of the present contribution is a pedagogical introduction to
the fascinating world of neutron stars by relying on relativistic density
functional theory. Density functional theory provides a powerful--and perhaps
unique--framework for the calculation of both the properties of finite nuclei
and neutron stars. Given the enormous densities that may be reached in the core
of neutron stars, it is essential that such theoretical framework incorporates
from the outset the basic principles of Lorentz covariance and special
relativity. After a brief historical perspective, we present the necessary
details required to compute the equation of state of dense, neutron-rich
matter. As the equation of state is all that is needed to compute the structure
of neutron stars, we discuss how nuclear physics--particularly certain kind of
laboratory experiments--can provide significant constrains on the behavior of
neutron-rich matter.",1502.01559v1
2012-04-29,On early onset of quark number density at zero temperature,"We study a longstanding problem in lattice QCD at low temperature and nonzero
quark chemical potential on an onset of the quark number density at
$\mu=m_\pi/2$. We introduce a physical parametrization of the eigenvalues in
the reduction formula of the fermion determinant. It is shown that the
parametrization reduces the quark number density operator to an expression with
the Fermi distribution of the quark. For each configuration, the eigenvalues of
the reduced matrix correspond to one-particle energy states of a quark. The gap
of the eigenspectrum of the reduced matrix corresponds to the gap of the energy
states, which causes the $\mu$-independence of the fermion determinant for
small $\mu$ at T=0. Once $\mu$ exceeds the gap, the quark number density
becomes nonzero for each configuration, which causes the early onset of the
quark number density.",1204.6480v1
2021-04-29,Machine learning band gaps from the electron density,"A remarkable consequence of the Hohenberg-Kohn theorem of density functional
theory is the existence of an injective map between the electronic density and
any observable of the many electron problem in an external potential. In this
work, we study the problem of predicting a particular observable, the band gap
of semiconductors and band insulators, from the knowledge of the local
electronic density. Using state-of-the-art machine learning techniques, we
predict the experimental band gaps from computationally inexpensive density
functional theory calculations. We propose a modified Behler-Parrinello (BP)
architecture that greatly improves the model capacity while maintaining the
symmetry properties of the BP architecture. Using this scheme, we obtain band
gaps at a level of accuracy comparable to those obtained with state of the art
and computationally intensive hybrid functionals, thus significantly reducing
the computational cost of the task.",2104.14351v2
2008-02-11,Local density of states of 1D Mott insulators and CDW states with a boundary,"We determine the local density of states (LDOS) of one-dimensional
incommensurate charge density wave (CDW) states in the presence of a strong
impurity potential, which is modeled by a boundary. We find that the CDW gets
pinned at the impurity, which results in a singularity in the Fourier transform
of the LDOS at momentum 2k_F. At energies above the spin gap we observe
dispersing features associated with the spin and charge degrees of freedom
respectively. In the presence of an impurity magnetic field we observe the
formation of a bound state localized at the impurity. All of our results carry
over to the case of one dimensional Mott insulators by exchanging the roles of
spin and charge degrees of freedom. We discuss the implications of our result
for scanning tunneling microscopy experiments on spin-gap systems such as
two-leg ladder cuprates and 1D Mott insulators.",0802.1544v2
2021-10-05,Peaks of sound velocity in two color dense QCD: quark saturation effects and semishort range correlations,"We discuss stiffening of dense matter in two color QCD (QC$_2$D) where
hadrons are mesons and diquark baryons. We study two models which describe a
transition of matter from the Bose-Einstein-Condensation regime at low density
to the Bardeen-Cooper-Schrieffer regime at high density. The first model is
based on coherent states of diquarks, and the second is the Nambu-Jona-Lasinio
model with diquark pairing terms. We particularly focus on how quark states are
occupied as baryon density increases. We find that, due to the occupied quark
levels, the ideal gas picture of diquarks breaks down at density significantly
less than the density where baryon cores overlap. The saturation of quark
states at low momenta stiffens equations of state. We also study the effects of
interactions which depend on the quark occupation probability. We argue that
equations of state become very stiff when the bulk part of the quark Fermi sea
has the effective repulsion but the Fermi surface enjoys the attractive
correlations. This disparity for different momentum domains is possible due to
the strong channel dependence in gluon exchanges with momentum transfer of
$0.2-1$ GeV. These concepts can be transferred from QC$_2$D to QCD in any
numbers of colors.",2110.02100v2
2009-12-28,Amplification of NOON States,"We examine the behavior of a Non Gaussian state like NOON state under phase
insensitive amplification. We derive analytical result for the density matrix
of the NOON state for arbitrary gain of the amplifier. We consider cases of
both symmetric and antisymmetric amplification of the two modes of the NOON
state. We quantitatively evaluate the loss of entanglement by the amplifier in
terms of the logarithmic negativity parameter. We find that NOON states are
more robust than their Gaussian counterparts.",0912.5134v1
2004-04-29,Vortex formation in quantum dots in high magnetic fields,"We study electronic structures of two-dimensional quantum dots in high
magnetic fields using the density-functional theory (DFT) and the exact
diagonalization (ED). With increasing magnetic field, beyond the formation of
the totally spin-polarized maximum density droplet (MDD) state, the DFT gives
the ground-state total angular momentum as a continuous function with
well-defined plateaus. The plateaus agree well with the magic angular momenta
of the ED calculation. By constructing a conditional wave function from the
Kohn-Sham states we show that vortices enter the quantum dot one-by-one at the
transition to the state with the adjacent magic angular momentum. Vortices are
also observed outside the high-density region of the quantum dot. These
findings are compared to the ED results and we report a significant agreement.
We study also interpretations and limitations of the density functional
approach in these calculations.",0404704v1
2009-06-27,Steady-state spin densities and currents,"This article reviews steady-state spin densities and spin currents in
materials with strong spin-orbit interactions. These phenomena are intimately
related to spin precession due to spin-orbit coupling which has no equivalent
in the steady state of charge distributions. The focus will be initially on
effects originating from the band structure. In this case spin densities arise
in an electric field because a component of each spin is conserved during
precession. Spin currents arise because a component of each spin is continually
precessing. These two phenomena are due to independent contributions to the
steady-state density matrix, and scattering between the conserved and
precessing spin distributions has important consequences for spin dynamics and
spin-related effects in general. In the latter part of the article extrinsic
effects such as skew scattering and side jump will be discussed, and it will be
shown that these effects are also modified considerably by spin precession.
Theoretical and experimental progress in all areas will be reviewed.",0906.5111v1
2011-08-03,A Density Matrix Renormalization Group Method Study of Optical Properties of Porphines and Metalloporphines,"The symmetrized Density-Matrix-Renormalization-Group (DMRG) method is used to
study linear and nonlinear optical properties of Free base porphine and
metallo-porphine. Long-range interacting model, namely, Pariser-Parr-Pople
(PPP) model is employed to capture the quantum many body effect in these
systems. The non-linear optical coefficients are computed within correction
vector method. The computed singlet and triplet low-lying excited state
energies and their charge densities are in excellent agreement with
experimental as well as many other theoretical results. The rearrangement of
the charge density at carbon and nitrogen sites, on excitation, is discussed.
From our bond order calculation, we conclude that porphine is well described by
the 18-annulenic structure in the ground state and the molecule expands upon
excitation. We have modelled the regular metalloporphine by taking an effective
electric field due to the metal ion and computed the excitation spectrum.
Metalloporphines have $D_{4h}$ symmetry and hence have more degenerate excited
states. The ground state of Metalloporphines show 20-annulenic structure, as
the charge on the metal ion increases. The linear polarizability seems to
increase with the charge initially and then saturates. The same trend is
observed in third order polarizability coefficients.",1108.0854v1
2015-07-24,Exogenous Quantum Operator Logic Based on Density Operators,"Although quantum logic by using exogenous approach has been proposed for
reasoning about closed quantum systems, an improvement would be worth to study
quantum logic based on density operators instead of unit vectors in the state
logic point of view. In order to achieve this, we build an exogenous quantum
operator logic(EQOL) based on density operators for reasoning about open
quantum systems. We show that this logic is sound and complete. Just as the
exogenous quantum propositional logic(EQPL), by applying exogenous approach,
EQOL is extended from the classical propositional logic, and is used to
describe the state logic based on density operators. As its applications, we
confirm the entanglement property about Bell states by reasoning and logical
argument, also verify the existence of eavesdropping about the basic BB84
protocol. As a novel type of mathematical formalism for open quantum systems,
we introduce an exogenous quantum Markov chain(EQMC) where its quantum states
are labelled using EQOL formulae. Then, an example is given to illustrate the
termination verification problem of a generalized quantum loop program
described using EQMC.",1507.06722v1
2018-06-22,Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems,"In this article we study transitions from low-density states towards
high-density states in bistable plasma-condensate systems. We take into account
an anisotropy in transference of adatoms between neighbour layers induced by
the electric field near substrate. We derive the generalized one-layer model by
assuming that the strength of the electric field is subjected to both periodic
oscillations and multiplicative fluctuations. By studying the homogeneous
system we discuss the corresponding mean passage time. In the limit of weak
fluctuations, we show the optimization of the mean passage time with variation
in the frequency of periodic driving in the non-adiabatic limit. Noise induced
effects corresponding to asynchronization and acceleration in the transition
dynamics are studied in detail.",1806.08526v2
2003-11-27,On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy,"The challenge of equality in the strong subadditivity inequality of entropy
is approached via a general additivity of correlation information in terms of
nonoverlapping clusters of subsystems in multipartite states (density
operators). A family of tripartite states satisfying equality is derived.",0311193v1
2021-12-23,Influence of the nuclear symmetry energy slope on observables of compact stars with $Δ$-admixed hypernuclear matter,"In this work, we study the effects of nuclear symmetry energy slope on
neutron star dense matter equation of state and its impact on neutron star
observables (mass-radius, tidal response). We construct the equation of state
within the framework of covariant density functional theory implementing
coupling schemes of non-linear and density-dependent models with viability of
heavier non-nucleonic degrees of freedom. The slope of symmetry energy
parameter ($L_{\text{sym}}$) is adjusted following density-dependence of
isovector meson coupling to baryons. We find that smaller values of
$L_{\text{sym}}$ at saturation favour early appearance of $\Delta$-resonances
in comparison to hyperons leading to latter's threshold at higher matter
densities. We also investigate the dependence of $L_{\text{sym}}$ on tidal
deformability and compactness parameter of a $1.4~M_\odot$ neutron star for
different equation of states and observe similar converging behaviour for
larger $L_{\text{sym}}$ values.",2112.12629v3
2021-07-11,Computational Complexity of the Ground State Energy Density Problem,"We study the complexity of finding the ground state energy density of a local
Hamiltonian on a lattice in the thermodynamic limit of infinite lattice size.
We formulate this rigorously as a function problem, in which we request an
estimate of the ground state energy density to some specified precision; and as
an equivalent promise problem, $\mathsf{GSED}$, in which we ask whether the
ground state energy density is above or below specified thresholds.
  The ground state energy density problem is unusual, in that it concerns a
single, fixed Hamiltonian in the thermodynamic limit, whose ground state energy
density is just some fixed, real number. The only input to the computational
problem is the precision to which to estimate this fixed real number,
corresponding to the ground state energy density. Hardness of this problem for
a complexity class therefore implies that the solutions to all problems in the
class are encoded in this single number (analogous to Chaitin's constant in
computability theory).
  This captures computationally the type of question most commonly encountered
in condensed matter physics, which is typically concerned with the physical
properties of a single Hamiltonian in the thermodynamic limit. We show that for
classical, translationally invariant, nearest neighbour Hamiltonians on a 2D
square lattice,
$\mathsf{P}^{\mathsf{NEEXP}}\subseteq\mathsf{EXP}^{\mathsf{GSED}}\subseteq
\mathsf{EXP}^{\mathsf{NEXP}}$, and for quantum Hamiltonians
$\mathsf{P}^{\mathsf{NEEXP}}\subseteq\mathsf{EXP}^{\mathsf{GSED}}\subseteq
\mathsf{EXP}^{\mathsf{QMA}_{EXP}}$. With some technical caveats on the oracle
definitions, the $\mathsf{EXP}$ in some of these results can be strengthened to
$\mathsf{PSPACE}$. We also give analogous complexity bounds for the function
version of $\mathsf{GSED}$.",2107.05060v1
2015-11-26,A Simple Hubbard Model for the Excited States of $π$ Conjugated -acene Molecules,"In this paper we present a model for the electronic excited states of $\pi$
conjugated -acene molecules such as tetracene, pentacene, and hexacene. We use
a simple Hubbard model with a limited basis to describe the low lying
excitations with reasonable quantitative accuracy. We are able to produce
semi-analytic wavefunctions for the electronic states of the system, which
allows us to compute the density correlation functions for various states such
as the ground state, the first two singly excited states, and the lowest lying
doubly excited state. We show that in this lowest lying doubly excited state, a
state speculated to play a role in the singlet fission process, the electrons
and holes behave in a triplet-like manner. We also compute the two-photon
absorption of these -acenes, and show that per number density it is comparable
to that of other organic molecules such as coronene and
hexa-peri-hexabenzocoronene (HBC).",1511.09396v3
2021-11-30,Saha equilibrium for metastable bound states and dark matter freeze-out,"The formation and decay of metastable bound states can significantly decrease
the thermal-relic dark matter density, particularly for dark matter masses
around and above the TeV scale. Incorporating bound-state effects in the dark
matter thermal decoupling requires in principle a set of coupled Boltzmann
equations for the bound and unbound species. However, decaying bound states
attain and remain in a quasi-steady state. Here we prove in generality that
this reduces the coupled system into a single Boltzmann equation of the
standard form, with an effective cross-section that describes the interplay
among bound-state formation, ionisation, transitions and decays. We derive a
closed-form expression for the effective cross-section for an arbitrary number
of bound states, and show that bound-to-bound transitions can only increase it.
Excited bound levels may thus decrease the dark matter density more
significantly than otherwise estimated. Our results generalise the Saha
ionisation equilibrium to metastable bound states, potentially with
applications beyond the dark matter thermal decoupling.",2112.00042v2
2000-03-24,Remark on multi-particle observables and entangled states with constant complexity,"We show that every density matrix of an n-particle system prepared by a
quantum network of constant depth is asymptotically commuting with the
mean-field observables. We introduce certain pairs of hypersurfaces in the
space of density matrices and give lower bounds for the depth of a network
which prepares states lying outside those pairs. The measurement of an
observable which is not asymptotically commuting with the mean-field
observables requires a network of depth in the order of log n, if one demands
the measurement to project the state into the eigenspace of the measured
observable.",0003117v1
2001-01-24,Quantum Data Compression of Ensembles of Mixed States with Commuting Density Operators,"We provide a rate distortion interpretation of the problem of quantum data
compression of ensembles of mixed states with commuting density operators.
There are two versions of this problem. In the visible case the sequence of
states is available to the encoder and in the blind or hidden case the encoder
may access only a sequence of measurements. We find the exact optimal
compression rates for both the visible and hidden cases. Our analysis includes
the scenario in which asymptotic reconstruction is imperfect.",0101119v1
2011-03-09,Self-consistent model of unipolar transport in organic semiconductor diodes: accounting for a realistic density-of-states distribution,"A self-consistent, mean-field model of charge-carrier injection and unipolar
transport in an organic semiconductor diode is developed utilizing the
effective transport energy concept and taking into account a realistic
density-of-states distribution as well as the presence of trap states in an
organic material. The consequences resulting from the model are discussed
exemplarily on the basis of an indium tin oxide/organic semiconductor/metallic
conductor structure. A comparison of the theory to experimental data of a
unipolar indium tin oxide/poly-3-hexyl-thiophene/Al device is presented.",1103.1752v1
2013-10-07,The Spectrum of Light States in Large N Minimal Models,"$W_{N,k}$ minimal models possess an interesting class of `light' primaries
which control much of the low energy density of states in the large $N$ 't
Hooft limit. In this paper we conduct a detailed exploration of their
distribution using a combination of numerical and analytical techniques. We
also make some observations about the density of states of the full CFT. Our
results appear to support the contention that there is no finite temperature
analogue of the Hawking-Page transition in these systems.",1310.1744v2
2013-11-15,Constraints on Skyrme Equations of State from Properties of Doubly Magic Nuclei and Ab-Initio Calculations of Low-Density Neutron Matter,"We use properties of doubly-magic nuclei and ab-initio calculations of
low-density neutron matter to constrain Skyrme equations of state for
neutron-rich conditions. All of these properties are consistent with a Skyrme
functional form and a neutron-matter equation of state that depends on three
parameters. With a reasonable range for the neutron-matter effective mass, the
values of the two other Skyrme parameters are well constrained. This leads to
predictions for other quantities. The neutron skins for $^{208}$Pb and
$^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Other
results including the dipole polarizability are discussed.",1311.3957v1
2023-12-07,Asymmetrical post quench transport in an embedded parity time symmetric Su-Schrieffer-Heeger system,"We study the effect of PT-symmetric non-hermiticity on the transport of edge
state probability density arising as a result of a quench. A hybrid system
involving a PT-symmetric SSH region sandwiched between two plain SSH systems is
designed to study the dynamics. Geometrical arguments and numerical
calculations were made to ascertain the nature of edge states. We then compute
the quench dynamics numerically and demonstrate that the post-quench
probability density light cones exhibit contrasting shapes as a result of
asymmetrical reflections from the non-Hermitian part of the system depending on
the direction of propagation of the transporting wave and, hence, on the
initial localization of the edge state.",2312.03997v1
2005-05-23,Singular behavior of an entangled state for a one-dimensional quantum spin system,"We studied the entangled state for a one-dimensional $S=1/2$
antiferromagnetic quantum spin chain in a transverse field. We calculate the
ground state using the density matrix renormalization group and discuss how the
entangled state changes around a quantum phase transition (QPT) point. By
analyzing concurrence $C(\rho)$ for two-qubit density matrix $\rho$ after the
Lewenstein-Sanpera decomposition, $\rho=\Lambda \rho_s + (1-\Lambda) \rho_e $,
where $\rho_s$ is a separable density matrix and $\rho_e$ is a pure entangled
state obtained by a linear combination of Bell states, we find singular
behaviors both in $C(\rho_e)$ and $1-\Lambda$ at the QPT point.&#12288;
$C(\rho_e)$ includes the effects of quantum fluctuations, which manifest the
competition between the antiferromagnetic spin fluctuation and the effect of
transverse field in the transverse Ising model. The quantum fluctuation shows
the singular maximum at the QPT point as expected from the general picture of
phase transition. In contrast, $1-\Lambda$ reveals the singular minimum at QPT
point.",0505168v2
2019-01-11,Bosonic Fractional Quantum Hall States on a Finite Cylinder,"We investigate the ground state properties of a bosonic Harper-Hofstadter
model with local interactions on a finite cylindrical lattice with filling
fraction $\nu=1/2$. We find that our system supports topologically ordered
states by calculating the topological entanglement entropy, and its value is in
good agreement with the theoretical value for the $\nu=1/2$ Laughlin state. By
exploring the behaviour of the density profiles, edge currents and
single-particle correlation functions, we find that the ground state on the
cylinder shows all signatures of a fractional quantum Hall state even for large
values of the magnetic flux density. Furthermore, we determine the dependence
of the correlation functions and edge currents on the interaction strength. We
find that depending on the magnetic flux density, the transition towards
Laughlin-like behaviour can be either smooth or happens abruptly for some
critical interaction strength.",1901.03595v2
2021-11-01,"Topological Phases in AB-Stacked MoTe$_2$/WSe$_2$: $\mathbb{Z}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves","We present a theory on the quantum phase diagram of AB-stacked
MoTe$_2$/WSe$_2$ using a self-consistent Hartree-Fock calculation performed in
the plane-wave basis, motivated by the observation of topological states in
this system. At filling factor $\nu=2$ (two holes per moir\'e unit cell),
Coulomb interaction can stabilize a $\mathbb{Z}_2$ topological insulator by
opening a charge gap. At $\nu=1$, the interaction induces three classes of
competing states, spin density wave states, an in-plane ferromagnetic state,
and a valley polarized state, which undergo first-order phase transitions tuned
by an out-of-plane displacement field. The valley polarized state becomes a
Chern insulator for certain displacement fields. Moreover, we predict a
topological charge density wave forming a honeycomb lattice with ferromagnetism
at $\nu=2/3$. Future directions on this versatile system hosting a rich set of
quantum phases are discussed.",2111.01152v3
2022-04-18,Challenges for variational reduced-density-matrix theory: Total angular momentum constraints,"The variational two-electron reduced density matrix (v2RDM) method is
generalized for the description of total angular momentum ($J$) and projection
of total angular momentum ($M_{J}$) states in atomic systems described by
non-relativistic Hamiltonians, and it is shown that the approach exhibits
serious deficiencies. Under ensemble $N$-representability constraints, v2RDM
theory fails to retain the appropriate degeneracies among various $J$ states
for fixed spin ($S$) and orbital angular momentum ($L$), and, for fixed $L$,
$S$, and $J$, the manifold of $M_{J}$ states are not necessarily degenerate.
Moreover, a substantial energy error is observed for a system for which the
two-electron reduced density matrix is exactly ensemble $N$-representable; in
this case, the error stems from violations in pure-state $N$-representability
conditions. Unfortunately, such violations do not appear to be good indicators
of the reliability of energies from v2RDM theory in general. Several states are
identified for which energy errors are near zero and yet pure-state conditions
are clearly violated.",2204.08539v3
2024-01-31,"Reversible, Irreversible and Mixed Regimes for Periodically Driven Disks in Random Obstacle Arrays","We examine an assembly of repulsive disks interacting with a random obstacle
array under a periodic drive, and find a transition from reversible to
irreversible dynamics as a function of drive amplitude or disk density. At low
densities and drives, the system rapidly forms a reversible state where the
disks return to their exact positions at the end of each cycle. In contrast, at
high amplitudes or high densities, the system enters an irreversible state
where the disks exhibit normal diffusion. Between these two regimes, there can
be a glassy irreversible state where most of the system is reversible, but
localized irreversible regions are present that are prevented from spreading
through the system due to a screening effect from the obstacles. We also find
states that we term combinatorial reversible states in which the disks return
to their original positions after multiple driving cycles. In these states,
individual disks exchange positions but form the same configurations during the
subcycles of the larger reversible cycle.",2401.18042v1
2008-05-31,Doping-insensitive density-of-states suppression in polycrystalline iron-based superconductor SmO$_{1-x}$F$_{x}$FeAs,"We investigated the temperature dependence of the density-of-states in the
iron-based superconductor SmO_1-xF_xFeAs (x=0, 0.12, 0.15, 0.2) with high
resolution angle-integrated photoemission spectroscopy. The density-of-states
suppression is observed with decreasing temperature in all samples, revealing
two characteristic energy scales (10meV and 80meV). However, no obvious doping
dependence is observed. We argue that the 10meV suppression is due to an
anomalously doping-independent normal state pseudogap, which becomes the
superconducting gap once in the superconducting state; and alert the
possibility that the 80meV-scale suppression might be an artifact of the
polycrystalline samples.",0806.0078v1
2019-05-28,Stationary states for underdamped anharmonic oscillators driven by Cauchy noise,"Using methods of stochastic dynamics, we have studied stationary states in
the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape
of stationary states depend both on the potential type and the damping. If the
damping is strong enough, for potential wells which in the overdamped regime
produce multimodal stationary states, stationary states in the underdamped
regime can be multimodal with the same number of modes like in the overdamped
regime. For the parabolic potential, the stationary density is always unimodal
and it is given by the two dimensional $\alpha$-stable density. For the mixture
of quartic and parabolic single-well potentials the stationary density can be
bimodal. Nevertheless, the parabolic addition, which is strong enough, can
destroy bimodlity of the stationary state.",1905.12078v2
2020-03-15,Multi-State Pair-Density Functional Theory,"Multiconfiguration pair-density functional theory (MC-PFDT) has previously
been applied successfully to carry out ground-state and excited-state
calculations. However, because it includes no interaction between electronic
states, MC-PDFT calculations can give an unphysical double crossing of
potential energy surfaces (PESs) in a region near a conical intersection. We
have recently proposed state-interaction pair-density functional theory
(SI-PDFT) to treat nearly degenerate states; although this method is
successful, it is inconvenient because two SCF calculations and two sets of
orbitals are required and because it puts the ground state on an unequal
footing with the excited states. Here we propose two new methods, called
extended-multi-state-PDFT (XMS-PDFT) and variational-multi-state-PDFT
(VMS-PDFT), that generate the intermediate states in a balanced way with a
single set of orbitals. The former uses the intermediate states proposed by
Granovsky for extended multiconfiguration quasidegenerate perturbation theory
(XMC-QDPT); the latter obtains the intermediate states by maximizing the sum of
the MC-PDFT energies for the intermediate states. We also propose a Fourier
series expansion to make the variational optimizations of the VMS-PDFT method
convenient, and we implement this method (FMS-PDFT) both for conventional
configuration-interaction solvers and for density-matrix-renormalization-group
solvers. The new methods are tested for eight systems exhibiting avoided
crossings among two to six states. The FMS-PDFT method is successful for all
eight test cases studied in the paper, and XMS-PDFT is successful for all of
them except the mixed-valence case. Since both XMS-PDFT and VMS-PDFT are less
expensive than XMS-CASPT2, they will allow well-correlated calculations on much
larger systems for which perturbation theory is unaffordable.",2003.06744v2
2021-04-12,Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning,"We use voxel deep neural networks to predict energy densities and functional
derivatives of electron kinetic energies for the Thomas-Fermi model and
Kohn-Sham density functional theory calculations. We show that the ground-state
electron density can be found via direct minimization for a graphene lattice
without any projection scheme using a voxel deep neural network trained with
the Thomas-Fermi model. Additionally, we predict the kinetic energy of a
graphene lattice within chemical accuracy after training from only 2 Kohn-Sham
density functional theory (DFT) calculations. We identify an important sampling
issue inherent in Kohn-Sham DFT calculations and propose future work to rectify
this problem. Furthermore, we demonstrate an alternative, functional
derivative-free, Monte Carlo based orbital free density functional theory
algorithm to calculate an accurate 2-electron density in a double inverted
Gaussian potential with a machine-learned kinetic energy functional.",2104.05408v3
2021-05-17,Nuclear energy density functionals from machine learning,"Machine learning is employed to build an energy density functional for
self-bound nuclear systems for the first time. By learning the kinetic energy
as a functional of the nucleon density alone, a robust and accurate
orbital-free density functional for nuclei is established. Self-consistent
calculations that bypass the Kohn-Sham equations provide the ground-state
densities, total energies, and root-mean-square radii with a high accuracy in
comparison with the Kohn-Sham solutions. No existing orbital-free density
functional theory comes close to this performance for nuclei. Therefore, it
provides a new promising way for future developments of nuclear energy density
functionals for the whole nuclear chart.",2105.07696v2
2007-03-21,Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in presence of a hard core potential:A stable ferromagnetic state,"We use different types of determinantal Hartree-Fock (HF) wave functions to
calculate variational bounds for the ground state energy of spin-half fermions
in volume V_0, with mass m, electric charge zero, and magnetic moment mu, which
are interacting through long range magnetic dipole-dipole interaction. We find
that at high densities when the average inter particle distance r_0 becomes
small compared to the magnetic length r_m, a ferromagnetic state with
spheroidal occupation function, involving quadrupolar deformation, gives a
lower energy compared to the variational energy for the uniform paramagnetic
state. This HF variational bound to the ground state energy turns out to have a
lower energy than our earlier calculation in which instead of a determinantal
wavefunction we had used a positive semi-definite single particle density
matrix operator whose eigenvalues, having quadrupolar deformation, were allowed
to take any value from 0 to 1. This system is of course still unstable towards
infinite density collapse, but we show here explicitly that a suitable short
range repulsive (hard core) interaction of strength U_0 and range a can stop
this collapse.The existence of a stable high density ferromagnetic state with
spheroidal occupation function is possible as long as the ratio of hard-core
and magnetic dipole coupling constants is not very small compared to 1.",0703547v1
2005-05-20,Spin-polarized surface states close to adatoms on Cu(111),"We present a theoretical study of surface states close to 3d transition metal
adatoms (Cr, Mn, Fe, Co, Ni and Cu) on a Cu(111) surface in terms of an
embedding technique using the fully relativistic Korringa-Kohn-Rostoker method.
For each of the adatoms we found resonances in the s-like states to be
attributed to a localization of the surface states in the presence of an
impurity. We studied the change of the s-like densities of states in the
vicinity of the surface state band-edge due to scattering effects mediated via
the adatom's d-orbitals. The obtained results show that a magnetic impurity
causes spin-polarization of the surface states. In particular, the long-range
oscillations of the spin-polarized s-like density of states around an Fe adatom
are demonstrated.",0505505v2
2013-06-21,How are mortality rates affected by population density?,"Biologists have found that the death rate of cells in culture depends upon
their spatial density. Permanent ""Stay alive"" signals from their neighbours
seem to prevent them from dying. In a previous paper (Wang et al. 2013) we gave
evidence for a density effect for ants. In this paper we examine whether there
is a similar effect in human demography. We find that although there is no
observable relationship between population density and overall death rates,
there is a clear relationship between density and the death rates of young
age-groups. Basically their death rates decrease with increasing density.
However, this relationship breaks down around 300 inhabitants per square
kilometre. Above this threshold the death rates remains fairly constant. The
same density effect is observed in Canada, France, Japan and the United States.
We also observe a striking parallel between the density effect and the
so-called marital status effect in the sense that they both lead to higher
suicide rates and are both enhanced for younger age-groups. However, it should
be noted that the strength of the density effect is only a fraction of the
strength of the marital status effect. In spite of the fact that this parallel
does not give us an explanation by itself, it invites us to focus on
explanations that apply to both effects. In this light the ""Stay alive""
paradigm set forth by Prof. Martin Raff appears as a natural interpretation. It
can be seen as an extension of the ""social ties"" framework proposed at the end
of the 19th century by the sociologist Emile Durkheim in his study about
suicide.",1306.5179v1
2021-06-02,Feedback Interconnected Mean-Field Density Estimation and Control,"Swarm robotic systems have foreseeable applications in the near future.
Recently, there has been an increasing amount of literature that employs
mean-field partial differential equations (PDEs) to model the time-evolution of
the probability density of swarm robotic systems and uses density feedback to
design stabilizing control laws that act on individuals such that their density
converges to a target profile. However, it remains largely unexplored
considering problems of how to estimate the mean-field density, how the density
estimation algorithms affect the control performance, and whether the
estimation performance in turn depends on the control algorithms. In this work,
we focus on studying the interplay of these algorithms. Specifically, we
propose new density control laws which use the mean-field density and its
gradient as feedback, and prove that they are globally input-to-state stable
(ISS) with respect to estimation errors. Then, we design filtering algorithms
to estimate the density and its gradient separately, and prove that these
estimates are convergent assuming the control laws are known. Finally, we show
that the feedback interconnection of these estimation and control algorithms is
still globally ISS, which is attributed to the bilinearity of the PDE system.
An agent-based simulation is included to verify the stability of these
algorithms and their feedback interconnection.",2106.00899v3
2023-04-19,Density-Insensitive Unsupervised Domain Adaption on 3D Object Detection,"3D object detection from point clouds is crucial in safety-critical
autonomous driving. Although many works have made great efforts and achieved
significant progress on this task, most of them suffer from expensive
annotation cost and poor transferability to unknown data due to the domain gap.
Recently, few works attempt to tackle the domain gap in objects, but still fail
to adapt to the gap of varying beam-densities between two domains, which is
critical to mitigate the characteristic differences of the LiDAR collectors. To
this end, we make the attempt to propose a density-insensitive domain adaption
framework to address the density-induced domain gap. In particular, we first
introduce Random Beam Re-Sampling (RBRS) to enhance the robustness of 3D
detectors trained on the source domain to the varying beam-density. Then, we
take this pre-trained detector as the backbone model, and feed the unlabeled
target domain data into our newly designed task-specific teacher-student
framework for predicting its high-quality pseudo labels. To further adapt the
property of density-insensitivity into the target domain, we feed the teacher
and student branches with the same sample of different densities, and propose
an Object Graph Alignment (OGA) module to construct two object-graphs between
the two branches for enforcing the consistency in both the attribute and
relation of cross-density objects. Experimental results on three widely adopted
3D object detection datasets demonstrate that our proposed domain adaption
method outperforms the state-of-the-art methods, especially over
varying-density data. Code is available at
https://github.com/WoodwindHu/DTS}{https://github.com/WoodwindHu/DTS.",2304.09446v1
2024-03-15,Experimental Measurements of the Granular Density of Modes via Impact,"The jamming transition is an important feature of granular materials, with
prior work showing an excess of low frequency modes in the granular analog to
the density of states, the granular density of modes. In this work, we present
an experimental method for acoustically measuring the granular density of modes
using a single impact event to excite vibrational modes in an experimental,
three dimensional, granular material. We test three different granular
materials, all of which are composed of spherical beads. The first two systems
are monodisperse collections of either 6 mm or 8 mm diameter beads. The third
system is a bidisperse mixture of the previous two bead sizes. During data
collection, the particles are confined to a box; on top of this box, and
resting on the granular material, is a light, rigid sheet onto which pressure
can be applied to the system. To excite the material, a steel impactor ball is
dropped on top of the system. The response of the granular material to the
impact pulse is recorded by piezoelectric sensors buried throughout the
material, and the density of modes is computed from the spectrum of the
velocity autocorrelation of these sensors. Our measurements of the density of
modes show more low frequency modes at low pressure, consistent with previous
experimental and numerical results, as well as several low frequency peaks in
the density of modes that shift with applied pressure. Finally, we also see
that the density of modes falls off at a wavelength on the order of twice the
particle diameter, which is reminiscent of the Debye frequency.",2403.10322v1
2010-05-03,Quantum theory for a total system including one internal measuring apparatus,"In this paper, we extend the standard formalism of quantum mechanics to a
quantum theory for a total system including one internal measuring apparatus.
The internality of the measuring apparatus implies that different decomposition
of a given density operator for the internal measuring apparatus into mixture
of pure states may have different physical implications. We use `specified
mixed-state description' to call a density operator with a specified
decomposition into mixture of pure states. The proposed theory has three basic
assumptions, which roughly speaking have the following contents: (i) Physical
states of the total system can be associated with vectors in the total Hilbert
space; (ii) the dynamical evolution of a state vector obeys Schr\""{o}dinger
equation; and (iii) under a principle of compatible description and certain
non-transition condition, a pure-vector description of the total system may
imply the existence of certain specified mixed-state description. The principle
of compatible description states that different mathematical descriptions for
the same physical state of the total system must give consistent predictions
for results of measurements performed by the internal measuring apparatus. This
principle imposes a restriction to vectors in the Hilbert space and this may
effectively break the time-reversal symmetry of Schr\""{o}dinger equation.",1005.0321v3
2011-03-25,"Electronic Structures, Born Effective Charges and Spontaneous Polarization in Magnetoelectric Gallium Ferrite","We present a theoretical study of the structure-property correlation in
gallium ferrite, based on the first principles calculations followed by a
subsequent comparison with the experiments. Local spin density approximation
(LSDA+U) of the density functional theory has been used to calculate the ground
state structure, electronic band structure, density of states and Born
effective charges. Calculations reveal that the ground state structure is
orthorhombic Pc21n having A-type antiferromagnetic spin configuration, with
lattice parameters matching well with those obtained experimentally. Plots of
partial density of states of constituent ions exhibit noticeable hybridization
of Fe 3d, Ga 4s, Ga 4p and O 2p states. However, the calculated charge density
and electron localization function show largely ionic character of the Ga/Fe-O
bonds which is also supported by lack of any significant anomaly in the
calculated Born effective charges with respect to the corresponding nominal
ionic charges. The calculations show a spontaneous polarization of ~ 59
microC/cm^2 along b-axis which is largely due to asymmetrically placed Ga1,
Fe1, O1, O2 and O6 ions.",1103.4935v2
1997-12-01,Stripes in a three-chain Hubbard ladder: a comparison of density-matrix renormalization group and constrained-path Monte Carlo results,"Using both the density-matrix renormalization group method and the
constrained-path quantum Monte Carlo method, we have studied the ground-state
energies and the spin and hole densities of a $12 \times 3$ Hubbard model with
open boundary conditions and 6 holes doped away from half-filling. Results
obtained with these two methods agree well in the small and intermediate $U$
regimes. For $U/t \geq 6$ we find a ground-state with stripes.",9712018v1
2007-01-25,The density of states method at non-zero chemical potential,"We study the QCD phase diagram by first principle lattice calculations at so
far unreached high densities. For this purpose we employ the density of states
method. Unimproved staggered fermions, which describe four quark flavors in the
continuum are used in this analysis. Though the method is quite expensive,
small lattices show an indication for a triple-point connecting three different
phases on the phase diagram.",0701022v2
2006-05-16,QCD Correction to Neutralino Annihilation Process and Dark Matter Density in Supersymmetric Models,"We calculate QCD correction to the neutralino annihilation cross section into
quark anti-quark final state and discuss its implications to the calculation of
neutralino relic density. We see that the QCD correction enhances the
pair-annihilation cross section by O(10 %) when final-state quarks are
non-relativistic. Consequently, when the lightest neutralinos dominantly
annihilate into a t\bar{t} pair, the relic density of the lightest neutralino
is significantly affected by the QCD correction, in particular when the
lightest-neutralino mass is close to the top-quark mass.",0605181v1
2010-05-31,Quantum quench in 1D: Coherent inhomogeneity amplification and 'supersolitons',"We study a quantum quench in a 1D system possessing Luttinger liquid (LL) and
Mott insulating ground states before and after the quench, respectively. We
show that the quench induces power law amplification in time of any particle
density inhomogeneity in the initial LL ground state. The scaling exponent is
set by the fractionalization of the LL quasiparticle number relative to the
insulator. As an illustration, we consider the traveling density waves launched
from an initial localized density bump. While these waves exhibit a particular
rigid shape, their amplitudes grow without bound.",1006.0012v1
2011-03-30,The lowest scattering state of one-dimensional Bose gas with attractive interactions,"We investigate the lowest scattering state of one-dimensional Bose gas with
attractive interactions trapped in a hard wall trap. By solving the Bethe
ansatz equation numerically we determine the full energy spectrum and the exact
wave function for different attractive interaction parameters. The resultant
density distribution, momentum distribution, reduced one body density matrix
and two body correlation show that the decreased attractive interaction induces
rich density profiles and specific correlation properties in the weakly
attractive Bose gas.",1103.5804v1
2010-05-18,Fidelity is a sub-martingale for discrete-time quantum filters,"Fidelity is known to increase through any Kraus map: the fidelity between two
density matrices is less than the fidelity between their images via a Kraus
map. We prove here that, in average, fidelity is also increasing for any
discrete-time quantum filter: fidelity between the density matrix of the
underlying Markov chain and the density matrix of its associated quantum filter
is a sub-martingale. This result is not restricted to pure states. It also
holds true for mixed states.",1005.3119v3
2015-12-16,Magnetism in Co$_{1-{\rm x}}$Fe$_{\rm x}$Sb$_{3}$ skutterudites from density functional theory,"We have investigated the electronic and magnetic properties of Co$_{1-{\rm
x}}$Fe$_{\rm x}$Sb$_{3}$ skutterudites from density functional theory and Monte
Carlo simulations. We find that above a certain threshold in the Fe
concentration, somewhere between x=0.125 and x=0.25, Co$_{1-{\rm x}}$Fe$_{\rm
x}$Sb$_{3}$ is ferromagnetic with an atomic moment which increases
asymptotically towards about 1 $\mu_{B}$/Fe and a non-zero Curie temperature
which reaches 70 K for FeSb$_{3}$. Ferromagnetism is favored due to a Stoner
instability in the electronic structure, where a large density of states at the
Fermi-level makes it favorable to form the ferromagnetic ground state.",1512.05124v1
2016-12-20,"""$1k_F$"" Singularities and Finite Density ABJM Theory at Strong Coupling","We study non-analytic behavior in the static charge susceptibility in finite
density states of the ABJM theory using its holographic dual. Emphasis is
placed on a particular state characterized by vanishing entropy density at zero
temperature, and Fermi surface-like singularities in various fermionic
correlation functions. The susceptibility exhibits branch points in the complex
momentum plane, with a real part quantitatively very similar to the location of
the Fermi surface singularities.",1612.06823v2
2010-11-03,Compressibility of graphene,"We develop a theory for the compressibility and quantum capacitance of
disordered monolayer and bilayer graphene including the full hyperbolic band
structure and band gap in the latter case. We include the effects of disorder
in our theory, which are of particular importance at the carrier densities near
the Dirac point. We account for this disorder statistically using two different
averaging procedures: first via averaging over the density of carriers
directly, and then via averaging in the density of states to produce an
effective density of carriers. We also compare the results of these two models
with experimental data, and to do this we introduce a model for inter-layer
screening which predicts the size of the band gap between the low-energy
conduction and valence bands for arbitary gate potentials applied to both
layers of bilayer graphene. We find that both models for disorder give
qualitatively correct results for gapless systems, but when there is a band gap
at charge neutrality, the density of states averaging is incorrect and
disagrees with the experimental data.",1011.0995v2
2023-03-08,Quantum liquid droplets in Bose mixtures with weak disorder,"We study the properties of self-bound liquid droplets of three-dimensional
Bose mixtures in a weak random potential with Gaussian correlation function at
both zero and finite temperatures. Using the Bogoliubov theory, we derive
useful formulas for the ground-state energy, the equilibrium density, the
depletion, and the anomalous density of the droplet. The quantum fluctuation
induced by the disorder known as the glassy fraction is also systematically
computed. At finite temperature, we calculate the free energy, the thermal
equilibrium density, and the critical temperature in terms of the disorder
parameters. We show that when the strength and the correlation length of the
disorder potential exceed a certain critical value, the droplet evaporates and
is eventually entirely destroyed. We calculate the density profiles of this
exotic state by means of numerical simulations of the corresponding generalized
disorder Gross-Pitaevskii equation. Our predictions reveal that as the strength
of the disorder gets larger, the atomic density varies rapidly in the plateau
region. We point out in addition that the peculiar interplay of the disorder
and the repulsive Lee-Huang-Yang corrections play a pivotal role in the
collective modes of the self-bound droplet.",2303.04760v1
2000-01-27,Quasiparticle Spectrum of d-wave Superconductors in the Mixed State,"The quasiparticle spectrum of a two-dimensional d-wave superconductor in the
mixed state, H_{c1} << H << H_{c2}, is studied both analytically and
numerically using the linearized Bogoliubov-de Gennes equation. We consider
various values of the ""anisotropy ratio"" v_F/v_Delta for the quasiparticle
velocities at the Dirac points, and we examine the implications of symmetry.
For a Bravais lattice of vortices, we find there is always an isolated
energy-zero (Dirac point) at the center of the Brillouin zone, but for a
non-Bravais lattice with two vortices per unit cell there is generally an
energy gap. In both of these cases, the density of states should vanish at zero
energy, in contrast with the semiclassical prediction of a constant density of
states, though the latter may hold down to very low energies for large
anisotropy ratios. This result is closely related to the particle-hole symmetry
of the band structures in lattices with two vortices per unit cell. More
complicated non-Bravais vortex lattice configurations with at least four
vortices per unit cell can break the particle-hole symmetry of the linearized
energy spectrum and lead to a finite density of states at zero energy.",0001406v1
2010-02-27,Charmonium mass in hot asymmetric nuclear matter,"We calculate the in-medium masses of J/$\psi$ and of the excited states of
charmonium ($\psi$(3686) and $\psi$(3770)) in isospin asymmetric nuclear matter
at finite temperatures. These mass modifications arise due to the interaction
of the charmonium states with the gluon condensates of QCD, simulated by a
scalar dilaton field introduced to incorporate the broken scale invariance of
QCD within an effective chiral model. The change in the mass of J/$\psi$ in the
nuclear matter with density is seen to be rather small, as has been shown in
the literature by using various approaches, whereas, the masses of the excited
states of charmonium ($\psi$(3686) and $\psi$(3770)) are seen to have
considerable drop at high densities. The dependence of the masses of the
charmonium states on the isospin asymmetry has also been investigated in the
hot nuclear matter and is seen to be appreciable at moderate temperatures and
high densities. These medium modifications of the charmonium states should
modify the experimental observables arising from the compressed baryonic matter
produced in asymmetric heavy ion collision experiments in the future facility
of FAIR, GSI.",1003.0077v1
2010-03-23,Local electronic structures on the superconducting interface $LaAlO_{3}/SrTiO_{3}$,"Motivated by the recent discovery of superconductivity on the heterointerface
$LaAlO_{3}/SrTiO_{3}$, we theoretically investigate its local electronic
structures near an impurity considering the influence of Rashba-type spin-orbit
interaction (RSOI) originated in the lack of inversion symmetry. We find that
local density of states near an impurity exhibits the in-gap resonance peaks
due to the quasiparticle scattering on the Fermi surface with the reversal sign
of the pairing gap caused by the mixed singlet and RSOI-induced triplet
superconducting state. We also analyze the evolutions of density of states and
local density of states with the weight of triplet pairing component determined
by the strength of RSOI, which will be widely observed in thin films of
superconductors with surface or interface-induced RSOI, or various
noncentrosymmetric superconductors in terms of point contact tunneling and
scanning tunneling microscopy, and thus reveal an admixture of the spin singlet
and RSOI-induced triplet superconducting states.",1003.4370v2
2015-03-31,Magnetism of gadolinium: a first-principles perspective,"By calculating the spectral density of states in the ferromagnetic (FM)
ground state and in the high temperature paramagnetic (PM) phase we provide the
first concise study of finite temperature effects on the electronic structure
of the bulk and the surface of gadolinium metal. The variation of calculated
spectral properties of the Fermi surface and the density of states in the bulk
and at the surface are in good agreement with recent photoemission experiments
performed in both ferromagnetic and paramagnetic phases. In the paramagnetic
state we find vanishing spin splitting of the conduction band, but finite local
spin moments both in bulk and at the surface. We clearly demonstrate that the
formation of these local spin moments in the conduction band is due to the
asymmetry of the density of states in the two spin channels, suggesting a
complex, non-Stoner behavior. We, therefore, suggest that the vanishing or
nearly vanishing spin splitting of spectral features cannot be used as an
indicator for Stoner-like magnetism.",1503.08940v1
2016-08-12,Tetrahedral shape and surface density wave of $^{16}$O caused by $α$-cluster correlations,"$\alpha$-cluster correlations in the $0^+_1$ and $3^-_1$ states of $^{12}$C
and $^{16}$O are studied using the method of antisymmetrized molecular
dynamics, with which nuclear structures are described from nucleon degrees of
freedom without assuming existence of clusters. The intrinsic states of
$^{12}$C and $^{16}$O have triangle and tetrahedral shapes, respectively,
because of the $\alpha$-cluster correlations. These shapes can be understood as
spontaneous symmetry breaking of rotational invariance, and the resultant
surface density oscillation is associated with density wave (DW) caused by the
instability of Fermi surface with respect to particle-hole correlations with
the wave number $\lambda=3$. $^{16}$O($0^+_1$) and $^{16}$O($3^-_1$) are
regarded as a set of parity partners constructed from the rigid tetrahedral
intrinsic state, whereas $^{12}$C($0^+_1$) and $^{12}$C($3^-_1$) are not good
parity partners as they have triangle intrinsic states of different sizes with
significant shape fluctuation because of softness of the $3\alpha$ structure.
$E3$ transition strengths from the $3^-_1$ to $0^+_1$ states in $^{12}$C and
$^{16}$O are also discussed.",1608.03642v1
2020-01-13,Unlocked-relative-phase states in arrays of Bose-Einstein condensates,"Phase engineering techniques are used to control the dynamics of
long-bosonic-Josephson-junction arrays built by linearly coupling Bose-Einstein
condensates. Just at the middle point of the underlying discrete energy band of
the system, unlocked-relative-phase states are shown to be stationary along
with the locked-relative-phase Bloch waves. In finite, experimentally-feasible
systems, such states find ranges of dynamical stability that depend on the
ratio of coupling to interaction energy. The same ratio determines different
decay regimes, which include the recurrence of staggered-soliton trains in the
condensates around Josephson loop currents at the junctions. These transient
solitons are also found in their stationary configurations, which provide
striped-density states by means of either dark-soliton or bright-soliton
trains. Additionally, the preparation of maximally out-of-phase (or splay)
states is demonstrated to evolve into an oscillation of the uniform density of
the condensates that keeps constant the total density of the system and robust
against noise at low coupling.",2001.04033v2
2009-05-12,Reconstructing the Neutron-Star Equation of State from Astrophysical Measurements,"The properties of matter at ultra-high densities, low temperatures, and with
a significant asymmetry between protons and neutrons can be studied exclusively
through astrophysical observations of neutron stars. We show that measurements
of the masses and radii of neutron stars can lead to tight constraints on the
pressure of matter at three fiducial densities, from 1.85 to 7.4 times the
density of nuclear saturation, in a manner that is largely model-independent
and that captures the key characteristics of the equation of state. We
demonstrate that observations with 10% uncertainties of at least three neutron
stars can lead to measurements of the pressure at these fiducial densities with
an accuracy of 0.11 dex or ~ 30%. Observations of three neutron stars with 5%
uncertainties are sufficient to distinguish at a better than 3-sigma confidence
level between currently proposed equations of state. In the electromagnetic
spectrum, such accurate measurements will become possible for weakly-magnetic
neutron stars during thermonuclear flashes and in quiescence with future
missions such as the International X-ray Observatory (IXO).",0905.1959v2
2011-02-21,The algebraic geometry of Harper operators,"Following an approach developed by Gieseker, Kn\""orrer and Trubowitz for
discretized Schr\""odinger operators, we study the spectral theory of Harper
operators in dimension two and one, as a discretized model of magnetic
Laplacians, from the point of view of algebraic geometry. We describe the
geometry of an associated family of Bloch varieties and compute their density
of states. Finally, we also compute some spectral functions based on the
density of states.
  We discuss the difference between the cases with rational or irrational
parameters: for the two dimensional Harper operator, the compactification of
the Bloch variety is an ordinary variety in the rational case and an
ind-pro-variety in the irrational case. This gives rise, at the
algebro-geometric level of Bloch varieties, to a phenomenon similar to the
Hofstadter butterfly in the spectral theory. In dimension two, the density of
states can be expressed in terms of period integrals over Fermi curves, where
the resulting elliptic integrals are independent of the parameters.
  In dimension one, for the almost Mathieu operator, with a similar argument we
find the usual dependence of the spectral density on the parameter, which gives
rise to the well known Hofstadter butterfly picture.",1102.4136v2
2019-05-01,First Principles Study of Electronic Structure and Fermi Surface in Rare-earth Filled Skutterudites RPt4Ge12,"Experiments on rare-earth filled skutterudites demonstrate an intriguing
array of thermodynamic, transport and superconducting properties, and bring to
fore theoretical challenges posed by f-electron systems. First principle
calculations based density functional theory and its extensions for strongly
correlated systems such as the Hubbard U correction, provide valuable
information about electronic structure that can be used to understand
experiments. We present a comprehensive study of the electronic structure and
Fermi surface of a series of rare earth filled skutterudites, RPt4Ge12 (where R
= La, Ce, Pr), aimed at shedding light on: consequences of progressive increase
of f-orbital occupancy in the series; the effects of the Hubbard parameter U;
the Fermi surfaces, band structures and densities of states. The calculated
Fermi surfaces may be relevant to the question of multi-band versus single-band
superconductivity. Computed densities of states qualitatively explain the
available resonant photoemission spectroscopy experiments, and (together with
available specific heat measurements) provide estimates of the effective
masses. We also show the existence of pseudogaps in the total density of states
which may be relevant for the thermoelectric properties of these systems.",1905.00169v1
2001-09-28,Structure and Parametrization of Stochastic Maps of Density Matrices,"The generic linear evolution of the density matrix of a system with a
finite-dimensional state space is by stochastic maps which take a density
matrix linearly into the set of density matrices. These dynamical stochastic
maps form a linear convex set that may be viewed as supermatrices. The property
of hermiticity of density matrices renders an associated supermatrix hermitian
and hence diagonalizable; but the positivity of the density matrix does not
make this associated supermatrix positive. If it is positive, the map is called
completely positive and they have a simple parametrization. This is extended to
all positive (not completely positive) maps. A contraction of a norm-preserving
map of the combined system can be contracted to obtain all dynamical maps. The
reconstruction of the extended dynamics is given.",0109158v1
1997-08-07,Fidelity for displaced squeezed states and the oscillator semigroup,"The fidelity for two displaced squeezed thermal states is computed using the
fact that the corresponding density operators belong to the oscillator
semigroup.",9708013v1
1993-09-13,Quantum State and Spontaneous Symmetry Breaking in Gravity,"A spontaneous symmetry breaking mechanism is used in quantum gravity to
obtain a convergent positive definite density-matrix as the most general
quantum state of Euclidean wormholes",9309008v1
2011-02-09,Heavy Long-lived Mossbauer State of Niobium,"A heavy niobium state showing 1/3 residual resistance is discovered below the
superconducting transition temperature. This niobium sample contains
high-density long-lived Mossbauer excitation.",1102.1766v2
2013-04-24,Universal Longtime Dynamics in Dense Simple Fluids,"There appears to be a longtime, very slowly evolving state in dense simple
fluids which, for high enough density, approaches a glassy nonergodic state.
The nature of the nonergodic state can be characterized by the associated
static equilibrium state. In particular, systems driven by Smoluchowski or
Newtonian dynamics share the same static equilibrium and nonergodic states.
That these systems share the same nonergodic states is a highly nontrivial
statement and requires establishing a number of results. In the high-density
regime one finds that an equilibrating system decays via a three-step process
identified in mode-coupling theory (MCT). For densities greater than a critical
density one has time-power-law decay with exponents a and b. There are sets of
linear fluctuation dissipation relations (FDRs) which connect the cumulants of
these two fields. The form of the FDRs is the same for both Smoluchowski or
Newtonian dynamics. While we show this universality of nonergodic states within
perturbation theory, we expect it to be true more generally.
  The nature of the approach to the nonergodic state has been suggested by MCT.
It has been a point of contention that MCT is a phenomenological theory and not
a systematic theory with prospects for improvement. Recently a systematic
theory has been developed. It naturally allows one to calculate
self-consistently density cumulants in a perturbation expansion in a
pseudo-potential. At leading order one obtains a kinetic kernel quadratic in
the density. This is a ""one-loop"" theory like MCT. At this one-loop level one
finds vertex corrections which depend on the three-point equilibrium cumulants.
Here we assume these vertex-corrections can be ignored and focus on the
higher-order loops. We show that one can sum up all of the loop contributions.
The higher-order loops do not change the nonergodic state parameters
substantially.",1304.6631v1
2011-07-12,Metamorphosis and Taxonomy of Andreev Bound States,"We analyze the spatial and energy dependence of the local density of states
in a SNS junction. We model our system as a one-dimensional tight-binding chain
which we solve exactly by numerical diagonalization. We calculate the
dependence of the Andreev bound states on position, phase difference, gate
voltage, and coupling with the superconducting leads. Our results confirm the
physics predicted by certain analytical approximations, but reveal a much
richer set of phenomena beyond the grasp of these approximations, such as the
metamorphosis of the discrete states of the normal link (the normal bound
states) into Andreev bound states as the leads become superconducting.",1107.2228v1
2018-09-25,Geometric measure of mixing of quantum state,"We define the geometric measure of mixing of quantum state as a minimal
Hilbert-Schmidt distance between the mixed state and a set of pure states. An
explicit expression for the geometric measure is obtained. It is interesting
that this expression corresponds to the squared Euclidian distance between the
mixed state and the pure one in space of eigenvalues of the density matrix. As
an example, geometric measure of mixing for spin-1/2 states is calculated.",1809.09469v2
2011-05-25,Local suppression of the superfluid density of PuCoGa$_5$ in the Swiss Cheese model,"We present superfluid density calculations for the unconventional
superconductor PuCoGa$_5$ by solving the real-space Bogoliubov-de Gennes
equations on a square lattice within the Swiss Cheese model in the presence of
strong on-site disorder. We find that despite strong electronic inhomogeneity,
one can establish a one-to-one correspondence between the local maps of the
density of states, superconducting order parameter, and superfluid density. In
this model, strong on-site impurity scattering punches localized holes into the
fabric of d-wave superconductivity similar to a Swiss cheese. Already a
two-dimensional impurity concentration of $n_{\rm imp} = 4%$ gives rise to a
pronounced short-range suppression of the order parameter and a suppression of
the superconducting transition temperature $T_c$ by roughly 20% compared to its
pure limit value $T_{c0}$, whereas the superfluid density $\rho_s$ is reduced
drastically by about 70%. This result is consistent with available experimental
data for aged (400 day-old) and fresh (25 day-old) PuCoGa$_5$ superconducting
samples. In addition, we show that the $T^2-$dependence of the low-$T$
superfluid density, a signature of dirty d-wave superconductivity, originates
from a combined effect in the density of states of `gap filling' and `gap
closing'. Finally, we demonstate that the Uemuera plot of $T_c$ vs.\ $\rho_s$
deviates sharply from the conventional Abrikosov-Gor'kov theory for
radiation-induced defects in PuCoGa$_5$, but follows the same trend of
short-coherence-length high-$T_c$ cuprate superconductors.",1105.5109v2
2008-04-03,Mazur intersection property for Asplund spaces,"The main result of the present note states that it is consistent with the ZFC
axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund
space of density character $\omega_1$ has a renorming with the Mazur
intersection property. Combined with the previous result of Jim\' enez and
Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain
that the MIP normability of Asplund spaces of density $\omega_1$ is undecidable
in ZFC.",0804.0583v1
2009-04-30,Density matrix of a single photon produced in parametric down conversion derived,"We introduce an effective numerical method of density matrix determination of
fiber coupled single photon generated in process of spontaneous parametric down
conversion in type I non-collinear configuration. The presented theory has been
successfully applied in case of source exploited in Phys. Rev. Lett. 99, 123601
(2007) to demonstrate the experimental characterization of spectral state of
single photon.",0904.4920v1
2022-09-10,Discovery of a pair density wave state in a monolayer high-Tc iron-based superconductor,"The pair density wave (PDW) is an extraordinary superconducting state where
Cooper pairs carry nonzero momentum. It can emerge when the full condensation
of zero momentum Cooper pairs is frustrated. Evidence for the existence of
intrinsic PDW order in high-temperature (high-Tc) cuprate superconductors and
kagome superconductors has emerged recently. However, the PDW order in
iron-based high-Tc superconductors has not been observed experimentally. Here,
using scanning tunneling microscopy/spectroscopy, we report the discovery of
the PDW state in monolayer iron-based high-Tc Fe(Te,Se) films grown on
SrTiO3(001) substrates. The PDW state with a period of {\lambda}~3.6a_Fe (a_Fe
is the distance between neighboring Fe atoms) is observed at the domain walls
by the spatial electronic modulations of the local density of states,
superconducting gap, and the {\pi}-phase shift boundaries of the PDW around the
dislocations of the intertwined charge density wave order. The discovery of the
PDW state in the monolayer Fe(Te,Se) film provides a low-dimensional platform
to study the interplay between the correlated electronic states and
unconventional Cooper pairing in high-Tc superconductors.",2209.04592v2
2004-03-01,Granular contact force density of states and entropy in a modified Edwards ensemble,"A method has been found to analyze Edwards' granular contact force
probability functional for a special case. As a result, the granular contact
force probability density functions are obtained from first principles for this
case. The results are in excellent agreement with the experimental and
simulation data. The derivation assumes Edwards' flat measure -- a density of
states that is uniform within the metastable regions of phase space. The
enabling assumption, supported by physical arguments and empirical evidence, is
that correlating information is not significantly recursive through loops in
the packing. Maximizing a state-counting entropy results in a transport
equation that can be solved numerically. For the present this has been done
using the ""mean structure approximation,"" projecting the density of states
across all angular coordinates to more clearly identify its predominant
non-uniformities. These features are: (1) the grain factor (Psi) related to
grain stability and strong correlation between the contact forces on the same
grain, and (2) the structure factor (Upsilon) related to Newton's third law and
strong correlation between neighboring grains.",0403034v2
2008-10-20,Metal-insulator transition in the Hartree-Fock phase diagram of the fully polarized homogeneous electron gas in two dimensions,"We determine numerically the ground state of the two-dimensional, fully
polarized electron gas within the Hartree-Fock approximation without imposing
any particular symmetries on the solutions. At low electronic densities, the
Wigner crystal solution is stable, but for higher densities ($r_s$ less than
$\sim 2.7$) we obtain a ground state of different symmetry: the charge density
forms a triangular lattice with about 11% more sites than electrons. We prove
analytically that this conducting state with broken translational symmetry has
lower energy than the uniform Fermi gas state in the high density region giving
rise to a metal to insulator transition.",0810.3559v1
2011-05-09,Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in an XXZ chain,"We compute the dynamics of localized excitations produced by a quantum quench
in the spin 1/2 XXZ chain. Using numerics combining the density matrix
renormalization group and exact time evolution, as well as analytical
arguments, we show that fractionalization due to interactions in the pre-quench
state gives rise to ""ultrarelativistic"" density waves that travel at the
maximum band velocity. The system is initially prepared in the ground state of
the chain within the gapless XY phase, which admits a Luttinger liquid (LL)
description at low energies and long wavelengths. The Hamiltonian is then
suddenly quenched to a band insulator, after which the chain evolves unitarily.
Through the gapped dispersion of the insulator spectrum, the post-quench
dynamics serve as a ""velocity microscope,"" revealing initial state particle
correlations via space time density propagation. We show that the
ultrarelativistic wave production is tied to the particular way in which
fractionalization evades Pauli-blocking in the zero-temperature initial LL
state.",1105.1786v2
2015-02-20,Accelerated rare event sampling,"A sampling procedure for the transition matrix Monte Carlo method is
introduced that generates the density of states function over a wide parameter
range with minimal coding effort.",1502.05842v1
2015-04-21,Cluster Density Matrix Embedding Theory for Quantum Spin Systems,"We applied cluster density matrix embedding theory, with some modifications,
to a spin lattice system. The reduced density matrix of the impurity cluster is
embedded in the bath states, which are a set of block-product states. The
ground state of the impurity model is formulated using a variational wave
function. We tested this theory in a two-dimensional (2-D) spin-1/2 J1-J2 model
for a square lattice. The ground-state energy (GSE) and the location of the
phase boundaries agree well with the most accurate previous results obtained
using the quantum Monte Carlo and coupled cluster methods. Moreover, this
cluster density matrix embedding theory is cost-effective and convenient for
calculating the von Neumann entropy, which is related to the quantum phase
transition.",1504.05344v1
2019-01-16,Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties,"We introduce a new relativistic energy density functional constrained by the
ground state properties of atomic nuclei along with the isoscalar giant
monopole resonance energy and dipole polarizability in $^{208}$Pb. A unified
framework of the relativistic Hartree-Bogoliubov model and random phase
approximation based on the relativistic density-dependent point coupling
interaction is established in order to determine the DD-PCX parameterization by
$\chi^2$ minimization. This procedure is supplemented with the co-variance
analysis in order to estimate statistical uncertainties in the model parameters
and observables. The effective interaction DD-PCX accurately describes the
nuclear ground state properties including the neutron-skin thickness, as well
as the isoscalar giant monopole resonance excitation energies and dipole
polarizabilities. The implementation of the experimental data on nuclear
excitations allows constraining the symmetry energy close to the saturation
density, and the incompressibility of nuclear matter by using genuine
observables on finite nuclei in the $\chi^2$ minimization protocol, rather than
using pseudo-observables on the nuclear matter, or by relying on the ground
state properties only, as it has been customary in the previous studies.",1901.05552v1
2021-07-12,"Mechanism of exotic density-wave and beyond-Migdal unconventional superconductivity in kagome metal AV3Sb5 (A=K, Rb, Cs)","Exotic quantum phase transitions in metals, such as the nematic and smectic
states, were discovered one after another and found to be universal now. The
emergence of unconventional density-wave order in frustrated kagome metal
AV$_3$Sb$_5$ and its interplay with exotic superconductivity attract increasing
attention. We reveal that the smectic bond-density-wave is naturally caused by
the paramagnon interference mechanism, because strong scatterings among
different van-Hove singularity points are induced. In addition, the
fluctuations of the bond-order induce sizable ""beyond-Migdal"" pairing glue, and
therefore both singlet nodal $s$-wave pairing and triplet $p$-wave pairing
states are expected to emerge. The coexistence of both states would explain
exotic superconducting states. Unexpected similarities between kagome metal and
some Fe-based superconductors are discussed. This study enables us to
understand the exotic density wave, superconductivity and their interplay in
kagome metals based on the interference mechanism.",2107.05372v6
2022-09-23,Pair density wave in doped three-band Hubbard model on two-leg square cylinders,"A pair density wave (PDW) is a superconducting (SC) state with spatially
modulated order parameter. Although much is known about the properties of the
PDW state, its realization in microscopic models with divergent susceptibility
has been challenging. Here we report a density-matrix renormalization group
study of a three-band Hubbard model (also known as the Emery model) for
cuprates on long two-leg square cylinders. Upon light doping, we find that the
ground state of the system is consistent with that of a PDW state with mutually
commensurate and power-law SC, charge (CDW) and spin (SDW) density wave
correlations. The SC correlations are dominant between neighboring Cu sites
with d-wave pairing symmetry. Interestingly, we find that the near-neighbor
interactions, especially the near-neighbor attractive $V_{pd}$ interaction
between neighboring Cu and oxygen sites, can notably enhance the SC
correlations while simultaneously suppressing the CDW correlations. For a
modestly strong attractive $V_{pd}$, the SC correlations become
quasi-long-ranged with a divergent PDW susceptibility.",2209.11381v3
2018-04-16,From cluster structures to nuclear molecules: the role of nodal structure of the single-particle wave functions,"The nodal structure of the density distributions of the single-particle
states occupied in rod-shaped, hyper- and megadeformed structures of
non-rotating and rotating $N\sim Z$ nuclei has been investigated in detail. The
single-particle states with the Nilsson quantum numbers of the $[NN0]1/2$ (with
$N$ from 0 to 5) and $[N,N-1,1]\Omega$ (with $N$ from 1 to 3 and $\Omega=1/2$,
3/2) types are considered. These states are building blocks of extremely
deformed shapes in the nuclei with mass numbers $A \leq 50$. Because of
(near)axial symmetry and large elongation of such structures, the wave
functions of the single-particle states occupied are dominated by a single
basis state in cylindrical basis. This basis state defines the nodal structure
of the single-particle density distribution. The nodal structure of the
single-particle density distributions allows to understand in a relatively
simple way the necessary conditions for $\alpha$-clusterization and the
suppression of the $\alpha$-clusterization with the increase of mass number. It
also explains in a natural way the coexistence of ellipsoidal mean-field type
structures and nuclear molecules at similar excitation energies and the
features of particle-hole excitations connecting these two types of the
structures. Our analysis of the nodal structure of the single-particle density
distributions does not support the existence of quantum liquid phase for the
deformations and nuclei under study.",1804.05811v1
1999-07-01,Transmission Through Carbon Nanotubes With Polyhedral Caps,"We study electron transport between capped carbon nanotubes and a substrate,
and relate the transmission probability to the local density of states in the
cap. Our results show that the transmission probability mimics the behavior of
the density of states at all energies except those that correspond to localized
states in the cap. Close proximity of a substrate causes hybridization of the
localized state. As a result, new transmission paths open from the substrate to
nanotube continuum states via the localized states in the cap. Interference
between various transmission paths gives rise to antiresonances in the
transmission probability, with the minimum transmission equal to zero at
energies of the localized states. Defects in the nanotube that are placed close
to the cap cause resonances in the transmission probability, instead of
antiresonances, near the localized energy levels. Depending on the spatial
position of defects, these resonant states are capable of carrying a large
current. These results are relevant to carbon nanotube based studies of
molecular electronics and probe tip applications.",9907020v2
2019-02-07,Fulde-Ferrell-Larkin-Ovchinnikov state in strongly correlated d-wave superconductors,"The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional
superconducting state found under the influence of strong Zeeman field. This
phase is identified by finite center-of-mass momenta in the Cooper pairs,
causing the pairing amplitude to oscillate in real space. Repulsive
correlations, on the other hand, smear out spatial inhomogeneities in d-wave
superconductors. We investigate the FFLO state in a strongly correlated d-wave
superconductor within a consolidated framework of Hartree-Fock-Bogoliubov
theory and Gutzwiller approximation. We find that the profound effects of
strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower
Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO
state, our calculation features a sharp mid-gap peak in the density of states,
indicating the formation of strongly localized Andreev bound states. We also
find that the signatures of the FFLO phase survive even in the presence of an
additional translational symmetry breaking competing order in the ground state.
This is demonstrated by considering a broken symmetry ground state with a
simultaneous presence of the d-wave superconducting order and a spin-density
wave order, often found in unconventional superconductors.",1902.02758v1
2004-04-26,Well-defined quasiparticles in interacting metallic grains,"We analyze spectral functions of mesoscopic systems with large dimensionless
conductance, which can be described by a universal Hamiltonian. We show that an
important class of spectral functions are dominated by one single state only,
which implies the existence of well-defined (i.e. infinite-lifetime)
quasiparticles. Furthermore, the dominance of a single state enables us to
calculate zero-temperature spectral functions with high accuracy using the
density-matrix renormalization group. We illustrate the use of this method by
calculating the tunneling density of states of metallic grains and the magnetic
response of mesoscopic rings.",0404614v1
2006-02-06,Superconducting Pairing Amplitude and Local Density of States in Presence of Repulsive Centers,"We study the properties of superconductor in presence of a finite
concentration of repulsive centers. The superconductor is described by the
negative $U$ Hubbard model while repulsive centers are treated as randomly
distributed impurities with repulsive interaction. Analyzing the paring
potential and local density of states at impurity sites we find a wide range of
the system parameters where the $\pi$ - like state could possibly be realized.
Comparison of our results to the single repulsive center case is also given.",0602120v1
2006-07-03,First principles molecular dynamics study of amorphous Si\sub{1-x}Ge\sub{x}:H alloys,"We study the structural, dynamical and electronic properties of amorphous
Si\sub{1-x}Ge\sub{x}:H alloys using first principles local basis molecular
dynamics simulation. The network topology and defects in the amorphous network
have been analyzed. Structural changes and an increase in number of defects
have been found as the Ge atomic percentage increases from x=0.1 to x=0.5. The
electronic density of states exhibits a decreasing band-gap and increased
mid-gap and band-tail defect states as Ge concentration increases.
Investigation of the band tails of the density of states show an exponential
(Urbach) behavior. The mobility gap is estimated as a function of Ge
concentration.",0607058v1
2006-12-01,Break-down of the density-of-states description of scanning tunneling spectroscopy in supported metal clusters,"Low-temperature scanning tunneling spectroscopy allows to probe the
electronic properties of clusters at surfaces with unprecedented accuracy. By
means of quantum transport theory, using realistic tunneling tips, we obtain
conductance curves which considerably deviate from the cluster's density of
states. Our study explains the remarkably small number of peaks in the
conductance spectra observed in recent experiments. We demonstrate that the
unambiguous characterization of the states on the supported clusters can be
achieved with energy-resolved images, obtained from a theoretical analysis
which mimics the experimental imaging procedure.",0612018v1
2001-09-26,Quantum times of arrival for multiparticle states,"Using the concept of crossing state and the formalism of second quantization,
we propose a prescription for computing the density of arrivals of particles
for multiparticle states, both in the free and the interacting case. The
densities thus computed are positive, covariant in time for time independent
hamiltonians, normalized to the total number of arrivals, and related to the
flux. We investigate the behaviour of this prescriptions for bosons and
fermions, finding boson enhancement and fermion depletion of arrivals.",0109133v1
2009-11-09,Triplet contribution to the Josephson current in the nonequilibrium superconductor/ferromagnet/superconductor junction,"The Josephson current through a long s-wave superconductor/weak
ferromagnet/s-wave superconductor weak link is studied theoretically in the
regime of nonequilibrium spin-dependent occupation of electron states in the
ferromagnetic intelayer. While under the considered nonequilibrium condition
the standard supercurrent, carried by the singlet part of current-carrying
density of states, is not modified, the additional supercurrent flowing via the
triplet part of the current-carrying density of states appears. Depending on
voltage, controlling the particular form of spin-dependent nonequilibrium in
the interlayer, this additional current can enhance or reduce the usual current
of the singlet component and also switch the junction between 0- and
$\pi$-states.",0911.1646v1
2011-05-09,Mixture of Quantum States: Thermal and Interaction Inducing Decoherence,"In this study, we show that the interaction energy plays an important role on
the quantum decoherence: If we pay attention to the oscillation phase factor,
$e^{-iE_{int}t/\hbar},$ we see that the time average of the macro-system's
density matrix becomes nearly diagonal, where the states giving extrema of
interaction energy are privileged to describe the quantum decoherence. This
approach is compatible with the von Neumann's old work, which has been recently
studied with renewed interest: The thermal mixture of states can be reached by
the time average of a density of matrix due to the oscillation phase factor,
$e^{-i(E_i-E_j)t/\hbar}.$ One of the direct results is the localization of
macroscopic objects.",1105.1581v1
2012-05-10,Deformed one-quasiparticle states in covariant density functional theory,"Systematic investigation of the accuracy of the description of the energies
of deformed one-quasiparticle states has been performed in covariant density
functional theory in actinide and rare-earth mass regions. The sources of the
discrepancies between theory and experiment are analyzed. Although some
improvements in the description of ground state configurations and
one-quasiparticle spectra can be achieved by better parametrization of the
relativistic mean field Lagrangian, the analysis suggests that spectroscopic
quality of their description can be achieved only in theoretical framework
which takes into account particle-vibration coupling.",1205.2135v1
2013-07-12,Bound states of the generalized spiked harmonic oscillator,"Bound states of the generalized spiked harmonic oscillator potential are
calculated accurately by using the generalized pseudospectral method. Energy
eigenvalues, various expectation values, radial densities are obtained through
a nonuniform, optimal spatial discretization of the radial Schr\""odinger
equation efficiently. Ground and excited states corresponding to arbitrary
values of $n$ and $\ell$ are reported for potential parameters covering a wide
range of interaction. Both weak and strong coupling is considered. The effect
of potential parameters on eigenvalues and densities are discussed. Almost all
of the results are reported here for the first time, which could be useful for
future studies.",1307.3323v1
2013-12-25,New theory of superfluidity. Method of equilibrium density matrix,"The variational theory of equilibrium boson system state to have been
previously developed by the author under the density matrix formalism is
applicable for researching equilibrium states and thermodynamic properties of
the quantum Bose gas which consists of zero-spin particles. Particle pulse
distribution function is obtained and duly employed for calculation of chemical
potential, internal energy and gas capacity temperature dependences. It is
found that specific phase transition, which is similar to transition of liquid
helium to its superfluid state, occurs at the temperature exceeding that of the
Bose condensation.",1412.6004v1
2018-02-04,"Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions","Multi-point probability measures along with the dielectric function of Dirac
Fermions in mono-layer graphene containing particle-particle and white-noise
(out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac
approximation is investigated. By calculating the one-body carrier density
probability measure of the graphene sheet, we show that the density fluctuation
($\zeta^{-1}$) is related to the disorder strength ($n_i$), the interaction
parameter ($r_s$) and the average density ($\bar{n}$) via the relation
$\zeta^{-1}\propto r_sn_i^2\bar{n}^{-1}$ for which $\bar{n}\rightarrow 0$ leads
to strong density inhomogeneities, i.e. electron-hole puddles (EHPs), in
agreement with the previous works. The general equation governing the two-body
distribution probability is obtained and analyzed. We present the analytical
solution for some limits which is used for calculating density-density response
function. We show that the resulting function shows power-law behaviors in
terms of $\zeta$ with fractional exponents which are reported. The
disorder-averaged polarization operator is shown to be a decreasing function of
momentum like ordinary 2D parabolic band systems. It is seen that a
disorder-driven momentum $q_{\text{ch}}$ emerges in the system which controls
the behaviors of the screened potential. We show that in small densities an
instability occurs in which imaginary part of the dielectric function becomes
negative and the screened potential changes sign. Corresponding to this
instability, some oscillations in charge density along with a
screening-anti-screening transition are observed. These effects become dominant
in very low densities, strong disorders and strong interactions, the state in
which EHPs appear. The total charge probability measure is another quantity
which has been investigated in this paper.",1802.01175v1
2023-03-09,Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights,"Energy barriers, which control the rates of chemical reactions, are seriously
underestimated by computationally-efficient semi-local approximations for the
exchange-correlation energy. The accuracy of a semi-local density functional
approximation is strongly boosted for reaction barrier heights by evaluating
that approximation non-self-consistently on Hartree-Fock electron densities, as
known for about 30 years. The conventional explanation is that Hartree-Fock
theory yields the more accurate density. This article presents a benchmark
Kohn-Sham inversion of accurate coupled-cluster densities for the reaction
H$_2$ + F $\rightarrow$ HHF $\rightarrow$ H + HF, and finds a strong,
understandable cancellation between positive (excessively over-corrected)
density-driven and large negative functional-driven errors (expected from
stretched radical bonds in the transition state) within this Hartree-Fock
density functional theory. This confirms earlier conclusions [Kaplan et al., J.
Chem. Theory Comput. 19, 532--543 (2023)] based on 76 barrier heights and three
less reliable, but less expensive, fully-nonlocal density-functional proxies
for the exact density.",2303.05318v3
2013-07-10,Kondo effect in f-electron superlattices,"We demonstrate the importance of the Kondo effect in artificially created
{\it f}-electron superlattices. We show that the Kondo effect does not only
change the density of states of the {\it f}-electron layers, but is also the
cause of pronounced resonances at the Fermi energy in the density of states of
the non-interacting layers in the superlattice, which are between the {\it
f}-electron layers. Remarkably, these resonances strongly depend on the
structure of the superlattice; due to interference, the density of states at
the Fermi energy can be strongly enhanced or even shows no changes at all.
Furthermore, we show that by inserting the Kondo lattice layer into a
three-dimensional (3D) metal, the gap of the Kondo insulating state changes
from a full gap to a pseudo gap with quadratically vanishing spectral weight
around the Fermi energy. Due to the formation of the Kondo insulating state in
the {\it f}-electron layer, the superlattice becomes strongly anisotropic below
the Kondo temperature. We prove this by calculating the in-plane and
out-of-plane conductivity of the superlattice.",1307.2675v2
2010-05-26,Experimental determination of the state-dependent enhancement of the electron-positron momentum density in solids,"The state-dependence of the enhancement of the electron-positron momentum
density is investigated for some transition and simple metals (Cr, V, Ag and
Al). Quantitative comparison with linearized muffin-tin orbital calculations of
the corresponding quantity in the first Brillouin zone is shown to yield a
measurement of the enhancement of the s, p and d states, independent of any
parameterizations in terms of the electron density local to the positron. An
empirical correction that can be applied to a first-principles state-dependent
model is proposed that reproduces the measured state-dependence very well,
yielding a general, predictive model for the enhancement of the momentum
distribution of positron annihilation measurements, including those of angular
correlation and coincidence Doppler broadening techniques.",1005.4909v2
2018-05-17,Multidimensional Triple Sum-Frequency Spectroscopy of MoS2 and Comparisons with Absorption and Second Harmonic Generation Spectroscopies,"Triple sum-frequency (TSF) spectroscopy is a recently-developed methodology
that enables collection of multidimensional spectra by resonantly exciting
multiple quantum coherences of vibrational and electronic states. This work
reports the first application of TSF to the electronic states of
semiconductors. Two independently tunable ultrafast pulses excite the A, B, and
C features of a MoS2 thin film. The measured TSF spectrum differs markedly from
absorption and second harmonic generation spectra. The differences arise
because of the relative importance of transition moments and the joint density
of states. We develop a simple model and globally fit the absorption and
harmonic generation spectra to extract the joint density of states and the
transition moments from these spectra. Our results validate previous
assignments of the C feature to a large joint density of states created by band
nesting.",1805.06985v3
2021-07-19,Saturation of Thermal Complexity of Purification,"We purify the thermal density matrix of a free harmonic oscillator as a
two-mode squeezed state, characterized by a squeezing parameter and squeezing
angle. While the squeezing parameter is fixed by the temperature and frequency
of the oscillator, the squeezing angle is otherwise undetermined, so that the
complexity of purification is obtained by minimizing the complexity of the
squeezed state over the squeezing angle. The resulting complexity of the
thermal state is minimized at non-zero values of the squeezing angle and
saturates to an order one number at high temperatures, indicating that there is
no additional operator cost required to build thermal states beyond a certain
temperature. We also review applications in which thermal density matrices
arise for quantum fields on curved spacetimes, including Hawking radiation and
a simple model of decoherence of cosmological density perturbations in the
early Universe. The complexity of purification for these mixed states also
saturates as a function of the effective temperature, which may have
interesting consequences for the quantum information stored in these systems.",2107.08969v1
2015-02-16,Fragmented Many-body States of Spin-2 Bose Gas,"We investigate the fragmented many-body ground states of a spin-2 Bose gas in
zero magnetic field.\ We point out that the exact ground state is not simply an
average over rotationally-invariant mean-field states, in contrast to the
spin-1 case with even number of particles N.\ We construct the exact ground
states and compare them with the angular-averaged polar and cyclic states.\ The
angular-averaged polar states fail to retrieve the exact eigenstate at $N$
$\ge$ $6$ while angular-averaged cyclic states sustain only for N with a
multiple of $3$.\ We calculate the density matrices and two-particle density
matrices to show how deviant the angular-averaged state is from the exact one.",1502.04437v2
2022-05-12,Engineering quasi-steady-state correlations in uncorrelated thermal states using stochastic driving,"Nonequilibrium quantum dynamics can give rise to the emergence of novel
steady states. We propose a scheme for driving an initially uncorrelated
thermal state to generate customized correlation functions by determining and
reverse engineering the steady-state two-point functions for a class of Markov
processes. We also extend the formalism to the calculation of four-point
functions. We then apply our method to generating power-law correlated
fermionic Green's functions. Furthermore, we find that the power-law patterns
emerge at much shorter times than the convergence to the steady state, at which
point the disorder in the two-point correlations disappears. On the other hand,
the density-density correlations exhibit steady-state disorder while following
a power-law trendline. These ideal steady states appear as intermediate-time
quasi-steady states in the presence of perturbations.",2205.06092v3
2003-07-17,On the Mott formula for the a.c. conductivity and binary correlators in the strong localization regime of disordered systems,"We present a method that allows us to find asymptotic form of various
characteristics of disordered systems in the strong localization regime, i.e.,
when either the random potential is big enough or the energy is close enough to
the spectrum edges. The method is based on the hypothesis that relevant
realizations of the random potential in the strong localization regime have the
form of deep random wells that are uniformly and chaotically distributed in the
space with a sufficiently small density. Assuming this and using the density
expansion, we show first that the density of wells coincides in the leading
order with the density of states. Thus the density of states is in fact the
small parameter of the theory in the strong localization regime. Then we derive
the Mott formula for the low frequency conductivity and the asymptotic formulas
for certain two-point correlators when the difference of respective energies is
small.",0307034v2
2008-05-28,First-Principles Studies of the Metallization and the Equation of State of Solid Helium,"The insulator-to-metal transition in solid helium at high pressure is studied
with first-principles simulations. Diffusion quantum Monte Carlo (DMC)
calculations predict that the band gap closes at a density of 21.3 g/cc and a
pressure of 25.7 terapascals, which is 20% higher in density and 40% higher in
pressure than predicted by density functional calculations based on the
generalized gradient approximation (GGA). The metallization density derived
from GW calculations is found to be in very close agreement with DMC
predictions. The zero point motion of the nuclei had no effect on the
metallization density within the accuracy of the calculation. Finally, fit
functions for the equation of state are presented and the magnitude of the
electronic correlation effects left out of the GGA approximation are discussed.",0805.4433v1
2009-11-19,Low-density neutron matter,"The properties of low-density neutron matter are important for the
understanding of neutron star crusts and the exterior of large neutron-rich
nuclei. We examine various properties of dilute neutron matter using quantum
Monte Carlo methods, with s- and p-wave terms in the interaction. Our results
provide a smooth evolution of the equation of state and pairing gap from
extremely small densities, where analytic expressions are available, up to the
strongly interacting regime probed experimentally and described theoretically
in cold atomic systems, where the Fermi momentum is approximately half an
inverse fermi and the pairing gap becomes of the order of magnitude of the
Fermi energy. We also present results for the momentum distribution and pair
distributions, displaying the same evolution from weak to strong coupling.
Combined with previous quantum Monte Carlo and other calculations at moderate
densities, these results provide strong constraints on the neutron matter
equation of state up to saturation densities.",0911.3907v2
2012-02-23,"Density Functional Resonance Theory: complex density functions, convergence, orbital energies, and functionals","Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett.
\textbf{107}, 163002 (2011)], a recently developed complex-scaled version of
ground-state Density Functional Theory (DFT), are studied in detail. The
asymptotic behavior of the complex density function is related to the complex
resonance energy and system's threshold energy, and the function's local
oscillatory behavior is connected with preferential directions of electron
decay. Practical considerations for implementation of the theory are addressed
including sensitivity to the complex-scaling parameter, $\theta$. In Kohn-Sham
DFRT, it is shown that almost all $\theta$-dependence in the calculated
energies and lifetimes can be extinguished via use of a proper basis set or
fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are
related to a physical affinity and width, and the threshold energy of the
Kohn-Sham system is shown to be equal to the threshold energy of the
interacting system shifted by a well-defined functional. Finally, various
complex-scaling conditions are derived which relate the functionals of
ground-state DFT to those of DFRT via proper scaling factors and a
non-Hermitian coupling constant system.",1202.5214v1
2014-07-09,"Charge transport in ion-gated mono-, bi-, and trilayer MoS2 field effect transistors","Charge transport in MoS2 in the low carrier density regime is dominated by
trap states and band edge disorder. The intrinsic transport properties of MoS2
emerge in the high density regime where conduction occurs via extended states.
Here, we investigate the transport properties of mechanically exfoliated mono-,
bi-, and trilayer MoS2 sheets over a wide range of carrier densities realized
by a combination of ion gel top gate and SiO2 back gate which allows us to
achieve high charge carrier (>10^13) density. We discuss the gating properties
of the devices as a function of layer thickness and demonstrate resistivities
of as low as 1 k{\Omega} for monolayer and 420{\Omega} for bilayer devices at
10 K. We show that from the capacitive coupling of the two gates, quantum
capacitance can be roughly estimated to be on the order of 1 {\mu}F/cm^2 for
all devices studied. Temperature dependence of the carrier mobility in the high
density regime indicates that short-range scatterers limit charge transport at
low temperatures.",1407.2439v1
2015-06-17,Local spin-density-wave order inside vortex cores in multiband superconductors,"Coexistence of antiferromagnetic order with superconductivity in many
families of newly discovered iron-based superconductors has renewed interest to
this old problem. Due to competition between the two types of order, one can
expect appearance of the antiferromagnetism inside the cores of the vortices
generated by the external magnetic field. The structure of a vortex in type II
superconductors holds significant importance from the theoretical and the
application points of view. Here we consider the internal vortex structure in a
two-band s$_\pm$ superconductor near a spin-density-wave instability. We treat
the problem in a completely self-consistent manner within the quasiclassical
Eilenberger formalism. We study the structure of the s$_\pm$ superconducting
order and magnetic field-induced spin-density-wave order near an isolated
vortex. We examine the effect of this spin-density-wave state inside the vortex
cores on the local density of states.",1506.05440v2
2014-06-29,Dealing with Zero Density Using Piecewise Phase-type Approximation,"Every probability distribution can be approximated up to a given precision by
a phase-type distribution, i.e. a distribution encoded by a continuous time
Markov chain (CTMC). However, an excessive number of states in the
corresponding CTMC is needed for some standard distributions, in particular
most distributions with regions of zero density such as uniform or shifted
distributions. Addressing this class of distributions, we suggest an
alternative representation by CTMC extended with discrete-time transitions.
Using discrete-time transitions we split the density function into multiple
intervals. Within each interval, we then approximate the density with standard
phase-type fitting. We provide an experimental evidence that our method
requires only a moderate number of states to approximate such distributions
with regions of zero density. Furthermore, the usage of CTMC with discrete-time
transitions is supported by a number of techniques for their analysis. Thus,
our results promise an efficient approach to the transient analysis of a class
of non-Markovian models.",1406.7527v1
2016-08-29,Wide-range shell correction to the Thomas--Fermi theory and equation of state for electrons,"Shell effects reflects irregularities of physical quantities caused by a
discrete energy spectrum. The theory of the shell effects by Kirzhnits and
Shpatakovskaya is valid only at relatively low densities providing for
oscillations of thermodynamic functions. Similar effects for the electronic
binding energy of a neutral atom were considered by Englert and Schwinger. In
this work we propose a method of calculation of shell effects applicable in a
wide range of density and temperature. The model is based on the
finite-temperature Thomas-Fermi theory. Shell corrections to thermodynamic
functions are obtained by special accounting of semiclassical states of bound
electrons in the Thomas-Fermi potential. The results are in good correspondence
with the precise Saha approach for the low density plasma and density
functional theory simulation at high density.",1608.08124v1
2022-06-19,Equation of state of fermions in neutron stars,"Employing both the number density and energy density, the equation of state
of fermions for each microscopic region of a neutron star is derived in the
presence of various statistical effects. It is computed as functions of
temperature (T), chemical potential (\mu) and magnetic field (B) based on the
statistical properties and corresponding phases of neutron stars. It is
revealed that the measurable properties describing the dynamic behavior of a
neutron star are determined by the unusual statistical conditions. It is
demonstrated that, in a strong magnetic field (B larger than\mu), the pressure
(P) shows a logarithmic dependence on B (P is proportional to logarithm
of(\mu/B). It is found that the regions with a higher (lower) magnetic field
(density) have a shorter (longer) life time. Moreover, the relationship between
the magnetic field and chemical potential confirms that the large magnetic
field and high density are short lived as compared to low magnetic field and
low density at the same temperature.",2206.09486v1
1998-08-08,The Influence of the Bulk Density on the Intergranular Properties of YBa2Cu3-xFexOy (0<x<0.01) Ceramics,"The influence of the bulk density of YBa2Cu3-xFexOy (0 < x < 0.01) ceramics
on the intergranular superconducting (SC) properties was studied using the
temperature dependence of AC magnetic susceptibility measurements. It was found
that the simultaneous variation of the sample's density and the iron impurity
concentration does not influence effectively the onset temperature of the
superconducting state Tc(on). While only increasing of the sample's density
shifts the intergranular hysteresis losses peak temperature Tm(J) to the lower
values which connects with the decreasing of the Josephson magnetic vortices
pinning role. It was established that the shielding capability and Tm(J)
display a plateau with X in the 0.003 < X < 0..007 region which is due to the
monotonous decrease of the sample's density. It was shown that the shielding
capability at the T=78K for the sample with 3.8g/cm3 is two times higher than
that for the sample with the density of 5.0g/cm3. The possible interpretations
of the observed results are discussed.",9808086v1
1998-10-07,Energy Transport in the Integrable System in Contact with Various Types of Phonon Reservoirs,"We study how energy transport in an integrable system is affected by the
spectral densities of heat reservoirs. The model investigated here is the
quantum harmonic chain whose both ends are in contact with two heat reservoirs
at different temperatures. The master equation for the reduced density matrix
is derived on the assumption that the reservoirs are composed of an infinite
number of independent harmonic oscillators. We evaluate temperature profile and
energy flux in the stationary state for the master equation and discuss how
they depend on the types of spectral densities. When we attach the reservoirs
of the same type of spectral density, we find that the temperature profile is
independent of the types. On the other hand, when the two reservoirs have
different types of spectral densities, the energy profile near the ends of the
chain depends on the types. When the coupling is finite, the temperature
profile near the ends shows wide variation of behavior dependent on spectral
densities and temperatures of reservoirs. This dependence is discussed with the
Fokker-Planck equations obtained in the classical limit.",9810069v2
2023-01-30,High-Density behavior of symmetry energy and speed of sound in the dense matter within an effective chiral model,"With an effective chiral model, we investigate how the mesonic cross
couplings $\sigma-\rho$ and $\omega-\rho$ affect the density content of the
symmetry energy and its higher-order slope parameters. Earlier mentioned
cross-couplings are crucial to controlling the density content of symmetry
energy. For this purpose, we did a case study for different values of the
symmetry energy $J_1$, defined at density 0.1 fm$^{-3}$ in the range (23.4 -
25.2) for a fixed value of the slope of the symmetry energy $L_0 = 60$ MeV at
saturation density and investigate its effect on the higher-order coefficients
and their influence on the underlying equation of state. We found that the
model with $J_1= 24.6$ MeV is more favorable with the pure neutron matter (PNM)
constraints obtained from $\chi$EFT calculations. In addition, we show that all
of our models predict a monotonically increasing speed of sound up to four
times the saturation density. The speed of sound decreases/saturates above that
point and approaches the conformal limit approximately $\sqrt{1/3}~c$ at the
center of the maximum mass star.",2301.12690v1
2014-08-26,Energy density of variational states,"We show, in several important and general cases, that a low variational
energy density of a trial state is possible even when the trial state
represents a different phase from the ground state. Specifically, we ask
whether the ground state energy density of a Hamiltonian whose ground state is
in phase A can be approximated to arbitrary accuracy by a wavefunction which
represents a different phase B. We show this is indeed the case when A has
discrete symmetry breaking order in one dimension or topological order in two
dimensions, while B is disordered. We argue that, if reasonable conditions of
physicality are imposed upon the trial wavefunction, then this is not possible
when A has discrete symmetry breaking in dimensions greater than one and B is
symmetric, or when A is topologically trivial and B has topological order.",1408.6268v1
2021-09-13,Holographic bottomonium formation in a cooling strong-interaction medium at finite baryon density,"The shrinking of the bottomonium spectral function towards narrow
quasi-particle states in a cooling strong-interaction medium at finite baryon
density is followed within a holographic bottom-up model. The 5-dimensional
Einstein-dilaton-Maxwell background is adjusted to lattice-QCD results of sound
velocity and susceptibilities. The zero-temperature bottomonium spectral
function is adjusted to experimental $\Upsilon$ ground-state mass and first
radial excitations. At baryo-chemical potential $\mu_B = 0$, these two pillars
let emerge the narrow quasi-particle state of the $\Upsilon$ ground state at a
temperature of about 150 MeV. Excited states are consecutively formed at lower
temperatures by about 10 (20) MeV for the $2S$ ($3S$) vector states. The baryon
density, i.e. $\mu_B > 0$, pulls that formation pattern to lower temperatures.
At $\mu_B =$ 200 MeV, we find a shift by about 15 MeV.",2109.05824v1
2007-06-07,Correlation Properties of the Electron-Hole Plasma Interecting with the Exciton Gas and the Formation of Inhomogeneous State,"The correlation properties of the cold system consisting of the electron-hole
plasma interacting with the exciton gas are analyzed. It is shown that the
homogeneous state of the system is unstable and in the stationary state the
densities of the electron-hole plasma and exciton gas are modulated.",0706.0994v2
2015-03-12,About Factorization of Quantum States with Few Qubits,"We study the factorization conditions of a wave function made up of states of
two, three and four qubits and propose and analytical expression which can
characterize entangled states in terms of the coefficients of the wave function
and density matrix elements.",1503.03557v1
2007-06-29,Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States,"We develop the Density Matrix Renormalization Group (DMRG) technique for
numerically studying incompressible fractional quantum Hall (FQH) states on the
sphere. We calculate accurate estimates for ground state energies and
excitationgaps at FQH filling fractions \nu=1/3 and \nu=5/2 for systems that
are almost twice as large as the largest ever studied by exact diagonalization.
We establish, by carefully comparing with existing numerical results on smaller
systems, that DMRG is a highly effective numerical tool for studying
incompressible FQH states.",0706.4469v2
2007-06-13,Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum,"In this paper we consider the question of the degree to which negative and
positive energy are intertwined. We examine in more detail a previously studied
quantum state of the massless minimally coupled scalar field, which we call a
``Helfer state''. This is a state in which the energy density can be made
arbitrarily negative over an arbitrarily large region of space, but only at one
instant in time. In the Helfer state, the negative energy density is
accompanied by rapidly time-varying energy fluxes. It is the latter feature
which allows the quantum inequalities, bounds which restrict the magnitude and
duration of negative energy, to hold for this class of states. An observer who
initially passes through the negative energy region will quickly encounter
fluxes of positive energy which subsequently enter the region. We examine in
detail the correlation between the energy density and flux in the Helfer state
in terms of their expectation values. We then study the correlation function
between energy density and flux in the Minkowski vacuum state, for a massless
minimally coupled scalar field in both two and four dimensions. In this latter
analysis we examine correlation functions rather than expectation values.
Remarkably, we see qualitatively similar behavior to that in the Helfer state.
More specifically, an initial negative energy vacuum fluctuation in some region
of space is correlated with a subsequent flux fluctuation of positive energy
into the region. We speculate that the mechanism which ensures that the quantum
inequalities hold in the Helfer state, as well as in other quantum states
associated with negative energy, is, at least in some sense, already
``encoded'' in the fluctuations of the vacuum.",0706.1970v2
2013-08-20,A consistent determination of the temperature of the intergalactic medium at redshift z=2.4,"We present new measurements of the thermal state of the intergalactic medium
(IGM) at $z\sim2.4$ derived from absorption line profiles in the Ly$\alpha$
forest. We use a large set of high-resolution hydrodynamical simulations to
calibrate the relationship between the temperature-density ($T$--$\Delta$)
relation in the IGM and the distribution of HI column densities, $N_{\rm HI}$,
and velocity widths, $b_{\rm HI}$, of discrete Ly$\alpha$ forest absorbers.
This calibration is then applied to the measurement of the lower cut-off of the
$b_{\rm HI}$--$N_{\rm HI}$ distribution recently presented by Rudie et al.
(2012). We infer a power-law $T$--$\Delta$ relation,
$T=T_{0}\Delta^{\gamma-1}$, with a temperature at mean density,
$T_{0}=[1.00^{+0.32}_{-0.21}]\times10^{4}\rm\,K$ and slope
$(\gamma-1)=0.54\pm0.11$. The slope is fully consistent with that advocated by
the analysis of Rudie et al (2012); however, the temperature at mean density is
lower by almost a factor of two, primarily due to an adjustment in the
relationship between column density and physical density assumed by these
authors. These new results are in excellent agreement with the recent
temperature measurements of Becker et al. (2011), based on the curvature of the
transmitted flux in the Ly$\alpha$ forest. This suggests that the thermal state
of the IGM at this redshift is reasonably well characterised over the range of
densities probed by these methods.",1308.4411v2
1999-11-18,Gapped Phases of Quantum Wires,"We investigate possible nontrivial phases of a two-subband quantum wire. It
is found that inter- and intra-subband interactions may drive the electron
system of the wire into a gapped state. If the nominal electron densities in
the two subbands are sufficiently close to each other, then the leading
instability is the inter-subband charge-density wave (CDW). For large density
imbalance, the interaction in the inter-subband Cooper channel may lead to a
superconducting instability. The total charge-density mode, responsible for the
conductance of an ideal wire, always remains gapless, which enforces the
two-terminal conductance to be at the universal value of 2e^2/h per occupied
subband. On the contrary, the tunneling density of states (DOS) in the bulk of
the wire acquires a hard gap, above which the DOS has a non-universal
singularity. This singularity is weaker than the square-root divergency
characteristic for non-interacting quasiparticles near a gap edge due to the
""dressing"" of massive modes by a gapless total charge density mode. The DOS for
tunneling into the end of a wire in a CDW-gapped state preserves the power-law
behavior due to the frustration the edge introduces into the CDW order. This
work is related to the vast literature on coupled 1D systems, and most of all,
on two-leg Hubbard ladders. Whenever possible, we give derivations of the
important results by other authors, adopted for the context of our study.",9911286v1
2018-06-20,Chiral topological states in Bose-Fermi mixtures,"Topological states were initially discovered in solid state systems and have
generated widespread interest in many areas of physics. The advances in cold
atoms create novel settings for studying topological states that would be quite
unrealistic in solid state systems. One example is that the constituents of
quantum gases can be various types of bosons, fermions, and their mixtures.
This paper explores interaction-induced topological states in two-dimensional
Bose-Fermi mixture. We propose a class of topological states which have no
fractionalized excitations but possess maximally chiral edge states. For
previously known topological states, these two features can only be found
simultaneously in the integer quantum Hall states of fermions and the $E_{8}$
state of bosons. The existences of some proposed states in certain continuum
and lattice models are corroborated by exact diagonalization and density matrix
renormalization group calculations. This paper suggests that Bose-Fermi mixture
is a very appealing platform for studying topological states.",1806.07634v2
2000-11-23,"su(2) and su(1,1) displaced number states and their nonclassical properties","We study su(2) and su(1,1) displaced number states. Those states are
eigenstates of density-dependent interaction systems of quantized radiation
field with classical current. Those states are intermediate states
interpolating between number and displaced number states. Their photon number
distribution, statistical and squeezing properties are studied in detail. It is
show that these states exhibit strong nonclassical properties.",0011096v1
2019-07-12,A Criterion to identify maximally entangled nine-qubit state,"We present a generalized criterion for maximally entangled nine-qubit states,
whose minimum averaged subsystem purity should be equal to 1/14. In this note,
we prove that absolutely maximally entangled state for nine qubits does not
exist. Further, we construct a new genuine nine-qubit maximally entangled
states of 110,15 and 1 balanced purities equal to 1/16, , 1/8 and and 1/4,
respectively. We found that, the marginal density matrices for subsystems of
1,2,3- qubits all completely mixed in these states, therefore, maximally
entangled nine-qubit state is a 3-uniform state.",1907.05612v1
2012-05-12,Laplacian matrices of weighted digraphs represented as quantum states,"Representing graphs as quantum states is becoming an increasingly important
approach to study entanglement of mixed states, alternate to the standard
linear algebraic density matrix-based approach of study. In this paper, we
propose a general weighted directed graph framework for investigating
properties of a large class of quantum states which are defined by three types
of Laplacian matrices associated with such graphs. We generalize the standard
framework of defining density matrices from simple connected graphs to density
matrices using both combinatorial and signless Laplacian matrices associated
with weighted directed graphs with complex edge weights and with/without
self-loops. We also introduce a new notion of Laplacian matrix, which we call
signed Laplacian matrix associated with such graphs. We produce necessary
and/or sufficient conditions for such graphs to correspond to pure and mixed
quantum states. Using these criteria, we finally determine the graphs whose
corresponding density matrices represent entangled pure states which are well
known and important for quantum computation applications. We observe that all
these entangled pure states share a common combinatorial structure.",1205.2747v2
2021-09-10,Ensemble Density Functional Theory of Neutral and Charged Excitations,"Recent progress in the field of (time-independent) ensemble
density-functional theory (DFT) for excited states are reviewed. Both
Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are
mathematically very similar and allow for an in-principle-exact description of
neutral and charged electronic excitations, respectively, are discussed. Key
exact results like, for example, the equivalence between the infamous
derivative discontinuity problem and the description of weight dependencies in
the ensemble exchange-correlation density functional, are highlighted. The
variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx)
energies is discussed in detail. We show in passing that state-averaging
individual exact Hx energies can lead to severe (solvable though)
$v$-representability issues. Finally, we explore the possibility to use the
concept of density-driven correlation, which has been recently introduced and
does not exist in regular ground-state DFT, for improving state-of-the-art
correlation density-functional approximations for ensembles. The present review
reflects the efforts of a growing community to turn ensemble DFT into a
rigorous and reliable low-cost computational method for excited states. We hope
that, in the near future, this contribution will stimulate new formal and
practical developments in the field.",2109.04943v2
2012-08-20,The density number of filaments in the state of the weak and optical turbulence,"We consider the statistics of density number of filaments for the propagation
of a laser beam subjected to multiple filamentation in a closed area with
reflecting boundaries. Dissipation arrests the catastrophic collapse of
filaments, causing their disintegration into almost linear waves.These waves
form a nearly gaussian random field that seeds new filaments. The evolution of
the energy distribution function of the angular spectrum and accordingly law of
the dynamics of formation of the thermodynamic characteristics of the light
field such as the effective temperature and entropy was found. It is
established that the growth rate of the thermodynamic functions and the
Hamiltonian of the system grows in proportion to the number density of
filaments. Also found that depending on the level of the average (background)
intensity of the light field can move in two steady state. The first mode is
realized for the steady state level of the background intensity does not exceed
the value, and is characterized by typical classical (linear) of a closed
thermodynamic system, a constant level of entropy and temperature, while the
number density of the filaments is equal to zero. In a strongly nonlinear
regime, steady state when the number density of filaments goes to a constant
level, depending on a cubic, but the entropy and the effective temperature rise
in a linear fashion from the distance of propagation. Patterns of development
of the number density of filaments with access to a steady state, are
nonmonotonic and significantly determined by the initial angular spectral
energy distribution of the light field. The average value of filament density
depends on the intensity of the complex way the linear growth stage is replaced
with the output of the nonlinear saturation, nonlinear growth, corresponding to
the transition to the regime of developed turbulence with growth rate in the
third degree.",1208.3916v1
2005-01-20,Density of states modulation in the pseudogap state of high-$T_c$ superconductors,"The density of states modulation recently observed by the scanning tunneling
microscopic experiment in the pseudogap state of high-$T_c$ superconductors is
explained by the pairing assisted particle transitions under perturbation of a
periodic pairing interaction. In such a transition process, a particle with
momentum ${\bf k}$ firstly picks up another particle of inverse spin to produce
a pair leaving a hole. Under the perturbation of periodic pairing interaction
of modulation wave vector ${\bf Q}$, the pair absorbs a momentum ${\bf Q}$ and
then breaks into two single-particles: one propagates with momentum ${\bf
k+Q}$, and another one fills in the hole. The transition is significant at low
energies within the pseudogap since where the pairing excitations most
favorably survive. We calculate the Fourier component of the modulated density
of states using two different models. Both of the theoretical results are
consistent with the experiment.",0501480v1
2002-08-08,Determination of the Equation of State of Dense Matter,"Nuclear collisions can compress nuclear matter to densities achieved within
neutron stars and within core-collapse supernovae. These dense states of matter
exist momentarily before expanding. We analyzed the flow of matter to extract
pressures in excess of 10^34 pascals, the highest recorded under
laboratory-controlled conditions. Using these analyses, we rule out strongly
repulsive nuclear equations of state from relativistic mean field theory and
weakly repulsive equations of state with phase transitions at densities less
than three times that of stable nuclei, but not equations of state softened at
higher densities because of a transformation to quark matter.",0208016v2
2004-07-19,Construction of accurate Kohn-Sham potentials for the lowest states of the helium atom: Accurate test of the ionization-potential theorem,"Accurate local Kohn-Sham potentials have been constructed for the ground
$1s^2 ^1S$ state and, in particular, for the lowest triplet $1s2s ^{3}S$ state
of the helium atom, using electron densities from many-body calculations and
the procedure of van Leeuwen and Baerends (Phys. Rev. A{\bf49}, 2138 (1994)).
The resulting Kohn-Sham orbitals reproduce the many-body densities very
accurately, and furthermore we have demonstrated that the negative of the
energy eigenvalue of the outermost electron orbital agrees with the
corresponding ionization energy with extreme accuracy. The procedure is also
applied to the Hartree-Fock density of the $1s2s ^{3}S$ state, and the
Kohn-Sham eigenvalue of the $2s$ orbital is found to agree very well with the
corresponding Hartree-Fock eigenvalue, which is the negative of the ionization
energy in this model due to Koopmans' theorem. The results for the $1s2s ^{3}S$
state clearly demonstrate that there is no conflict between the locality of the
Kohn-Sham potential and the exclusion principle, as claimed by Nesbet (Phys.
Rev. A{\bf58}, R12 (1998)).",0407095v1
2007-06-18,Electron-Electron Interactions on the Edge States of Graphene: A Many Body Configuration Interaction Study,"We have studied zigzag and armchair graphene nano ribbons (GNRs), described
by the Hubbard Hamiltonian using quantum many body configuration interaction
methods. Due to finite termination, we find that the bipartite nature of the
graphene lattice gets destroyed at the edges making the ground state of the
zigzag GNRs a high spin state, whereas the ground state of the armchair GNRs
remains a singlet. Our calculations of charge and spin densities suggest that,
although the electron density prefers to accumulate on the edges, instead of
spin polarization, the up and down spins prefer to mix throughout the GNR
lattice. While the many body charge gap results in insulating behavior for both
kinds of GNRs, the conduction upon application of electric field is still
possible through the edge channels because of their high electron density.
Analysis of optical states suggest differences in quantum efficiency of
luminescence for zigzag and armchair GNRs, which can be probed by simple
experiments.",0706.2528v2
2011-06-15,Future cosmological evolution in $f(R)$ gravity using two equations of state parameters,"We investigate the issues of future oscillations around the phantom divide
for $f(R)$ gravity. For this purpose, we introduce two types of energy density
and pressure arisen from the $f(R)$-higher order curvature terms. One has the
conventional energy density and pressure even in the beginning of the Jordan
frame, whose continuity equation provides the native equation of state $w_{\rm
DE}$. On the other hand, the other has the different forms of energy density
and pressure which do not obviously satisfy the continuity equation. This needs
to introduce the effective equation of state $w_{\rm eff}$ to describe the
$f(R)$-fluid, in addition to the native equation of state $\tilde{w}_{\rm DE}$.
We confirm that future oscillations around the phantom divide occur in $f(R)$
gravities by introducing two types of equations of state. Finally, we point out
that the singularity appears ar $x=x_c$ because the stability condition of
$f(R)$ gravity violates.",1106.2865v2
2013-11-18,Dynamically Optimized Wang-Landau Sampling with Adaptive Trial Moves and Modification Factors,"The density of states of continuous models is known to span many orders of
magnitudes at different energies due to the small volume of phase space near
the ground state. Consequently, the traditional Wang-Landau sampling which uses
the same trial move for all energies faces difficulties sampling the low
entropic states. We developed an adaptive variant of the Wang-Landau algorithm
that very effectively samples the density of states of continuous models across
the entire energy range. By extending the acceptance ratio method of Bouzida,
Kumar, and Swendsen such that the step size of the trial move and acceptance
rate are adapted in an energy-dependent fashion, the random walker efficiently
adapts its sampling according to the local phase space structure. The
Wang-Landau modification factor is also made energy-dependent in accordance
with the step size, enhancing the accumulation of the density of states.
Numerical simulations show that our proposed method performs much better than
the traditional Wang-Landau sampling.",1311.4237v1
2015-07-02,Hyperfine transitions of 13CN from pre-protostellar sources,"Recent quantum mechanical calculations of rate coefficients for collisional
transfer of population between the hyperfine states of 13CN enable their
population densities to be determined. We have computed the relative
populations of the hyperfine states of the N = 0, 1, 2 rotational states for
kinetic temperatures 5 $\le$ T $\le$ 20 K and molecular hydrogen densities 1
$\le$ n(H2) $\le$10 10 cm --3. Spontaneous and induced radiative transitions
were taken into account. Our calculations show that, if the lines are optically
thin, the populations of the hyperfine states, F, within a given rotational
manifold are proportional to their statistical weights, (2F + 1) -- i.e. in
local thermodynamic equilibrium -- over the entire range of densities. We have
re-analysed IRAM 30 m telescope observations of 13CN hyperfine transitions (N =
1 $\rightarrow$ 0) in four starless cores. A comparison of these observations
with our calculations confirms that the hyperfine states are statistically
populated in these sources.",1507.00709v1
2015-11-26,Theoretical study on density of microscopic states in configuration space via Random Matrix,"In classical systems, our recent theoretical study provides new insight into
how spatial constraint on the system connects with macroscopic properties,
which lead to universal representation of equilibrium macroscopic physical
property and structure in disordered states. These important characteristics
rely on the fact that statistical interdependence for density of microscopic
states (DOMS) in configuration space appears numerically vanished at
thermodynamic limit for a wide class of spatial constraints, while such
behavior of the DOMS is not quantitatively well-understood so far. The present
study theoretically address this problem based on the Random Matrix with
Gaussian Orthogonal Ensemble, where corresponding statistical independence is
mathematically guaranteed. Using the generalized Ising model, we confirm that
lower-order moment of density of eigenstates (DOE) of covariance matrix of DOMS
shows asymptotic behavior to those for Random Matrix with increase of system
size. This result supports our developed theoretical approach, where
equilibrium macroscopic property in disordered states can be decomposed into
individual contribtion from each generalized coordinate with the sufficiently
high number of constituents in the given system, leading to representing
equilibrium macroscopic properties by a few special microscopic states.",1511.08312v1
2020-07-29,Density of states and current-voltage characteristics in SIsFS junctions,"We study the density of states (DOS) inside superconducting Josephson SIsFS
junctions with complex interlayer consisting of a thin superconducting spacer
's' between insulator I and a ferromagnetic metal F. The consideration is
focused on the local density of states in the vicinity of a tunnel barrier, and
it permits to estimate the current-voltage characteristics in the resistive
state of such junctions. We study the influence of the proximity effect and
Zeeman splitting on the properties of the system, and we find significant
sub-gap regions with non-vanishing DOS. We also find manifestations of the
0-$\pi$ transition in the behavior of DOS in a thin s-layer. These properties
lead to appearance of new characteristic features on I-V curves which provide
additional information about electronic states inside the junction.",2007.15054v2
2020-06-05,Absence of superconducting dome at the charge-density-wave quantum phase transition in 2H-NbSe2,"Superconductivity is often found in a dome around quantum critical points,
i.e. 2nd-order quantum phase transitions. Here, we show that an enhancement of
superconductivity is avoided at the critical pressure of the
charge-density-wave (CDW) state in NbSe$_2$. We present comprehensive
high-pressure Hall effect and magnetic susceptibility measurements of the CDW
and superconducting state in NbSe$_2$. Initially, the 2nd-order CDW transition
is suppressed smoothly but it drops to zero abruptly at PCDW = 4.4 GPa thus
indicating a change to 1st order whilstthe superconducting transition
temperature Tc rises continuously up to PCDW but is constant above. The
putative 1st-order nature of the CDW transition is suggested as the cause for
the absence of a superconducting dome at PCDW. Indeed, we show that the
suppression of the superconducting state at low pressures is due to the loss of
density of states inside the CDW phase whilst the initial suppression of the
CDW state is accounted for by the stiffening of the underlying bare phonon
mode.",2006.03422v3
2020-11-11,Long-lived non-thermal states in pumped one-dimensional systems of hard-core bosons,"We study a unitary time evolution of a symmetry-broken state in a form of a
charge density wave in a finite system of interacting hard-core bosons, which
can be mapped onto the XXZ Heisenberg chain. Moreover, we introduce a
spatially-homogenous and time-dependent vector potential that mimics a short
laser pulse. We establish the range of amplitudes of the vector potential for
which the onset of charge density wave order can be controlled. We propose a
protocol that reveals non-thermal long-lived states, which are characterized by
a non-zero charge density wave order translated by one lattice site with
respect to its initial formation. The life times of these states are large in
comparison to all typical times given by the parameters of the system. They
increase with the number of lattice sites, but are significantly suppressed by
the integrablility breaking perturbations. In view of these findings, we
speculate that the long-lived non-thermal states exist in the thermodynamic
limit.",2011.05849v2
2021-01-02,Density profile of multi-state fuzzy dark matter,"Equations of motion for excited states of weakly self-interacting bosons
forming fuzzy dark matter are solved using the WKB approximation. The
contribution of self-interactions are neglected in the equations of motion.
Wave functions of excited states are expressed in terms of a yet undetermined
gravitational potential. At equilibrium, the contributions of states to the
density distribution are summed using Bose-Einstein statistics. Combined with
the Poisson equation, a differential equation is obtained for the gravitational
potential, which has physically acceptable solutions only if the energy
spectrum of excited states has a finite gap, corresponding to a finite virial
radius. Such a gap could be created by decay processes, in first order
perturbation of the self-interaction potential. The obtained density profile is
found to be similar to the Burkert profile.",2101.00349v1
2021-05-11,Coulomb impurity on a Dice lattice: atomic collapse and bound states,"The modification of the quantum states in a Dice lattice due to a Coulomb
impurity are investigated. The energy band structure of a pristine Dice lattice
consists of a Dirac cone and a flat band at the Dirac point. We use the tight
binding formalism and find that the flat band states transform into a set of
discrete bound states whose electron density is localized on a ring around the
impurity mainly on two of the three sublattices. The energy is proportional to
the strength of the Coulomb impurity. Beyond a critical strength of the Coulomb
potential atomic collapse states appear that have some similarity with those
found in graphene with the difference that the flat band states contribute with
an additional ring-like electron density that is spatially decoupled from the
atomic collapse part. At large value of the strength of the Coulomb impurity
the flat band bound states anti-cross with the atomic collapse states.",2105.05065v1
2012-12-24,Interplay between the symmetry energy and the strangeness content of neutron stars,"The effect of the density dependence of the nucleonic equation of state and
the hyperon meson couplings on the star properties, including strangeness
content, mass and radius, are studied within a relativistic mean field
formalism. It is shown that there is still lacking information on the nucleonic
equation of state at supra-saturation densities and on the hyperon interactions
in nuclear matter that will allow a clear answer to the question whether the
mass of the pulsar J1614-2230 could rule out exotic degrees of freedom from the
interior of compact stars. We show that some star properties are affected in a
similar way by the density dependence of the symmetry energy and the hyperon
content of the star. To disentangle these two effects it is essential to have a
good knowledge of the equation of state at supra-saturation densities. A linear
correlation between the radius and the strangeness content of a star with a
fixed mass is obtained.",1212.5911v3
2021-06-16,Electronic and Band Structure Calculation of Wurtzite CdS Using GGA and GGA+U functionals,"The wurtzite (wz) structure of CdS is analyzed using density functional
theory within the generalized gradient approximation (GGA) and Hubbard
correction (GGA+U). The total energy convergence evaluation is carried out
concerning energy cut-off (ecutwfc) and k-point sampling. The geometry
optimization of wz-CdS is calculated using the total energy and force
minimization process, which is based on the Broyden Fletcher Goldfarb Shanno
(BFGS) optimization algorithm. Bulk modulus and lattice parameters are
estimated to ensure accuracy of the calculations. The electronic band
structure, density of states (DOS), and projected density of states (PDOS) of
wz-CdS are analyzed. The band structure calculation shows CdS as direct band
gap semiconductor. The electronic correlation in CdS is altered by varying
U-parameters of valence orbitals of Cd and S. The alteration of electronic
correlation results in convergence of the band gap to the experimental value
2.4 eV. The alteration of U-parameter affects substantially the density of
states near the band edges.",2106.08875v1
1999-06-16,Measuring the equation of state of the intergalactic medium,"(Abridged) Numerical simulations indicate that the intergalactic medium (IGM)
responsible for the low column density Lyman-alpha forest follows a well
defined temperature-density relation. We demonstrate that such an equation of
state results in a cutoff in the distribution of line widths (b-parameters) as
a function of column density (N) for the low column density absorption lines.
This explains the existence of the lower envelope which is clearly seen in
scatter plots of the b(N)-distribution in observed QSO spectra. We show that
the parameters of the cutoff in the b(N)-distribution are strongly correlated
with the parameters of the underlying equation of state. We use simulations to
determine these relations, which can then be applied to the observed cutoff in
the b(N)-distribution to measure the equation of state of the IGM. Using Monte
Carlo simulations of Keck spectra at z=3, we show that determining the slope of
the equation of state will be difficult, but that the amplitude can be
determined to within ten per cent, even from a single QSO spectrum. Measuring
the evolution of the equation of state with redshift will allow us to put tight
constraints on the reionization history of the universe.",9906271v1
2023-03-22,$CrowdDiff$: Multi-hypothesis Crowd Density Estimation using Diffusion Models,"Crowd counting is a fundamental problem in crowd analysis which is typically
accomplished by estimating a crowd density map and summing over the density
values. However, this approach suffers from background noise accumulation and
loss of density due to the use of broad Gaussian kernels to create the ground
truth density maps. This issue can be overcome by narrowing the Gaussian
kernel. However, existing approaches perform poorly when trained with ground
truth density maps with broad kernels. To deal with this limitation, we propose
using conditional diffusion models to predict density maps, as diffusion models
show high fidelity to training data during generation. With that, we present
$CrowdDiff$ that generates the crowd density map as a reverse diffusion
process. Furthermore, as the intermediate time steps of the diffusion process
are noisy, we incorporate a regression branch for direct crowd estimation only
during training to improve the feature learning. In addition, owing to the
stochastic nature of the diffusion model, we introduce producing multiple
density maps to improve the counting performance contrary to the existing crowd
counting pipelines. We conduct extensive experiments on publicly available
datasets to validate the effectiveness of our method. $CrowdDiff$ outperforms
existing state-of-the-art crowd counting methods on several public crowd
analysis benchmarks with significant improvements.",2303.12790v3
2011-07-07,Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes,"We classify, up to local unitary equivalence, local unitary stabilizer Lie
algebras for symmetric mixed states into six classes. These include the
stabilizer types of the Werner states, the GHZ state and its generalizations,
and Dicke states. For all but the zero algebra, we classify entanglement types
(local unitary equivalence classes) of symmetric mixed states that have those
stabilizers. We make use of the identification of symmetric density matrices
with polynomials in three variables with real coefficients and apply the
representation theory of SO(3) on this space of polynomials.",1107.1372v2
2012-06-12,Operational typicality of the nonequilibrium states: a thermodynamic lower bound of the deviation from equilibrium,"The typicality of the canonical state shows that majority of the states are
indistinguishable from equilibrium, and thus the nonequilibrium states are
exceptionally rare in the extremely high-dimensional Hilbert space. On the
contrary, we can easily apply an external force acting on the system, and then
the actual density matrix quantitatively deviates from the canonical state
specified by the system Hamiltonian at each instance. To express how the
external forcing amounts to the deviation from equilibrium, we give a universal
thermodynamic expression of the lower bound of Hilbert-Schmidt distance between
the actual nonequilibrium and corresponding canonical states. The lower bound
is expressed only by the amount of forcing and its consequent entropy
production rate.",1206.2577v1
2023-04-24,QCD bound states in motion,"I consider the frame dependence of QCD bound states in the presence of a
confining, spatially constant gluon field energy density. The states are
quantized at equal time in $A^0=0$ (temporal) gauge. I derive the frame
dependence of the wave functions, and demonstrate the Lorentz covariance of the
electromagnetic (transition) form factors for states of any spin. The wave
functions of $J^{PC}=0^{-+}$ states with CM momentum $P \neq 0$ are considered
in some detail, verifying their local normalizability and the expected frame
dependence of the bound state energy.",2304.11903v2
1997-11-05,Quantum-Mechanical Analysis of Single-Particle Level Density,"A quantum-mechanical calculation of the single-particle level (s.p.l.)
density $g(\epsilon)$ is carried on by using the connection with the
single-particle Green's function. The relation between the imaginary part of
Green's function and single-particle wave functions is used separately for the
discrete and continuous states. Within the bound-states region the imaginary
part of the Green's function is calculated by using the wronskian theorem. The
Green's function corresponding to the continuum is written by using the regular
and Jost solutions of the radial Schrodinger equation. The smooth part of the
rapidly fluctuating s.p.l. density is calculated by means of the Strutinski
procedure. The continuum component of the s.p.l. density has rather close
values within either exact quantum-mechanical calculations with the Woods-Saxon
(WS) potential, or Thomas-Fermi approximation with WS as well as finite-square
potential wells, provided that the free-gas contribution is subtracted. A
similar trend is obtained by means of the simple FGM formula for the s.p.l.
density if the continuum effect is taken into account.",9711007v3
2011-06-17,Scaling properties of induced density of chiral and non-chiral Dirac fermions in magnetic fields,"We find that a repulsive potential of graphene in the presence of a magnetic
field has bound states that are peaked inside the barrier with tails extending
over \ell(N + 1), where \ell and N are the magnetic length and Landau level(LL)
index. We have investigated how these bound states affect scaling properties of
the induced density of filled Landau levels of massless Dirac fermions. For
chiral fermions we find, in strong coupling regime, that the density inside the
repulsive potential can be greater than the value in the absence of the
potential while in the weak coupling regime we find negative induced density.
Similar results hold also for non-chiral fermions. As one moves from weak to
strong coupling regimes the effective coupling constant between the potential
and electrons becomes more repulsive, and then it changes sign and becomes
attractive. Different power-laws of induced density are found for chiral and
non-chiral fermions.",1106.3387v2
2014-11-27,Levy-Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo,"The constrained-search principle introduced by Levy and Lieb, is proposed as
a practical, though conceptually rigorous, link between Density Functional
Theory (DFT) and Quantum Monte Carlo (QMC). The resulting numerical protocol
realizes in practice the implicit key statement of DFT: ""Given the three
dimensional electron density of the ground state of a system of N electrons
with external potential v(r) it is possible to find the corresponding
3N-dimensional wavefunction of ground state."" From a numerical point of view,
the proposed protocol can be employed to speed up the QMC procedure by
employing DFT densities as a pre-selection criterion for the sampling of
wavefunctions.",1411.7535v1
2020-01-04,Transverse density fluctuations around the ground state distribution of counterions near one charged plate: stochastic density functional view,"We consider the Dean-Kawasaki (DK) equation of overdamped Brownian particles
that forms the basis of the stochastic density functional theory. Recently, the
linearized DK equation has successfully reproduced the full Onsager theory of
symmetric electrolyte conductivity. In this paper, the linear DK equation is
applied to investigate density fluctuations around the ground state
distribution of strongly coupled counterions near a charged plate, focusing
especially on the transverse dynamics along the plate surface. Consequently, we
find a crossover scale above which the transverse density dynamics appears
frozen and below which diffusive behavior of counterions can be observed on the
charged plate. The linear DK equation provides a characteristic length of the
dynamical crossover that is similar to the Wigner-Seitz radius used in
equilibrium theory for the 2D one-component plasma, which is our main result.
Incidentally, general representations of longitudinal dynamics vertical to the
plate further suggest the existence of advective and electrically reverse
flows; these effects remain to be quantitatively investigated.",2001.01039v1
2020-05-27,On the complexity of finding the maximum entropy compatible quantum state,"Herein we study the problem of recovering a density operator from a set of
compatible marginals, motivated from limitations of physical observations.
Given that the set of compatible density operators is not singular, we adopt
Jaynes' principle and wish to characterize a compatible density operator with
maximum entropy. We first show that comparing the entropy of compatible density
operators is QSZK-complete, even for the simplest case of 3-chains. Then, we
focus on the particular case of quantum Markov chains and trees and establish
that for these cases, there exists a quantum polynomial circuit that constructs
the maximum entropy compatible density operator. Finally, we extend the
Chow-Liu algorithm to the same subclass of quantum states.",2005.13371v1
2021-07-20,Imposing multi-physics constraints at different densities on the Neutron Star Equation of State,"Neutron star matter spans a wide range of densities, from that of nuclei at
the surface to exceeding several times normal nuclear matter density in the
core. While terrestrial experiments, such as nuclear or heavy-ion collision
experiments, provide clues about the behaviour of dense nuclear matter, one
must resort to theoretical models of neutron star matter to extrapolate to
higher density and finite neutron/proton asymmetry relevant for neutron stars.
In this work, we explore the parameter space within the framework of the
Relativistic Mean Field model allowed by present uncertainties compatible with
state-of-the-art experimental data. We apply a cut-off filter scheme to
constrain the parameter space using multi-physics constraints at different
density regimes: chiral effective field theory, nuclear and heavy-ion collision
data as well as multi-messenger astrophysical observations of neutron stars.
Using the results of the study, we investigate possible correlations between
nuclear and astrophysical observables.",2107.09371v3
2021-12-01,"Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids","Electron density $\rho(\vec{r})$ is the fundamental variable in the
calculation of ground state energy with density functional theory (DFT). Beyond
total energy, features and changes in $\rho(\vec{r})$ distributions are often
used to capture critical physicochemical phenomena in functional materials. We
present a machine learning framework for the prediction of $\rho(\vec{r})$. The
model is based on equivariant graph neural networks and the electron density is
predicted at special query point vertices that are part of the message passing
graph, but only receive messages. The model is tested across multiple data sets
of molecules (QM9), liquid ethylene carbonate electrolyte (EC) and
LixNiyMnzCo(1-y-z)O2 lithium ion battery cathodes (NMC). For QM9 molecules, the
accuracy of the proposed model exceeds typical variability in $\rho(\vec{r})$
obtained from DFT done with different exchange-correlation functionals. The
accuracy on all three datasets is beyond state of the art and the computation
time is orders of magnitude faster than DFT.",2112.00652v2
2013-07-16,Neutron skin uncertainties of Skyrme energy density functionals,"Background: Neutron-skin thickness is an excellent indicator of isovector
properties of atomic nuclei. As such, it correlates strongly with observables
in finite nuclei that depend on neutron-to-proton imbalance and the nuclear
symmetry energy that characterizes the equation of state of neutron-rich
matter. A rich worldwide experimental program involving studies with rare
isotopes, parity violating electron scattering, and astronomical observations
is devoted to pinning down the isovector sector of nuclear models. Purpose: We
assess the theoretical systematic and statistical uncertainties of neutron-skin
thickness and relate them to the equation of state of nuclear matter, and in
particular to nuclear symmetry energy parameters. Methods: We use the nuclear
superfluid Density Functional Theory with several Skyrme energy density
functionals and density dependent pairing. To evaluate statistical errors and
their budget, we employ the statistical covariance technique. Results: We find
that the errors on neutron skin increase with neutron excess. Statistical
errors due to uncertain coupling constants of the density functional are found
to be larger than systematic errors, the latter not exceeding 0.06 fm in most
neutron-rich nuclei across the nuclear landscape. The single major source of
uncertainty is the poorly determined slope L of the symmetry energy that
parametrizes its density dependence. Conclusions: To provide essential
constraints on the symmetry energy of the nuclear energy density functional,
next-generation measurements of neutron skins are required to deliver precision
better than 0.06 fm.",1307.4223v1
2019-01-31,Equation of state of dense matter in the multimessenger era,"While the equation of state (EOS) of symmetric nuclear matter (SNM) at
suprasaturation densities has been relatively well constrained from heavy-ion
collisions, the EOS of high-density neutron-rich matter is still largely
uncertain due to the poorly known high-density behavior of the symmetry energy.
Using the constraints on the EOS of SNM at suprasaturation densities from
heavy-ion collisions together with the data of finite nuclei and the existence
of $2M_\odot$ neutron stars from electromagnetic (EM) observations, we show
that the high-density symmetry energy cannot be too soft, which leads to lower
bounds on dimensionless tidal deformability of $\Lambda_{1.4} \ge 193$ and
radius of $R_{1.4} \ge 11.1$ km for $1.4M_\odot$ neutron star. Furthermore, we
find that the recent constraint of $\Lambda_{1.4} \le 580$ from the
gravitational wave signal GW170817 detected from the binary neutron star merger
by the LIGO and Virgo Collaborations rules out too stiff high-density symmetry
energy, leading to an upper limit of $R_{1.4} \le 13.3$ km. All these
terrestrial nuclear experiments and astrophysical observations based on strong,
EM and gravitational measurements together put stringent constraints on the
high-density symmetry energy and the EOS of SNM, pure neutron matter and
neutron star matter.",1901.11364v2
2023-08-15,Bound state breaking and the importance of thermal exchange-correlation effects in warm dense hydrogen,"Hydrogen at extreme temperatures and pressures is ubiquitous throughout our
universe and naturally occurs in a variety of astrophysical objects. In
addition, it is of key relevance for cutting-edge technological applications,
with inertial confinement fusion research being a prime example. In the present
work, we present exact \emph{ab initio} path integral Monte Carlo (PIMC)
results for the electronic density of warm dense hydrogen along a line of
constant degeneracy across a broad range of densities. Using the well-known
concept of reduced density gradients, we develop a new framework to identify
the breaking of bound states due to pressure ionization in bulk hydrogen.
Moreover, we use our PIMC results as a reference to rigorously assess the
accuracy of a variety of exchange--correlation (XC) functionals in density
functional theory calculations for different density regions. Here a key
finding is the importance of thermal XC effects for the accurate description of
density gradients in high-energy density systems. Our exact PIMC test set is
freely available online and can be used to guide the development of new
methodologies for the simulation of warm dense matter and beyond.",2308.07916v2
1999-06-21,The Schrödinger formulation of the Feynman path centroid density,"We present an analysis of the Feynman path centroid density that provides new
insight into the correspondence between the path integral and the Schr\""odinger
formulations of statistical mechanics. The path centroid density is a central
concept for several approximations (centroid molecular dynamics, quantum
transition state theory, and pure quantum self-consistent harmonic
approximation) that are used in path integral studies of thermodynamic and
dynamical properties of quantum particles. The centroid density is related to
the quasi-static response of the equilibrium system to an external force. The
path centroid dispersion is the canonical correlation of the position operator,
that measures the linear change in the mean position of a quantum particle upon
the application of a constant external force. At low temperatures, this
quantity provides an approximation to the excitation energy of the quantum
system. In the zero temperature limit, the particle's probability density
obtained by fixed centroid path integrals corresponds to the probability
density of minimum energy wave packets, whose average energy define the Feynman
effective classical potential.",9906318v1
2003-08-11,Divergence of the effective mass near a density wave instability in a MOSFET system,"We study the renormalization of the Fermi-liquid parameters in the vicinity
of a density wave quantum phase transition, which should occur in MOSFET
systems at low densities. First, using a perturbative RPA treatment of
fluctuations, we calculate the electronic self-energy and show that the
effective mass diverges at the density wave transition point. Second, we go
beyond perturbation theory, making use of the exact Pitaevskii identities.
Within this exact analysis, we also find a divergence of the effective mass,
which occurs at higher densities in the fluctuation region, as compared to the
perturbation theory. This result signals the break-down of conventional
Fermi-liquid description in the vicinity of the transition point. The
divergence of the effective mass gives rise to a singular behavior of the
electronic compressibility. We suggest that the experimentally observed
enhancement of the effective mass is a precursor to a second order
thermodynamic phase transition into a glassy density wave state.",0308203v1
2007-08-21,Symmetry Energy as a Function of Density and Mass,"Energy in nuclear matter is, in practice, completely characterized at
different densities and asymmetries, when the density dependencies of symmetry
energy and of energy of symmetric matter are specified. The density dependence
of the symmetry energy at subnormal densities produces mass dependence of
nuclear symmetry coefficient and, thus, can be constrained by that latter
dependence. We deduce values of the mass dependent symmetry coefficients, by
using excitation energies to isobaric analog states. The coefficient
systematic, for intermediate and high masses, is well described in terms of the
symmetry coefficient values of a_a^V=(31.5-33.5) MeV for the volume coefficient
and a_a^S=(9-12) MeV for the surface coefficient. These two further correspond
to the parameter values describing density dependence of symmetry energy, of
L~95 MeV and K_{sym}~25 MeV.",0708.2830v1
2011-05-11,"Finite Temperature Scaling, Bounds, and Inequalities for the Non-interacting Density Functionals","Finite temperature density functional theory requires representations for the
internal energy, entropy, and free energy as functionals of the local density
field. A central formal difficulty for an orbital-free representation is
construction of the corresponding functionals for non-interacting particles in
an arbitrary external potential. That problem is posed here in the context of
the equilibrium statistical mechanics of an inhomogeneous system. The density
functionals are defined and shown to be equal to the extremal state for a
functional of the reduced one-particle statistical operators. Convexity of the
latter functionals implies a class of general inequalities. First, it is shown
that the familiar von Weizs\""acker lower bound for zero temperature functionals
applies at finite temperature as well. An upper bound is obtained in terms of a
single-particle statistical operator corresponding to the Thomas-Fermi
approximation. Next, the behavior of the density functionals under coordinate
scaling is obtained. The inequalities are exploited to obtain a class of upper
and lower bounds at constant temperature, and a complementary class at constant
density. The utility of such constraints and their relationship to
corresponding results at zero temperature are discussed.",1105.2276v1
2011-12-20,Probing Mach's principle,"The principle of least action in its original form \'a la Maupertuis is used
to explain geodetic and frame-dragging precessions which are customarily
accounted for a curved spacetime by general relativity. The obtained least-time
equations of motion agree with observations and are also in concert with
general relativity. Yet according to the least-time principle, gravitation does
not relate to the mathematical metric of spacetime, but to a tangible energy
density embodied by photons. The density of free space is in balance with the
total mass of the Universe in accord with Planck's law. Likewise, a local
photon density and its phase distribution are in balance with mass and charge
distribution of a local body. Here gravitational force is understood as an
energy density difference that will diminish when the oppositely polarized
pairs of photons co-propagate from the energy-dense system of bodies to the
energy-sparse system of the surrounding free space. Thus when the body changes
its state of motion, the surrounding energy density must accommodate the
change. The concurrent resistance in restructuring of the surroundings,
ultimately involving the entire Universe, is known as inertia. The all-around
propagating energy density couples everything with everything else in accord
with Mach's principle.",1205.4628v1
1998-10-07,Wavelength limits on isobaricity of perturbations in a thermally unstable radiatively cooling medium,"Nonlinear evolution of one-dimensional planar perturbations in an optically
thin radiatively cooling medium in the long-wavelength limit is studied
numerically. The accepted cooling function generates in thermal equilibrium a
bistable equation of state $P(\rho)$. The unperturbed state is taken close to
the upper (low-density) unstable state with infinite compressibility
($dP/d\rho= 0$). The evolution is shown to proceed in three different stages.
At first stage, pressure and density set in the equilibrium equation of state,
and velocity profile steepens gradually as in case of pressure-free flows. At
second stage, those regions of the flow where anomalous pressure (i.e. with
negative compressibility) holds, create velocity profile more sharp than in
pressure-free case, which in turn results in formation of a very narrow
(short-wavelength) region where gas separates the equilibrium equation of state
and pressure equilibrium sets in rapidly. On this stage, variation in pressure
between narrow dense region and extended environment does not exceed more than
0.01 of the unperturbed value. On third stage, gas in the short-wavelength
region reaches the second (high-density) stable state, and pressure balance
establishes through the flow with pressure equal to the one in the unperturbed
state. In external (long-wavelength) regions, gas forms slow isobaric inflow
toward the short-wavelength layer. The duration of these stages decreases when
the ratio of the acoustic time to the radiative cooling time increases. Limits
in which nonlinear evolution of thermally unstable long-wavelength
perturbations develops in isobaric regime are obtained.",9810104v1
1999-06-08,Final State Effects in the high q response of $^3$He-$^4$He mixtures,"A modified Gersch-Rodriguez formalism describing the leading Final State
Effects in the high momentum transfer response of low concentration
$^3$He-$^4$He mixtures is presented and discussed. The leading corrections to
the Impulse Approximation are expressed in terms of the interatomic potentials
and the semidiagonal two-body density matrices of both the mixture and its
boson-boson approximation, in which the $^3$He atoms are replaced by bosons of
the same mass and at the same partial density. Numerical calculations of the
Final State Effects functions of $^3$He and $^4$He are finally presented and
discussed.",9906106v2
1999-08-03,Semiclassical mechanics of a non-integrable spin cluster,"We study detailed classical-quantum correspondence for a cluster system of
three spins with single-axis anisotropic exchange coupling. With autoregressive
spectral estimation, we find oscillating terms in the quantum density of states
caused by classical periodic orbits: in the slowly varying part of the density
of states we see signs of nontrivial topology changes happening to the energy
surface as the energy is varied. Also, we can explain the hierarchy of quantum
energy levels near the ferromagnetic and antiferromagnetic states with EKB
quantization to explain large structures and tunneling to explain small
structures.",9908055v1
1999-11-10,Ground-state energy of a high-density electron gas in a strong magnetic field,"The high-density electron gas in a strong magnetic field B and at zero
temperature is investigated. The quantum strong-field limit is considered in
which only the lowest Landau level is occupied. It is shown that the
perturbation series of the ground-state energy can be represented in analogy to
the Gell-Mann Brueckner expression of the ground-state energy of the field-free
electron gas. The role of the expansion parameter is taken by $r_B= (2/3 \pi^2)
(B/m^2) (\hbar r_S/e)^3$ instead of the field-free Gell-Mann Brueckner
parameter r_s.",9911139v1
2003-06-09,Probing many-body states of ultra-cold atoms via noise correlations,"We propose to utilize density-density correlations in the image of an
expanding gas cloud to probe complex many body states of trapped ultra-cold
atoms. In particular we show how this technique can be used to detect
superfluidity of fermionic gases and reveal broken spin symmetries in
Mott-states of atoms in optical lattices. The feasibility of the method is
investigated by analysis of the relevant signal to noise ratio including
experimental imperfections.",0306226v1
2004-11-02,Quantum Monte Carlo simulation of a two-dimensional Bose gas,"The equation of state of a homogeneous two-dimensional Bose gas is calculated
using quantum Monte Carlo methods. The low-density universal behavior is
investigated using different interatomic model potentials, both finite-ranged
and strictly repulsive and zero-ranged supporting a bound state. The condensate
fraction and the pair distribution function are calculated as a function of the
gas parameter, ranging from the dilute to the strongly correlated regime. In
the case of the zero-range pseudopotential we discuss the stability of the
gas-like state for large values of the two-dimensional scattering length, and
we calculate the critical density where the system becomes unstable against
cluster formation.",0411049v1
2004-11-17,The Structure of Ultrathin Ag Films on Pd(111),"We have performed ab initio density functional calculations of thin Ag films
on the Pd(111) surface. We have calculated the structural properties and the
electronic bands of the Ag/Pd systems. There is a band gap in the electronic
density of states around the centre of the two-dimensional Brillouin zone of
the Pd(111) surface, which makes possible the formation of localised states in
the adsorbed silver films. We find that quantum well states may form at binding
energies around 4 eV.",0411447v1
2003-01-15,QCD Equations of State and the QGP Liquid Model,"Recent advances in the study of equations of state of thermal lattice Quantum
Chromodynamics obtained at non-zero baryon density allow validation of the
quark-gluon plasma (QGP) liquid model equations of state (EoS). We study here
the properties of the QGP-EoS near to the phase transformation boundary at
finite baryon density and show a close agreement with the lattice results.",0301099v1
2000-02-24,Quantum-classical correspondence for local density of states and eigenfunctions of a chaotic periodic billiard,"Classical-quantum correspondence for conservative chaotic Hamiltonians is
investigated in terms of the structure of the eigenfunctions and the local
density of states, using as a model a 2D rippled billiard in the regime of
global chaos. The influence of the observed localized and sparsed states in the
quantum-classical correspondence is discussed.",0002044v2
2002-03-15,Ergodic Properties of Local Spectral Density for a Conservative System of Coupled Quantum States,"The shape and the inverse participation ratio (IPR) of local spectral density
(LSD) are studied for a generic isolated system of coupled quantum states, the
Hamiltonian of which is represented by a band random matrix with the disordered
leading diagonal. We find for the matrices with arbitrary small band that the
lack of ergodicity for LSD can be associated with an exponential increase in
IPR with the ratio $v/\Delta_c$ ($v$ - the root of mean square for off-diagonal
matrix elements, $\Delta_c$ - the energy spacing between directly coupled basis
states). Criterions specifying transition to localization and ergodicity for
LSD are considered.",0203071v1
2002-10-24,A note on separability criteria for multipartite state,"The recent proposed realignment separability criterion for mixed is analyzed.
We identify the essential part of this criterion is a swap operator followed by
a partial transposition. Then we analyze the separability criterion of
permutation indices of the density matrix for multipartite state which is a
generalization of the realignment criterion. We give a method to solve the
equivalence problem of the separability criterion of permutation indices of the
density matrix. For tripartite state, we show the non-trivial separability
criteria are either partial transposition criterion or realignment criterion.",0210168v1
2006-02-03,The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach,"We present here a formulation of the electronic ground-state energy in terms
of the second order reduced density matrix, using a duality argument. It is
shown that the computation of the ground-state energy reduces to the search of
the projection of some two-electron reduced Hamiltonian on the dual cone of
$N$-representability conditions. Some numerical results validate the approach,
both for equilibrium geometries and for the dissociation curve of N$_2$.",0602042v2
2006-02-24,Density Matrix Tomography of Entangled Electron and Nuclear Spin States in 15N:C60,"We discuss details of the preparation and detection of entangled
electron-nuclear spin states in 15N:C60 together with a quantitative evaluation
of the complete density matrix. All four Bell states of a two qubit subsystem
were analyzed. In addition we find a quantum critical temperature of Tq = 7.73
K for this system at an electron spin resonance frequency of 95 GHz.",0602201v1
2008-04-18,Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions,"The formalism for exactly calculating the retarded and advanced Green's
functions of strongly correlated lattice models in a uniform electric field is
derived within dynamical mean-field theory. To illustrate the method, we solve
for the nonequilibrium density of states of the Hubbard model in both the
metallic and Mott insulating phases at half-filling (with an arbitrary strength
electric field) by employing the numerical renormalization group as the
impurity solver. This general approach can be applied to any strongly
correlated lattice model in the limit of large dimensions.",0804.3077v1
2009-03-16,The States of Matter in QCD,"Quantum chromodynamics predicts that the interaction between its fundamental
constituents, quarks and gluons, can lead to different states of strongly
interacting matter, dependent on its temperature and baryon density. We first
survey the possible states of matter in QCD and discuss the transition from a
color-confining hadronic phase to a plasma of deconfined colored quarks and
gluons. Next, we summarize the results from non-perturbative studies of QCD at
finite temperature and baryon density, and address the origin of deconfinement
in the different regimes. Finally, we consider possible probes to test the
basic features of bulk matter in QCD.",0903.2778v1
2009-07-10,Measurement of Conduction Electron Polarization Via the Pairing Resonance,"We show that the pairing resonance in the Pauli-limited normal state of
ultra-thin superconducting Al films provides a spin-resolved probe of
conduction electron polarization in thin magnetic films. A
superconductor-insulator-ferromagnet tunneling junction is used to measure the
density of states in supercritical parallel magnetic fields that are well
beyond the Clogston-Chandresekhar limit, thus greatly extending the field range
of the tunneling density of states technique. The applicability and limitations
of using the pairing resonance as a spin probe are discussed.",0907.1800v1
2009-10-13,Metallic proximity effect in ballistic graphene with resonant scatterers,"We study the effect of resonant scatterers on the local density of states in
a rectangular graphene setup with metallic leads. We find that the density of
states in a vicinity of the Dirac point acquires a strong position dependence
due to both metallic proximity effect and impurity scattering. This effect may
prevent uniform gating of weakly-doped samples. We also demonstrate that even a
single-atom impurity may essentially alter electronic states at low-doping on
distances of the order of the sample size from the impurity.",0910.2339v1
2013-01-28,Impurity scattering effect on the zero-energy peak of the local density of states in a multi-quantum vortex core,"We theoretically study a non-magnetic impurity effect on the vortex bound
states of a multi-quantum vortex. The zero-energy peak of the local density of
states is investigated for vortex cores with the winding numbers 2 and 4 within
the framework of the quasiclassical theory of superconductivity. We find that
the zero-energy peaks, which appear away from the vortex center in the clean
limit, move towards the vortex center with increasing the impurity scattering
rate, resolving a contradiction between an experimental result and previous
theoretical predictions.",1301.6445v1
2013-05-12,Hermite Polynomial Representation of the Spin States,"The invertable map of spin state density operator onto quasiprobability
distribution of three continuous variables is constructed. The connection with
two-mode electromagnetic field oscillators is discussed. The inversion formula
for spin-density matrix is given in terms of Hermite polynomials. The
connection with the spin-tomographic representation is examined. The problem of
the magnetic moment rotation in the magnetic field is considered in the
suggested representation of spin states.",1305.2596v1
2014-10-19,Characterization of Electron Density of States in Laser-superposed Channeling Regime,"We present low-dimensional functionalization and characterization of electron
density of states (DOS) using highly correlated/precisely guided proton beam
trajectories and a silicon nanocrystal as a target, representing at a same time
a versatile nanolaser technique capable for coherent control of atomic quantum
states and for scanning the interior of an atom with resolution comparable to
10% of the Bohr radius.",1410.5417v1
2014-11-13,Signatures of a momentum independent pseudogap in the electronic density of states and Raman spectroscopy of the underdoped cuprates,"We propose a hybridization phenomenology to describe the pseudogap state of
the underdoped cuprates. We show how a momentum independent pseudogap opens
asymmetrically from the Fermi-surface but symmetric to the zeroes of the
hybridized bonding dispersion, which results in false d-wave characteristics of
the pseudogap at the Fermi level. By comparing against a d-wave form factor we
illustrate the difficulty in identifying a momentum independent order in
momentum averaged quantities such as the electronic Raman response. We identify
a suppression in the single-particle density of states which produces a hump
feature which should be observable experimentally in tunnelling $dI/dV$ spectra
and distinguishes the s-wave and d-wave ordering scenarios.",1411.3641v1
2018-11-13,On instability of ground states in 2D CP(N-1) and O(N) models at large N,"We consider properties of the inhomogeneous solution found recently for
\mbox{$\mathbb{CP}^{\,N-1}$} model. The solution was interpreted as a soliton.
We reevaluate its energy in three different ways and find that it is negative
contrary to the previous claims. Hence, instead of the solitonic interpretation
it calls for reconsideration of the issue of the true ground state. While
complete resolution is still absent we show that the energy density of the
periodic elliptic solution is lower than the energy density of the homogeneous
ground state. We also discuss similar solutions for the ${\mathbb{O}}(N)$ model
and for SUSY extensions.",1811.05449v1
2018-03-18,High frequency limits for invariant Ruelle densities,"We establish an equidistribution result for Ruelle resonant states on compact
locally symmetric spaces of rank one. More precisely, we prove that among the
first band Ruelle resonances there is a density one subsequence such that the
respective products of resonant and co-resonant states converge weakly to the
Liouville measure. We prove this result by establishing an explicit
quantum-classical correspondence between eigenspaces of the scalar Laplacian
and the resonant states of the first band of Ruelle resonances which also leads
to a new description of Patterson-Sullivan distributions.",1803.06717v2
2012-01-05,Density of States for a Specified Correlation Function and the Energy Landscape,"The degeneracy of two-phase disordered microstructures consistent with a
specified correlation function is analyzed by mapping it to a ground-state
degeneracy. We determine for the first time the associated density of states
via a Monte Carlo algorithm. Our results are described in terms of the
roughness of the energy landscape, defined on a hypercubic configuration space.
The use of a Hamming distance in this space enables us to define a roughness
metric, which is calculated from the correlation function alone and related
quantitatively to the structural degeneracy. This relation is validated for a
wide variety of disordered systems.",1201.1142v1
2022-05-06,Probability density functions of quantum mechanical observable uncertainties,"We study the uncertainties of quantum mechanical observables, quantified by
the standard deviation (square root of variance) in Haar-distributed random
pure states. We derive analytically the probability density functions (PDFs) of
the uncertainties of arbitrary qubit observables. Based on these PDFs, the
uncertainty regions of the observables are characterized by the supports of the
PDFs. The state-independent uncertainty relations are then transformed into the
optimization problems over uncertainty regions, which opens a new vista for
studying state independent uncertainty relations. Our results may be
generalized to multiple observable case in higher dimensional spaces.",2205.03193v1
2012-11-07,Gaussification through decoherence,"We investigate the loss of nonclassicality and non-Gaussianity of a
single-mode state of the radiation field in contact with a thermal reservoir.
The damped density matrix for a Fock-diagonal input is written using the Weyl
expansion of the density operator. Analysis of the evolution of the
quasiprobability densities reveals the existence of two successive
characteristic times of the reservoir which are sufficient to assure the
positivity of the Wigner function and, respectively, of the $P$ representation.
We examine the time evolution of non-Gaussianity using three recently
introduced distance-type measures. They are based on the Hilbert-Schmidt
metric, the relative entropy, and the Bures metric. Specifically, for an
$M$-photon-added thermal state, we obtain a compact analytic formula of the
time-dependent density matrix that is used to evaluate and compare the three
non-Gaussianity measures. We find a good consistency of these measures on the
sets of damped states. The explicit damped quasiprobability densities are shown
to support our general findings regarding the loss of negativities of Wigner
and $P$ functions during decoherence. Finally, we point out that Gaussification
of the attenuated field mode is accompanied by a nonmonotonic evolution of the
von Neumann entropy of its state conditioned by the initial value of the mean
photon number.",1211.1701v3
2021-10-22,Pseudo-gap and Localization of Light in Correlated Disordered Media,"Among the remarkable scattering properties of correlated disordered
materials, the origin of pseudo-gaps and the formation of localized states are
some of the most puzzling features. Fundamental differences between scalar and
vector waves in both these aspects make their comprehension even more
problematic. Here we present an in-depth and comprehensive analysis of the
order-to-disorder transition in 2D resonant systems. We show with exact ab
initio numerical simulations in hyperuniform media that localization of 2D
vector waves can occur in the presence of correlated disorder, in a regime of
moderate density of scatterers. On the contrary, no signature of localization
is found for white noise disorder. This is in striking contrast with scalar
waves which localize at high density whatever the amount of correlation. For
correlated materials, localization is associated with the formation of
pseudo-gap in the density of states. We develop two complementary models to
explain these observations. The first one uses an effective photonic
crystal-type framework and the second relies on a diagrammatic treatment of the
multiple scattering sequences. We provide explicit theoretical evaluations of
the density of states and localization length in good agreement with numerical
simulations. In this way, we identify the microscopic processes at the origin
of pseudo-gap formation and clarify the role of the density of states for wave
localization in resonant correlated systems.",2110.12034v1
2006-10-18,"Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor","We derive general relations between grain boundaries, rotational
deformations, and stress-free states for the mesoscale continuum Nye
dislocation density tensor. Dislocations generally are associated with
long-range stress fields. We provide the general form for dislocation density
fields whose stress fields vanish. We explain that a grain boundary (a
dislocation wall satisfying Frank's formula) has vanishing stress in the
continuum limit. We show that the general stress-free state can be written
explicitly as a (perhaps continuous) superposition of flat Frank walls. We show
that the stress-free states are also naturally interpreted as configurations
generated by a general spatially-dependent rotational deformation. Finally, we
propose a least-squares definition for the spatially-dependent rotation field
of a general (stressful) dislocation density field.",0610492v2
2008-04-07,Metal-insulator transition in the two-dimensional fully polarized homogeneous electron gas from Hartree-Fock solutions,"We determine the ground state of the two-dimensional, fully polarized
electron gas within the Hartree-Fock approximation without imposing any
particular symmetries on the solutions. At low electronic densities, the Wigner
crystal solution is stable, but for higher densities ($r_s$ less than $\sim 3$)
we obtain a ground state of different symmetry: the charge density forms a
triangular lattice with about 11% more sites than electrons. We argue that this
conducting state with broken translational symmetry remains the ground state of
the high density region in the thermodynamic limit giving rise to a metal to
insulator transition.",0804.1025v2
2009-03-09,Uniform current in graphene strip with zigzag edges,"Graphene exhibits zero-gap massless-Dirac fermion and zero density of states
at E = 0. These particles form localized states called edge states on finite
width strip with zigzag edges at E = 0. Naively thinking, one may expect that
current is also concentrated at the edge, but Zarbo and Nikolic numerically
obtained a result that the current density shows maximum at the center of the
strip. We derive a rigorous relation for the current density, and clarify the
reason why the current density of edge state has a maximum at the center.",0903.1483v2
2017-01-19,"Density-scaling exponents and virial potential-energy correlation coefficients for the (2n,n) Lennard-Jones system","This paper investigates the relation between the density-scaling exponent
$\gamma$ and the virial potential-energy correlation coefficient $R$ at several
thermodynamic state points in three dimensions for the generalized $(2n,n)$
Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard
$n=6$ LJ system in two, three, and four dimensions. The state points studied
include many low-density states at which the virial potential-energy
correlations are not strong. For these state points we find the roughly linear
relation $\gamma\cong 3nR/d$ in $d$ dimensions. This result is discussed in
light of the approximate ""extended inverse power law"" description of
generalized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508
(2008)]. In the plot of $\gamma$ versus $R$ there is in all cases a transition
around $R\approx 0.9$, above which $\gamma$ starts to decrease as $R$
approaches unity. This is consistent with the fact that $\gamma\rightarrow
2n/d$ for $R\rightarrow 1$, a limit that is approached at high densities and/or
temperatures at which the repulsive $r^{-2n}$ term dominates the physics.",1701.05470v2
2021-01-04,Building Kohn-Sham potentials for ground and excited states,"We analyze the inverse problem of Density Functional Theory using a
regularized variational method. First, we show that given $k$ and a target
density $\rho$, there exist potentials having $k^{\text{th}}$ bound mixed
states which densities are arbitrarily close to $\rho$. The state can be chosen
pure in dimension $d=1$ and without interactions, and we provide numerical and
theoretical evidence consistently leading us to conjecture that the same pure
representability result holds for $d=2$, but that the set of pure-state
$v$-representable densities is not dense for $d=3$. Finally, we present an
inversion algorithm taking into account degeneracies, removing the generic
blocking behavior of standard ones.",2101.01127v2
1993-12-28,Meson phase space density from interferometry,"The interferometric analysis of meson correlations provides a measure of the
average phase space density of the mesons in the final state. This quantity is
a useful indicator of the statistical properties of the system, and it can be
extracted with a minimum of model assumptions. Values obtained from recent
measurements are consistent with the thermal value, but do not rule out
superradiance effects.",9312021v1
2015-12-08,Critical density of a soliton gas,"We quantify the notion of a dense soliton gas by establishing an upper bound
for the integrated density of states of the quantum-mechanical Schr\""odinger
operator associated with the KdV soliton gas dynamics. As a by-product of our
derivation we find the speed of sound in the soliton gas with Gaussian spectral
distribution function.",1512.02470v2
2007-02-09,Mean field exact solutions showing charge density wave crossover at low fillings in the fractional quantum Hall regime,"A general analytical framework for the determination of the mean field states
at arbitrary rational filling factors for the 2DEG in FQHE regime is given. Its
use allows to obtain analytic expressions for the solutions at filling factors
of the form $\nu=1/q$ for arbitrary odd $q$. The analysis can be performed for
two general classes of states characterized by $\gamma=1$ or $\gamma={1/2}$
particles per unit cell. Instead of the periodic peaks of the Wigner solid
solution, the new states show electron densities forming percolating ridges
that may favor an energy decrease through correlated ring of exchange
contributions. Therefore, we estimate that they can realize mean field versions
of the so called Hall Crystal (HC) states. The obtained analytic HC solution
shows the same crystalline symmetry that the corresponding WC state in its
class $\gamma=1$, but a qualitatively different charge density distribution.
The energy dependence of the corresponding HC and WC states on the filling
factor is also evaluated here for the class $\gamma=1/2$. The results show a
crossover between HC state and the Wigner crystal, close to filling 1/7.
Therefore, transitions may occur from one to the other as the electron density
is varied. This result is consistent with recent experimental findings.",0702251v1
2022-09-23,Automatic hermiticity for mixed states,"We previously proposed a mechanism to effectively obtain, after a long time
development, a Hamiltonian being Hermitian with regard to a modified inner
product $I_Q$ that makes a given non-normal Hamiltonian normal by using an
appropriately chosen Hermitian operator $Q$. We studied it for pure states. In
this letter we show that a similar mechanism also works for mixed states by
introducing density matrices to describe them and investigating their
properties explicitly both in the future-not-included and future-included
theories. In particular, in the latter, where not only a past state at the
initial time $T_A$ but also a future state at the final time $T_B$ is given, we
study a couple of candidates for it, and introduce a ``skew density matrix''
composed of both ensembles of the future and past states such that the trace of
the product of it and an operator ${\cal O}$ matches a normalized matrix
element of ${\cal O}$. We argue that the skew density matrix defined with $I_Q$
at the present time $t$ for large $T_B-t$ and large $t-T_A$ approximately
corresponds to another density matrix composed of only an ensemble of past
states and defined with another inner product $I_{Q_J}$ for large $t-T_A$.",2209.11619v2
2005-01-31,The electronic structure of liquid water within density functional theory,"In the last decade, computational studies of liquid water have mostly
concentrated on ground state properties. However recent spectroscopic
measurements have been used to infer the structure of water, and the
interpretation of optical and x-ray spectra requires accurate theoretical
models of excited electronic states, not only of the ground state. To this end,
we investigate the electronic properties of water at ambient conditions using
ab initio density functional theory within the generalized gradient
approximation (DFT/GGA), focussing on the unoccupied subspace of Kohn-Sham
eigenstates. We generate long (250 ps) classical trajectories for large
supercells, up to 256 molecules, from which uncorrelated configurations of
water molecules are extracted for use in DFT/GGA calculations of the electronic
structure. We find that the density of occupied states of this molecular liquid
is well described with 32 molecule supercells using a single k-point (k = 0) to
approximate integration over the first Brillouin zone. However, the description
of the density of unoccupied states (u-EDOS) is sensitive to finite size
effects. Small, 32 molecule supercell calculations, using Gamma-the point
approximation, yield a spuriously isolated state above the Fermi level.
Nevertheless, the more accurate u-EDOS of large, 256 molecule supercells may be
reproduced using smaller supercells and increased k-point sampling. This
indicates that the electronic structure of molecular liquids like water is
relatively insensitive to the long-range disorder in the molecular structure.
These results have important implications for efficiently increasing the
accuracy of spectral calculations for water and other molecular liquids.",0502008v1
2021-05-26,The Schwarzschild Mass in General Relativity,"The central (surface) energy-density, $E_0 (E_R)$, which appears in the
expression of total static and spherical mass, $M$ (corresponding to the total
radius $R$) is defined as the density measured only by one observer located at
the centre (surface) in the Momentarily Co-moving Reference Frame (MCRF). Since
the mass, $M$, depends only on the central (surface) density for most of the
equations of state (EOSs) and/or exact analytic solutions of Einstein's field
equations available in the literature, the central (surface) density measured
in the preferred frame (that is, in the MCRF) appears to be not in agreement
with the coordinate invariant form of the field equations that result for the
source mass, $M$. In order to overcome the use of any preferred coordinate
system (the MCRF) defined for the central (surface) density in the literature,
we argue for the first time that the said density may be defined in the
coordinate invariant form, that is, in the form of the average density
($3M/4\pi R^3)$ of the the configuration which turns out to be independent of
the radial coordinate $`r'$ and depends only on the central (surface) density
of the configuration. In this connection, we further argue that the central
(surface) density of the structure should be {\em independent} of the density
measured on the other boundary (surface/central) because there exists no a
priori relation between the radial coordinate $`r'$ and the proper distance
from the centre of the sphere to its surface \cite{Ref1}. In the light of this
reasoning, the various EOSs and analytic solutions of Einstein's field
equations in which the central and the surface density are {\em interdependent}
can not fulfill the definition of central (surface) density measured only by
one observer located in the MCRF at the centre (surface) of the configuration.",2105.12535v1
2009-08-10,Spin polarized states in neutron matter at a strong magnetic field,"Spin polarized states in neutron matter at a strong magnetic field are
considered in the model with the Skyrme effective interaction (SLy4, SLy7
parametrizations). Analyzing the self-consistent equations at zero temperature,
it is shown that a thermodynamically stable branch of solutions for the spin
polarization parameter as a function of density corresponds to the negative
spin polarization when the majority of neutron spins are oriented oppositely to
the direction of the magnetic field. Besides, beginning from some threshold
density being dependent on the magnetic field strength the self-consistent
equations have also two other branches (upper and lower) of solutions for the
spin polarization parameter with the positive spin polarization.
  The free energy corresponding to the upper branch turns out to be very close
to the free energy corresponding to the thermodynamically preferable branch
with the negative spin polarization. As a consequence, at a strong magnetic
field, the state with the positive spin polarization can be realized as a
metastable state at the high density region in neutron matter which under
decreasing density at some threshold density changes into a thermodynamically
stable state with the negative spin polarization. The calculations of the
neutron spin polarization parameter and energy per neutron as functions of the
magnetic field strength show that the influence of the magnetic field remains
small at the field strengths up to $10^{17}$ G.",0908.1368v2
2004-05-07,The role of anisotropy and inhomogeneity in Lemaitre-Tolman-Bondi collapse,"We study the effects of shear and density inhomogeneities in the formation of
naked singularities in spherically symmetric dust space--times. We find that in
general neither of these physical features alone uniquely specifies the end
state of the gravitational collapse. We do this by (i) showing that, for open
sets of initial data, the same initial shear (or initial density contrast) can
give rise to both naked and covered solutions. In particular this can happen
for zero initial shear or zero initial density contrast; (ii) demonstrating
that both shear and density contrast are invariant under a one parameter set of
linear transformations acting on the initial data set and (iii) showing that
asymptotically (near the singularities) one cannot in general establish a
direct relationship between the rate of change of shear (or density contrast)
and the nature of the singularities. However, one can uniquely determine the
nature of the singularity if both the initial shear and initial density
contrast are known.
  These results are important in understanding the effects of the initial
physical state and in particular the role of shear, in determiming the end
state of the gravitational collapse.",0405041v1
2016-06-14,Separability and entanglement of n-qubits and a qubit with a qudit using Hilbert-Schmidt decompositions,"Hilbert-Schmidt (HS) decompositions are employed for analyzing systems of
n-qubits, and a qubit with a qudit. Negative eigenvalues, obtained by
partial-transpose (PT) plus local unitary transformations (PTU) for one qubit
from the whole system, are used for indicating inseparability. A sufficient
criterion for full separability of the n-qubits and qubit-qudit systems is
given. We use the singular value decomposition (SVD) for improving the
criterion for full separability. General properties of entanglement and
separability are analyzed for a system of a qubit and a qudit and n-qubits
systems, with emphasis on maximally disordered subsystems (MDS) (i.e., density
matrices rho(MDS) for which tracing over any subsystem gives the unit density
matrix). A sufficient condition that rho(MDS) is not separable is that it has
an eigenvalue larger than 1/d for a qubit and a qudit, and larger than
1/2^(n-1) for n-qubits system. The PTU transformation does not change the
eigenvalues of the n-qubits MDS density matrices for odd n. Thus the
Peres-Horodecki criterion does not give any information about entanglement of
these density matrices, but this criterion is useful for indicating
inseparability for even n. The changes of the entanglement and separability
properties of the GHZ state, the Braid entangled state and the W state by
mixing them with white noise are analyzed by the use of the present methods.
The entanglement and separability properties of the GHZ-diagonal density
matrices, composed of mixture of 8 GHZ density matrices with probabilities
p(i), is analyzed as function of these probabilities. In some cases we show
that the Peres-Horodecki criterion is both sufficient and necessary.",1606.04304v2
2023-08-30,Density Stabilization Strategies for Nonholonomic Agents on Compact Manifolds,"In this article, we consider the problem of stabilizing a class of degenerate
stochastic processes, which are constrained to a bounded Euclidean domain or a
compact smooth manifold, to a given target probability density. Most existing
works on modeling and control of robotic swarms that use partial differential
equation (PDE) models assume that the robots' dynamics are holonomic, and
hence, the associated stochastic processes have generators that are elliptic.
We relax this assumption on the ellipticity of the generator of the stochastic
processes, and consider the more practical case of the stabilization problem
for a swarm of agents whose dynamics are given by a controllable driftless
control-affine system. We construct state-feedback control laws that
exponentially stabilize a swarm of nonholonomic agents to a target probability
density that is sufficiently regular. State-feedback laws can stabilize a swarm
only to target probability densities that are positive everywhere. To stabilize
the swarm to probability densities that possibly have disconnected supports, we
introduce a semilinear PDE model of a collection of interacting agents governed
by a hybrid switching diffusion process. The interaction between the agents is
modeled using a (mean-field) feedback law that is a function of the local
density of the swarm, with the switching parameters as the control inputs. We
show that under the action of this feedback law, the semilinear PDE system is
globally asymptotically stable about the given target probability density. The
stabilization strategies with and without agent interactions are verified
numerically for agents that evolve according to the Brockett integrator; the
strategy with interactions is additionally verified for agents that evolve
according to an underactuated system on the sphere $S^2$.",2308.15755v1
1999-05-27,Measuring the temperature of the intergalactic medium,"Numerical simulations indicate that the smooth, photoionized intergalactic
medium (IGM) responsible for the low column density Lyman-alpha forest follows
a well defined temperature-density relation. We show that such an equation of
state results in a cutoff in the distribution of line widths (b-parameters) as
a function of column density (N) for the low column density absorption lines.
This explains the existence of the lower envelope which is clearly seen in
scatter plots of the b(N)-distribution in observed QSO spectra. The intercept
and slope of this cutoff can be used to measure the equation of state of the
IGM. Measuring the evolution of the equation of state with redshift will allow
us to put tight constraints on the reionization history of the universe.",9905364v1
1996-12-14,Off-Diagonal Density Profiles and Conformal Invariance,"Off-diagonal profiles of local densities (e.g. order parameter or energy
density) are calculated at the bulk critical point, by conformal methods, for
different types of boundary conditions (free, fixed and mixed). Such profiles,
which are defined by a non-vanishing matrix element of the appropriate operator
between the ground state and the corresponding lowest excited state of the
strip Hamiltonian, enter into the expression of two-point correlation functions
on a strip. They are of interest in the finite-size scaling study of bulk and
surface critical behaviour since they allow the elimination of regular
contributions. The conformal profiles, which are obtained through a conformal
transformation of the correlation functions from the half-plane to the strip,
are in agreement with the results of a direct calculation, for the energy
density of the two-dimensional Ising model.",9612128v5
2018-09-17,"Dynamics Phases, Stratification, Laning, and Pattern Formation for Driven Bidisperse Disk Systems in the Presence of Quenched Disorder","Using numerical simulations, we examine the dynamics of driven
two-dimensional bidisperse disks flowing over quenched disorder. The system
exhibits a series of distinct dynamical phases as a function of applied driving
force and packing fraction including a phase separated state as well as a
smectic state with liquid like or polycrystalline features. At low driving
forces, we find a clogged phase with an isotropic density distribution, while
at intermediate driving forces the disks separate into bands of high and low
density with either liquid like or polycrystalline structure in the high
density bands. In addition to the density phase separation, we find that in
some cases there is a fractionation of the disk species, particularly when the
disk size ratio is large. The species phase separated regimes form a variety of
patterns such as large disks separated by chains of smaller disks. Our results
show that the formation of laning states can be enhanced by tuning the ratio of
disk radius of the two species, due to the clumping of small disks in the
interstitial regions between the large disks.",1809.06335v1
2023-11-23,Semiclassical analysis of two-scale electronic Hamiltonians for twisted bilayer graphene,"This paper investigates the mathematical properties of independent-electron
models for twisted bilayer graphene by examining the density-of-states of
corresponding single-particle Hamiltonians using tools from semiclassical
analysis. This study focuses on a specific atomic-scale Hamiltonian
$H_{d,\theta}$ constructed from Density-Functional Theory, and a family of
moir\'e-scale Hamiltonians $H_{d,K,\theta}^{\rm eff}$ containing the
Bistritzer-MacDonald model. The parameter $d$ represents the interlayer
distance, and $\theta$ the twist angle. It is shown that the density-of-states
of $H_{d,\theta}$ and $H_{d,K,\theta}^{\rm eff}$ admit asymptotic expansions in
the twist angle parameter $\epsilon:=\sin(\theta/2)$. The proof relies on a
twisted version of the Weyl calculus and a trace formula for an exotic class of
pseudodifferential operators suitable for the study of twisted 2D materials. We
also show that the density-of-states of $H_{d,\theta}$ admits an asymptotic
expansion in $\eta:=\tan(\theta/2)$ and comment on the differences between the
expansions in $\epsilon$ and $\eta$.",2311.14011v1
2024-03-20,Nonlocality of the energy density of a spontaneously emitted single-photon from a Hydrogen atom,"We analyze through the expectation value of the energy density the spatial
nonlocality of single photons emitted by the spontaneous decay of a Hydrogen
atom. By using a minimal coupling between the quantized electromagnetic field
and the atom, we compute the state of the photon under the assumption that only
a single-photon is produced. The calculations are thus performed in the
subspace of single-photon states which is essentially equivalent to the
rotating wave approximation. We obtain a characterization of the spatial decay
of the energy density. We compute the asymptotic limit of large distances from
the atom at each given time, and find an algebraic behavior of $1/r^6$. This
result confirms that the energy density of single-photon states is nonlocal and
the algebraic decay is far from the maximal quasiexponential localization
predicted by the theory.",2403.13622v1
2018-11-23,Surface pair-density-wave superconducting and superfluid states,"Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous
superconducting and superfluid ground states, spontaneously breaking
translation symmetries. In this Letter, we demonstrate that the transition from
the FFLO to the normal state as a function of temperature or increased Fermi
surface splitting is not a direct one. Instead the system has an additional
phase transition to a different state where pair-density-wave superconductivity
(or superfluidity) exists only on the boundaries of the system, while the bulk
of the system is normal. The surface pair-density-wave state is very robust and
exists for much larger fields and temperatures than the FFLO state.",1811.09590v3
2007-06-28,Free energy density for mean field perturbation of states of a one-dimensional spin chain,"Motivated by recent developments on large deviations in states of the spin
chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the
variational expression of free energy density in the presence of a mean field
type perturbation. We extend their results from the product state case to the
Gibbs state case in the setting of translation-invariant interactions of finite
range. In the special case of a locally faithful quantum Markov state, we
clarify the relation between two different kinds of free energy densities (or
pressure functions).",0706.4148v2
2016-02-10,Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential,"It is observed that the exact interacting ground-state electronic energy of
interest may be obtained directly, in principle, as a simple sum of orbital
energies when a universal density-dependent term is added to $w\left(\left[
\rho \right];\mathbf{r} \right)$, the familiar Hartree plus
exchange-correlation component in the Kohn-Sham effective potential. The
resultant shifted potential, $\bar{w}\left(\left[ \rho \right];\mathbf{r}
\right)$, actually changes less on average than $w\left(\left[ \rho
\right];\mathbf{r} \right)$ when the density changes, including the fact that
$\bar{w}\left(\left[ \rho \right];\mathbf{r} \right)$ does not undergo a
discontinuity when the number of electrons increases through an integer. Thus
the approximation of $\bar{w}\left(\left[ \rho \right];\mathbf{r} \right)$
represents an alternative direct approach for the approximation of the
ground-state energy and density.",1602.03267v1
2021-04-26,Entropy of quantum states,"Given the algebra of observables of a quantum system subject to selection
rules, a state can be represented by different density matrices. As a result,
different von Neumann entropies can be associated with the same state.
Motivated by a minimality property of the von Neumann entropy of a density
matrix with respect to its possible decompositions into pure states, we give a
purely algebraic definition of entropy for states of an algebra of observables,
thus solving the above ambiguity. The entropy so defined satisfies all the
desirable thermodynamic properties, and reduces to the von Neumann entropy in
the quantum mechanical case. Moreover, it can be shown to be equal to the von
Neumann entropy of the unique representative density matrix belonging to the
operator algebra of a multiplicity-free Hilbert-space representation.",2104.12611v1
2012-07-09,About the posterior distribution in hidden Markov models with unknown number of states,"We consider finite state space stationary hidden Markov models (HMMs) in the
situation where the number of hidden states is unknown. We provide a
frequentist asymptotic evaluation of Bayesian analysis methods. Our main result
gives posterior concentration rates for the marginal densities, that is for the
density of a fixed number of consecutive observations. Using conditions on the
prior, we are then able to define a consistent Bayesian estimator of the number
of hidden states. It is known that the likelihood ratio test statistic for
overfitted HMMs has a nonstandard behaviour and is unbounded. Our conditions on
the prior may be seen as a way to penalize parameters to avoid this phenomenon.
Inference of parameters is a much more difficult task than inference of
marginal densities, we still provide a precise description of the situation
when the observations are i.i.d. and we allow for $2$ possible hidden states.",1207.2064v2
2017-02-03,Dressed coherent states in finite quantum systems: a cooperative game theory approach,"A quantum system with variables in Z(d) is considered. Coherent density
matrices and coherent projectors of rank n are introduced, and their properties
(e.g., the resolution of the identity) are dis- cussed. Cooperative game theory
and in particular the Shapley methodology, is used to renormalize coherent
states, into a particular type of coherent density matrices (dressed coherent
states). The Q-function of a Hermitian operator, is then renormalized into a
physical analogue of the Shapley values. Both the Q-function and the Shapley
values, are used to study the relocation of a Hamilto- nian in phase space as
the coupling constant varies, and its effect on the ground state of the system.
The formalism is also generalized for any total set of states, for which we
have no resolution of the identity. The dressing formalism leads to density
matrices that resolve the identity, and makes them practically useful.",1702.01055v1
2018-08-11,Evolution of infinite populations of immigrants: micro- and mesoscopic description,"A model is proposed of an infinite population of entities immigrating to a
noncompact habitat, in which the newcomers are repelled by the already existing
population. The evolution of such a population is described at micro- and
mesoscopic levels. The microscopic states are probability measures on the
corresponding configuration space. States of populations without interactions
are Poisson measures, fully characterized by their densities. The evolution of
micro-states is Markovian and obtained from the Kolmogorov equation with the
use of correlation functions. The mesoscopic description is made by a kinetic
equation for the densities. We show that the micro-states are approximated by
the Poissonian states characterized by the densities obtained from the kinetic
equation. Both micro- and mesoscopic descriptions are performed and their
interrelations are analyzed, that includes also discussing the problem of the
appearance of a spatial diversity in such populations.",1808.03789v1
2009-12-21,Normalization procedure for relaxation studies in NMR quantum information processing,"NMR quantum information processing studies rely on the reconstruction of the
density matrix representing the so-called pseudo-pure states (PPS). An
initially pure part of a PPS state undergoes unitary and non-unitary
(relaxation) transformations during a computation process, causing a ""loss of
purity"" until the equilibrium is reached. Besides, upon relaxation, the nuclear
polarization varies in time, a fact which must be taken into account when
comparing density matrices at different instants. Attempting to use time-fixed
normalization procedures when relaxation is present, leads to various anomalies
on matrices populations. On this paper we propose a method which takes into
account the time-dependence of the normalization factor. From a generic form
for the deviation density matrix an expression for the relaxing initial pure
state is deduced. The method is exemplified with an experiment of relaxation of
the concurrence of a pseudo-entangled state, which exhibits the phenomenon of
sudden death, and the relaxation of the Wigner function of a pseudo-cat state.",0912.4073v1
2020-10-09,Random State Technology,"We review and extend, in a self-contained way, the mathematical foundations
of numerical simulation methods that are based on the use of random states. The
power and versatility of this simulation technology is illustrated by
calculations of physically relevant properties such as the density of states of
large single particle systems, the specific heat, current-current correlations,
density-density correlations, and electron spin resonance spectra of many-body
systems. We explore a new field of applications of the random state technology
by showing that it can be used to analyze numerical simulations and experiments
that aim to realize quantum supremacy on a noisy intermediate-scale quantum
processor. Additionally, we show that concepts of the random state technology
prove useful in quantum information theory.",2010.04621v1
2015-10-13,Simple permutation-based measure of quantum correlations and maximally-3-tangled states,"Quantities invariant under local unitary transformations are of natural
interest in the study of entanglement. This paper deduces and studies a
particularly simple quantity that is constructed from a combination of two
standard permutations of the density matrix, namely realignment and partial
transpose. This bipartite quantity, denoted here as $R_{12}$, vanishes on large
classes of separable states including classical-quantum correlated states,
while being maximum for only maximally entangled states. It is shown to be
naturally related to the 3-tangle in three qubit states via their two-qubit
reduced density matrices. Upper and lower bounds on concurrence and negativity
of two-qubit density matrices for all ranks are given in terms of $R_{12}$.
Ansatz states satisfying these bounds are given and verified using various
numerical methods. In rank-2 case it is shown that the states satisfying the
lower bound on $R_{12}$ {\it vs} concurrence define a class of three qubit
states that maximizes the tripartite entanglement (the 3-tangle) given an
amount of entanglement between a pair of them. The measure $R_{12}$ is
conjectured, via numerical sampling, to be always larger than the concurrence
and negativity. In particular this is shown to be true for the physically
interesting case of $X$ states.",1510.03656v2
2018-06-05,Fulde-Ferrell-Larkin-Ovchinnikov pairing states of a polarized dipolar Fermi gas trapped in a one-dimensional optical lattice,"We study the interplay between the long- and short-range interaction of a
one-dimensional optical lattice system of two-component dipolar fermions by
using the density matrix renormalization group method. The atomic density
profile, pairing-pairing correlation function, and the compressibility are
calculated in the ground state, from which we identify the parameter region of
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state, half-metal (HM)
state, FFLO-HM state, and the normal polarized state, and thus the phase
diagram in the coordinates of the long- and short-range interaction strength.
The effect of the long-range dipolar interaction on the FFLO state is discussed
in details. We find that the long-range part of the dipole-dipole interaction
does not sweep away the FFLO superconducting region that is driven by the
short-range interaction in the Hubbard model, and thus the FFLO state survives
in the wide parameter space of the long-range interaction, polarization and the
filling.",1806.01582v3
2021-03-08,Orbital Optimized Density Functional Theory for Electronic Excited States,"Density functional theory (DFT) based modeling of electronic excited states
is of importance for investigation of the photophysical/photochemical
properties and spectroscopic characterization of large systems. The widely used
linear response time-dependent DFT (TDDFT) approach is however not effective at
modeling many types of excited states, including (but not limited to)
charge-transfer states, doubly excited states and core-level excitations. In
this perspective, we discuss state-specific orbital optimized (OO) DFT
approaches as an alterative to TDDFT for electronic excited states. We motivate
the use of OO-DFT methods and discuss reasons behind their relatively
restricted historical usage (vs TDDFT). We subsequently highlight modern
developments that address these factors and allow efficient and reliable OO-DFT
computations. Several successful applications of OO-DFT for challenging
electronic excitations are also presented, indicating their practical efficacy.
OO-DFT approaches are thus increasingly becoming a useful route for computing
excited states of large chemical systems. We conclude by discussing the
limitations and challenges still facing OO-DFT methods, as well as some
potential avenues for addressing them.",2103.04573v1
2021-10-02,On states of quantum theory,"In this paper the generalized quantum states, i.e. positive and normalized
linear functionals on $C^{*}$-algebras, are studied. Firstly, we study normal
states, i.e. states which are represented by density operators, and singular
states, i.e. states can not be represented by density operators. It is given an
approach to the resolution of bounded linear functionals into quantum states by
applying the GNS construction, i.e. the fundamental result of Gelfand, Neumark
and Segal on the representation theory of $C^{*}$-algebras, and theory of
projections. Secondly, it is given an application in quantum information
theory. We study covariant cloners, i.e. quantum channels in the Heisenberg and
the Schr\""{o}dinger pictures which are covariant by shifting, and it is shown
that the optimal cloners can not have a singular component. Finally, we discuss
on the representation of pure states in the sense of the Gelfand-Pettis
integral. We also give physical interpretations and examples in different
sections of the present work.",2110.00793v4
2023-08-03,Quantum entropies of realistic states of a topological insulator,"Nanowires of BiSe show topological states localized near the surface of the
material. The topological nature of these states can be analyzed using
well-known quantities. In this paper, we calculate the topological entropy
suggested by Kitaev and Preskill for these states together with a new entropy
based on a reduced density matrix that we propose as a measure to distinguish
topological one-electron states. Our results show that the topological entropy
is a constant independent of the parameters that characterize a topological
state as its angular momentum, longitudinal wave vector, and radius of the
nanowire. The new entropy is always larger for topological states than for
normal ones, allowing the identification of the topological ones. We show how
the reduced density matrices associated with both entropies are constructed
from the pure state using positive maps and explicitly obtaining the Krauss
operators.",2308.01799v1
2016-11-17,Bell-CHSH Violation Under Global Unitary Operations: Necessary and Sufficient conditions,"The relation between Bell-CHSH violation and factorization of Hilbert space
is considered here. That is, a state which is local in the sense of the
Bell-CHSH inequality under a certain factorization of the underlying Hilbert
space can be Bell-CHSH non-local under a different factorization. While this
question has been addressed with respect to separability , the relation of the
factorization with Bell-CHSH violation has remained hitherto unexplored. We
find here, that there is a set containing density matrices which do not exhibit
Bell-CHSH violation under any factorization of the Hilbert space brought about
by global unitary operations. Using the Cartan decomposition of $ SU(4) $,we
characterize the set in terms of a necessary and sufficient criterion based on
the spectrum of density matrices. Sufficient conditions are obtained to
characterize such density matrices based on their bloch representations. For
some classes of density matrices, necessary and sufficient conditions are
derived in terms of bloch parameters. Furthermore, an estimation of the volume
of such density matrices is achieved in terms of purity. The criterion is
applied to some well-known class of states in two qubits.Since, both local
filtering and global unitary operations influence Bell-CHSH violation of a
state, a comparative study is made between the two operations. The
inequivalence of the two operations(in terms of increasing Bell-CHSH violation)
is exemplified through their action on some classes of states.",1611.05586v2
1998-07-04,Time-dependent linear response of an inhomogeneous Bose superfluid: Microscopic theory and connection to current-density functional theory,"The dynamics of a confined fluid of Bose atoms is treated within the linear
response regime, with a view to establishing a current-density functional
formalism for an inhomogeneous superfluid state. After evaluating in full
detail a simplified case of an external coupling to the density and phase of
the condensate, the theory is extended to include the coupling to the total
current density. The Kohn-Sham response functions of the condensate and all the
exchange-correlation kernels for the superfluid are introduced from the
microscopic equations of motion and are expressed in a physically transparent
way through functional derivatives of correlation functions. A microscopic
formula for the superfluid density is derived and used to introduce a
generalized hydrodynamic approach for a weakly inhomogeneous two-fluid model in
isothermal conditions. Local-density expressions are thereby derived for the
velocities of first and second sound in the weakly inhomogeneous superfluid and
for visco-elastic functions describing the transition from the hydrodynamic to
the collisionless regime. Landau's hydrodynamic theory and known results in
Green's functions language are recovered in the limiting case of a homogeneous
superfluid.",9807064v1
2003-05-23,Development of a density inversion in driven granular gases,"Granular materials fluidized by a rapidly vibrating bottom plate often
develop a fascinating density inversion: a heavier layer of granulate supported
by a lower-density region. We employ the Navier-Stokes granular hydrodynamics
to follow a density inversion as it develops in time. Assuming a dilute
low-Mach-number flow, we derive a reduced time-dependent model of the late
stage of the dynamics. The model looks especially simple in the Lagrangian
coordinates. The time-dependent solution describes the growth of a density peak
at an intermediate height. A transient temperature minimum is predicted to
develop in the region of the density peak. The temperature minimum disappears
at later times, as the system approaches the steady state. At late times, the
predictions of the low-Mach-number model are in good agreement with a numerical
solution of the full hydrodynamic equations. At an early stage of the dynamics,
pressure oscillations are predicted.",0305557v1
2008-11-26,Assessing the spatial and field dependence of the critical current density in YBCO bulk superconductors by scanning Hall probes,"Although the flux density map of a bulk superconductor provides in principle
sufficient information for calculating the magnitude and the direction of the
supercurrent flow, the inversion of the Biot-Savart law is ill conditioned for
thick samples, thus rendering this method unsuitable for state of the art bulk
superconductors. If a thin (< 1 mm) slab is cut from the bulk, the inversion is
reasonably well conditioned and the variation of the critical current density
in the sample can be calculated with adequate spatial resolution. Therefore a
novel procedure is employed, which exploits the symmetry of the problem and
solves the equations non-iteratively, assuming a planar z-independent current
density. The calculated current density at a certain position is found to
depend on the magnetic induction. In this way the average field dependence of
the critical current density Jc(B) is obtained also at low fields, which is not
accessible to magnetisation measurements due to the self-field of the sample.
It is further shown that an evaluation of magnetisation loops, taking the
self-field into account, results in a similar dependence in the field range
accessible to this experiment.",0811.4279v1
2012-02-14,An analytical approach to the thermal instability of superconducting films under high current densities,"Using the Green's function of the 3D heat equation, we develop an analytical
account of the thermal behaviour of superconducting films subjected to
electrical currents larger than their critical current in the absence of an
applied magnetic field. Our model assumes homogeneity of films and current
density, and besides thermal coefficients employs parameters obtained by
fitting to experimental electrical field - current density characteristics at
constant bath temperature. We derive both a tractable dynamic equation for the
real temperature of the film up to the supercritical current density J^\ast
(the lowest current density inducing transition to the normal state), and a
thermal stability criterion that allows prediction of J^\ast . For two typical
YBCO films, J^\ast predictions agree with observations to within 5%. These
findings strongly support the hypothesis that a current-induced thermal
instability is generally the origin of the breakdown of superconductivity under
high electrical current densities, at least at temperatures not too far from
Tc.",1202.3010v1
2014-02-27,Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations,"Spectral density of quantum Ising model in two fields for large but finite
number of spins $N$, is discussed in detail. When all coupling constants are of
the same order, spectral densities in the bulk are well approximated by a
Gaussian function which is typical behaviour for many-body models with
short-range interactions. The main part of the paper is devoted to the
investigation of a different characteristic case when spectral densities have
peaks related with strong degeneracies of unperturbed states in certain limits
of coupling constants. In the strict limit $N\to\infty$, peaks overlap and
disappear but for values of $N$ accessible in numerical calculations they often
strongly influence spectral densities and other quantities as well. A simple
method is developed which permits to find general approximation formulae for
multi-peak structure of spectral density in good agreement with numerics.",1402.6858v1
2014-08-18,Density functional theory of a trapped Bose gas with tunable scattering length: from weak-coupling to unitarity,"We study an interacting Bose gas at T=0 under isotropic harmonic confinement
within Density Functional Theory in the Local Density approximation. The energy
density functional, which spans the whole range of positive scattering lengths
up to the unitary regime (infinite scattering length), is obtained by fitting
the recently calculated Monte Carlo bulk equation of state [Phys. Rev. A 89,
041602(R) (2014)]. We compare the density profiles of the trapped gas with
those obtained by MC calculations. We solve the time-dependent Density
Functional equation to study the effect of increasing values of the interaction
strength on the frequencies of monopole and quadrupole oscillations of the
trapped gas. We find that the monopole breathing mode shows a non-monotonous
behavior as a function of the scattering length. We also consider the damping
effect of three-body losses on such modes.",1408.3945v2
2016-05-21,Density shift of Bose gas due to the Casimir effect and mean field potential,"The shift of density of Bose gas due to the mean field potential (MFP) and
the Casimir effect is systematically investigated in the $d$-dimensional
configuration space from the point of thermodynamic consideration. We show
that, for $d=3$, the shift of density arises completely due to the Casimir
effect and, the MFP remains totally ineffective regardless of the state,
condensate or non-condensate. But for dimension $d>3$ the MFP plays an active
role in shifting the density of Bose gas along with the Casimir interaction.
The sign of density shift becomes positive in the present case. So, the
corresponding critical temperature shift would be negative, because these two
shifts are related as $\Delta n_{c}$/$n_{c}$ $\approx$ -$\Delta T_{c}$/$T_{c}$.
It is important to note that, the MFP causes a shift of density for $d>3$ even
when the Casimir effect is not there, and the sign of shift becomes negative
then; consequently, the critical temperature shift would be positive with MFP
alone in this particular situation.",1605.06633v1
2017-07-24,Lyapunov Stability Analysis for Invariant States of Quantum Systems,"In this article, we propose a Lyapunov stability approach to analyze the
convergence of the density operator of a quantum system. In contrast to many
previously studied convergence analysis methods for invariant density operators
which use weak convergence, in this article we analyze the convergence of
density operators by considering the set of density operators as a subset of
Banach space. We show that the set of invariant density operators is both
closed and convex, which implies the impossibility of having multiple isolated
invariant density operators. We then show how to analyze the stability of this
set via a candidate Lyapunov operator.",1707.07372v3
2021-06-08,Marginalizable Density Models,"Probability density models based on deep networks have achieved remarkable
success in modeling complex high-dimensional datasets. However, unlike kernel
density estimators, modern neural models do not yield marginals or conditionals
in closed form, as these quantities require the evaluation of seldom tractable
integrals. In this work, we present the Marginalizable Density Model
Approximator (MDMA), a novel deep network architecture which provides closed
form expressions for the probabilities, marginals and conditionals of any
subset of the variables. The MDMA learns deep scalar representations for each
individual variable and combines them via learned hierarchical tensor
decompositions into a tractable yet expressive CDF, from which marginals and
conditional densities are easily obtained. We illustrate the advantage of exact
marginalizability in several tasks that are out of reach of previous deep
network-based density estimation models, such as estimating mutual information
between arbitrary subsets of variables, inferring causality by testing for
conditional independence, and inference with missing data without the need for
data imputation, outperforming state-of-the-art models on these tasks. The
model also allows for parallelized sampling with only a logarithmic dependence
of the time complexity on the number of variables.",2106.04741v1
2024-01-18,Higher bracket structure of density operators in Weyl fermion systems and topological insulators,"We study the algebraic structure of electron density operators in gapless
Weyl fermion systems in $d=3,5,7,\cdots$ spatial dimensions and in topological
insulators (without any protecting symmetry) in $d=4,6,8,\cdots$ spatial
dimensions. These systems are closely related by the celebrated bulk-boundary
correspondence. Specifically, we study the higher bracket -- a generalization
of commutator for more than two operators -- of electron density operators in
these systems. For topological insulators, we show that the higher-bracket
algebraic structure of density operators structurally parallels with the
Girvin-MacDonald-Platzman algebra (the $W_{1+\infty}$ algebra), the algebra of
electron density operators projected onto the lowest Landau level in the
quantum Hall effect. By the bulk-boundary correspondence, the bulk
higher-bracket structure mirrors its counterparts at the boundary.
Specifically, we show that the density operators of Weyl fermion systems, once
normal-ordered with respect to the ground state, their higher bracket acquires
a c-number part. This part is an analog of the Schwinger term in the commutator
of the fermion current operators. We further identify this part with a cyclic
cocycle, which is a topological invariant and an element of Connes'
noncommutative geometry.",2401.09683v1
2006-08-29,Exact calculation of robustness of entanglement via convex semi-definite programming,"In general the calculation of robustness of entanglement for the mixed
entangled quantum states is rather difficult to handle analytically. Using the
the convex semi-definite programming method, the robustness of entanglement of
some mixed entangled quantum states such as: $2\otimes 2$ Bell decomposable
(BD) states, a generic two qubit state in Wootters basis, iso-concurrence
decomposable states, $2\otimes 3$ Bell decomposable states, $d\otimes d$ Werner
and isotropic states, a one parameter $3\otimes 3$ state and finally multi
partite isotropic state, is calculated exactly, where thus obtained results are
in agreement with those of :$2\otimes 2$ density matrices, already calculated
by one of the authors in \cite{Bell1,Rob3}. Also an analytic expression is
given for separable states that wipe out all entanglement and it is further
shown that they are on the boundary of separable states as pointed out in
\cite{du}.
  {\bf Keywords: Robustness of entanglement, Semi-definite programming, Bell
decomposable states, Werner and isotropic states.}",0608225v1
2003-06-12,Kirkwood Phase Transition for Boson and Fermion Hard-Sphere Systems,"The London ground-state energy formula as a function of number density $\rho
$ for a system of boson hard spheres of diameter $c$ at zero temperature
(corrected for the reduced mass of a pair of particles in a
``sphere-of-influence'' picture) generalized to describe fermion hard-sphere
systems with four and two intrinsic degrees of freedom such as helium-three or
neutron matter and symmetric nuclear matter, respectively, is proposed as the
crystalline energy branch for hard-sphere systems. For the fluid branch we use
the well-known, exact, low-density equation-of-state expansions for many-boson
and many-fermion systems, appropriately extrapolated to physical densities.
Here, via a double-tangent construction the crystallization and melting
densities for boson and fermion hard spheres are determined. They agree well
with variational Monte Carlo, density-functional, and Green Function Monte
Carlo calculations.",0306338v1
2004-07-15,Large-N limit of a magnetic impurity in unconventional density waves,"We investigate the effect of unconventional density wave (UDW) condensate on
an Anderson impurity using large-N technique at T=0. In accordance with
previous treatments of a Kondo impurity in pseudogap phases, we find that Kondo
effect occurs only in a certain range of parameters. The f-electron density of
states reflects the influence of UDW at low energies and around the maximum of
the density wave gap. The static spin susceptibility diverges at the critical
coupling, indicating the transition from strong to weak coupling. In the
dynamic spin susceptibility an additional peak appears showing the presence the
UDW gap. Predictions concerning non-linear density of states are made. Our
results apply to other unconventional condensates such as d-wave
superconductors and d-density waves as well.",0407387v1
2002-09-05,Relativistic Random-Phase Approximation with density-dependent meson-nucleon couplings,"The matrix equations of the relativistic random-phase approximation (RRPA)
are derived for an effective Lagrangian characterized by density-dependent
meson-nucleon vertex functions. The explicit density dependence of the
meson-nucleon couplings introduces rearrangement terms in the residual two-body
interaction, that are essential for a quantitative description of excited
states. Illustrative calculations of the isoscalar monopole, isovector dipole
and isoscalar quadrupole response of $^{208}$Pb, are performed in the fully
self-consistent RRPA framework, based on effective interactions with a
phenomenological density dependence adjusted to nuclear matter and ground-state
properties of spherical nuclei. The comparison of the RRPA results on multipole
giant resonances with experimental data constrains the parameters that
characterize the isoscalar and isovector channel of the density-dependent
effective interactions.",0209016v1
2010-03-23,The equilibrium state of a trapped two-dimensional Bose gas,"We study experimentally and numerically the equilibrium density profiles of a
trapped two-dimensional $^{87}$Rb Bose gas, and investigate the equation of
state of the homogeneous system using the local density approximation. We find
a clear discrepancy between in-situ measurements and Quantum Monte Carlo
simulations, which we attribute to a non-linear variation of the optical
density of the atomic cloud with its spatial density. However, good agreement
between experiment and theory is recovered for the density profiles measured
after time-of-flight, taking advantage of their self-similarity in a
two-dimensional expansion.",1003.4545v1
2011-07-27,Phase diagram of the ABC model with nonequal densities,"The ABC model is a driven diffusive exclusion model, composed of three
species of particles that hop on a ring with local asymmetric rates. In the
weak asymmetry limit, where the asymmetry vanishes with the length of the
system, the model exhibits a phase transition between a homogenous state and a
phase separated state. We derive the exact solution for the density profiles of
the three species in the hydrodynamic limit for arbitrary average densities.
The solution yields the complete phase diagram of the model and allows the
study of the nature of the first order phase transition found for average
densities that deviate significantly from the equal densities point.",1107.5471v1
2018-11-12,Laboratory Probes of the Neutron-Matter Equation of State,"To relate constraints from nuclear physics to the tidal deformabilities of
neutron stars, we construct a neutron star model that accepts input from a
large collection of Skyrme density functions to calculate properties of 1.4
solar-mass neutron stars. We find that restricting this set of Skyrme to
density functions that describe nuclear masses, isobaric analog states, and low
energy nuclear reactions does not sufficiently restrict the predicted
neutron-star radii and the tidal deformabilities. However, pressure constraints
on the EoS around twice saturation density ($2\times2.74\times10^{14}g/cm^3$),
obtained from high energy nucleus-nucleus collisions, does constrain predicted
tidal deformabilities with uncertainties smaller than those obtained from the
analysis of GW170817. We also found that the density-pressure constraint on the
EoS obtained from a recent analysis of the neutron-star merger event agree very
well with the density pressure constraints obtained from nuclear physics
experiments published in 2002.",1811.04888v1
2018-11-29,Lower Bound on the Hartree-Fock Energy of the Electron Gas,"The Hartree-Fock ground state of the Homogeneous Electron Gas is never
translation invariant, even at high densities. As proved by Overhauser, the
(paramagnetic) free Fermi Gas is always unstable under the formation of spin or
charge density waves. We give here the first explicit bound on the energy gain
due to the breaking of translational symmetry. Our bound is exponentially small
at high density, which justifies posteriori the use of the non-interacting
Fermi Gas as a reference state in the large-density expansion of the
correlation energy of the Homogeneous Electron Gas. We are also able to discuss
the positive temperature phase diagram and prove that the Overhauser
instability only occurs at temperatures which are exponentially small at high
density. Our work sheds a new light on the Hartree-Fock phase diagram of the
Homogeneous Electron Gas.",1811.12461v2
2020-09-11,Electron-Phonon Interactions in Flat Band Systems,"Existing Quantum Monte Carlo studies have investigated the properties of
fermions on a Lieb (CuO$_2$) lattice interacting with an on-site, or
near-neighbor electron-electron coupling. Attention has focused on the
interplay of such interactions with the macroscopic degeneracy of local zero
energy modes, from which Bloch states can be formed to produce a flat band in
which energy is independent of momentum. The resulting high density of states,
in combination with the Stoner criterion, suggests that there should be
pronounced instabilities to ordered phases. Indeed, a theorem by Lieb
rigorously establishes the existence of ferrimagnetic order. Here we study the
charge density wave phases induced by electron-phonon coupling on the Lieb
lattice, as opposed to previous work on electron-electron interactions. Our key
result is the demonstration of charge density wave (CDW) phases at one-third
and two-thirds fillings, characterized by long-range density density
correlations between doubly occupied sites on the minority or majority
sublattice, and an accompanying gap. We also compute the transition temperature
to the ordered phase as a function of the electron-phonon coupling.",2009.05595v3
2020-06-17,Regularity of transition densities and ergodicity for affine jump-diffusion processes,"In this paper we study the transition density and exponential ergodicity in
total variation for an affine process on the canonical state space
$\mathbb{R}_{\geq0}^{m}\times\mathbb{R}^{n}$. Under a H\""ormander-type
condition for diffusion components as well as a boundary non-attainment
assumption, we derive the existence and regularity of the transition density
for the affine process and then prove the strong Feller property. Moreover, we
also show that under these and the additional subcritical conditions the
corresponding affine process on the canonical state space is exponentially
ergodic in the total variation distance. To prove existence and regularity of
the transition density we derive some precise estimates for the real part of
the characteristic function of the process. Our ergodicity result is a
consequence of a suitable application of a Harris-type theorem based on a local
Dobrushin condition combined with the regularity of the transition densities.",2006.10009v1
2021-04-11,Time-Dependent Atomistic Simulations of the CP29 Light-Harvesting Complex,"Light harvesting as the first step in photosynthesis is of prime importance
for life on earth. For a theoretical description of photochemical processes
during light harvesting, spectral densities are key quantities. They serve as
input functions for modeling the excitation energy transfer dynamics and
spectroscopic properties. Herein, a recently developed procedure is applied to
determine the spectral densities of the pigments in the minor antenna complex
CP29 of photosystem II which has recently gained attention because of its
active role in non-photochemical quenching processes in higher plants. To this
end, the density functional based tight binding (DFTB) method has been employed
to enable simulation of the ground state dynamics in a
quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll
pigment. Subsequently, the time-dependent extension of the long-range corrected
DFTB approach has been used to obtain the excitation energy fluctuations along
the ground-state trajectories also in a QM/MM setting. From these results the
spectral densities have been determined and compared for different force fields
and to spectral densities from other light-harvesting complexes. In addition,
the excitation energy transfer in the CP29 complex has been studied using
ensemble-average wave packet dynamics.",2104.05034v1
2023-03-06,A Crossover phase transition based on the phenomenology of hadronic matter and quark matter,"The phase transition calculations are utilized for an in-depth understanding
of the thermodynamics of the deconfinement transition to perform the best
analysis of the QCD phase diagram. The phenomenological justifications for a
mathematical approach to constructing the phase transition are found based on
the properties of hadronic matter at low densities as well as quark matter at
high densities. We modify both the quark matter equation of state by confining
effects at low densities and the hadronic matter equation of state by excluded
volume effects at higher densities. Over the intermediate densities, the
transition from the hadronic phase to the quark phase is modified by the
surface tension between to phases. The results are in agreement with the
observational constraints of neutron stars.",2303.03030v1
2023-03-18,Self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo using mixed estimators,"We propose a new scheme to implement the self-consistent optimization of the
trial wave-function in constrained path auxiliary field Quantum Monte Carlo
(CP-AFQMC) in the framewok of natural orbitals. In this scheme, a new trial
wave-function in the form of Slater determinant is constructed from the
CP-AFQMC results by diagonalizing the mixed estimator of the one-body reduced
density matrix. We compare two ways (from real and mixed estimators in
CP-AFQMC) to calculate the one-body reduced density matrix in the
self-consistent process and study the ground state of doped two dimensional
Hubbard model to test the accuracy of the two schemes. By comparing the local
density, occupancy, and ground state energy we find the scheme in which
one-body reduced density matrix is calculated from mixed estimator is
computational more efficient and provides more accurate result with less
fluctuation. The local densities from mixed estimator scheme agree well with
the numerically exact values. This scheme provides a useful tool for the study
of strongly correlated electron systems.",2303.10301v2
2024-01-09,Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective,"This work merges two different types of many-electron ensembles, namely the
Theophilou-Gross-Oliveira-Kohn ensembles of ground and neutrally-excited
states, and the more recent $N$-centered ensembles of neutral and charged
ground states. On that basis, an in-principle exact and general, so-called
extended $N$-centered, ensemble density-functional theory of charged and
neutral electronic excitations is derived. We revisit in this context the
concept of density-functional derivative discontinuity for neutral excitations,
without ever invoking nor using the asymptotic behavior of the ensemble
electronic density. The present mathematical construction fully relies on the
weight dependence of the ensemble Hartree-exchange-correlation
density-functional energy, which makes the theory applicable to lattice models
and opens new perspectives for the description of gaps in mesoscopic systems.",2401.04685v2
2024-04-04,Nuclear Matter Equation of State in the Brueckner-Hartree-Fock Approach and Standard Skyrme Energy-Density Functionals,"The equation of state of asymmetric nuclear matter as well as the neutron and
proton effective masses and their partial-wave and spin-isospin decomposition
are analyzed within the Brueckner--Hartree--Fock approach. Theoretical
uncertainties for all these quantities are estimated by using several
phase-shift-equivalent nucleon-nucleon forces together with two types of
three-nucleon forces, phenomenological and microscopic. It is shown that the
choice of the three-nucleon force plays an important role above saturation
density, leading to different density dependencies of the energy per particle.
These results are compared to the standard form of the Skyrme energy-density
functional and we find that it is not possible to reproduce the BHF predictions
in the $(S,T)$ channels in symmetric and neutron matter above saturation
density, already at the level of the two-body interaction, and even more
including the three-body interaction.",2404.03583v1
2002-05-07,Compatibility of quantum states,"We introduce a measure of the compatibility between quantum states--the
likelihood that two density matrices describe the same object. Our measure is
motivated by two elementary requirements, which lead to a natural definition.
We list some properties of this measure, and discuss its relation to the
problem of combining two observers' states of knowledge.",0205033v1
2003-04-10,Von Neumann Measurement is Optimal for Detecting Linearly Independent Mixed Quantum States,"We consider the problem of designing a measurement to minimize the
probability of a detection error when distinguishing between a collection of
possibly non-orthogonal mixed quantum states. We show that if the quantum state
ensemble consists of linearly independent density operators then the optimal
measurement is an orthogonal Von Neumann measurement consisting of mutually
orthogonal projection operators and not a more general positive operator-valued
measure.",0304077v1
2007-06-29,Equation-of-state model for shock compression of hot dense matter,"A quantum equation-of-state model is presented and applied to the calculation
of high-pressure shock Hugoniot curves beyond the asymptotic fourfold density,
close to the maximum compression where quantum effects play a role. An
analytical estimate for the maximum attainable compression is proposed. It
gives a good agreement with the equation-of-state model.",0707.0010v1
2007-10-22,Collapsing Layers on Schwarzschild-Lemaitre Geodesics,"We discuss Israel layers collapsing inward from rest at infinity along
Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its
equation of state are developed. There is a general equation of state which is
approximately polytropic in the limit of very low pressure. The equation of
state establishes a new limit on the stress-density ratio.",0710.4058v1
2010-08-05,The structure of strongly additive states and Markov triplets on the CAR algebra,"We find a characterization of states satisfying equality in strong
subadditivity of entropy and of Markov triplets on the CAR algebra. For even
states, a more detailed structure of the density matrix is given.",1008.0982v1
2013-04-02,Entanglement of one-magnon Schur-Weyl states,"We investigate the entanglement properties of symmetry states of the
Schur-Weyl duality. Our approach based on reduced two-qubit density matrices,
and concurrence as the measure of entanglement. We show that all kinds of
entangled graphs, which describe the entanglement structure in Schur-Weyl
states are completely coded in the corresponding Young tableau.",1304.0590v1
2022-05-07,The Exact Exchange-Correlation Potential in Time-Dependent Density Functional Theory: Choreographing Electrons with Steps and Peaks,"The time-dependent exchange-correlation potential has an unusual task in
directing fictitious non-interacting electrons to move with exactly the same
probability density as true interacting electrons. This has intriguing
implications for its structure, especially in the non-perturbative regime,
leading to step and peak features that cannot be captured by bootstrapping any
ground-state functional approximations. We review what has been learned about
these features in the exact exchange-correlation potential in time-dependent
density functional theory in the past decade or so, and implications for the
performance of simulations when electrons are driven far from any ground-state.",2205.03691v2
2013-04-26,Energy trapping from Hagedorn densities of states,"In this note, we construct simple stochastic toy models for holographic gauge
theories in which distributions of energy on a collection of sites evolve by a
master equation with some specified transition rates. We build in only energy
conservation, locality, and the standard thermodynamic requirement that all
states with a given energy are equally likely in equilibrium. In these models,
we investigate the qualitative behavior of the dynamics of the energy
distributions for different choices of the density of states for the individual
sites. For typical field theory densities of states (\log(\rho(E)) ~
E^{\alpha<1}), the model gives diffusive behavior in which initially localized
distributions of energy spread out relatively quickly. For large N gauge
theories with gravitational duals, the density of states for a finite volume of
field theory degrees of freedom typically includes a Hagedorn regime
(\log(\rho(E)) ~ E). We find that this gives rise to a trapping of energy in
subsets of degrees of freedom for parametrically long time scales before the
energy leaks away. We speculate that this Hagedorn trapping may be part of a
holographic explanation for long-lived gravitational bound states (black holes)
in gravitational theories.",1304.7275v1
2004-10-14,"Relativistic Mean-Field Models with Effective Hadron Masses and Coupling Constants, and rho^- Condensation","We study relativistic mean-field models with hadron masses and coupling
constants depending self-consistently on a scalar meson field. We demonstrate
that by the field redefinition some models can be equivalently transformed into
each other. Thereby the large variety of scaling functions for masses and
couplings can be reduced to a restricted set of functions with a constrained
dependence on a scalar field. We show how by choosing properly the latter
scaling functions one may stiffen or soften the equation of state at high
densities and simultaneously increase the threshold density for the direct Urca
process without any change of the description of nuclear matter close to the
saturation density. The stiffening of the equation of state might be motivated
by recent neutron star mass measurements, whereas the increase of the threshold
density for the direct Urca process is required by the analysis of neutron star
cooling data. We demonstrate that if a rho meson is included in a mean-field
model as a non-Abelian gauge boson, then there is a possibility for a charged
rho-meson condensation in dense nuclear matter. We show that such a novel phase
can be realized in neutron star interiors already for sufficiently low
densities, typically $\sim 3\div 4 n_0$, where $n_0$ is the nuclear saturation
density. In the framework of the relativistic mean field model the new phase
arises in a second-order phase transition. The appearance of a $\rho^-$
condensate significantly alters the proton fraction in a neutron star but
changes moderately the equation of state. The neutrino emissivity of the
processes involving a $\rho^-$ meson condensate is estimated.",0410063v1
2020-05-11,Correlated electron-hole State in Twisted Double Bilayer Graphene,"When twisted to angles near 1{\deg}, graphene multilayers provide a new
window on electron correlation physics by hosting gate-tuneable
strongly-correlated states, including insulators, superconductors, and unusual
magnets. Here we report the discovery of a new member of the family,
density-wave states, in double bilayer graphene twisted to 2.37{\deg}. At this
angle the moir\'e states retain much of their isolated bilayer character,
allowing their bilayer projections to be separately controlled by gates. We use
this property to generate an energetic overlap between narrow isolated electron
and hole bands with good nesting properties. Our measurements reveal the
formation of ordered states with reconstructed Fermi surfaces, consistent with
density-wave states, for equal electron and hole densities. These states can be
tuned without introducing chemical dopants, thus opening the door to a new
class of fundamental studies of density-waves and their interplay with
superconductivity and other types of order, a central issue in quantum matter
physics.",2005.05373v3
2019-05-26,Effects of $φ_0$-meson on the EOS of hyperon star in the relativistic mean field model,"Nuclear effective interactions are considered as a vital tool to guide into
the region of the high degree of isospin asymmetry and density. We take
varieties of parameter sets of the RMF model to show the parametric dependence
of the hyperon star properties. We add $\phi_0$-meson to
$\sigma$-$\omega$-$\rho$ model. The effects of $\phi_0$-meson on the equation
of state and consequently on the maximum mass of the hyperon star are
discussed. Due to the inclusion of $\phi_0$-meson the threshold density of
different hyperon production shift to higher density region. The effects of the
hyperon-meson coupling constants on the maximum mass and radius of the hyperon
stars are discussed.",1905.10880v1
2005-06-17,Quantum state tomography with quantum shotnoise,"We propose a scheme for a complete reconstruction of one- and two-particle
orbital quantum states in mesoscopic conductors. The conductor in the transport
state continuously emits orbital quantum states. The orbital states are
manipulated by electronic beamsplitters and detected by measurements of average
currents and zero frequency current shotnoise correlators. We show how, by a
suitable complete set of measurements, the elements of the density matrices of
the one- and two-particle states can be directly expressed in terms of the
currents and current correlators.",0506446v1
1996-04-21,Symplectic Tomography of Nonclassical States of Trapped Ion,"The marginal distribution of squeezed and rotated quadrature for two types of
nonclassical states of trapped ion -- for squeezed and correlated states and
for squeezed even and odd coherent states (squeezed Schr\""odinger cat states)
is studied. The obtained marginal distribution for the two types of states is
shown to satisfy classical dynamical equation equivalent to standard quantum
evolution equation for density matrix (wave function) derived in symplectic
tomography scheme.",9604018v1
2012-11-14,Robust entangled qutrit states in atmospheric turbulence,"The entangled quantum state of a photon pair propagating through atmospheric
turbulence suffers decay of entanglement due to the scintillation it
experiences. Here we investigate the robustness against this decay for
different qutrit states. We use an infinitesimal-propagation equation to obtain
the density matrix as a function of the propagation distance and we use the
tangle to quantify the entanglement between a pair of qutrits. The evolution of
various initial states as they propagate through turbulence is considered.
Using optimization of the initial parameters, we obtain expressions for
bipartite qutrit states that retain their initial entanglement longer than the
initially maximally entangled states.",1211.3203v1
2015-11-07,Entropic lower bound for distinguishability of quantum states,"For a system randomly prepared in a number of quantum states, we present a
lower bound for the distinguishability of the quantum states, that is, the
success probability of determining the states in the form of entropy. When the
states are all pure, acquiring the entropic lower bound requires only the
density operator and the number of the possible states. This entropic bound
shows a relation between the von Neumann entropy and the distinguishability.",1511.02309v2
2016-09-16,Schmidt number of bipartite and multipartite states under local projections,"The Schmidt number is a fundamental parameter characterizing the properties
of quantum states, and the local projections are a fundamental operation in
quantum physics. We investigate the relation between the Schmidt numbers of
bipartite states and their projected states. We show that there exist bipartite
positive-partial-transpose (PPT) entangled states of any given Schmidt number.
We further construct the notion of joint Schmidt number for multipartite
states, and its relation with the Schmidt number of bipartite reduced density
operators.",1609.05100v1
2016-10-24,"Multi-photon subtracted thermal states: description, preparation and reconstruction","We present a study of optical quantum states generated by subtraction of
photons from the thermal state. Some aspects of their photon number and
quadrature distributions are discussed and checked experimentally. We
demonstrate an original method of up to ten photon subtracted state preparation
with use of just one single-photon detector. All the states where measured with
use of balanced homodyne technique, and the corresponding density matrices
where reconstructed. The fidelity between desired and reconstructed states
exceeds 99%",1610.07321v2
1995-06-09,"Transport Properties of ""Extended-s"" State Superconductors","Superconducting states with ""extended s-wave"" symmetry have been suggested in
connection with recent ARPES experiments on BSCCO. In the presence of
impurities, thermodynamic properties of such states reflect a residual density
of states $N(0)$ for a range of concentrations. While properties reflecting
$N(\omega)$ alone will be similar to those of d-wave states, transport
measurements may be shown to qualitatively distinguish between the two. In
contrast to the d-wave case with unitarity limit scattering, limiting
low-temperature residual conductivities in the s-wave state are large and scale
inversely with impurity concentration.",9506039v1
2011-03-01,Young's Double Slit Experiment in Quantum Field Theory,"Young's double slit experiment is formulated in the framework of canonical
quantum field theory in view of the modern quantum optics. We adopt quantum
scalar fields instead of quantum electromagnetic fields ignoring the vector
freedom in gauge theory. The double slit state is introduced in Fock space
corresponding to experimental setup. As observables, expectation values of
energy density and positive frequency part of current with respect to the
double slit state are calculated which give the interference term. Classical
wave states are realized by coherent double slit states in Fock space which
connect quantum particle states with classical wave states systematically. In
case of incoherent sources, the interference term vanishes by averaging random
phase angles as expected.",1103.0100v1
2013-02-05,On separable decompositions of quantum states with strong positive partial transposes,"We analyze a class of positive partial transpose states (PPT) such that the
positivity of its partial transposition is recognized with respect to canonical
factorization of the original density operator (Cholesky block decomposition).
We call such PPT states strong PPT states (SPPT). This property, contrary to
PPT, is basis dependent. It is shown that there exists a proper subset of SPPT
states which are separable and provide a separable decomposition for any of
these states.",1302.1049v1
2020-01-12,Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder,"Phyllotactic states are regular lattice-like structures on cylinders and are
a botanical classification scheme. In this communication, we report a sequence
of transitions between phyllotactic states for particles with a repulsive
particle-particle interaction on a cylindrical geometry at zero temperature. We
can infer the transition points as a function of density via Monte Carlo
simulations, as well as the mathematical descriptions of the ground states. The
lattices we generate are described as phyllotactic states that fit onto the
cylindrical surface as a set of helical chains. Our analysis shows how all
state energies lie on the same parabola which we exploit to find the
transitions.",2001.03948v1
2024-02-29,Nuclear spin relaxation in solid state defect quantum bits via electron-phonon coupling in their optical excited state,"Optically accessible solid state defect spins are primary platform for
quantum information processing where tight control of the electron spin and
ancilla nuclear spins is pivotal for the operation. We demonstrate on the
exemplary nitrogen-vacancy (NV) color center in diamond by means of a combined
group theory and density functional theory study that spin-phonon relaxation
rate of the nitrogen nuclear spin is with several orders of magnitude enhanced
by the strong electron-phonon coupling in the optical excited state of the
defect. The mechanism is common to other solid state defect spins sharing
similar optical excited states with that of the NV center.",2402.19418v1
2018-01-21,Information loss in effective field theory: entanglement and thermal entropies,"Integrating out high energy degrees of freedom to yield a low energy
effective field theory leads to a loss of information with a concomitant
increase in entropy. We obtain the effective field theory of a light scalar
field interacting with heavy fields after tracing out the heavy degrees of
freedom from the time evolved density matrix. The initial density matrix
describes the light field in its ground state and the heavy fields in
equilibrium at a common temperature $T$. For $T=0$, we obtain the reduced
density matrix in a perturbative expansion, it reveals an emergent mixed state
as a consequence of the entanglement between light and heavy fields. We obtain
the effective action that determines the time evolution of the \emph{reduced}
density matrix for the light field in a non-perturbative Dyson resummation of
one-loop correlations of the heavy fields. The Von-Neumann \emph{entanglement
entropy} associated with the reduced density matrix is obtained for the
non-resonant and resonant cases in the asymptotic long time limit. In the
non-resonant case the reduced density matrix displays an \emph{incipient}
thermalization albeit with a wave-vector, time and coupling dependent
\emph{effective temperature} as a consequence of memory of initial conditions.
The entanglement entropy is time independent and is the \emph{thermal entropy}
for this effective, non-equilibrium temperature. In the resonant case the light
field fully \emph{thermalizes} with the heavy fields, the reduced density
matrix looses memory of the initial conditions and the entanglement entropy
becomes the \emph{thermal entropy} of the light field. We discuss the relation
between the entanglement entropy ultraviolet divergences and renormalization.",1801.06840v2
2021-11-09,How perturbative QCD constrains the Equation of State at Neutron-Star densities,"We demonstrate in a general and analytic way how high-density information
about the equation of state (EoS) of strongly interacting matter obtained using
perturbative Quantum Chromodynamics (pQCD) constrains the same EoS at densities
reachable in physical neutron stars. Our approach is based on utilizing the
full information of the thermodynamic potentials at the high-density limit
together with thermodynamic stability and causality. This requires considering
the pressure as a function of chemical potential $p(\mu)$ instead of the
commonly used pressure as a function of energy density $p(\epsilon)$. The
results can be used to propagate the pQCD calculations reliable around 40$n_s$
to lower densities in the most conservative way possible. We constrain the EoS
starting from only few times the nuclear saturation density $n \gtrsim 2.2 n_s$
and at $n = 5 n_s$ we exclude at least 65% of otherwise allowed area in the
$(\epsilon - p)$-plane. This provides information complementary to
astrophysical observations that should be taken into account in any complete
statistical inference study of the EoS. These purely theoretical results are
independent of astrophysical neutron-star input, and hence, they can also be
used to test theories of modified gravity and BSM physics in neutron stars.",2111.05350v2
2007-10-22,Equilibrium sequences of non rotating and rapidly rotating crystalline color superconducting hybrid stars,"The three-flavor crystalline color-superconducting (CCS) phase of quantum
chromodynamics (QCD) is a candidate phase for the ground state of cold matter
at moderate densities above the density of the deconfinement phase transition.
Apart from being a superfluid, the CCS phase has properties of a solid, such as
a lattice structure and a shear modulus, and hence the ability to sustain
multipolar deformations in gravitational equilibrium. We construct equilibrium
configurations of hybrid stars composed of nuclear matter at low, and CCS quark
matter at high, densities. Phase equilibrium between these phases is possible
only for rather stiff equations of state of nuclear matter and large couplings
in the effective Nambu--Jona-Lasinio Lagrangian describing the CCS state. We
identify a new branch of stable CCS hybrid stars within a broad range of
central densities which, depending on the details of the equations of state,
either bifurcate from the nuclear sequence of stars when the central density
exceeds that of the deconfinement phase transition or form a new family of
configurations separated from the purely nuclear sequence by an instability
region. The maximum masses of our non-rotating hybrid configurations are
consistent with the presently available astronomical bounds. The sequences of
hybrid configurations that rotate near the mass-shedding limit are found to be
more compact and thus support substantially larger spins than their same mass
nuclear counterparts.",0710.3874v2
2016-09-29,Sub-system fidelity for ground states in one dimensional interacting systems,"We propose to utilize the sub-system fidelity (SSF), defined by comparing a
pair of reduced density matrices derived from the degenerate ground states, to
identify and/or characterize symmetry protected topological (SPT) states in
one-dimensional interacting many-body systems. The SSF tells whether two states
are locally indistinguishable (LI) by measurements within a given sub-system.
Starting from two polar states (states that could be distinguished on either
edge), the other combinations of these states can be mapped onto a Bloch
sphere. We prove that a pair of orthogonal states on the equator of the Bloch
sphere are LI, independently of whether they are SPT states or cat states
(symmetry-preserving states by linear combinations of states that break
discrete symmetries). Armed with this theorem, we provide a scheme to construct
zero-energy exitations that swap the LI states. We show that the zero mode can
be located anywhere for cat states, but is localized near the edge for SPT
states. We also show that the SPT states are LI in a finite fraction of the
bulk (excluding the two edges), whereas the symmetry-breaking states are
distinguishable. This can be used to pinpoint the transition from SPT states to
the symmetry-breaking states.",1609.09309v1
2001-12-06,Two effective temperatures in traffic flow models: analogies with granular flow,"We present a model of traffic flow, with rules that describe the behaviour of
automated vehicles in an open system. We show first of all that the fundamental
diagram of this system collapses to a point, where states of free and jammed
traffic can coexist in phase space. This leads us to consider separately the
roles of average velocities and densities as better descriptors of the actual
state of the traffic. Next, we observe that the transition between free and
jammed traffic as a function of the braking parameter R is different for high
and low initial densities, in the steady state; it turns out to be 'smeared
out' for low densities, a behaviour which is already portended by the transient
behaviour of the system. Our results indicate strongly that, at least for such
models, two effective temperatures (one related to R, and the other to the
density) are needed to describe the global behaviour of this system in
statistical mechanical terms. Analogies with granular flow are discussed in
this context.",0112102v1
2001-06-01,High Temperature Electron Localization in dense He Gas,"We report new accurate mesasurements of the mobility of excess electrons in
high density Helium gas in extended ranges of temperature $[(26\leq T\leq 77) K
]$ and density $[ (0.05\leq N\leq 12.0) {atoms} \cdot {nm}^{-3}]$ to ascertain
the effect of temperature on the formation and dynamics of localized electron
states. The main result of the experiment is that the formation of localized
states essentially depends on the relative balance of fluid dilation energy,
repulsive electron-atom interaction energy, and thermal energy. As a
consequence, the onset of localization depends on the medium disorder through
gas temperature and density. It appears that the transition from delocalized to
localized states shifts to larger densities as the temperature is increased.
This behavior can be understood in terms of a simple model of electron
self-trapping in a spherically symmetric square well.",0106004v1
2010-09-09,Virial Expansion of the Nuclear Equation of State,"We study the equation of state (EOS) of nuclear matter as function of
density. We expand the energy per particle (E/A) of symmetric infinite nuclear
matter in powers of the density to take into account 2,3,. . .,N-body forces.
New EOS are proposed by fitting ground state properties of nuclear matter
(binding energy, compressibility and pressure) and assuming that at high
densities a second order phase transition to the Quark Gluon Plasma (QGP)
occurs. The latter phase transition is due to symmetry breaking at high density
from nuclear matter (locally color white) to the QGP (globally color white). In
the simplest implementation of a second order phase transition we calculate the
critical exponent ? by using Landau's theory of phase transition. We find ? =
3. Refining the properties of the EOS near the critical point gives ? = 5 in
agreement with experimental results. We also discuss some scenarios for the EOS
at finite temperatures.",1009.1812v1
2018-04-04,Wide Ranging Equation of State with Tartarus: a Hybrid Green's Function/Orbital based Average Atom Code,"Average atom models are widely used to make equation of state tables and for
calculating other properties of materials over a wide range of conditions, from
zero temperature isolated atom to fully ionized free electron gases. The
numerical challenge of making these density functional theory based models work
for any temperature, density or nuclear species is formidable. Here we present
in detail a hybrid Green's function/orbital based approach that has proved to
be stable and accurate for wide ranging conditions. Algorithmic strategies are
discussed. In particular the decomposition of the electron density into
numerically advantageous parts is presented and a robust and rapid self
consistent field method based on a quasi-Newton algorithm is given. Example
application to the equation of state of lutetium (Z=71) is explored in detail,
including the effect of relativity, finite temperature exchange and
correlation, and a comparison to a less approximate method. The hybrid scheme
is found to be numerically stable and accurate for lutetium over at least 6
orders of magnitude in density and 5 orders of magnitude in temperature.",1804.01613v1
2020-01-17,Parallelity of mixed quantum ensembles,"A unifying framework for identifying distance and holonomy for decompositions
of density operators is introduced. Parallelity between quantum ensembles is
defined by minimizing this distance over allowed decompositions. The minimum is
a property of a pair of states and coincides with the Bures distance. The
parallelity condition imposes a connection (rule for parallel transport) that
results in the Uhlmann holonomy for sequences of density operators. A distance
and holonomy for spectral decompositions of density operators is identified as
a sub-group restriction of the full decomposition freedom. These spectral
concepts are gauge invariant (decomposition independent) properties of mixed
quantum ensembles, as long as the corresponding density operators are
non-degenerate. A gauge invariant spectral geometric phase for discrete
sequences of mixed quantum states is obtained as the phase of the trace of the
spectral holonomy. This geometric phase differs from the interferometric mixed
state geometric phase in the continuous limit.",2001.06360v1
2022-10-28,Symmetry protected topological phases under decoherence,"We study ensembles described by density matrices with potentially nontrivial
topological features. In particular, we study a class of symmetry protected
topological (SPT) phases under various types of decoherence, which can drive a
pure SPT state into a mixed state. We demonstrate that the system can still
retain the nontrivial topological information from the SPT ground state even
under decoherence. In the ""doubled Hilbert space"", we provide a general
definition for symmetry protected topological ensemble (SPT ensemble), and the
main quantity that we investigate is various types of (boundary) anomalies in
the doubled Hilbert space. We show that the notion of the strange correlator,
previously proposed to as a diagnosis for the SPT ground states, can be
generalized to capture these anomalies in mixed-state density matrices. Using
both exact calculations of the stabilizer Hamiltonians and field theory
evaluations, we demonstrate that under decoherence the nontrivial features of
the SPT state can persist in the two types of strange correlators: type-I and
type-II. We show that the nontrivial type-I strange correlator corresponds to
the presence of the SPT information that can be efficiently identified and
utilized from experiments, such as for the purpose of preparing for long-range
entangled states. The nontrivial type-II strange correlator encodes the full
topological response of the decohered mixed state density matrix, i.e., the
information about the presence of the SPT state before decoherence. Therefore,
our work provides a unified framework to understand decohered SPT phases from
the information-theoretic viewpoint.",2210.16323v4
2006-06-05,"Ultra-Dense Neutron Star Matter, Strange Quark Stars, and the Nuclear Equation of State","With central densities way above the density of atomic nuclei, neutron stars
contain matter in one of the densest forms found in the universe. Depending of
the density reached in the cores of neutron stars, they may contain stable
phases of exotic matter found nowhere else in space. This article gives a brief
overview of the phases of ultra-dense matter predicted to exist deep inside
neutron stars and discusses the equation of state associated with such matter.",0606093v1
1999-10-01,Carrier relaxation dynamics in intra-gap states: the case of the superconductor Y Ba_2 Cu_3O_7-delta and the charge-density-wave semiconductor K_0.3MoO_3,"The unusual slow carrier relaxation dynamics - observed in femtosecond
pump-probe experiments on high-temperature superconductors and recently also in
a charge-density-wave system - is analyzed in terms of a model for relaxation
of carriers in intra-gap states. The data on YBa_2Cu_3O_7-delta near optimum
doping and K_0.3$MoO_3 are found to be described very well with the model using
a BCS-like gap which closes at T_c. From the analysis of the data we conclude
that a significant intra-gap density of localized states exists in these
materials, which can be clearly distinguished from quasiparticle states by the
time-resolved optical experiments because of the different time- and
temperature-dependences of the photoinduced transmission or reflection.
Localized charges are suggested to be the most likely origin of the intra-gap
states, while the similarity of the response in the two materials appear to
exclude spin and vortex excitations.",9910003v1
2002-08-23,Periodic Density of States Modulations in Superconducting $\rm Bi_2Sr_2CaCu_2O_{8+δ}$,"In this paper we show, using scanning tunneling spectroscopy (STS), the
existence of static striped density of electronic states in nearly optimally
doped $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ in zero field. The observed modulation
is strongest at roughly half the superconducting gap energy and is aligned with
the Cu-O bonds, with a periodicity of four lattice constants, exhibiting
features characteristic of a two-dimensional system of line objects. These
features also exhibit asymmetries between the two orthogonal directions
locally, pointing to a possible broken symmetry state (i. e., stripe phase). We
further show that the density of states modulation manifests itself as a shift
of states from above to below the superconducting gap. The fact that a single
energy scale (i. e., the gap) appears for both superconductivity and stripes
suggests that these two effects have the same microscopic origin.",0208442v1
2007-09-08,High-field vortices in Josephson junctions with alternating critical current density,"We study long Josephson junctions with the critical current density
alternating along the junction. New equilibrium states, which we call the field
synchronized or FS states, are shown to exist if the applied field is from
narrow intervals centered around equidistant series of resonant fields, $H_m$.
The values of $H_m$ are much higher than the flux penetration field, $H_s$. The
flux per period of the alternating critical current density, $\phi_i$, is fixed
for each of the FS states. In the $m$-th FS state the value of $\phi_i$ is
equal to an integer amount of flux quanta, $\phi_i =m\phi_0$. Two types of
single Josephson vortices carrying fluxes $\phi_0$ or/and $\phi_0/2$ can exist
in the FS states. Specific stepwise resonances in the current-voltage
characteristics are caused by periodic motion of these vortices between the
edges of the junction.",0709.1217v1
2019-05-08,Scaling behaviour of the ground-state antihydrogen yield from CTMC simulation as a function of positron density and temperature,"Antihydrogen production has reached such a level that precision spectroscopic
measurements of its properties are within reach. In particular, the
ground-state level population is of central interest for experiments aiming at
antihydrogen spectroscopy. The positron density and temperature dependence of
the ground-state yield is a result of the interplay between recombination,
collisional, and radiative processes. Considering the fact that antihydrogen
atoms with the principal quantum number n=15 or lower quickly cascade down to
the ground state within 1ms, the number of such states are adopted as a measure
of useful antihydrogen atoms. It has been found that the scaling behaviour of
the useful antihydrogen yield is different depending on the positron density
and positron temperature.",1905.03242v1
2012-01-03,Photonic-Crystal Waveguides with Disorder: Measurement of a Band-Edge Tail in the Density of States,"We measure localized and extended mode profiles at the band edge of
slow-light photonic-crystal waveguides using phase-sensitive near-field
microscopy. High-resolution band structures are obtained and interpreted,
allowing the retrieval of the optical density of states (DOS). This constitutes
a first observation of the DOS of a periodic system with weak disorder. The Van
Hove singularity in the DOS expected at the band edge of an ideal 1D periodic
structure is removed by the disorder. The Anderson-localized states form a
""tail"" in the density of states, as predicted by Lifshitz for solid-state
systems.",1201.0624v1
2012-04-02,Emergent states in dense systems of active rods: from swarming to turbulence,"Dense suspensions of self-propelled rod-like particles exhibit a fascinating
variety of non-equilibrium phenomena. By means of computer simulations of a
minimal model for rigid self-propelled colloidal rods with variable shape we
explore the generic diagram of emerging states over a large range of rod
densities and aspect ratios. The dynamics is studied using a simple numerical
scheme for the overdamped noiseless frictional dynamics of a many-body system
in which steric forces are dominant over hydrodynamic ones. The different
emergent states are identified by various characteristic correlation functions
and suitable order parameter fields. At low density and aspect ratio, a
disordered phase with no coherent motion precedes a highly-cooperative swarming
state at large aspect ratio. Conversely, at high densities weakly anisometric
particles show a distinct jamming transition whereas slender particles form
dynamic laning patterns. In between there is a large window corresponding to
strongly vortical, turbulent flow. The different dynamical states should be
verifiable in systems of swimming bacteria and artificial rod-like
micro-swimmers.",1204.0381v1
2016-08-22,Geometric criterion for separability based on local measurement,"A geometric understanding of entanglement is proposed based on local
measurements. Taking recourse to the general structure of density matrices in
the framework of Euclidean geometry, we first illustrate our approach for
bipartite Werner states. It is demonstrated that separable states satisfy
certain geometric constraints that entangled states do not. A separability
criterion for multiparty Werner states of arbitrary dimension is derived. This
approach can be used to determine separability across any bipartition of a
general density matrix and leads naturally to a computable measure of
entanglement for multiparty pure states. It is known that all density matrices
within a certain distance of the normalized identity are separable. This
distance is determined for a general setting of $n$ qudits, each of dimension
$d$.",1608.06145v3
2022-04-20,Optical conductivity and orbital magnetization of Floquet vortex states,"Motivated by recent experimental demonstrations of Floquet topological
insulators, there have been several theoretical proposals for using structured
light, either spatial or spectral, to create other properties such as flat band
and vortex states. In particular, the generation of vortex states in a massive
Dirac fermion insulator irradiated by light carrying nonzero orbital angular
momentum (OAM) has been proposed [Kim et al. Phys. Rev. B 105, L081301(2022)].
Here, we evaluate the orbital magnetization and optical conductivity as
physical observables for such a system. We show that the OAM of light induces
nonzero orbital magnetization and current density. The orbital magnetization
density increases linearly as a function of OAM degree. In certain regimes, we
find that orbital magnetization density is independent of the system size,
width, and Rabi frequency of light. It is shown that the orbital magnetization
arising from our Floquet theory is large and can be probed by magnetometry
measurements. Furthermore, we study the optical conductivity for various types
of electron transitions between different states such as vortex, edge, and bulk
that are present in the system. Based on conductance frequency peaks, a scheme
for the detection of vortex states is proposed.",2204.09488v2
2022-08-23,Topological states in chiral electronic chains,"We consider the influence of topological phases, or their vicinity, on the
spin density and spin polarization through a chiral chain. We show the
quantization of the Berry phase in a one-dimensional polarization helix
structure, under the presence of an external magnetic field, and show its
influence on the spin density. The polar angle of the momentum space spin
density becomes quantized in the regime that the Berry phase is quantized, as a
result of the combined effect of the induced spin-orbit coupling and the
external transverse magnetic field, while the edge states do not show the polar
angle quantization, in contrast with the bulk states. Under appropriate
conditions, the model can be generalized to have similarities with a chain with
nonhomogeneous Rashba spin- orbit couplings, with zero- or low-energy edge
states. Due to the breaking of time-reversal symmetry, we recover the effect of
chiral-induced spin polarization and spin transport across the chiral chain,
when coupling to external leads. Some consequences of the quantized spin
polarization and low-energy states on the spin transport are discussed.",2208.10807v1
2023-05-23,Liouville Space Neural Network Representation of Density Matrices,"Neural network quantum states as ansatz wavefunctions have shown a lot of
promise for finding the ground state of spin models. Recently, work has been
focused on extending this idea to mixed states for simulating the dynamics of
open systems. Most approaches so far have used a purification ansatz where a
copy of the system Hilbert space is added which when traced out gives the
correct density matrix. Here, we instead present an extension of the Restricted
Boltzmann Machine which directly represents the density matrix in Liouville
space. This allows the compact representation of states which appear in
mean-field theory. We benchmark our approach on two different version of the
dissipative transverse field Ising model which show our ansatz is able to
compete with other state-of-the-art approaches.",2305.13992v1
1993-06-08,Slater Decomposition of Laughlin States,"The second-quantized form of the Laughlin states for the fractional quantum
Hall effect is discussed by decomposing the Laughlin wavefunctions into the
$N$-particle Slater basis. A general formula is given for the expansion
coefficients in terms of the characters of the symmetric group, and the
expansion coefficients are shown to possess numerous interesting symmetries.
For expectation values of the density operator it is possible to identify
individual dominant Slater states of the correct uniform bulk density and
filling fraction in the physically relevant $N\to\infty$ limit.",9306022v1
1997-07-24,Pade approximants for the ground-state energy of closed-shell quantum dots,"Analytic approximations to the ground-state energy of closed-shell quantum
dots (number of electrons from 2 to 210) are presented in the form of two-point
Pade approximants. These Pade approximants are constructed from the small- and
large-density limits of the energy. We estimated that the maximum error,
reached for intermediate densities, is less than 3%. Within the present
approximation the ground-state is found to be unpolarized.",9707258v1
1998-05-22,Quantum shot-noise at local tunneling contacts on mesoscopic multiprobe conductors,"New experiments that measure the low-frequency shot-noise spectrum at local
tunneling contacts on mesoscopic structures are proposed. The current
fluctuation spectrum at a single tunneling tip is determined by local partial
densities of states. The current-correlation spectrum between two tunneling
tips is sensitive to non-diagonal density of states elements which are
expressed in terms of products of scattering states of the conductor. Thus such
an experiment permits to investigate correlations of electronic wave functions.
We present specific results for a clean wire with a single barrier and for
metallic diffusive conductors.",9805295v1
1998-06-22,Ground-state energy of confined charged bosons in two dimensions,"The Pade approximant technique and the variational Monte Carlo method are
applied to determine the ground-state energy of a finite number of charged
bosons in two dimensions confined by a parabolic trap. The particles interact
repulsively through a Coulombic, 1/r, potential. Analytic expressions for the
ground-state energy are obtained. The convergence of the Pade sequence and
comparison with the Monte Carlo results show that the error of the Pade
estimate is less than 4% at any boson density and is exact in the extreme
situations of very dilute and high density.",9806256v1
1998-11-23,Exact Density of States in a System of Disordered Two Dimensional Dirac Fermions in the Unitarity Limit: The d-wave Superconductor,"In this paper we present a method to compute the exact density of states
induced by $N$ non magnetic impurities in a system of two dimensional Dirac
fermions in the unitarity limit. We review the case of the $\pi$-flux phase of
the Heisenberg model and also treat the disordered d-wave superconductor. In
both case we find additional states in the gap with $\delta \rho (\omega)
\simeq n_i/ |\omega(\ln^2 |\omega/\Delta_0| + (\pi/2)^2)|$.",9811328v2
1999-11-07,Nonlinear conduction of sliding electronic crystals: Charge and Spin Density Waves,"A model of local metastable states due to the pinning induces plastic
deformations allows to describe the nonlinear I-V curves in sliding density
waves -DW. With increasing the DW velocity v, the metastable states of
decreasing lifetimes ~1/v are accessed. The characteristic second threshold
field is reached when configurations of shortest life time are accessed by the
fast moving DW. Thus the DW works as a kind of a ``linear accelerator'' testing
virtual states.",9911100v1
2000-10-02,Quantal Andreev billiards: Density of states oscillations and the spectrum-geometry relationship,"Andreev billiards are finite, arbitrarily-shaped, normal-state regions,
surrounded by superconductor. At energies below the superconducting energy gap,
single-quasiparticle excitations are confined to the normal region and its
vicinity, the mechanism for confinement being Andreev reflection. Short-wave
quantal properties of these excitations, such as the connection between the
density of states and the geometrical shape of the billiard, are addressed via
a multiple scattering approach. It is shown that one can, inter alia, hear the
stationary chords of Andreev billiards.",0010016v2
2001-10-01,Metastable states in the Blume-Emery-Griffiths spin glass model,"We study the Blume-Emery-Griffiths spin glass model in presence of an
attractive coupling between real replicas, and evaluate the effective potential
as a function of the density overlap. We find that there is a region, above the
first order transition of the model, where metastable states with a large
density overlap exist. The line where these metastable states appear should
correspond to a purely dynamical transition, with a breaking of ergodicity.
Differently from what happens in p-spin glasses, in this model the dynamical
transition would not be the precursor of a 1-step RSB transition, but
(probably) of a full RSB transition.",0110029v1
2003-09-22,Exchange and correlation as a functional of the local density of states,"A functional $E_{xc}[\rho(\r,\epsilon)]$ is presented, in which the exchange
and correlation energy of an electron gas depends on the local density of
occupied states. A simple local parametrization scheme is proposed, entirely
from first principles, based on the decomposition of the exchange-correlation
hole in scattering states of different relative energies. In its practical
Kohn-Sham-like form, the single-electron orbitals become the independent
variables, and an explicit formula for the functional derivative is obtained.",0309507v2
2005-06-27,Unrestricted renormalized mean field theory of strongly correlated electron systems,"We generalized systematically the renormalized mean field theory in the case
of uniform states to the unrestricted case of general inhomogeneous states with
competing spin-, charge- and superconducting orders. Applying the theory to
high-$T_c$ superconductors, we discuss the issues of electronic inhomogeneity,
the superfluid density, and in particular the local electron density of states.
The results account for many intriguing aspects of the phenomenology.",0506712v2
2006-04-29,Impact of the transport supercurrent on the density of states in the weak link,"The impact of the transport supercurrent on the density of states in the
superconducting thin film with the weak link is investigated. At the weak link
the order parameter is locally suppressed due to the order parameter phase
difference. This results in the appearance of the zero-energy states, which are
strongly influenced by the supercurrent especially at the phase difference
close to Pi. The observability of these effects with the scanning tunneling
spectroscopy is discussed.",0605016v2
1994-10-18,Landau Hamiltonians with Random Potentials: Localization and the Density of States,"We prove the existence of localized states at the edges of the bands for the
two-dimensional Landau Hamiltonian with a random potential, of arbitrary
disorder, provided that the magnetic field is sufficiently large. The
corresponding eigenfunctions decay exponentially with the magnetic field and
distance. We also prove that the integrated density of states is Lipschitz
continuous away from the Landau energies. The proof relies on a Wegner estimate
for the finite-area magnetic Hamiltonians with random potentials and
exponential decay estimates for the finite-area Green's functions. The proof of
the decay estimates for the Green's functions uses fundamental results from
two-dimensional bond percolation theory.",9410005v1
1994-07-03,The Partonic Content of $h_1(x)$ and $h_2(x),"A light-cone wavefunction interpretation is presented for the polarized
distribution functions $h_1(x)$ and $h_2(x)$. All matrix elements for moments
of these distributions are given in terms of overlap integrals between Fock
state amplitudes of the target state. In a suitable spinor basis, $h_1(x)$
involves only diagonal matrix elements so can be interpreted as a density.
Matrix elements of $h_2(x)$ connect Fock states differing by one gluon so that
$h_2(x)$ has no simple interpretation as a density. Nevertheless, in the
wavefunction decomposition, $h_2(x)$ is described through a compact set of
elementary quark-gluon processes which are averaged over the target
wavefunction.",9407213v1
2004-09-30,Equilibrium states and their entropy densities in gauge-invariant C*-systems,"A gauge-invariant C*-system is obtained as the fixed point subalgebra of the
infinite tensor product of full matrix algebras under the tensor product
unitary action of a compact group. In the paper, thermodynamics is studied on
such systems and the chemical potential theory developed by Araki, Haag,
Kastler and Takesaki is used. As a generalization of quantum spin system, the
equivalence of the KMS condition, the Gibbs condition and the variational
principle is shown for translation-invariant states. The entropy density of
extremal equilibrium states is also investigated in relation to macroscopic
uniformity.",0409601v2
1999-07-22,Hartree--Fock--Bogoliubov Approximation for Finite Systems,"Some general features of the spectrum of the Hartree-Fock-Bogoliubov
equations are examined. Special attention is paid to the asymptotic behavior of
the single quasiparticle wave functions (s.qp.w.fs.), matter density
distribution and density of the pair condensate. It is shown that due to the
coupling between hole and particle states,the deeply bound hole states acquire
a width and have to be treated as continuum states. The proper normalization of
the s.qp.w.fs. is discussed.",9907088v2
2000-12-25,Multi-gap superfluidity in nuclear matter,"It is shown that under lowering density or temperature a nucleon Fermi
superfluid can undergo a phase transition to a new superfluid state
corresponding to superposition of states with singlet-triplet (ST) and
triplet-singlet (TS) pairing of nucleons (in spin and isospin spaces). Such
states arise as a result of branching from one-gap solution of the
self-consistent equations, describing ST pairing of nucleons. The density and
temperature dependence of the order parameters for new two-gap solutions is
determined in the model with Skyrme effective forces.",0012089v1
2007-10-25,Electronic structure of the c(4 x 2) reconstructed Ge(001) surface,"We investigate the electronic structure of the c(4 x 2) reconstructed Ge(001)
surface using band structure calculations based on density functional theory
and the generalized gradient approximation. In particular, we take into account
the details of surface reconstruction by means of well relaxed crystal
structures. The surface electronic states are identified and the local density
of states is compared to recent data from scanning tunneling spectroscopy. We
obtain almost perfect agreement between theory and experiment for both the
occupied and unoccupied states, which allows us to clarify the interpretation
of the experimental data.",0710.4841v1
2007-11-06,Universal Behavior in Heavy Electron Materials,"We present our finding that an especially simple scaling expression describes
the formation of a new state of quantum matter, the Kondo Fermi liquid (KL) in
heavy electron materials. Emerging at $T^*$ as a result of the collective
coherent hybridization of localized f electrons and conduction electrons, the
KL possesses a non-Landau density of states varying as
$(1-T/T^*)^{3/2}[1+\ln(T^*/T)]$. We show that four independent experimental
probes verify this scaling behavior and that for CeIrIn$_5$ the KL state
density is in excellent agreement with the recent microscopic calculations of
hybridization in this material by Shim, Haule, and Kotliar.",0711.0789v1
2009-01-09,Surface density of states of s+-wave Cooper pairs in a two-band model,"We calculate surface density of state (SDOS) of s+-wave Cooper pair in
two-band superconductor model, where gap functions have different signs between
two bands. We find that Andreev bound state appears at surface due to the sign
change in the gap function in the interband quasiparticle scattering. However,
we do not obtain the zero-energy peak of SDOS in contrast to the d-wave case.
The tunneling spectroscopy of s+-wave is much more complex as compared to the
d-wave case realized in high-Tc cuprates.",0901.1166v2
2009-03-23,Spin-polarized electronic structures and transport properties of Fe-Co alloys,"The electrical resistivities of Fe-Co alloys owing to random alloy disorder
are calculated using the Kubo-Greenwood formula. The obtained electrical
esistivities agree well with experimental data quantitatively at low
temperature. The spin-polarization of Fe50Co50 estimated from the conductivity
(86%) has opposite sign to that from the densities of the states at the Fermi
level (-73%). It is found that the conductivity is governed mainly by
s-electrons, and the s-electrons in the minority spin states are less
conductive due to strong scattering by the large densities of the states of
d-electrons than the majority spin electrons.",0903.3842v1
2009-06-16,Spectral density and Sobolev inequalities for pure and mixed states,"We prove some general Sobolev-type and related inequalities for positive
operators A of given ultracontractive spectral decay, without assuming e^{-tA}
is submarkovian. These inequalities hold on functions, or pure states, as
usual, but also on mixed states, or density operators in the quantum mechanical
sense. This provides universal bounds of Faber-Krahn type on domains, that
apply to their whole Dirichlet spectrum distribution, not only the first
eigenvalue. Another application is given to relate the Novikov-Shubin numbers
of coverings of finite simplicial complexes to the vanishing of the torsion of
some l^{p,2}-cohomology.",0906.2902v1
2010-03-31,Phonon Density of States and Thermodynamic Behavior in Highly Amorphous Media,"We calculate the phonon density of states (DOS) for strongly amorphous
materials with a short-ranged interatomic potential. Exponentially decaying and
abruptly truncated interatomic potentials are examined. Thermally excited mean
square deviations from equilibrium are calculated with rapid increases noted as
the average number of neighbors is reduced. The Inverse Participation Ratio
(IPR) is used to characterize the phonon states and identify localized phonon
modes as the bonding range (and hence the average number of neighbors per atom)
is diminished. For the truncated potential, the characteristics of the IPR
histogram change qualitatively below $n_{\mathrm{neigh}}$ with the appearance
of localized phonon modes below $n_{\mathrm{neigh}} = 6.0$.",1003.6131v1
2012-03-08,Origin of Magnetic Circular Dichroism in GaMnAs: Giant Zeeman Splitting versus Spin Dependent Density of States,"We present a unified interpretation of experimentally observed magnetic
circular dichroism (MCD) in the ferromagnetic semiconductor (Ga,Mn)As, based on
theoretical arguments, which demonstrates that MCD in this material arises
primarily from a difference in the density of spin-up and spin-down states in
the valence band brought about by the presence of the Mn impurity band, rather
than being primarily due to the Zeeman splitting of electronic states.",1203.1853v1
2012-06-11,Chemical Bonds and Spin State Splittings in Spin Crossover Complexes. A DFT and QTAIM Analysis,"Density functional theory (DFT) calculations have been performed for the
high-spin (HS) and low-spin (LS) isomers of a series of iron(II) spin crossover
complexes with nitrogen ligands. The calculated charge densities have been
analyzed in the framework of the quantum theory of atoms in molecules (QTAIM).
For a number of iron(II) complexes with substituted tris(pyrazolyl) ligands the
energy difference between HS and LS isomers, the spin state splitting, has been
decomposed into atomic contributions in order to rationalize changes of the
spin state splitting due to substituent effects.",1206.2136v1
2013-02-20,Proton scattering on an electron gas,"It is shown in the case of proton scattering on an electron gas target that
the Closed Time Path formalism can handle final state interactions of the
target in equilibrium in a simple and natural manner. The leading order cross
section is proportional to the photon density of states. The scattering needs a
partial resummation of the perturbation series when the electron gas forms long
living quasi-particles with high density of state during the collision. A
strong cancellation between real and virtual electron-hole pairs is found in
this case.",1302.5126v2
2013-04-01,Decay behavior of localized states at reconstructed armchair graphene edges,"Density functional theory calculations are used to investigate the electronic
structures of localized states at reconstructed armchair graphene edges. We
consider graphene nanoribbons with two different edge types and obtain the
energy band structures and charge densities of the edge states. By examining
the imaginary part of the wavevector in the forbidden energy region, we reveal
the decay behavior of the wavefunctions in graphene. The complex band
structures of graphene in the armchair and zigzag directions are presented in
both tight-binding and first-principles frameworks.",1304.0314v2
2014-02-14,Structural and vibrational properties of nitrogen-rich energetic material guanidinium 2-methyl-5-nitraminotetrazolate,"We present density functional theory calculations on the crystal structure,
equation of state, vibrational properties and electronic structure of
nitrogen-rich solid energetic material guanidinium
2-methyl-5-nitraminotetrazolate (G-MNAT). The ground state structural
properties calculated with dispersion corrected density functionals are in good
agreement with experiment. The computed equilibrium crystal structure is
further used to calculate the equation of state and zone-center vibrational
frequencies of the material. The electronic band structure is calculated and
found that the material is an indirect band gap semiconductor with a value of
3.04 eV.",1402.3432v1
2014-02-27,Joint Hitting-Time Densities for Finite State Markov Processes,"For a finite state Markov process and a finite collection $\{ \Gamma_k, k \in
K \}$ of subsets of its state space, let $\tau_k$ be the first time the process
visits the set $\Gamma_k$. We derive explicit/recursive formulas for the joint
density and tail probabilities of the stopping times $\{ \tau_k, k \in K\}$.
The formulas are natural generalizations of those associated with the jump
times of a simple Poisson process. We give a numerical example and indicate the
relevance of our results to credit risk modeling.",1402.7093v1
2014-12-12,Non-Resonant Thermal Admittance Spectroscopy,"Thermal Admittance Spectroscopy (TAS) as become a popular technique to
determine trap state density and energetic position in semiconductors. In the
limit of a large number of trap states ($>10^{16} \text{cm}^{-3}$), Fermi-level
pinning undermines the assumptions used in the analysis of TAS data, which
leads to a significant underestimation of the trap state density. Here, we
develop the tools to detect and account for the occurrence of Fermi-level
pinning in TAS measurements.",1412.4087v1
2014-11-04,Self-graviting Gas Spheres in Equilibrium State,"In the paper we discuss equilibrium states of stars, using a simplified
analytic model. A star is considered as self-graviting body of gas. We use a
condition for the equilibrium state of the body in the form of a differential
equation, which relates the pressure distribution and mass density in the body.
The density distributions of constant, potential, gaussian, and exponential
forms are discussed. Exact expressions for the distribution of mass and
pressure along the radial direction, and the central pressure were obtained.",1504.05819v1
2018-07-06,Inverse Structure Problem for Neutron-Star Binaries,"Gravitational wave detectors in the LIGO/Virgo frequency band are able to
measure the individual masses and the composite tidal deformabilities of
neutron-star binary systems. This paper demonstrates that high accuracy
measurements of these quantities from an ensemble of binary systems can in
principle be used to determine the high density neutron-star equation of state
exactly. This analysis assumes that all neutron stars have the same
thermodynamically stable equation of state, but does not use simplifying
approximations for the composite tidal deformability or make additional
assumptions about the high density equation of state.",1807.02538v2
2017-11-20,Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group,"We present a state interaction spin-orbit coupling method to calculate
electron paramagnetic resonance (EPR) $g$-tensors from density matrix
renormalization group wavefunctions. We apply the technique to compute
$g$-tensors for the \ce{TiF3} and \ce{CuCl4^2-} complexes, a [2Fe-2S] model of
the active center of ferredoxins, and a \ce{Mn4CaO5} model of the S2 state of
the oxygen evolving complex. These calculations raise the prospects of
determining $g$-tensors in multireference calculations with a large number of
open shells.",1711.07195v3
2019-01-31,Impurity states and Localization in Bilayer Graphene: the Low Impurity Concentration Regime,"We study the problem of non-magnetic impurities adsorbed on bilayer graphene
in the diluted regime. We analyze the impurity spectral densities for various
concentrations and gate fields. We also analyze the effect of the adsorbate on
the local density of states (LDOS) of the different C atoms in the structure
and present some evidence of strong localization for the electronic states with
energies close to the Dirac point.",1902.00034v1
2021-05-17,Completeness of coherent state subsystems for nilpotent Lie groups,"Let $G$ be a nilpotent Lie group and let $\pi$ be a coherent state
representation of $G$. The interplay between the cyclicity of the restriction
$\pi|_{\Gamma}$ to a lattice $\Gamma \leq G$ and the completeness of subsystems
of coherent states based on a homogeneous $G$-space is considered. In
particular, it is shown that necessary density conditions for Perelomov's
completeness problem can be obtained via density conditions for the cyclicity
of $\pi|_{\Gamma}$.",2105.07699v2
2022-03-30,Experimental Activation of Strong Local Passive States with Quantum Information,"Strong local passivity is a property of multipartite quantum systems from
which it is impossible to extract energy locally. Surprisingly, if the strong
local passive state displays entanglement, it could be possible to locally
activate energy density by adding classical communication between different
partitions of the system, through so-called ""quantum energy teleportation""
protocols. Here, we report both the first experimental observation of local
activation of energy density on an entangled state and the first realization of
a quantum energy teleportation protocol using nuclear magnetic resonance on a
bipartite quantum system.",2203.16269v2
2016-03-11,Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches,"We study properties of the single-site reduced density matrix in the
Bose-Bose resonance model as a function of system parameters. This model
describes a single-component Bose gas with a resonant coupling to a diatomic
molecular state, here defined on a lattice. A main goal is to demonstrate that
the eigenstates of the single-site reduced density matrix have structures that
are characteristic for the various quantum phases of this system. Since the
Hamiltonian conserves only the global particle number but not the number of
bosons and molecules individually, these eigenstates, referred to as optimal
modes, can be nontrivial linear combinations of bare eigenstates of the
molecular and boson particle number. We numerically analyze the optimal modes
and their weights, the latter giving the importance of the corresponding state,
in the ground state of the Bose-Bose resonance model. We find that the
single-site von Neumann entropy is sensitive to the location of the phase
boundaries. We explain the structure of the optimal modes and their weight
spectra using perturbation theory and via a comparison to results for the
single-component Bose-Hubbard model. We further study the dynamical evolution
of the optimal modes and of the single-site entanglement entropy in two quantum
quenches that cross phase boundaries of the model and show that these
quantities are thermal in the steady state. For our numerical calculations, we
use the density matrix renormalization group method for ground-state
calculations and time evolution in a Krylov subspace for the quench dynamics as
well as exact diagonalization.",1603.03592v1
1998-12-16,Cosmological Tracking Solutions,"A substantial fraction of the energy density of the universe may consist of
quintessence in the form of a slowly-rolling scalar field. Since the energy
density of the scalar field generally decreases more slowly than the matter
energy density, it appears that the ratio of the two densities must be set to a
special, infinitesimal value in the early universe in order to have the two
densities nearly coincide today.
  Recently, we introduced the notion of tracker fields to avoid this initial
conditions problem. In the paper, we address the following questions: What is
the general condition to have tracker fields? What is the relation between the
matter energy density and the equation-of-state of the universe imposed by
tracker solutions? And, can tracker solutions explain why quintessence is
becoming important today rather than during the early universe?",9812313v1
2007-08-28,Exact density matrix of the Gutzwiller wave function: II. Minority spin component,"The density matrix, i.e. the Fourier transform of the momentum distribution,
is obtained analytically for all magnetization of the Gutzwiller wave function
in one dimension with exclusion of double occupancy per site. The present
result complements the previous analytic derivation of the density matrix for
the majority spin. The derivation makes use of a determinantal form of the
squared wave function, and multiple integrals over particle coordinates are
performed with the help of a diagrammatic representation. In the thermodynamic
limit, the density matrix at distance x is completely characterized by
quantities v_c x and v_s x, where v_s and v_c are spin and charge velocities in
the supersymmetric t-J model for which the Gutzwiller wave function gives the
exact ground state. The present result then gives the exact density matrix of
the t-J model for all densities and all magnetization at zero temperature.
Discontinuity, slope, and curvature singularities in the momentum distribution
are identified. The momentum distribution obtained by numerical Fourier
transform is in excellent agreement with existing result.",0708.3773v1
2013-07-09,Nuclear matter EOS with light clusters within the mean-field approximation,"The crust of a neutron star is essentially determined by the low-density
region ($\rho<\rho_0\approx0.15-0.16\unit{fm}^{-3}$) of the equation of state.
At the bottom of the inner crust, where the density is $\rho\lesssim0.1\rho_0$,
the formation of light clusters in nuclear matter will be energetically
favorable at finite temperature. At very low densities and moderate
temperatures, the few body correlations are expected to become important and
light nuclei like deuterons, tritons, helions and $\alpha$-particles will form.
Due to Pauli blocking, these clusters will dissolve at higher densities
$\rho\gtrsim 0.1\rho_0$.
  The presence of these clusters influences the cooling process and quantities,
such as the neutrino emissivity and gravitational waves emission. The
dissolution density of these light clusters, treated as point-like particles,
will be studied within the Relativistic Mean Field approximation. In
particular, the dependence of the dissolution density on the clusters-meson
couplings is studied.",1307.2534v1
2015-03-13,Rabi-coupled Countersuperflow in Binary Bose-Einstein Condensates,"We show theoretically that periodic density patterns are stabilized in two
counter-propagating Bose-Einstein condensates of atoms in different hyperfine
states under Rabi coupling. In the presence of coupling, the relative velocity
between two components is localized around density depressions in
quasi-one-dimensional systems. When the relative velocity is sufficiently
small, the periodic pattern reduces to a periodic array of topological solitons
as kinks of relative phase. According to our variational and numerical
analyses, the soliton solution is well characterized by the soliton width and
density depression. We demonstrate the dependence of the depression and width
on the Rabi frequency and the coupling constant of inter-component
density-density interactions. The periodic pattern of the relative phase
transforms continuously from a soliton array to a sinusoidal pattern as the
period becomes smaller than the soliton width. These patterns become unstable
when the localized relative velocity exceeds a critical value. The
stability-phase diagram of this system is evaluated with a stability analysis
of countersuperflow, by taking into account the finite-size-effect owing to the
density depression.",1503.04010v1
2019-12-15,N-centered ensemble density-functional theory for open systems,"Two (so-called left and right) variants of N-centered ensemble
density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513
(2018)] are presented. Unlike the original formulation of the theory, these
variants allow for the description of systems with a fractional electron
number. While conventional DFT for open systems uses only the true electron
density as basic variable, left/right N-centered ensemble DFT relies instead on
(i) a fictitious ensemble density that integrates to a central (integral)
number N of electrons, and (ii) a grand canonical ensemble weight $\alpha$
which is equal to the deviation of the true electron number from N. Within such
a formalism, the infamous derivative discontinuity that appears when crossing
an integral number of electrons is described exactly through the dependence in
$\alpha$ of the left and right N-centered ensemble Hartree-exchange-correlation
density functionals. Incorporating N-centered ensembles into existing
density-functional embedding theories is expected to pave the way towards the
in-principle-exact description of an open fragment by means of a pure-state
N-electron many-body wavefunction. Work is currently in progress in this
direction",1912.07125v3
2021-06-24,A Many-Body Density Energy Functional,"The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the
basis of the Density Functional Theory, are reformulated in terms of a
particular many-body density, which is translational invariant and therefore is
relevant for self-bound systems. In a similar way that there is a unique
relation between the one-body density and the external potential that gives
rise to it, we demonstrate that there is a unique relation between that
particular many-body density and a definite many-body potential. The energy is
then a functional of this density and its minimization leads to the
ground-state energy of the system. As a proof of principle, the analogous of
the Kohn-Sham equation is solved in the specific case of $^4$He atomic
clusters, to put in evidence the advantages of this new formulation in terms of
physical insights.",2106.13582v1
2022-03-23,A density description of a bounded-confidence model of opinion dynamics on hypergraphs,"Social interactions often occur between three or more agents simultaneously.
Examining opinion dynamics on hypergraphs allows one to study the effect of
such polyadic interactions on the opinions of agents. In this paper, we
consider a bounded-confidence model (BCM), in which opinions take continuous
values and interacting agents comprise their opinions if they are close enough
to each other. We study a density description of a Deffuant--Weisbuch BCM on
hypergraphs. We derive a rate equation for the mean-field opinion density as
the number of agents becomes infinite, and we prove that this rate equation
yields a probability density that converges to noninteracting opinion clusters.
Using numerical simulations, we examine bifurcations of the density-based BCM's
steady-state opinion clusters and demonstrate that the agent-based BCM
converges to the density description of the BCM as the number of agents becomes
infinite.",2203.12189v2
2024-02-15,Variational Density Functional Perturbation Theory for Metals,"Density functional perturbation theory is a well-established method to study
responses of molecules and solids, especially responses to atomic displacements
or to different perturbing fields (electric, magnetic). Like for density
functional theory, the treatment of metals is delicate, due to the Fermi-Dirac
statistics and electronic bands crossing the Fermi energy. At zero temperature,
there is an abrupt transition from occupied states to unoccupied ones, usually
addressed with smearing schemes. Also, at finite temperature, fractional
occupations are present, and the occupation numbers may vary in response to the
perturbation. The present work establishes the characteristics of density
functional perturbation theory stemming from the underlying variational
principle, in the case of metals. After briefly reviewing variational density
functional theory for metals, the convexity of the entropy function of the
occupation number is analyzed, and, at finite temperature, the benefit of
resmearing the Fermi-Dirac broadening with the Methfessel-Paxton one is
highlighted. Then the variational expressions for the second-order derivative
of the free energy are detailed, exposing the different possible gauge choices.
The influence of the inaccuracies in the unperturbed wavefunctions from the
prior density functional theory calculation is studied. The whole formalism is
implemented in the ABINIT software package.",2402.09806v1
2005-07-07,A cosmic equation of state for the inhomogeneous Universe: can a global far-from-equilibrium state explain Dark Energy?,"A system of effective Einstein equations for spatially averaged scalar
variables of inhomogeneous cosmological models can be solved by providing a
`cosmic equation of state'. Recent efforts to explain Dark Energy focus on
`backreaction effects' of inhomogeneities on the effective evolution of
cosmological parameters in our Hubble volume, avoiding a cosmological constant
in the equation of state. In this Letter it is argued that, if kinematical
backreaction effects are indeed of the order of the averaged density (or larger
as needed for an accelerating domain of the Universe), then the state of our
regional Hubble volume would have to be in the vicinity of a
far-from-equilibrium state that balances kinematical backreaction and average
density. This property, if interpreted globally, is shared by a stationary
cosmos with effective equation of state $p_{\rm eff} = -1/3 \rho_{\rm eff}$. It
is concluded that a confirmed explanation of Dark Energy by kinematical
backreaction may imply a paradigmatic change of cosmology.",0507028v2
2015-05-05,Helical bound states in the continuum of the edge states in two dimensional topological insulators,"We study bound states embedded into the continuum of edge states in
two-dimensional topological insulators. These states emerge in the presence of
a short-range potential of a structural defect coupled to the boundary. In this
case the edge states flow around the defect and have two resonances in the
local density of states. The bound state in continuum (BIC) arises due to an
interference of the resonances when they are close to the degeneracy. We find
the condition under which the BIC appears, study the spacial distribution of
the electron density, and show that the BIC has a helical structure with an
electron current circulating around the defect.",1505.01119v2
2016-03-28,Orbital-FFLO state in a chain of high spin ultracold atoms,"Recent experiments with Yb-173 and Sr-87 isotopes provide new possibilities
to study high spin two-orbital systems. Within these experiments part of the
atoms are excited to a higher energy metastable electronic state mimicking an
additional internal (orbital) degree of freedom. The interaction between the
atoms depends on the orbital states, therefore four different scattering
channels can be identified in the system characterized by four independent
couplings. When the system is confined into a one-dimensional chain the
scattering lengths can be tuned by changing the transverse confinement, and
driven through four resonances. Using the new available experimental data of
the scattering lengths we analyze the phase diagram of the one-dimensional
system as the couplings are tuned via transverse confinement, and the
populations of the two orbital states are changed. We found that three orders
compete showing power law decay: a state with dominant density wave
fluctuations, another one with spin density fluctuations, and a third one
characterized by exotic Fulde-Ferrell-Larkin-Ovchinnikov-like pairs consisting
one atom in the electronic ground state and one in the excited state. We also
show that sufficiently close to the resonances the compressibility of the
system starts to diverge indicating that the emerging order is unstable and
collapses to a phase separated state with a first order phase transition.",1603.08505v1
2016-09-09,Signature of magnetic-dependent gapless odd frequency states at superconductor/ferromagnet interfaces,"The theory of superconductivity developed by Bardeen, Cooper and Schrieffer
(BCS) explains the stabilization of electron pairs into a spin-singlet, even
frequency, state by the formation of an energy gap within which the density of
states is zero. At a superconductor interface with an inhomogeneous
ferromagnet, a gapless odd frequency superconducting state is predicted, in
which the Cooper pairs are in a spin-triplet state. Although indirect evidence
for such a state has been obtained, the gap structure and pairing symmetry have
not so far been determined. Here we report scanning tunnelling spectroscopy of
Nb superconducting films proximity coupled to epitaxial Ho. These measurements
reveal pronounced changes to the Nb subgap superconducting density of states on
driving the Ho through a metamagnetic transition from a helical
antiferromagnetic to a homogeneous ferromagnetic state for which a BCS-like gap
is recovered. The results prove odd frequency spin-triplet superconductivity at
superconductor/inhomogeneous magnet interfaces.",1609.02905v1
2016-05-14,First-principle study on compensated half metallic double perovskite compound $Ba_2PrVO_6$,"The first-principle study on double perovskite compound Ba$_2$PrVO$_6$ has
been presented in this paper. By analysing band structures and integrated
density of states, it is found that Ba$_2$PrVO$_6$ is ferromagnetic metallic
within LSDA and compensated half metallic whithin LSDA+U. According to the
total and partial density of states, the anti-ferromagnetism of Ba$_2$PrVO$_6$
is originated from the spin down state Pr$^{4+}$ ($4f_{-2}$) and the spin up
hybridized state between the partially filled $t_{2g}$ state of V and the
partially filled triple-degeneration state $4f_{-1}$, $4f_{+1}$, $4f_{+3}$ of
Pr. We have investigated the magnetic evaluation of Ba$_2$PrVO$_6$ through
fixed spin moment calculations, and the results indicate that the compensated
half-metallic state is the ground state. The thermodynamic properties of
Ba$_2$PrVO$_6$ are also studied by employing the quasi-harmonic Debye model.",1605.04383v1
2023-11-07,Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces,"Bogoliubov Fermi surfaces of superconducting states arise from point or line
nodes by breaking time-reversal symmetry. Because line and point nodes often
accompany topologically protected zero-energy surface Andreev bound states
(ASBSs) and thereby lead to a characteristic zero-bias conductance peak (ZBCP)
in tunneling spectroscopy, we investigate how these properties change when the
line and point nodes deform into BFSs. In this paper, we consider spin-quintet
$J_{\rm pair}=2$ pairing states of spin-3/2 electrons with BFSs and calculate
the surface density of states and the charge conductance. Comparing the
obtained results with the cases of spin-singlet $d$-wave pairing states having
the same symmetry, we find that the ZBCP associated with point and/or line
nodes is blunted or split in accordance with the appearance of the BFSs. On the
other hand, when the spin-singlet $d$-wave state has point nodes but does not
have SABS on the surface, we obtain a nonzero small electron conductivity at
zero bias through the zero-energy states on the BFSs.",2311.03717v1
2002-10-01,"Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity","An analysis of insular solutions of Einstein's field equations for static,
spherically symmetric, source mass, on the basis of exterior Schwarzschild
solution is presented. Following the analysis, we demonstrate that the {\em
regular} solutions governed by a self-bound (that is, the surface density does
not vanish together with pressure) equation of state (EOS) or density variation
can not exist in the state of hydrostatic equilibrium, because the source mass
which belongs to them, does not represent the `actual mass' appears in the
exterior Schwarzschild solution. The only configuration which could exist in
this regard is governed by the homogeneous density distribution (that is, the
interior Schwarzschild solution). Other structures which naturally fulfill the
requirement of the source mass, set up by exterior Schwarzschild solution (and,
therefore, can exist in hydrostatic equilibrium) are either governed by
gravitationally-bound regular solutions (that is, the surface density also
vanishes together with pressure), or self-bound singular solutions (that is,
the pressure and density both become infinity at the centre).",0210018v3
2007-12-21,Off-diagonal Ground State Properties of a 1D Gas of Fermi Hard Rods,"A variational Monte Carlo calculation of the one-body density matrix and
momentum distribution of a system of Fermi hard rods (HR) is presented and
compared with the same quantities for its bosonic counterpart. The calculation
is exact within statistical errors since we sample the exact ground state wave
function, whose analytical expression is known. The numerical results are in
good agreement with known asymptotic expansions valid for Luttinger liquids. We
find that the difference between the absolute value of the bosonic and
fermionic density matrices becomes marginally small as the density increases.
In this same regime, the corresponding momentum distributions merge into a
common profile that is independent of the statistics. Non-analytical
contributions to the one--body density matrix are also discussed and found to
be less relevant with increasing density.",0712.3593v1
2011-08-24,The hydrogen equation of state at high densities,"We use a two-fluid model combining the quantum Green's function technique for
the electrons and a classical HNC description for the ions to calculate the
high-density equation of state of hydrogen. This approach allows us to describe
fully ionized plasmas of any electron degeneracy and any ionic coupling
strength which are important for the modeling of a variety of astrophysical
objects and inertial confinement fusion targets. We have also performed density
functional molecular dynamics simulations (DFT-MD) and show that the data
obtained agree with our approach in the high density limit. Good agreement is
also found between DFT-MD and quantum Monte Carlo simulations. The
thermodynamic properties of dense hydrogen can thus be obtained for the entire
density range using only calculations in the physical picture.",1108.4826v1
2012-06-25,Resummation in nonlinear equation for high energy factorizable gluon density and its extension to include coherence,"Motivated by forthcoming p-Pb experiments at Large Hadron Collider which
require both knowledge of gluon densities accounting for saturation and for
processes at a wide range of $p_t$ we study basic momentum space evolution
equations of high energy QCD factorization. Solutions of those equations might
be used to form a set of gluon densities to calculate observables in
generalized high energy factorization. Moreover in order to provide a framework
for predictions for exclusive final states in p-Pb scattering with high $p_t$
we rewrite the equation for the high energy factorizable gluon density in a
resummed form, similarly to what has been done in \cite{Kutak:2011fu} for the
BK equation. The resummed equation is then extended to account for colour
coherence. This introduces an external scale to the evolution of the gluon
density, and therefore makes it applicable in studies of final states.",1206.5757v2
2015-03-23,Temporal behavior of microwave sheath-voltage combination plasma,"Microwave sheath-Voltage combination Plasma (MVP) is a high density plasma
source and can be used as a suitable plasma processing device (e.g., ionized
physical vapor deposition). In the present report, the temporal behavior of an
argon MVP sustained along a direct-current biased Ti rod is investigated. Two
plasma modes are observed, one is an ""oxidized state"" (OS) at the early time of
the microwave plasma and the other is ""ionized sputter state"" (ISS) at the
later times. Transition of the plasma from OS to ISS, results a prominent
change in the visible color of the plasma, resulting from a significant
increase in the plasma density, as measured by a Langmuir probe. In the OS,
plasma is dominated by Ar ions and the density is order 10^11 cm^-3. In the
ISS, metal ions from the Ti rod contribute significantly to the ion composition
and higher density plasma (10^12 cm^-3) is produced. Nearly uniform high
density plasma along the length of the Ti rod is produced at very low input
microwave powers (around 30 W). Optical emission spectroscopy measurements
confirm the presence of sputtered Ti ions and Ti neutrals in the ISS.",1503.06530v1
2016-01-12,Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics,"In this paper we study a (1+1)-dimensional version of the famous
Nambu-Jona-Lasinio model of Quantum Chromodynamics (QCD2) both at zero and
finite hadron density. We use non-perturbative techniques (non-Abelian
bosonization and Truncated Conformal Space Approach). At zero density we
describe a formation of fermion three-quark (nucleons and $\Delta$-baryons) and
boson (two-quark mesons, six-quark deuterons) bound states and also a formation
of a topologically nontrivial phase. At finite hadron density, the model has a
rich phase diagram which includes phases with density wave and superfluid
quasi-long-range (QLR) order and also a phase of a baryon Tomonaga-Luttinger
liquid (strange metal). The QLR order results as a condensation of scalar
mesons (the density wave) or six-quark bound states (deuterons).",1601.02979v5
2002-08-13,Wigner molecules in polygonal quantum dots: A density functional study,"We investigate the properties of many-electron systems in two-dimensional
polygonal (triangle, square, pentagon, hexagon) potential wells by using the
density functional theory. The development of the ground state electronic
structure as a function of the dot size is of particular interest. First we
show that in the case of two electrons, the Wigner molecule formation agrees
with the previous exact diagonalization studies. Then we present in detail how
the spin symmetry breaks in polygonal geometries as the spin density functional
theory is applied. In several cases with more than two electrons, we find a
transition to the crystallized state, yielding coincidence with the number of
density maxima and the electron number. We show that this transition density,
which agrees reasonably well with previous estimations, is rather insensitive
to both the shape of the dot and the electron number.",0208244v1
2003-06-06,Non-linear electrical response in a charge/orbital ordered $\Pr_{0.63}$Ca$_{0.37}$MnO$_3$ crystal : the charge density wave analogy,"Non-linear conduction in a charge-ordered manganese oxide
Pr$_{0.63}$Ca$_{0.37}$MnO$_3$ is reported. To interpret such a feature, it is
usually proposed that a breakdown of the charge or orbitally ordered state is
induced by the current. The system behaves in such a way that the bias current
may generate metallic paths giving rise to resistivity drop. One can describe
this feature by considering the coexistence of localized and delocalized
electron states with independent paths of conduction. This situation is
reminiscent of what occurs in charge density wave systems where a similar
non-linear conduction is also observed. In the light of recent experimental
results suggesting the development of charge density waves in charge and
orbitally ordered manganese oxides, a phenomenological model for charge density
waves motion is used to describe the non-linear conduction in
Pr$_{0.63}$Ca$_{0.37}$MnO$_3$. In such a framework, the non-linear conduction
arises from the motion of the charge density waves condensate which carries a
net electrical current.",0306161v1
2007-03-23,Phase transitions in isolated strongly interacting systems,"Thermodynamical properties of the nuclear matter at sub-saturation densities
were investigated using a simple van der Waals-like equation of state with an
additional term representing the symmetry energy. First-order
isospin-asymmetric liquid-gas phase transition appears restricted to isolated
isospin-asymmetric systems while the symmetric systems will undergo
fragmentation decay resembling the second-order phase transition. The density
dependence of the symmetry energy scaling with the Fermi energy satisfactorily
describes the symmetry energy at sub-saturation nuclear densities. The
deconfinement-confinement phase transition from the quark-gluon plasma to the
confined quark matter appears in the isolated systems continuous in energy
density while discontinuous in quark density. A transitional state of the
confined quark matter has a negative pressure and after hadronization an
explosion scenario can take place which can offer explanation for the HBT
puzzle as a signature of the phase transition.",0703077v2
2008-03-10,Analysis of Incident-Photon-Energy and Polarization Dependent Resonant Inelastic X-Ray Scattering from La$_{2}$CuO$_{4}$,"We present a detailed analysis of the incident-photon-energy and polarization
dependences of the resonant inelastic x-ray scattering (RIXS) spectra at the Cu
$K$ edge in La$_{2}$CuO$_{4}$. Our analysis is based on the formula developed
by Nomura and Igarashi, which describes the spectra by a product of an
incident-photon-dependent factor and a density-density correlation function for
3d states. We calculate the former factor using the $4p$ density of states from
an ab initio band structure calculation and the latter using a multiorbital
tight-binding model within the Hartree-Fock approximation and the random phase
approximation. We obtain spectra with rich structures in the energy-loss range
2-5 eV, which vary with varying momentum and incident-photon energy, in
semi-quantitative agreement with recent experiments. We clarify the origin of
such changes as a combined effect of the incident-photon-dependent factor and
the density-density correlation function.",0803.1337v2
2013-04-08,Electronic phase separation in iron pnictides,"A mechanism for electronic phase separation in iron pnictides is proposed. It
is based on the competition between commensurate and incommensurate
spin-density-wave phases in a system with an imperfect doping-dependent nesting
of a multi-sheeted Fermi surface. We model the Fermi surface by two elliptical
electron pockets and three circular hole pockets. The interaction between a
charge carrier in a hole band and a carrier in an electron band leads to the
formation of spin-density-wave order. The commensurate spin density wave in the
parent compound transforms to the incommensurate phase when doping is
introduced. We show that, for certain parameter values, the uniform state is
unstable with respect to phase separation. The resulting inhomogeneous state
consists of regions of commensurate and incommensurate spin-density-wave
phases. Our results are in qualitative agreement with recent observations of
incommensurate spin density waves and electronic inhomogeneity in iron
pnictides.",1304.2175v2
2015-01-01,A hybrid-exchange density-functional theory study of the electronic structure of $\mathrm{MnV}_2\mathrm{O}_4$: Exotic orbital ordering in the cubic structure,"The electronic structures of the cubic and tetragonal
$\mathrm{MnV}_2\mathrm{O}_4$ have been studied by using hybrid-exchange density
functional theory. The computed electronic structure of the tetragonal phase
shows an anti-ferro orbital ordering on V sites and a ferrimagnetic ground
state (the spins on V and Mn are anti-aligned). These results are in a good
agreement with the previous theoretical result obtained from the local-density
approximation+$U$ methods [S. Sarkar, et. al., Phys. Rev. Lett. 102, 216405
(2009)]. Moreover, the electronic structure, especially the projected density
of states of the cubic phase has been predicted with a good agreement with the
recent soft x-ray spectroscopy experiment. Similar to the tetragonal phase, the
spins on V and Mn in the cubic structure favour a ferrimagnetic configuration.
Most interesting is that the computed charge densities of the spin-carrying
orbitals on V in the cubic phase show an exotic orbital ordering, i.e., a
ferro-orbital ordering along [110] but an anti-ferro-orbital ordering along
[$\overline{1}$10].",1501.00322v4
2015-04-03,Appearance of the prolate and the toroidal magnetic field dominated stars - Analytic approach,"We have analyzed magnetized equilibrium states and showed a condition for
appearance of the prolate and the toroidal magnetic field dominated stars by
analytic approaches. Both observations and numerical stability analysis support
that the magnetized star would have the prolate and the large internal toroidal
magnetic fields. In this context, many investigations concerning magnetized
equilibrium states have tried to obtain the prolate and the toroidal dominant
solutions, but many of them have failed to obtain such configurations. Since
the Lorentz force is a cross product of current density and magnetic field, the
prolate shaped configurations and the large toroidal magnetic fields in stars
require a special relation between current density and the Lorentz force. We
have analyzed simple analytical solutions and found that the prolate and the
toroidal dominant configuration require non force-free toroidal current density
that flows in the opposite direction with respect to the bulk current within
the star. Such current density results in the Lorentz force which makes the
stellar shape prolate. Satisfying this special relation between the current
density and the Lorentz force is a key for appearance of the prolate and the
toroidal magnetic field dominated magnetized star.",1504.00713v1
2013-09-16,Seeing Hofstadter's Butterfly in Atomic Fermi Gases,"We propose a novel way to detect the fractal energy spectrum of the
Hofstadter model from the density distributions of ultracold fermions in an
external trap. At low temperature, the local compressibility is proportional to
the density of states of the system which reveals the fractal energy spectrum.
However, thermal broadening and noises in the real experimental situation
inevitably smear out fine features in the density distribution. To overcome
this difficulty, we use the maximum entropy method to extract the density of
states directly from the noisy thermal density distributions. Simulations show
that one is able to restore the core feature of the Hofstadter's butterfly
spectrum with current experimental techniques. By further reducing the noise or
the temperature, one can refine the resolution and observe fine structures of
the butterfly spectrum.",1309.4097v1
2021-08-12,Dissipative dynamics in the free massive boson limit of the sine-Gordon model,"We study the dissipative dynamics of one-dimensional fermions, described in
terms of the sine-Gordon model in its free massive boson or semi-classical
limit, while keeping track of forward scattering processes. The system is
prepared in the gapped ground state, and then coupled to environment through
local currents within the Lindblad formalism. The heating dynamics of the
system is followed using bosonization. The single particle density matrix
exhibits correlations between the left and right moving particles. While the
density matrix of right movers and left movers is translationally invariant,
the left-right sector is not, corresponding to a translational symmetry
breaking charge density wave state. Asymptotically, the single particle density
matrix decays exponentially with exponent proportional to $-\gamma
t|x|\Delta^2$ where $\gamma$ and $\Delta$ are the dissipative coupling and the
gap, respectively. The charge density wave order parameter decays exponentially
in time with an interaction independent decay rate. The second R\'enyi entropy
grows linearly with time and is essentially insensitive to the presence of the
gap.",2108.05865v2
2021-09-28,Dense matter equation of state and phase transitions from a Generalized Skyrme model,"Skyrmion crystals are the field configurations which minimize the energy per
baryon in the infinitely large topological charge sector of the Skyrme model,
at least for sufficiently high density. They are, therefore, an important tool
to describe the ground state of cold, symmetric nuclear matter at high density
regimes. In this work, we analyze different crystalline phases and the
existence of phase transitions between them within the generalized Skyrme
model, with the ultimate goal of describing symmetric nuclear matter in a wide
regime of densities. Furthermore, we propose a new energy-minimizing phase for
densities lower than the nuclear saturation point ($n_0$) which also presents a
good qualitative behavior in the zero density limit, thereby improving the
description of strongly interacting matter in the region $n<n_0$.",2109.13946v2
2023-04-17,Pileup density estimate independent on jet multiplicity,"The hard-scatter processes in hadronic collisions are often largely
contaminated with soft background coming from pileup in proton-proton
collisions, or underlying event in heavy-ion collisions. There are multiple
methods to remove the effect of pileup for jets. Two such methods, Area
Subtraction and Constituent Subtraction, use the pileup density as the main
ingredient to estimate the magnitude of pileup contribution on an
event-by-event basis. The state-of-the-art approaches to estimating pileup
density are sensitive to the number of hard-scatter jets in the event. This
paper presents a new pileup-density estimation method that minimizes the
sensitivity on the presence of hard-scatter jets in the event. Using a
detector-level simulation, we provide a comparison of the new method with the
state-of-the-art estimation methods. We observe a significantly lower bias for
the estimated pileup density when using the new method. We conclude that the
new method has the potential to significantly improve pileup mitigation in
proton-proton collisions or the underlying event subtraction in heavy-ion
collisions.",2304.08383v2
2012-11-29,Nucleon-nucleon momentum correlation function as a probe of the density distribution of valence neutron in neutron-rich nucleus,"Proton-neutron, neutron-neutron and proton-proton momentum correlation
functions ($C_{pn}$, $C_{nn}$, $C_{pp}$) are systematically investigated for
$^{15}$C and other C isotopes induced collisions at different entrance channel
conditions within the framework of the isospin-dependent quantum molecular
dynamics (IDQMD) model complemented by the CRAB (correlation after burner)
computation code. $^{15}$C is a prime exotic nucleus candidate due to the
weakly bound valence neutron coupling with closed-neutron shell nucleus
$^{14}$C. In order to study density dependence of correlation function by
removing the isospin effect, the initialized $^{15}$C projectiles are sampled
from two kinds of density distribution from RMF model, in which the valence
neutron of $^{15}$C is populated on both 1$d$5/2 and 2$s$1/2 states,
respectively. The results show that the density distributions of valence
neutron significantly influence nucleon-nucleon momentum correlation function
at large impact parameter and high incident energy. The extended density
distribution of valence neutron largely weakens the strength of correlation
function. The size of emission source is extracted by fitting correlation
function using Gaussian source method. The emission source size as well as the
size of final state phase space is larger for projectiles sampling from more
extended density distribution of valence neutron corresponding 2$s$1/2 state in
RMF model. Therefore momentum correlation function can be considered as a
potential valuable tool to diagnose the exotic nuclear structure such as skin
and halo.",1211.6906v1
2010-05-11,Energy density functional on a microscopic basis,"In recent years impressive progress has been made in the development of
highly accurate energy density functionals, which allow to treat medium-heavy
nuclei. In this approach one tries to describe not only the ground state but
also the first relevant excited states. In general, higher accuracy requires a
larger set of parameters, which must be carefully chosen to avoid redundancy.
Following this line of development, it is unavoidable that the connection of
the functional with the bare nucleon-nucleon interaction becomes more and more
elusive. In principle, the construction of a density functional from a density
matrix expansion based on the effective nucleon-nucleon interaction is
possible, and indeed the approach has been followed by few authors. However, to
what extent a density functional based on such a microscopic approach can reach
the accuracy of the fully phenomenological ones remains an open question. A
related question is to establish which part of a functional can be actually
derived by a microscopic approach and which part, on the contrary, must be left
as purely phenomenological. In this paper we discuss the main problems that are
encountered when the microscopic approach is followed. To this purpose we will
use the method we have recently introduced to illustrate the different aspects
of these problems. In particular we will discuss the possible connection of the
density functional with the nuclear matter Equation of State and the distinct
features of finite size effects proper of nuclei.",1005.1810v1
2018-03-10,Effect of population density on epidemics,"Investigations of a possible connection between population density and the
propagation and magnitude of epidemics have so far led to mixed and
unconvincing results. There are three reasons for that. (i) Previous studies
did not focus on the appropriate density interval. (ii) For the density to be a
meaningful variable the population must be distributed as uniformly as
possible. If an area has towns and cities where a majority of the population is
concentrated its average density is meaningless. (iii) In the propagation of an
epidemic the initial proportion of susceptibles (that is to say persons who
have not developed an immunity) is an essential, yet usually unknown, factor.
The assumption that most of the population is susceptible holds only for new
strain of diseases.
  It will be shown that when these requirements are taken care of, the size of
epidemics is indeed closely connected with the population density. This
empirical observation comes as a welcome confirmation of the classical KMK
(Kermack-McKendrick 1927) model. Indeed, one of its key predictions is that the
size of the epidemic increases strongly (and in a non linear way) with the
initial density of susceptibles.
  An interesting consequence is that, contrary to common beliefs, in sparsely
populated territories, like Alaska, Australia or the west coast of the United
states the size of epidemics among native populations must have been limited by
the low density even for diseases for which the natives had no immunity (i.e.,
were susceptibles).",1803.03809v1
2009-05-21,Droplet minimizers for the Gates-Lebowitz-Penrose free energy functional,"We study the structure of the constrained minimizers of the
Gates-Lebowitz-Penrose free-energy functional ${\mathcal F}_{\rm GLP}(m)$,
non-local functional of a density field $m(x)$, $x\in {\mathcal T}_L$, a
$d$-dimensional torus of side length $L$. At low temperatures, ${\mathcal
F}_{\rm GLP}$ is not convex, and has two distinct global minimizers,
corresponding to two equilibrium states. Here we constrain the average density
$L^{-d}\int_{{\cal T}_L}m(x)\dd x$ to be a fixed value $n$ between the
densities in the two equilibrium states, but close to the low density
equilibrium value. In this case, a ""droplet"" of the high density phase may or
may not form in a background of the low density phase, depending on the values
$n$ and $L$. We determine the critical density for droplet formation, and the
nature of the droplet, as a function of $n$ and $L$. The relation between the
free energy and the large deviations functional for a particle model with
long-range Kac potentials, proven in some cases, and expected to be true in
general, then provides information on the structure of typical microscopic
configurations of the Gibbs measure when the range of the Kac potential is
large enough.",0905.3583v1
2011-08-23,Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions,"We study smoothness of densities for the solutions of SDEs whose coefficients
are smooth and nondegenerate only on an open domain $D$. We prove that a smooth
density exists on $D$ and give upper bounds for this density. Under some
additional conditions (mainly dealing with the growth of the coefficients and
their derivatives), we formulate upper bounds that are suitable to obtain
asymptotic estimates of the density for large values of the state variable
(""tail"" estimates). These results specify and extend some results by Kusuoka
and Stroock [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1--76], but our
approach is substantially different and based on a technique to estimate the
Fourier transform inspired from Fournier [Electron. J. Probab. 13 (2008)
135--156] and Bally [Integration by parts formula for locally smooth laws and
applications to equations with jumps I (2007) The Royal Swedish Academy of
Sciences]. This study is motivated by existing models for financial securities
which rely on SDEs with non-Lipschitz coefficients. Indeed, we apply our
results to a square root-type diffusion (CIR or CEV) with coefficients
depending on the state variable, that is, a situation where standard techniques
for density estimation based on Malliavin calculus do not apply. We establish
the existence of a smooth density, for which we give exponential estimates and
study the behavior at the origin (the singular point).",1108.4558v1
2011-12-09,The Josephson relation for the superfluid density and the connection to the Goldstone theorem in dilute Bose atomic gasses,"We derive the Josephson relation for a dilute Bose gas in the framework of an
auxiliary-field resummation of the theory in terms of the normal- and
anomalous-density condensates. The mean-field phase diagram of this theory
features two critical temperatures, T_c and $T^*, associated with the presence
in the system of the Bose-Einstein condensate (BEC) and superfluid state,
respectively. In this context, the Josephson relation shows that the superfluid
density is related to a second order parameter, the square of the
anomalous-density condensate. This is in contrast with the corresponding result
in the Bose gas theory without an anomalous condensate, which predicts that the
superfluid density is proportional to the BEC condensate density. Our findings
are consistent with the prediction that in the temperature range between T_c
and T^* a fraction of the system is in the superfluid state in the absence of
the BEC condensate. This situation is similar to the case of dilute Fermi
gases, where the superfluid density is proportional to the square of the gap
parameter. The Josephson relation relies on the existence of zero energy and
momentum excitations showing the intimate relationship between superfluidity
and the Goldstone theorem.",1112.2233v1
2023-12-12,Sliding Dynamics of Current-Driven Skyrmion Crystal and Helix in Chiral Magnets,"The skyrmion crystal (SkX) and helix (HL) phases, present in typical chiral
magnets, can each be considered as forms of density waves but with distinct
topologies. The SkX exhibits gyrodynamics analogous to electrons under a
magnetic field, while the HL state resembles topological trivial spin density
waves. However, unlike the charge density waves, the theoretical analysis of
the sliding motion of SkX and HL remains unclear, especially regarding the
similarities and differences in sliding dynamics between these two spin density
waves. In this work, we systematically explore the sliding dynamics of SkX and
HL in chiral magnets in the limit of large current density. We demonstrate that
the sliding dynamics of both SkX and HL can be unified within the same
theoretical framework as density waves, despite their distinct microscopic
orders. Furthermore, we highlight the significant role of gyrotropic sliding
induced by impurity effects in the SkX state, underscoring the impact of
nontrivial topology on the sliding motion of density waves. Our theoretical
analysis shows that the effect of impurity pinning is much stronger in HL
compared with SkX, i.e., $\chi^{SkX}/\chi^{HL}\sim \alpha^2$ ($\chi^{SkX}$,
$\chi^{HL}$: susceptibility to the impurity potential, $\alpha$ ($\ll 1$) is
the Gilbert damping). Moreover, the velocity correction is mostly in the
transverse direction to the current in SkX. These results are further
substantiated by realistic Landau-Lifshitz-Gilbert simulations.",2312.07116v2
2020-09-21,AQUA: A Collection of H$_2$O Equations of State for Planetary Models,"Water is one of the key chemical elements in planetary structure modelling.
Due to its complex phase diagram, equations of state cover often only parts of
the pressure - temperature space needed in planetary modelling. We construct an
equation of state of H$_2$O spanning a very wide range from 0.1 Pa to 400 TPa
and 150 K to $10^{5}$ K, which can be used to model the interior of planets. We
combine equations of state valid in localised regions to form a continuous
equation of state spanning over said pressure and temperature range. We provide
tabulated values for the most important thermodynamic quantities, i.e.,
density, adiabatic temperature gradient, entropy, internal energy and bulk
speed of sound of water over this pressure and temperature range. For better
usability we also calculated density - temperature and density - internal
energy grids. We discuss further the impact of this equation of state on the
mass radius relation of planets compared to other popular equation of states
like ANEOS and QEOS. AQUA is a combination of existing equation of state useful
for planetary models. We show that AQUA is in most regions a thermodynamic
consistent description of water. At pressures above 10 GPa AQUA predicts
systematic larger densities than ANEOS or QEOS. A feature which was already
present in a previously proposed equation of state, which is the main
underlying equation of this work. We show that the choice of the equation of
state can have a large impact on the mass-radius relation, which highlights the
importance of future developments in the field of equation of states and
regarding experimental data of water at high pressures.",2009.10098v1
2013-02-18,"A link between Quantum Entanglement, Secant varieties and Sphericity","In this paper, we shed light on relations between three concepts studied in
representations theory, algebraic geometry and quantum information theory.
First - spherical actions of reductive groups on projective spaces. Second -
secant varieties of homogeneous projective varieties, and the related notions
of rank and border rank. Third - quantum entanglement. Our main result concerns
the relation between the problem of the state reconstruction from its reduced
one-particle density matrices and the minimal number of separable summands in
its decomposition. More precisely, we show that sphericity implies that states
of a given rank cannot be approximated by states of a lower rank. We call
states for which such approximation is possible exceptional states. For three,
important from quantum entanglement perspective cases of distinguishable,
fermionic and bosonic particles, we also show that non-sphericity implies the
existence of exceptional states. Remarkably, the exceptional states belong to
non-bipartite entanglement classes. In particular, we show that the $W$-type
states and their appropriate modifications are exceptional states stemming from
the second secant variety for three cases above. We point out that the
existence of the exceptional states is a physical obstruction for deciding the
local unitary equivalence of states by means of the one-particle reduced
density matrices. Finally, for a number of systems of distinguishable particles
with known orbit structure we list all exceptional states and discuss their
possible importance in entanglement theory.",1302.4459v1
2021-06-16,Level Densities from 0-30 MeV,"Photon strength, $f(E_{\gamma})$, measured in photonuclear reactions, is the
product of the average level density per MeV, $\rho(E_x)$, and the average
reduced level width, $\Gamma_{\gamma}/E_{\gamma}^3$ for levels populated
primarily by E1 transitions at an excitation energy $E_x=E_{\gamma}$. It can be
calculated with the Brink-Axel (BA) formulation modified to include
contributions from the Giant Dipole Resonance (GDR) and higher lying
resonances. Level densities and reduced widths have been calculated for 17
nuclei with atomic numbers between Z=14-92. Level densities below the GDR
energy were calculated with the CT-JPI model and combined with the BA photon
strength to determine the associated reduced widths. The reduced widths varied
exponentially with level energy and could be extrapolated up to higher
energies. The extrapolated widths were then combined with the BA photon
strength to determine the level densities at higher energies. The level
densities are found to increase exponentially at low energies, peak near the
GDR energy due to the appearance of new states at the $2\hbar\omega$ shell
closure, and continue to increase less rapidly up to at least 30 MeV. The
average level densities have been compared with the Fermi Gas Level Density
(FGLD), Back-Shifted Fermi Gas (BSFG), and Hartree-Fock-Bogoliubov (HFB)
models. Good agreement is found with the nearly identical FGLD and BDFG models,
while the HFB models gives substantially lower level densities. A universal set
of FGLD model parameters were determined as a function of mass and temperature
that are applicable to all nuclei.",2106.09088v1
2003-06-17,Bose-Einstein Condensation of Molecular Hydrogen in Nanotube Bundles,"We evaluate the effects of heterogeneity on the density of states of H$_2$
molecules inside interstitial channels within bundles of carbon nanotubes. As
temperature (T) falls, the density increases within those tubes having the
greatest binding energy. At T ~ 10 mK, the molecules undergo Bose-Einstein
condensation, exhibiting a singular heat capacity.",0306450v1
2005-08-18,Density operator and entropy of the damped quantum harmonic oscillator,"The expression for the density operator of the damped harmonic oscillator is
derived from the master equation in the framework of the Lindblad theory for
open quantum systems. Then the von Neumann entropy and effective temperature of
the system are obtained. The entropy for a state characterized by a Wigner
distribution function which is Gaussian in form is found to depend only on the
variance of the distribution function.",0508141v1
2010-02-17,Anomalous Hall effects and electron polarizability,"A theory of the anomalous and spin Hall effects, based on the space
distribution of the current densities, is presented. Spin-orbit coupling gives
rise to a space separation of the mass centers, as well as a current density
separation of the quasiparticle states having opposite group velocities. It is
shown that this microscopic property is essential for existence of both Hall
effects.",1002.3212v1
2017-12-21,Wave function representation of probability distributions,"Orthogonal decomposition of the square root of a probability density function
in the Hermite basis is a useful low-dimensional parameterization of continuous
probability distributions over the reals. This representation is formally
similar to the representation of quantum mechanical states as wave functions,
whose squared modulus is a probability density.",1712.07764v2
2018-09-13,Effects of density-dependent migration on a population subjected to Allee effect,"This study assessed the effects of migration on the dynamics of a species
population. It was considered that the species in its natural state and without
the presence of migration exhibited Allee effect. This work also considered
migration as a density-dependent function, which, from a maximum rate,
decreases to a minimum of zero when the population reaches its carrying
capacity.",1809.05025v1
2019-02-19,Fundamental gaps of quantum dots on the cheap,"We show that the fundamental gaps of quantum dots can be accurately estimated
at the computational effort of a standard ground-state calculation supplemented
with a non self-consistent step of negligible cost, all performed within
density-functional theory at the level of the local-density approximation.",1902.07001v1
2022-06-04,Electronic and magnetic properties of the BaTiO$_{3}$/LaMnO$_{3}$ interface: a DFT study,"By means of ab initio calculations within the density functional theory (DFT)
electronic and magnetic properties of BaTiO3/LaMnO3 interface were
investigated. An impact of ferroelectric overlayer thickness onto the interface
properties was analysed through the spin-polarized density of states.",2206.01935v1
2022-06-17,"Excellent thermoelectric performance and impressive optoelectronic properties of Janus monolayer of ZrXY(X=O, S) (Y=S, Se)","Lower-dimensional TMDC materials are suitable for thermoelectric applications
for their specific quantum confinement and being distinct in the density of
states (DOS). Here we investigated thermoelectric parameters of the 2D TMDC
monolayer of ZrXY ((X=O, S,) (Y=S, Se)) by using Density Functional Theory
(DFT) combined with Boltzmann Transport Equation (BTE)",2206.08997v1
1998-12-04,Interlayer Coherence in the $ν=1$ and $ν=2$ Bilayer Quantum Hall States,"We have measured the Hall-plateau width and the activation energy of the
bilayer quantum Hall (BLQH) states at the Landau-level filling factor $\nu=1$
and 2 by tilting the sample and simultaneously changing the electron density in
each quantum well. The phase transition between the commensurate and
incommensurate states are confirmed at $\nu =1$ and discovered at $\nu =2$. In
particular, three different $\nu =2$ BLQH states are identified; the compound
state, the coherent commensurate state, and the coherent incommensurate state.",9812064v1
2010-06-08,Hierarchy of Separability Conditions for Bipartite Systems,"A new hierarchy of separability conditions for bipartite states is obtained.
All the conditions in the hierarchy are necessary for separability. The
conditions are expressed in terms of higher powers of the density operator of
the bipartite system and the reduced density operators of the subsystems.
Violation of any of the conditions in the hierarchy implies entanglement. As a
consequence of the hierarchy, another separability condition, expressed in
terms of the eigenvalues of the density operators of the total system and
subsystems, is obtained.",1006.1533v2
2015-12-18,Upper bound for SL-invariant entanglement measures of mixed states,"An algorithm is proposed that serves to handle full rank density matrices,
when coming from a lower rank method to compute the convex-roof. This is in
order to calculate an upper bound for any polynomial SL invariant multipartite
entanglement measure E. Here, it is exemplifyed how this algorithm works, based
on a method for calculating convex-roofs of rank two density matrices. It
iteratively considers the decompositions of the density matrix into two states
each, exploiting the knowledge for the rank-two case. The algorithm is
therefore quasi exact as far as the two rank case is concerned, and it also
gives hints where it should include more states in the decomposition of the
density matrix. Focusing on the threetangle, I show the results the algorithm
gives for two states, one of which being the $GHZ$-Werner state, for which the
exact convex roof is known. It overestimates the threetangle in the state,
thereby giving insight into the optimal decomposition the $GHZ$-Werner state
has. As a proof of principle, I have run the algorithm for the threetangle on
the transverse quantum Ising model. I give qualitative and quantitative
arguments why the convex roof should be close to the upper bound found here.",1512.05987v2
2002-05-10,Modelling charge self-trapping in wide-gap dielectrics: Localization problem in local density functionals,"We discuss the adiabatic self-trapping of small polarons within the density
functional theory (DFT). In particular, we carried out plane-wave
pseudo-potential calculations of the triplet exciton in NaCl and found no
energy minimum corresponding to the self-trapped exciton (STE) contrary to the
experimental evidence and previous calculations. To explore the origin of this
problem we modelled the self-trapped hole in NaCl using hybrid density
functionals and an embedded cluster method. Calculations show that the
stability of the self-trapped state of the hole drastically depends on the
amount of the exact exchange in the density functional: at less than 30% of the
Hartree-Fock exchange, only delocalized hole is stable, at 50% - both
delocalized and self-trapped states are stable, while further increase of exact
exchange results in only the self-trapped state being stable. We argue that the
main contributions to the self-trapping energy such as the kinetic energy of
the localizing charge, the chemical bond formation of the di-halogen quasi
molecule, and the lattice polarization, are represented incorrectly within the
Kohn-Sham (KS) based approaches.",0205218v1
2005-05-14,Origin of charge density wave formation in insulators from a high resolution photoemission study of BaIrO3,"We investigate the origin of charge density wave (CDW) formation in
insulators by studying BaIrO3 using high resolution (1.4 meV) photoemission
spectroscopy. The spectra reveal the existence of localized density of states
at the Fermi level in the vicinity of room temperature. These localized states
are found to vanish as the temperature is lowered thereby, opening a soft gap
at the Fermi level, as a consequence of CDW transition. In addition, the energy
dependence of the spectral density of states reveals the importance of magnetic
interactions, rather than well-known Coulomb repulsion effect, in determining
the electronic structure thereby implying a close relationship between
ferromagnetism and CDW observed in this compound. Also, Ba core level spectra
surprisingly exhibit an unusual behavior prior to CDW transition.",0505361v1
2013-04-22,A Time Dependent Local Isospin Density Approximation Study of Asymmetric Nuclear Matter,"The dynamic response of asymmetric nuclear matter is studied by using a
Time-Dependent Local Isospin Density (TDLIDA) approximation approach.
Calculations are based on a local density energy functional derived by an
Auxiliary Field Diffusion Monte Carlo (AFDMC) calculation of bulk nuclear
matter. Three types of excited states emerge: collective states, a continuum of
quasi-particle-quasi-hole excitations and unstable solutions. These states are
analyzed and discussed for different values of the nuclear density $\rho$ and
isospin asymmetry $\xi=(N-Z)/A$. An analytical expression of the
compressibility as a function of $\rho$ and $\xi$ is derived which show
explicitly an instability of the neutron matter around $\rho\simeq 0.09
fm^{-3}$ when a small fraction of protons is added to the system.",1304.5858v1
2019-03-07,$d_{x^2-y^2}$-wave density wave and $d_{x^2-y^2}$-wave superconducting gap on the extended Hubbard model on a square lattice,"The extended Hubbard model with a nearest-neighbor Coulomb repulsion on the
square lattice is studied to obtain insight into the phase diagram of cuprate
high $T_c$ superconductors (HTS). To pursue the hidden-order scenario proposed
in [S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001)], we derive an
effective Hamiltonian by using the canonical transformation and develop a
mean-field theory. The calculated phase diagrams are qualitatively consistent
with the experimental phase diagrams of HTS, and we thus conclude that the
pseudogap can be interpreted as the order parameter of the $d_{x^2-y^2}$-wave
density wave (DDW) state, and the $d_{x^2-y^2}$-wave superconducting (DSC)
rises based on the DDW order. Furthermore, the analytical representation of the
density of states is obtained and, near the optimal doping of the DSC, the van
Hove singular point of the density of states is located at the Fermi level.",1903.02902v1
2024-01-04,Spinodal decomposition and phase separation in polar active matter,"We develop and study the hydrodynamic theory of flocking with autochemotaxis.
This describes large collections of self-propelled entities all spontaneously
moving in the same direction, each emitting a substance which attracts the
others (e.g., ants). The theory combines features of the Keller-Segel model for
autochemotaxis with the Toner-Tu theory of flocking. We find that sufficiently
strong autochemotaxis leads to an instability of the uniformly moving state
(the ``flock""), in which bands of different density form moving parallel to the
mean flock velocity with different speeds. These bands, which are reminiscent
of ant trails, coarsen over time to reach a phase-separated state, in which one
high density and one low density band fill the entire system. The same
instability, described by the same hydrodynamic theory, can occur in flocks
phase separating due to any microscopic mechanism (e.g., sufficiently strong
attractive interactions). Although in many ways analogous to equilibrium phase
separation via spinodal decomposition, the two steady state densities here are
determined not by a common tangent construction, as in equilibrium, but by an
uncommon tangent construction very similar to that found for motility induced
phase separation (MIPS) of disordered active particles. Our analytic theory
agrees well with our numerical simulations of our equations of motion.",2401.09461v1
2010-04-13,Charge orderings and phase separations in the atomic limit of the extended Hubbard model with intersite density-density interactions,"A simple effective model of charge ordered insulators is studied. The tight
binding Hamiltonian consists of the effective on-site interaction U and the
intersite density-density interactions Wij (both: nearest-neighbour and
next-nearest-neighbour). In the analysis of the phase diagrams we have adopted
the variational approach, which treats the on-site interaction term exactly and
the intersite interactions within the mean-field approximation. The phase
separated states have not been taken into account in previous analyses. Our
investigations of two cases of the on-site interaction: attraction
(U/(-W_Q)=-10) and repulsion (U/(-W_Q)=1.1) show that, depending on the values
of the next-nearest-neighbour attraction, the system can exhibit not only
homogeneous phases: charge ordered (CO) and nonordered (NO), but also various
phase separated states (CO--NO, CO--CO).",1004.2243v2
2014-08-29,Entropy-energy inequalities for qudit states,"We establish a procedure to find the extremal density matrices for any finite
Hamiltonian of a qudit system. These extremal density matrices provide an
approximate description of the energy spectra of the Hamiltonian. In the case
of restricting the extremal density matrices by pure states, we show that the
energy spectra of the Hamiltonian is recovered for $d=2$ and $3$. We conjecture
that by means of this approach the energy spectra can be recovered for the
Hamiltonian of an arbitrary finite qudit system. For a given qudit system
Hamiltonian, we find new inequalities connecting the mean value of the
Hamiltonian and the entropy of an arbitrary state. We demonstrate that these
inequalities take place for both the considered extremal density matrices and
generic ones.",1408.7099v3
2018-03-30,"Universal non-phononic density of states in 2D, 3D and 4D glasses","It is now well established that structural glasses possess disorder- and
frustration-induced soft quasilocalized excitations, which play key roles in
various glassy phenomena. Recent work has established that in model
glass-formers in three dimensions, these non-phononic soft excitations may
assume the form of quasilocalized, harmonic vibrational modes whose frequency
follows a universal density of states $D(\omega)\!\sim\!\omega^4$,
independently of microscopic details, and for a broad range of glass
preparation protocols. Here we further establish the universality of the
non-phononic density of vibrational modes by direct measurements in model
structural glasses in two dimensions and four dimensions. We also investigate
their degree of localization, which is generally weaker in lower spatial
dimensions, giving rise to a pronounced system-size dependence of the
non-phononic density of states in two dimensions, but not in higher dimensions.
Finally, we identify a fundamental glassy frequency scale $\omega_c$ above
which the universal $\omega^4$ law breaks down.",1803.11383v2
2018-01-22,Functionalization of Silicon Surface by Thiadiazole Molecule : a DFT Study,"The first principles density functional theory (DFT) calculations have been
used to investigate the atomic and electronic properties of thiadiazole
adsorption on the Si(001) surface. A (2x2) reconstructed clean substrate
surface has been chosen to give the molecule sufficient space to relax into its
most favorable position. A total of eighteen bonding model including
bridge-type bonding, and [2+2]/[4+2] cycloaddition mechanisms for four
structural isomers of thiadiazole molecule have been discussed in these
calculations. The most stable bonding configuration for each of the four
isomers on the clean silicon surface has been determined by performing total
energy calculations. Electronic structures of the stable surfaces have been
investigated by plotting the total density of states (TDOS) and energy band
diagrams. Charge densities have been plotted to determine the origin of the
surface states appeared in the fundamental band gap of silicon. Finally,
partial density of states (PDOS) have been plotted to see the contributions
from s- and p-orbitals.",1801.07056v2
2023-11-08,Traversable Wormholes supported by Holographic Dark Energy with a modified Equation of State,"Inspired by holographic dark energy models, we consider different energy
density profiles as possible sources needed to have traversable wormholes
solutions. Since such energy densities are all positive, we are forced to
introduce an equation of state of the form $p_{r}% (r)=\omega_{r}\left(
r\right) \rho(r)$. We will find that Zero Tidal Forces can be imposed at the
price of having the function $\omega_{r}\left( r\right) $ divergent for
$r\rightarrow\infty$. To overcome this inconvenient, we abandon the request of
having Zero Tidal Forces, by introducing appropriate modifications on the
function $\omega_{r}\left( r\right) $ in such a way to obtain a finite result
everywhere. We will find that such modifications will leave the behavior of the
Equation of State close to the throat invariant. Moreover, despite of the
initial assumption, we will find that every dark energy profile will be moved
into the phantom region. Among the different energy density proposals, only one
profile will not require a modification of the original $\omega
_{r}\left(r\right) $ to have Zero Tidal Forces. Such an energy density profile
will be consistent with the appearance of a Global Monopole.",2311.04620v1
2009-02-19,Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions,"For the Euler equations governing compressible isentropic fluid flow with a
barotropic equation of state (where pressure is a function only of the
density), local conservation laws in $n>1$ spatial dimensions are fully
classified in two primary cases of physical and analytical interest: (1)
kinematic conserved densities that depend only on the fluid density and
velocity, in addition to the time and space coordinates; (2) vorticity
conserved densities that have an essential dependence on the curl of the fluid
velocity. A main result of the classification in the kinematic case is that the
only equation of state found to be distinguished by admitting extra
$n$-dimensional conserved integrals, apart from mass, momentum, energy, angular
momentum and Galilean momentum (which are admitted for all equations of state),
is the well-known polytropic equation of state with dimension-dependent
exponent $\gamma=1+2/n$. In the vorticity case, no distinguished equations of
state are found to arise, and here the main result of the classification is
that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's
two-dimensional circulation theorem is obtained for a general equation of
state.",0902.3405v3
2010-09-28,Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states,"We determine the local density of states (LDOS) for spin-gapped
one-dimensional charge density wave (CDW) states and Mott insulators in the
presence of a hard-wall boundary. We calculate the boundary contribution to the
single-particle Green function in the low-energy limit using field theory
techniques and analyze it in terms of its Fourier transform in both time and
space. The boundary LDOS in the CDW case exhibits a singularity at momentum
2kF, which is indicative of the pinning of the CDW order at the impurity. We
further observe several dispersing features at frequencies above the spin gap,
which provide a characteristic signature of spin-charge separation. This
demonstrates that the boundary LDOS can be used to infer properties of the
underlying bulk system. In presence of a boundary magnetic field mid-gap states
localized at the boundary emerge. We investigate the signature of such bound
states in the LDOS. We discuss implications of our results on STM experiments
on quasi-1D systems such as two-leg ladder materials like Sr14Cu24O41. By
exchanging the roles of charge and spin sectors, all our results directly carry
over to the case of one-dimensional Mott insulators.",1009.5587v3
2013-08-09,"Pre- and post-selected quantum states: density matrices, tomography, and Kraus operators","We present a general formalism for charecterizing 2-time quantum states,
describing pre- and post-selected quantum systems. The most general 2-time
state is characterized by a `density vector' that is independent of
measurements performed between the preparation and post-selection. We provide a
method for performing tomography of an unknown 2-time density vector. This
procedure, which cannot be implemented by weak or projective measurements,
brings new insight to the fundamental role played by Kraus operators in quantum
measurements. Finally, after showing that general states and measurements are
isomorphic, we show that any measurement on a 2-time state can be mapped to a
measurement on a preselected bipartite state.",1308.2089v1
2016-12-15,Precursor of Laughlin state of hard core bosons on a two leg ladder,"We study hard core bosons on a two leg ladder lattice under the orbital
effect of a uniform magnetic field. At densities which are incommensurate with
flux, the ground state is a Meissner state, or a vortex state, depending on the
strength of the flux. When the density is commensurate with the flux,
analytical arguments predict the existence of a ground state of central charge
$c = 1$, which displays signatures compatible with the expected Laughlin state
at $\nu=1/2$. This differs from the coupled wire construction of the Laughlin
state in that there exists a nonzero backscattering term in the edge
Hamiltonian. We construct a phase diagram versus density and flux in order to
delimit the region where this precursor to the Laughlin state is the ground
state, by using a combination of bosonization and numerics based on the density
matrix renormalization group (DMRG) and exact diagonalization. We obtain the
phase diagram from local observables and central charge. We use bipartite
charge fluctuations to deduce the Luttinger parameter for the edge Luttinger
liquid corresponding to the Laughlin state. The properties studied with local
observables are confirmed by the long distance behavior of correlation
functions. Our findings are consistent with a calculation of the many body
ground state transverse conductivity in a thin torus geometry for parameters
corresponding to the Laughlin state. The model considered is simple enough such
that the precursor to the Laughlin state could be realized in current ultracold
atom, Josephson junction array, and quantum circuit experiments.",1612.05134v2
2004-07-10,"N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature","We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions
at finite temperature. The partition function is constructed by finding a
numerical approximation to the entire spectrum. We solve numerically for the
spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the
large-N_c approximation and calculate the density of states. We find that the
density of states grows exponentially and the theory has a Hagedorn
temperature, which we extract. We find that the Hagedorn temperature at
infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2).
We use the density of states to also calculate a standard set of thermodynamic
functions below the Hagedorn temperature. In this temperature range, we find
that the thermodynamics is dominated by the massless states of the theory.",0407076v2
2006-03-02,Gibbs States and the Consistency of Local Density Matrices,"Suppose we have an n-qubit system, and we are given a collection of local
density matrices rho_1,...,rho_m, where each rho_i describes some subset of the
qubits. We say that rho_1,...,rho_m are ""consistent"" if there exists a global
state sigma (on all n qubits) whose reduced density matrices match
rho_1,...,rho_m.
  We prove the following result: if rho_1,...,rho_m are consistent with some
state sigma > 0, then they are also consistent with a state sigma' of the form
sigma' = (1/Z) exp(M_1+...+M_m), where each M_i is a Hermitian matrix acting on
the same qubits as rho_i, and Z is a normalizing factor. (This is known as a
Gibbs state.) Actually, we show a more general result, on the consistency of a
set of expectation values <T_1>,...,<T_r>, where the observables T_1,...,T_r
need not commute. This result was previously proved by Jaynes (1957) in the
context of the maximum-entropy principle; here we provide a somewhat different
proof, using properties of the partition function.",0603012v1
2013-11-18,On Instability and Stability of Three-Dimensional Gravity Driven Viscous Flows in a Bounded Domain,"We investigate the instability and stability of some steady-states of a
three-dimensional nonhomogeneous incompressible viscous flow driven by gravity
in a bounded domain $\Omega$ of class $C^2$. When the steady density is heavier
with increasing height (i.e., the Rayleigh-Taylor steady-state), we show that
the steady-state is linear unstable (i.e., the linear solution grows in time in
$H^2$) by constructing a (standard) energy functional and exploiting the
modified variational method. Then, by introducing a new energy functional and
using a careful bootstrap argument, we further show that the steady-state is
nonlinear unstable in the sense of Hadamard. When the steady density is lighter
with increasing height, we show, with the help of a restricted condition
imposed on steady density, that the steady-state is linearly globally stable
and nonlinearly locally stable in the sense of Hadamard.",1311.4364v1
2017-09-27,Effects of geometrical frustration on ferromagnetism in the Hubbard model on the Shastry-Sutherland lattice,"The small-cluster exact-diagonalization calculations and the projector
quantum Monte Carlo method are used to examine the competing effects of
geometrical frustration and interaction on ferromagnetism in the Hubbard model
on the Shastry-Sutherland lattice. It is shown that the geometrical frustration
stabilizes the ferromagnetic state at high electron concentrations ($n \gtrsim
7/4$), where strong correlations between ferromagnetism and the shape of the
noninteracting density of states are observed. In particular, it is found that
ferromagnetism is stabilized only for these values of frustration parameters,
which lead to the single peaked noninterating density of states at the band
edge. Once, two or more peaks appear in the noninteracting density of states at
the band egde the ferromagnetic state is suppressed. This opens a new route
towards the understanding of ferromagnetism in strongly correlated systems.",1709.09461v1
2018-10-10,Hole-pocket-driven superconductivity and its universal features in the electron-doped cuprates,"After three decades of enormous scientific inquiry, the emergence of
superconductivity in the cuprates remains an unsolved puzzle. One major
challenge has been to arrive at a satisfactory understanding of the unusual
metallic normal state from which the superconducting state emerges upon
cooling. A second challenge has been to achieve a unified understanding of
hole- and electron-doped compounds. Here we report detailed magnetoresistivity
measurements for the archetypal electron-doped cuprate
Nd$_{2-x}$Ce$_x$CuO$_{4+{\delta}}$ that, in combination with prior data,
provide crucial links between the normal and superconducting states and between
the electron- and hole-doped parts of the phase diagram. The characteristics of
the normal state (magnetoresistivity, quantum oscillations, and Hall
coefficient) and those of the superconducting state (superfluid density and
upper critical field) consistently indicate two-band (electron and hole)
features and clearly point to hole-pocket-driven superconductivity in these
nominally electron-doped materials. We show that the approximate Uemura scaling
between the superconducting transition temperature and the superfluid density
found for hole-doped cuprates also holds for the small hole component of the
superfluid density in the electron-doped cuprates.",1810.04634v1
2023-08-10,Topological soliton molecule in quasi 1D charge density wave,"Soliton molecules, bound states of two solitons, can be important for the
informatics using solitons and the quest for exotic particles in a wide range
of physical systems from unconventional superconductors to nuclear matter and
Higgs field, but have been observed only in temporal dimension for classical
wave optical systems. Here, we identify a topological soliton molecule formed
spatially in an electronic system, a quasi 1D charge density wave of indium
atomic wires. This system is composed of two coupled Peierls chains, which are
endowed with a Z$_4$ topology and three distinct, right-chiral, left-chiral,
and non-chiral, solitons. Our scanning tunneling microscopy measurements
identify a bound state of right- and left-chiral solitons with distinct in-gap
states and net zero phase shift. Our density functional theory calculations
reveal the attractive interaction of these solitons and the hybridization of
their electronic states. This result initiates the study of the interaction
between solitons in electronic systems, which can provide novel manybody
electronic states and extra data-handling capacity beyond the given soliton
topology.",2308.05495v1
2024-03-01,Understanding Trap States in InP and GaP Quantum Dots Through Density Functional Theory,"The widespread application of III-V colloidal quantum dots (QDs) as
non-toxic, highly tunable emitters is stymied by their high density of trap
states. Here, we utilize density functional theory (DFT) to investigate trap
state formation in a diverse set of realistically passivated core-only InP and
GaP QDs. Through orbital localization techniques, we deconvolute the dense
manifold of trap states to allow for detailed assignment of surface defects. We
find that the three-coordinate species dominate trapping in III-V QDs and
identify features in the geometry and charge environment of trap centers
capable of deepening, or sometimes passivating, traps. Furthermore, we observe
stark differences in surface reconstruction between InP and GaP, where the more
labile InP reconstructs to passivate three-coordinate indium at the cost of
distortion elsewhere. These results offer explanations for experimentally
observed trapping behavior and suggest new avenues for controlling trap states
in III-V QDs.",2403.00703v1
2008-04-04,Astrophysical Implications of Equation of State for Hadron-Quark Mixed Phase: Compact Stars and Stellar Collapses,"We construct an equation of state including the hadron-quark phase
transition. The mixed phase is obtained by the Gibbs conditions for finite
temperature. We adopt the equation of state based on the relativistic mean
field theory for the hadronic phase taking into account pions. As for the quark
phase, the MIT bag model of the deconfined 3-flavor strange quark matter is
used. As a result, our equation of state is thermodynamically stable and
exhibits qualitatively the desired properties of hadron-quark mixed matter,
such as the temperature dependence of the transition density. The pions raise
the transition density because they make the equation of state softer. Using
the equation of state constructed here, we study its astrophysical
implications. The maximum mass of compact stars is investigated, and our
equation of state is consistent with recent observations. We also compute the
collapse of a massive star with 100 solar masses using our equation of state
and find that the interval time from the bounce to the black hole formation
becomes shorter for the model with pions and quarks. The pions and quarks
affect the total energy of the emitted neutrinos because the duration time of
the neutrino emission becomes shorter. The neutrino luminosity rises under the
effect of pions since the density of the proto-neutron star becomes high.",0804.0661v1
2016-05-04,Quark Matter at High Density based on Extended Confined-isospin-density-dependent-mass Model,"We investigate the effect of the inclusion of relativistic Coulomb terms in a
confined-isospin-density-dependent-mass (CIDDM) model of strange quark matter
(SQM). We found that if we include Coulomb term in scalar density form, SQM
equation of state (EOS) at high densities is stiffer but if we include Coulomb
term in vector density form is softer than that of standard CIDDM model. We
also investigate systematically the role of each term of the extended CIDDM
model. Compared with what was reported in Ref.~\cite {ref:isospin}, we found
the stiffness of SQM EOS is controlled by the interplay among the the
oscillator harmonic, isospin asymmetry and Coulomb contributions depending on
the parameter's range of these terms. We have found that the absolute stable
condition of SQM and the mass of 2 $M_\odot$ pulsars can constrain the
parameter of oscillator harmonic $\kappa_1$ $\approx 0.53$ in the case Coulomb
term excluded. If the Coulomb term is included, for the models with their
parameters are consistent with SQM absolute stability condition, the
$2.0~M_{\odot}$ constraint more prefer the maximum mass prediction of model
with scalar Coulomb term than that of model with vector Coulomb term. On
contrary, the high densities EOS predicted by model with vector Coulomb is more
compatible with recent pQCD result \cite{ref:pressure} than that predicted by
model with scalar Coulomb. Furthermore, we also observed the quark composition
in a very high density region depends quite sensitively on the kind of Coulomb
term used.",1605.01154v1
2017-12-13,Role of fluctuations for density-wave instabilities: Failure of the mean-field description,"Density-wave instabilities have been observed and studied in a multitude of
materials. Most recently, in the context of unconventional superconductors like
the iron-based superconductors, they have excited considerable interest. We
analyze the fluctuation corrections to the equation of state of the
density-wave order parameter for commensurate charge-density waves and
spin-density waves due to perfect nesting. For XY magnets, we find that
contributions due to longitudinal and transverse fluctuations cancel each
other, making the mean-field analysis of the problem controlled. This is
consistent with the analysis of fluctuation corrections to the BCS theory of
superconductivity [S. Kos, A. J. Millis, and A. I. Larkin, Phys. Rev. B 70,
214531 (2004)]. However, this cancellation does not occur in density-wave
systems when the order parameter is a real $N$-component object with $N\neq2$.
Then, the number of transverse fluctuating modes differs from the number of
longitudinal fluctuating modes. Indeed, in the case of charge-density waves as
well as spin-density waves with Heisenberg symmetry, we find that fluctuation
corrections are not negligible, and hence mean-field theories are not
justified. These singular fluctuations originate from the intermediate
length-scale regime, with wavelengths between the lattice constant and the
$T=0$ correlation length. The resulting logarithmic fluctuation contributions
to the gap equation originate from the derivative of the anomalous polarization
function, and the crucial process is an interaction of quasiparticles through
the exchange of fluctuations.",1712.04679v2
2012-03-25,Harmonic analysis on Cayley Trees II: the Bose Einstein condensation,"We investigate the Bose-Einstein Condensation on non homogeneous non amenable
networks for the model describing arrays of Josephson junctions on perturbed
Cayley Trees. The resulting topological model has also a mathematical interest
in itself. The present paper is then the application to the Bose-Einstein
Condensation phenomena, of the harmonic analysis aspects arising from additive
and density zero perturbations, previously investigated by the author in a
separate work. Concerning the appearance of the Bose-Einstein Condensation, the
results are surprisingly in accordance with the previous ones, despite the lack
of amenability. We indeed first show the following fact. Even when the critical
density is finite (which is implied in all the models under consideration,
thanks to the appearance of the hidden spectrum), if the adjacency operator of
the graph is recurrent, it is impossible to exhibit temperature locally normal
states (i.e. states for which the local particle density is finite) describing
the condensation at all. The same occurs in the transient cases for which it is
impossible to exhibit locally normal states describing the Bose--Einstein
Condensation at mean particle density strictly greater than the critical
density . In addition, for the transient cases, in order to construct locally
normal temperature states through infinite volume limits of finite volume Gibbs
states, a careful choice of the the sequence of the finite volume chemical
potential should be done. For all such states, the condensate is essentially
allocated on the base--point supporting the perturbation. This leads that the
particle density always coincide with the critical one. It is shown that all
such temperature states are Kubo-Martin-Schwinger states for a natural
dynamics. The construction of such a dynamics, which is a very delicate issue,
is also done.",1203.5522v2
2021-08-07,The area operator and fixed area states in conformal field theories,"The fixed area states are constructed by gravitational path integrals in
previous studies.In this paper we show the dual of the fixed area states in
conformal field theories (CFTs).These CFT states are constructed by using
spectrum decomposition of reduced density matrix $\rho_A$ for a subsystem $A$.
For 2 dimensional CFTs we directly construct the bulk metric, which is
consistent with the expected geometry of the fixed area states. For arbitrary
pure geometric state $|\psi\rangle$ in any dimension we also find the
consistency by using the gravity dual of R\'enyi entropy. We also give the
relation of parameters for the bulk and boundary state. The pure geometric
state $|\psi\rangle$ can be expanded as superposition of the fixed area states.
Motivated by this, we propose an area operator $\hat A^\psi$. The fixed area
state is the eigenstate of $\hat A^\psi$, the associated eigenvalue is related
to R\'enyi entropy of subsystem $A$ in this state. The Ryu-Takayanagi formula
can be expressed as the expectation value $\langle \psi| {\hat
A}^\psi|\psi\rangle$ divided by $4G$, where $G$ is the Newton constant. We also
show the fluctuation of the area operator in the geometric state $|\psi\rangle$
is suppressed in the semiclassical limit $G\to0$.",2108.03346v1
2004-01-08,Exact Solutions of Einstein's Field Equations,"We examine various well known exact solutions available in the literature to
investigate the recent criterion obtained in ref. [20] which should be
fulfilled by any static and spherically symmetric solution in the state of
hydrostatic equilibrium. It is seen that this criterion is fulfilled only by
(i) the regular solutions having a vanishing surface density together with the
pressure, and (ii) the singular solutions corresponding to a non-vanishing
density at the surface of the configuration . On the other hand, the regular
solutions corresponding to a non-vanishing surface density do not fulfill this
criterion. Based upon this investigation, we point out that the exterior
Schwarzschild solution itself provides necessary conditions for the types of
the density distributions to be considered inside the mass, in order to obtain
exact solutions or equations of state compatible with the structure of general
relativity. The regular solutions with finite centre and non-zero surface
densities which do not fulfill the criterion [20], in fact, can not meet the
requirement of the `actual mass' set up by exterior Schwarzschild solution. The
only regular solution which could be possible in this regard is represented by
uniform (homogeneous) density distribution.
  The criterion [20] provides a necessary and sufficient condition for any
static and spherical configuration (including core-envelope models) to be
compatible with the structure of general relativity. Thus, it may find
application to construct the appropriate core-envelope models of stellar
objects like neutron stars and may be used to test various equations of state
for dense nuclear matter and the models of relativistic stellar structures like
star clusters.",0401024v1
2001-10-15,Out of Equilibrium Dynamics of Supersymmetry at High Energy Density,"We investigate the out of equilibrium dynamics of global chiral supersymmetry
at finite energy density. We concentrate on two specific models. The first is
the massive Wess-Zumino model which we study in a selfconsistent one-loop
approximation. We find that for energy densities above a certain threshold, the
fields are driven dynamically to a point in field space at which the fermionic
component of the superfield is massless. The state, however is found to be
unstable, indicating a breakdown of the one-loop approximation. To investigate
further, we consider an O(N) massive chiral model which is solved exactly in
the large $N$ limit. For sufficiently high energy densities, we find that for
late times the fields reach a nonperturbative minimum of the effective
potential degenerate with the perturbative minimum. This minimum is a true
attractor for O(N) invariant states at high energy densities, and this provides
a mechanism for determining which of the otherwise degenerate vacua is chosen
by the dynamics. The final state for large energy density is a cloud of
massless particles (both bosons and fermions) around this new nonperturbative
supersymmetric minimum. By introducing boson masses which softly break the
supersymmetry, we demonstrate a see-saw mechanism for generating small fermion
masses. We discuss some of the cosmological implications of our results.",0110205v1
2008-01-31,Investigating a Class of $2\otimes2\otimes d$ Chessboard Density Matrices via Linear and Non-linear Entanglement Witnesses Constructed by Exact Convex Optimization,"Here we consider a class of $2\otimes2\otimes d$ chessboard density matrices
starting with three-qubit ones which have positive partial transposes with
respect to all subsystems. To investigate the entanglement of these density
matrices, we use the entanglement witness approach. For constructing
entanglement witnesses (EWs) detecting these density matrices, we attempt to
convert the problem to an exact convex optimization problem. To this aim, we
map the convex set of separable states into a convex region, named feasible
region, and consider cases that the exact geometrical shape of feasible region
can be obtained. In this way, various linear and non-linear EWs are
constructed. The optimality and decomposability of some of introduced EWs are
also considered. Furthermore, the detection of the density matrices by
introduced EWs are discussed analytically and numerically.
  {\bf Keywords: chessboard density matrices, optimal non-linear entanglement
witnesses, convex optimization}
  {\bf PACs Index: 03.65.Ud}",0801.4953v1
2013-02-26,Pressure dependence of the charge density wave in 1T-TaS2 and its relation to superconductivity,"We present a state-of-the-art x-ray diffraction study of the charge density
wave order in 1T-TaS2 as a function of temperature and pressure. Our results
prove that the charge density wave, which we characterize in terms of wave
vector, amplitude and the coherence length, indeed exists in the
superconducting region of the phase diagram. The data further imply that the
ordered charge density wave structure as a whole becomes superconducting at low
temperatures, i. e, superconductivity and charge density wave coexist on a
macroscopic scale in real space. This result is fundamentally different from a
previously proposed separation of superconducting and insulating regions in
real space and, instead, provides evidence that the superconducting and the
charge density wave gap exist in separate regions of reciprocal space.",1302.6449v1
2013-07-05,Nuclear Pasta Formation,"The formation of complex nonuniform phases of nuclear matter, known as
nuclear pasta, is studied with molecular dynamics simulations containing 51200
nucleons. A phenomenological nuclear interaction is used that reproduces the
saturation binding energy and density of nuclear matter. Systems are prepared
at an initial density of 0.10fm$^{-3}$ and then the density is decreased by
expanding the simulation volume at different rates to densities of 0.01
fm$^{-3}$ or less. An originally uniform system of nuclear matter is observed
to form spherical bubbles (""swiss cheese""), hollow tubes, flat plates
(""lasagna""), thin rods (""spaghetti"") and, finally, nearly spherical nuclei with
decreasing density. We explicitly observe nucleation mechanisms, with
decreasing density, for these different pasta phase transitions. Topological
quantities known as Minkowski functionals are obtained to characterize the
pasta shapes. Different pasta shapes are observed depending on the expansion
rate. This indicates non equilibrium effects. We use this to determine the best
ways to obtain lower energy states of the pasta system from MD simulations and
to place constrains on the equilibration time of the system.",1307.1678v1
2015-01-09,Dipolar Bilayer with Antiparallel Polarization -- a Self-Bound Liquid,"Dipolar bilayers with antiparallel polarization, i.e. opposite polarization
in the two layers, exhibit liquid-like rather than gas-like behavior. In
particular, even without external pressure a self-bound liquid puddle of
constant density will form. We investigate the symmetric case of two identical
layers, corresponding to a two-component Bose system with equal partial
densities. The zero-temperature equation of state $E(\rho)/N$, where $\rho$ is
the total density, has a minimum, with an equilibrium density that decreases
with increasing distance between the layers. The attraction necessary for a
self-bound liquid comes from the inter-layer dipole-dipole interaction that
leads to a mediated intra-layer attraction. We investigate the regime of
negative pressure towards the spinodal instability, where the bilayer is
unstable against infinitesimal fluctuations of the total density, conformed by
calculations of the speed of sound of total density fluctuations.",1501.02091v1
2015-06-15,The Nuclear Symmetry Energy in Heavy Ion Collisions,"In this contribution I discuss the nuclear symmetry energy in the regime of
hadronic degrees of freedom. The density dependence of the symmetry energy is
important from very low densities in supernova explosions, to the structure of
neutron-rich nuclei around saturation density, and to several times saturation
density in neutron stars. Heavy ion collisions are the only means to study this
density dependence in the laboratory. Numerical simulations of transport
theories are used to extract the equation-of-state, and thus also the symmetry
energy. I discuss some examples, which relate particularly to the high density
symmetry energy, which is of particular interest today. I review the status and
point out some open problems in the determination of the symmetry energy in
heavy ion collisions.",1506.04687v1
2018-02-13,X-Ray sum frequency generation; direct imaging of ultrafast electron dynamics,"X-ray diffraction from molecules in the ground state produces an image of
their charge density, and time-resolved X-ray diffraction can thus monitor the
motion of the nuclei. However, the density change of excited valence electrons
upon optical excitation can barely be monitored with regular diffraction
techniques due to the overwhelming background contribution of the core
electrons. We present a nonlinear X-ray technique made possible by novel free
electron laser sources, which provides a spatial electron density image of
valence electron excitations. The technique, sum frequency generation carried
out with a visible pump and a broadband X-ray diffraction pulse, yields
snapshots of the transition charge densities, which represent the electron
density variations upon optical excitation. The technique is illustrated by ab
initio simulations of transition charge density imaging for the optically
induced electronic dynamics in a donor/acceptor substituted stilbene.",1802.04421v1
2019-07-12,Symmetric nuclear matter from the strong interaction,"We study the equation of state of symmetric nuclear matter at zero
temperature over a wide range of densities using two complementary theoretical
approaches. At low densities up to twice nuclear saturation density, we compute
the energy per particle based on modern nucleon-nucleon and three-nucleon
interactions derived within chiral effective field theory. For higher densities
we derive for the first time constraints in a Fierz-complete setting directly
based on quantum chromodynamics using functional renormalization group
techniques. We find remarkable consistency of the results obtained from both
approaches as they come together in density and the natural emergence of a
maximum in the speed of sound $c_S$ at supranuclear densities with a value
beyond the asymptotic $c_S^2 = 1/3$. The presence of a maximum appears tightly
connected to the formation of a diquark gap.",1907.05814v2
2020-04-20,Roundtrip: A Deep Generative Neural Density Estimator,"Density estimation is a fundamental problem in both statistics and machine
learning. In this study, we proposed Roundtrip as a general-purpose neural
density estimator based on deep generative models. Roundtrip retains the
generative power of generative adversarial networks (GANs) but also provides
estimates of density values. Unlike previous neural density estimators that put
stringent conditions on the transformation from the latent space to the data
space, Roundtrip enables the use of much more general mappings. In a series of
experiments, Roundtrip achieves state-of-the-art performance in a diverse range
of density estimation tasks.",2004.09017v4
2022-07-12,Seven Useful Questions in Density Functional Theory,"We explore a variety of unsolved problems in density functional theory, where
mathematicians might prove useful. We give the background and context of the
different problems, and why progress toward resolving them would help those
doing computations using density functional theory. Subjects covered include
the magnitude of the kinetic energy in Hartree-Fock calculations, the shape of
adiabatic connection curves, using the constrained search with input densities,
densities of states, the semiclassical expansion of energies, the tightness of
Lieb-Oxford bounds, and how we decide the accuracy of an approximate density.",2207.05794v4
1998-03-31,Crossover between polariton and phonon local states. Anisotropy-induced localization threshold,"We consider the impurity-induced polariton local states in a dipole-active
medium. These states present the local optical vibrations which are coherently
coupled with the induced electromagnetic field. We show that the crossover
between the polariton and phonon local states takes place within the
relativistically narrow interval near the bottom of the polariton gap. However,
the resonant phonon-photon interaction leads to the absence of the lower
threshold of the impurity strength. These results are due to the singularity of
the density of the polariton states, which is generic for any isotropic
dipole-active phonon mode with the negative dispersion. We show that a weak
anisotropy removes this singularity and sets a finite threshold for the local
polariton states.",9803375v1
1999-06-16,A novel superconducting glass state in disordered thin films in Clogston limit,"A theory of mesoscopic fluctuations in disordered thin superconducting films
in a parallel magnetic field is developed. At zero temperature, the
superconducting state undergoes a phase transition into a state characterized
by superfluid densities of random signs, instead of a spin polarized disordered
Fermi liquid phase. Consequently, the ground state belongs to the same
universality class as the 2D XY spin glass. As the magnetic field increases
further, mesoscopic pairing states are nucleated in an otherwise homogeneous
spin polarized disordered Fermi liquid. The statistics of these pairing states
is universal depending on the sheet conductance of the 2D film.",9906257v1
2000-02-08,Thermodynamic Properties of d_{x^2-y^2}+id_{xy} Superconductor,"In view of the current interest in d_{x^{2}-y^{2}}+id_{xy} superconductors
some of their thermodynamic properties have been studied to obtain relevant
information for experimental verification. The temperature dependence of the
specific heat and superfluid density show marked differences in
d_{x^{2}-y^{2}}+id_{xy} state compared to the pure d-wave state. A second order
phase transition is observed on lowering the temperature into a
d_{x^{2}-y^{2}}+id_{xy} state from the d_{x^{2}-y^{2}} state with the opening
up of a gap all over the fermi surface. The thermodynamic quantities in
d_{x^{2}-y^{2}}+id_{xy} state are dominated by this gap as in an s-wave
superconductor as opposed to the algebraic temperature dependence in pure
d-wave states coming from the low energy excitations across the node(s).",0002114v1
2003-05-08,Impurity and interface bound states in $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ superconductors,"Motivated by recent discoveries of novel superconductors such as
Na$_x$CoO$_2\cdot y$H$_2$O and Sr$_2$RuO$_4$, we analysize features of
quasi-particle scattering due to impurities and interfaces for possible gapful
$d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ Cooper pairing. A bound state appears near
a local impurity, and a band of bound states form near an interface. We
obtained analytically the bound state energy, and calculated the space and
energy dependent local density of states resolvable by high-resolution scanning
tunnelling microscopy. For comparison we also sketch results of impurity and
surface states if the pairing is nodal p- or d-wave.",0305152v1
2010-11-08,Quantum decoherence in strongly correlated electron systems,"Complexity in strongly correlated electron systems is analyzed by considering
decoherence process between the localized state, |L> and the itinerant state,
|I>. The coherent superposition state of a|I> + b|L> decoheres to the pointer
states in the proximity of both extremes of the correlation where the
symmetry-breaking ground states of the charge pairing emerge. For maximizing
the entropy of the system, the superconducting pairing and the spin density
wave coexist within the uncertainty principle, which invokes the metastable
states as like pseudogap phase and electronic inhomogenity.",1011.1782v2
2019-11-28,Floquet-state cooling,"We demonstrate that a periodically driven quantum system can adopt a
quasistationary state which is effectively much colder than a thermal reservoir
it is coupled to, in the sense that certain Floquet states of the
driven-dissipative system can carry much higher population than the ground
state of the corresponding undriven system in thermal equilibrium. This is made
possible by a rich Fourier spectrum of the system's Floquet transition matrix
elements, the components of which are addressed individually by a suitably
peaked reservoir density of states. The effect is expected to be important for
driven solid-state systems interacting with a phonon bath predominantly at
well-defined frequencies.",1911.12563v1
2014-06-10,Bound states in the continuum: localization of Dirac-like fermions,"We report the formation of bound states in the continuum for Dirac-like
fermions in structures composed by a trilayer graphene flake connected to
nanoribbon leads. The existence of this kind of localized states can be proved
by combining local density of states and electronic conductance calculations.
By applying a gate voltage, the bound states couple to the continuum, yielding
a maximum in the electronic transmission. This feature can be exploited to
identify bound states in the continuum in graphene-based structures.",1406.2627v1
2023-08-21,Simulation of Kerr Nonlinearity: Revealing Initial State Dependency,"We simulate coherent driven free dissipative Kerr nonlinear system
numerically using time evolving block decimation (TEBD) algorithm and time
propagation on the Heisenberg equation of motion using Eulers method to study
how the numerical results are analogous to classical bistability. The system
evolves through different trajectories to stabilize different branches for
different external drives and initial conditions. The Wigner state reprentation
confirms the system to suffer a residual effect of initial state throughout the
non-classical dynamical evolution and the steady state of the system.
Furthermore, we also see the numerically simulated spectral density remains
significantly different from analytical counterparts when initial states do not
lie to the same branch of the final state.",2308.10667v1
2004-06-07,Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant,"The energy density associated with Planck length is $\rho_{uv}\propto
L_P^{-4}$ while the energy density associated with the Hubble length is
$\rho_{ir}\propto L_H^{-4}$ where $L_H=1/H$. The observed value of the dark
energy density is quite different from {\it either} of these and is close to
the geometric mean of the two: $\rho_{vac}\simeq \sqrt{\rho_{uv} \rho_{ir}}$.
It is argued that classical gravity is actually a probe of the vacuum {\it
fluctuations} of energy density, rather than the energy density itself. While
the globally defined ground state, being an eigenstate of Hamiltonian, will not
have any fluctuations, the ground state energy in the finite region of space
bounded by the cosmic horizon will exhibit fluctuations $\Delta\rho_{\rm
vac}(L_P, L_H)$. When used as a source of gravity, this $\Delta \rho$ should
lead to a spacetime with a horizon size $L_H$. This bootstrapping condition
leads naturally to an effective dark energy density $\Delta\rho\propto
(L_{uv}L_H)^{-2}\propto H^2/G$ which is precisely the observed value. The model
requires, either (i) a stochastic fluctuations of vacuum energy which is
correlated over about a Hubble time or (ii) a semi- anthropic interpretation.
The implications are discussed.",0406060v1
2021-11-24,Inclusive rates from smeared spectral densities in the two-dimensional O(3) non-linear $σ$-model,"This work employs the spectral reconstruction approach of Ref. [1] to
determine an inclusive rate in the $1+1$ dimensional O(3) non-linear
$\sigma$-model, analogous to the QCD part of ${e}^+{e}^- \rightarrow \rm
{hadrons}$. The Euclidean two-point correlation function of the conserved
current $j$ is computed using Monte Carlo lattice field theory simulations for
a variety of spacetime volumes and lattice spacings. The spectral density of
this correlator is related to the inclusive rate for $j \rightarrow {\rm X}$ in
which all final states produced by the external current are summed. The
ill-posed inverse problem of determining the spectral density from the
correlation function is made tractable through the determination of smeared
spectral densities in which the desired density is convolved with a set of
known smearing kernels of finite width $\epsilon$. The smooth energy dependence
of the underlying spectral density enables a controlled $\epsilon \to 0$
extrapolation in the inelastic region, yielding the real-time inclusive rate
without reference to individual finite-volume energies or matrix elements.
Systematic uncertainties due cutoff effects and residual finite-volume effects
are estimated and taken into account in the final error budget. After taking
the continuum limit, the results are consistent with the known analytic rate to
within the combined statistical and systematic errors. Above energies where
20-particle states contribute, the overall precision is sufficient to discern
the four-particle contribution to the spectral density.",2111.12774v1
2022-03-29,Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis,"We theoretically investigate an electric-field-driven system of charged
spheres as a primitive model of concentrated electrolytes under an applied
electric field. First, we provide a unified formulation for the stochastic
charge and density dynamics of the electric-field-driven primitive model using
the stochastic density functional theory (DFT). The stochastic DFT integrates
various frameworks of the equilibrium and dynamic DFTs, the liquid state
theory, and the field-theoretic approach, which allows us to justify in a
unified manner various modifications previously made for the
Poisson-Nernst-Planck model. Next, we consider stationary density-density and
charge-charge correlation functions of the primitive model with a static
electric field. We focus on an electric-field-induced synchronization between
the emergence of density and charge oscillations, or the crossover from
monotonic to oscillatory decay of density-density and charge-charge
correlations. The correlation function analysis demonstrates the appearance of
stripe states formed by segregation bands perpendicular to the external field.
We also predict the following: (i) the electric-field-induced crossover occurs
prior to the conventional Kirkwood crossover without an applied electric field,
and (ii) the ion concentration dependence of the decay lengths at the
electric-field-induced crossovers bears a similarity to the underscreening
behavior found by simulation and theoretical studies on the oscillatory decay
length in equilibrium.",2203.15428v2
2022-04-12,Plane-Wave-Based Stochastic-Deterministic Density Functional Theory for Extended Systems,"Traditional finite-temperature Kohn-Sham density functional theory (KSDFT)
has an unfavorable scaling with respect to the electron number or at high
temperatures. The evaluation of the ground-state density in KSDFT can be
replaced by the Chebyshev trace (CT) method. In addition, the use of stochastic
orbitals within the CT method leads to the stochastic density functional theory
[Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed
stochastic-deterministic density functional theory [Phys. Rev. Lett. 125,
055002 (2020)] (MDFT). We have implemented the above four methods within the
first-principles package ABACUS. All of the four methods are based on the
plane-wave basis set with the use of norm-conserving pseudopotentials and the
periodic boundary conditions with the use of $k$-point sampling in the
Brillouin zone. By using the KSDFT calculation results as benchmarks, we
systematically evaluate the accuracy and efficiency of the CT, SDFT, and MDFT
methods via examining a series of physical properties, which include the
electron density, the free energy, the atomic forces, stress, and density of
states for a few condensed phase systems. The results suggest that our
implementations of CT, SDFT, and MDFT not only reproduce the KSDFT results with
a high accuracy, but also exhibit several advantages over the tradition KSDFT
method. We expect these methods can be of great help in studying
high-temperature and large-size extended systems such as warm dense matter and
dense plasma.",2204.05662v2
2003-09-25,On the one-particle reduced density matrices of a pure three-qutrit quantum state,"We present a necessary and sufficient condition for three qutrit density
matrices to be the one-particle reduced density matrices of a pure three-qutrit
quantum state. The condition consists of seven classes of inequalities
satisfied by the eigenvalues of these matrices. One of them is a generalization
of a known inequality for the qubit case. Some of these inequalities are proved
algebraically whereas the proof of the others uses the fact that a continuous
function of the state must have a minimum. Construction of states satisfying
these inequalities relies on a representation of the convex set of the allowed
set of eigenvalues in terms of corner points. We also present a result for a
more general quantum system concerning the nature of the boundary surface of
the set of the allowed set of eigenvalues.",0309186v2
2014-12-23,Distribution of dark energy in the vicinity of compact objects,"The distribution of dark energy density in the vicinity of compact static
objects is analyzed. Dark energy is assumed to be in the form of a scalar field
with three parameters: the background density, the equation of state parameter
and the effective sound speed. Compact object is assumed to be a homogeneous
spherical object of constant radius. We use the solutions of the hydrodynamical
equations for dark energy in the gravitational fields of such objects for cases
of static distribution of dark energy in the vicinity of star and stationary
accretion onto black hole in order to analyze the possibility of constraining
of the parameters of dark energy from astrophysical data. We show that
dependence of density of dark energy in the vicinity of such object on the
effective sound speed, background density and equation of state parameter of
dark energy makes it possible to try such tests. Here we exploit the accuracy
of determination of masses of Sun and black hole in the center of Milky Way to
obtain the lower limit on the effective sound speed of dark energy.",1412.7323v1
2003-11-13,Quasiparticle scattering and local density of states in the d-density wave phase,"We study the effects of single-impurity scattering on the local density of
states in the high-$T_c$ cuprates. We compare the quasiparticle interference
patterns in three different ordered states: d-wave superconductor (DSC),
d-density wave (DDW), and coexisting DSC and DDW (DSC-DDW). In the coexisting
state, at energies below the DSC gap, the patterns are almost identical to
those in the pure DSC state with the same DSC gap. However, they are
significantly different for energies greater than or equal to the DSC gap. This
transition at an energy around the DSC gap can be used to test the nature of
the superconducting state of the underdoped cuprates by scanning tunneling
microscopy. Furthermore, we note that in the DDW state the effect of the
coherence factors is stronger than in the DSC state. The new features arising
due to DDW ordering are discussed.",0311299v1
2009-05-22,Electronic and Magnetic Properties of $\rm{RMnO}_3/\rm{AMnO}_3$ Heterostructures,"In this paper, we investigate the ground state properties of the
$\rm{RMnO}_3/\rm{AMnO}_3$ ($\rm{RMO/AMO}$) heterostructures (R=trivalent
cation, and A=divalent cation) by using a two-orbital double-exchange model
supplemented by the Poisson's equation. We find that the state stabilized near
the interface of the heterostructure is similar to the state of the bulk
compound $\rm{(R,A)MO}$ at electronic density close to 0.5. Depending on the
bandwidth it will be a charge and orbital ordered CE state or an A-AF state
with $x^2-y^2$ orbital order. Our results can explain some properties of
long-period superlattices. As another interesting result, we find exotic
intermediate states stabilized in between the interface and the bulk-like
regimes of the heterostructure. For instance, a spin ""canted CE"" state and
others. They may not have an analog in experimentally known bulk phase
diagrams, but provide a natural interpolation between magnetically-ordered
states that are stable in the bulk at different electronic densities.",0905.3591v1
2023-07-31,Scalable Quantum State Tomography with Locally Purified Density Operators and Local Measurements,"Understanding quantum systems is of significant importance for assessing the
performance of quantum hardware and software, as well as exploring quantum
control and quantum sensing. An efficient representation of quantum states
enables realizing quantum state tomography with minimal measurements. In this
study, we propose a new approach to state tomography that uses tensor network
representations of mixed states through locally purified density operators and
employs a classical data postprocessing algorithm requiring only local
measurements. Through numerical simulations of one-dimensional pure and mixed
states and two-dimensional pure states up to size $8\times 8$, we demonstrate
the efficiency, accuracy, and robustness of our proposed methods. Experiments
on the IBM and Quafu Quantum platforms complement these numerical simulations.
Our study opens new avenues in quantum state tomography for two-dimensional
systems using tensor network formalism.",2307.16381v2
2002-11-14,Isometries of quantum states,"This paper treats the isometries of metric spaces of quantum states. We
consider two metrics on the set all quantum states, namely the Bures metric and
the one which comes from the trace-norm. We describe all the corresponding
(nonlinear) isometries and also present similar results concerning the space of
all (non-normalized) density operators.",0211221v1
1997-10-15,"Density Profiles, Casimir Amplitudes and Critical Exponents in the Two Dimensional Potts Model: A Density Matrix Renormalization Study","We use the density matrix renormalization group (DMRG) to perform a detailed
study of the critical properties of the two dimensional Q state Potts model,
including the magnetization and energy-density profiles, bulk and surface
critical exponents and the Casimir amplitudes. We apply symmetry breaking
boundary conditions to a $L \times \infty$ strip and diagonalize the
corresponding transfer matrix for a series of moderately large systems ($L \le
64$) by the DMRG method. The numerically very accurate finite lattice results
are then extrapolated by efficient sequence extrapolation techniques. The
critical density profiles and the Casimir amplitudes are found to follow
precisely the conformal predictions for Q=2 and 3. Similarly, the bulk and
surface critical exponents of the models are in very good agreement with the
conformal and exact values: their accuracy has reached or even exceeded the
accuracy of other available numerical methods. For the Q=4 model both the
profiles and the critical exponents show strong logarithmic corrections, which
are also studied.",9710144v1
2004-09-15,Reply to comment on ``Electronic structure and structural stability study of Li$_3$AlH$_6$'',"The nature of the bonding in Li$_3$AlH$_6$ has been re-examined with
additional analyses using density-functional calculations. From partial density
of states, charge density distribution, charge transfer, electron localization
function, crystal orbital Hamilton population and Mulliken population analyses
it is concluded that the interaction between Li and AlH$_6$ in Li$_3$AlH$_6$ is
ionic as earlier advocated. Based on charge density distribution, electron
localization function, and density of states analyses we earlier suggested that
the interaction between Al and H is largely of the covalent type. However, the
additional analyses indicate that the interaction between Al and H in the
AlH$_6$ structural sub-units is of a mixed covalent ionic (iono-covalent)
character.",0409399v1
2006-01-17,Collective excitations in unconventional charge-density wave systems,"The excitation spectrum of the t-J model is studied on a square lattice in
the large $N$ limit in a doping range where a $d$-$density$-$wave$ (DDW) forms
below a transition temperature $T^\star$. Characteristic features of the DDW
ground state are circulating currents which fluctuate above and condense into a
staggered flux state below $T^\star$ and density fluctuations where the
electron and the hole are localized at different sites. General expressions for
the density response are given both above and below $T^\star$ and applied to
Raman, X-ray, and neutron scattering. Numerical results show that the density
response is mainly collective in nature consisting of broad, dispersive
structures which transform into well-defined peaks mainly at small momentum
transfers. One way to detect these excitations is by inelastic neutron
scattering at small momentum transfers where the cross section (typically a few
per cents of that for spin scattering) is substantially enhanced, exhibits a
strong dependence on the direction of the transferred momentum and a
well-pronounced peak somewhat below twice the DDW gap. Scattering from the
DDW-induced Bragg peak is found to be weaker by two orders of magnitude
compared with the momentum-integrated inelastic part.",0601382v1
2004-05-21,Reflection Symmetries for Multiqubit Density Operators,"For multiqubit density operators in a suitable tensorial basis, we show that
a number of nonunitary operations used in the detection and synthesis of
entanglement are classifiable as reflection symmetries, i.e., orientation
changing rotations. While one-qubit reflections correspond to antiunitary
symmetries, as is known for example from the partial transposition criterion,
reflections on the joint density of two or more qubits are not accounted for by
the Wigner Theorem and are well-posed only for sufficiently mixed states. One
example of such nonlocal reflections is the unconditional NOT operation on a
multiparty density, i.e., an operation yelding another density and such that
the sum of the two is the identity operator. This nonphysical operation is
admissible only for sufficiently mixed states.",0405123v2
2014-08-27,Quantum electrodynamical time-dependent density functional theory on a lattice,"We present a rigorous formulation of the time-dependent density functional
theory for interacting lattice electrons strongly coupled to cavity photons. We
start with an example of one particle on a Hubbard dimer coupled to a single
photonic mode, which is equivalent to the single mode spin-boson model or the
quantum Rabi model. For this system we prove that the electron-photon wave
function is a unique functional of the electronic density and the expectation
value of the photonic coordinate, provided the initial state and the density
satisfy a set of well defined conditions. Then we generalize the formalism to
many interacting electrons on a lattice coupled to multiple photonic modes and
prove the general mapping theorem. We also show that for a system evolving from
the ground state of a lattice Hamiltonian any density with a continuous second
time derivative is locally $v$-representable.",1408.6324v2
2014-12-11,Quantum Control of Many-Body Systems by the Density,"In this work we focus on a recently introduced method [1] to construct the
external potential $v$ that, for a given initial state, produces a prescribed
time-dependent density in an interacting quantum many-body system. We show how
this method can also be used to perform flexible and efficient quantum control.
The simple interpretation of the density (the amount of electrons per volume)
allows us to use our physical intuition to consider interesting control
problems and to easily restrict the search space in optimization problems. The
method's origin in time-dependent density-functional theory makes studies of
large systems possible. We further discuss the generalization of the method to
higher dimensions and its numerical implementation in great detail. We also
present several examples to illustrate the flexibility, and to confirm that the
scheme is efficient and stable even for large and rapid density variations
irrespective of the initial state and interactions.",1412.3794v1
2015-01-21,Exotic topological density waves in cold atomic Rydberg fermions,"Versatile controllability of interactions in ultracold atomic and molecular
gases has now reached an unprecedented era where quantum correlations and
unconventional many-body phases can be studied with no corresponding analogs in
solid state systems. Recent experiments in Rydberg atomic gases have achieved
exquisite control over non-local interactions, allowing novel quantum phases
unreachable with the usual local interactions in atomic systems. Here, we study
Rydberg dressed atomic fermions in a three dimensional optical lattice
predicting the existence of hitherto unheard-of exotic mixed topological
density wave phases. We show that varying spatial range of the non-local
interaction leads to a rich phase diagram containing various bond density
waves, with unexpected spontaneous time-reversal symmetry breaking.
Quasiparticles in these chiral phases experience emergent gauge fields and form
three dimensional quantum Hall and Weyl semimetal states. Remarkably, certain
density waves even exhibit mixed topologies beyond the existing topological
classification. Experimental signatures of density waves and their topological
properties are predicted in time-of-flight measurements.",1501.05320v1
2017-04-06,Density inhomogeneities and Rashba spin-orbit coupling interplay in oxide interfaces,"There is steadily increasing evidence that the two-dimensional electron gas
(2DEG) formed at the interface of some insulating oxides like LaAlO3/SrTiO3 and
LaTiO3/SrTiO3 is strongly inhomogeneous. The inhomogeneous distribution of
electron density is accompanied by an inhomogeneous distribution of the
(self-consistent) electric field confining the electrons at the interface. In
turn this inhomogeneous transverse electric field induces an inhomogeneous
Rashba spin-orbit coupling (RSOC). After an introductory summary on two
mechanisms possibly giving rise to an electronic phase separation accounting
for the above inhomogeneity,we introduce a phenomenological model to describe
the density-dependent RSOC and its consequences. Besides being itself a
possible source of inhomogeneity or charge-density waves, the density-dependent
RSOC gives rise to interesting physical effects like the occurrence of
inhomogeneous spin-current distributions and inhomogeneous quantum-Hall states
with chiral ""edge"" states taking place in the bulk of the 2DEG. The
inhomogeneous RSOC can also be exploited for spintronic devices since it can be
used to produce a disorder-robust spin Hall effect.",1704.01852v1
2018-08-09,On Global Classical Solutions to 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum,"For the initial boundary value problem of compressible barotropic
Navier-Stokes equations in one-dimensional bounded domains with general
density-dependent viscosity and large external force, we prove that there
exists a unique global classical solution with large initial data containing
vacuum. Furthermore, we show that the density is bounded from above
independently of time which in particular yields the large time behavior of the
solution as time tends to infinity: the density and the velocity converge to
the steady states in $L^p$ and in $W^{1,p}$ ($1\le p<+\infty$) respectively.
Moreover, the decay rate in time of the solution is shown to be exponential.
Finally, we also prove that the spatial gradient of the density will blow up as
time tends to infinity when vacuum states appear initially even at one point.",1808.03042v1
2011-11-26,Drude and Superfluid Weights in Extended Systems: the Role of Discontinuities and $δ$-peaks in the One and Two-Body Momentum Densities,"The question of conductivity is revisited. Using the total momentum shift
operator to construct the perturbed many-body Hamiltonian and ground state wave
function the second derivative of the ground state energy with respect to the
perturbing field is expressed in terms of the one and two-body momentum
densities. The distinction between the adiabatic and envelope function
derivatives, hence that between the Drude and superfluid weights can be
introduced in a straightforward manner. It is shown that a discontinuity in the
momentum density leads to a contribution to the Drude weight, but not the
superfluid weight, however a $\delta$-function contribution in the two-body
momentum density (such as in the BCS wave-funtion) contributes to both
quantities. The connection between the discontinuity in the momentum density
and localization is also demonstrated.",1111.6166v2
2019-06-26,Level inversion in kaonic nuclei and the high-density nuclear equation of state,"It is very difficult for any nuclear model to pin down the saturation
property and high-density equation of state (EOS) simultaneously because of
high nonlinearity of the nuclear many-body problem. In this work, we propose,
for the first time, to use the special property of light kaonic nuclei to
characterize the relation between saturation property and high-density EOS.
With a series of relativistic mean-field models, this special property is found
to be the level inversion between orbitals $2S_{1/2}$ and $1D_{5/2}$ in light
kaonic nuclei. This level inversion can serve as a theoretical laboratory to
group the incompressibility at saturation density and the EOS at supra-normal
densities simultaneously.",1906.10868v1
2022-06-20,"The Lieb-Oxford Lower Bounds on the Coulomb Energy, Their Importance to Electron Density Functional Theory, and a Conjectured Tight Bound on Exchange","Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local
functionals of the electron density, on the indirect part of the Coulomb
repulsion energy. The greatest lower bound for a given electron number N
depends monotonically upon N, and the N-> infinity limit is a bound for all N.
These bounds have been shown to apply to the exact density functionals for the
exchange- and exchange-correlation energies that must be approximated for an
accurate and computationally efficient description of atoms, molecules, and
solids. A tight bound on the exact exchange energy has been derived therefrom
for two-electron ground states, and is conjectured to apply to all
spin-unpolarized electronic ground states. Some of these and other exact
constraints have been used to construct two generations of non-empirical
density functionals beyond the local density approximation: the
Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the
strongly constrained and appropriately normed (SCAN) meta-GGA.",2206.09974v1
2023-07-20,Cluster charge-density-wave glass in hydrogen-intercalated TiSe$_{2}$,"The topotactic intercalation of transition-metal dichalcogenides with atomic
or molecular ions acts as an efficient knob to tune the electronic ground state
of the host compound. A representative material in this sense is
1$T$-TiSe$_{2}$, where the electric-field-controlled intercalations of lithium
or hydrogen trigger superconductivity coexisting with the charge-density wave
phase. Here, we use the nuclear magnetic moments of the intercalants in
hydrogen-intercalated 1$T$-TiSe$_{2}$ as local probes for nuclear magnetic
resonance experiments. We argue that fluctuating mesoscopic-sized domains
nucleate already at temperatures higher than the bulk critical temperature to
the charge-density wave phase and display cluster-glass-like dynamics in the
MHz range tracked by the $^{1}$H nuclear moments. Additionally, we observe a
well-defined independent dynamical process at lower temperatures that we
associate with the intrinsic properties of the charge-density wave state. In
particular, we ascribe the low-temperature phenomenology to the collective
phason-like motion of the charge-density wave being hindered by structural
defects and chemical impurities and resulting in a localized oscillating
motion.",2307.10979v1
2023-10-25,Zero-sound modes for the nuclear equation of state at supra-normal densities,"The meaningful correlations between the zero-sound modes and the stiffness of
the nuclear equation of state (EOS) are uncovered in nuclear matter with the
relativistic mean-field theory. It is demonstrated that the high-density
zero-sound modes merely exist in models with the stiff EOS. While the stiff EOS
can be softened by including {\omega}-meson self-interactions (the {\omega}4
term), the weakened coupling of the {\omega}-meson self-interactions reignites
the zero sound at high density. These results suggest that the high-density
zero-sound modes can be used to probe the stiffness of the EOS at supra-normal
densities. The implications and effects of zero sounds are also discussed in
heavy ion collisions and neutron stars.",2310.16759v1
2023-12-21,Equation of state at neutron-star densities and beyond from perturbative QCD,"We explore the consequences of imposing robust thermodynamic constraints
arising from perturbative Quantum Chromodynamics (QCD) when inferring the
dense-matter equation-of-state (EOS). We find that the termination density, up
to which the EOS modeling is performed in an inference setup, strongly affects
the constraining power of the QCD input. This sensitivity in the constraining
power arises from EOSs that have a specific form, with drastic softening
immediately above the termination density followed by a strong stiffening. We
also perform explicit modeling of the EOS down from perturbative-QCD densities
to construct a new QCD likelihood function that incorporates additional
perturbative-QCD calculations of the sound speed and is insensitive to the
termination density, which we make publicly available.",2312.14127v2
2020-12-05,Deep learning Local Reduced Density Matrices for Many-body Hamiltonian Estimation,"Human experts cannot efficiently access the physical information of quantum
many-body states by simply ""reading"" the coefficients, but have to reply on the
previous knowledge such as order parameters and quantum measurements. In this
work, we demonstrate that convolutional neural network (CNN) can learn from the
coefficients of local reduced density matrices to estimate the physical
parameters of the many-body Hamiltonians, such as coupling strengths and
magnetic fields, provided the states as the ground states. We propose QubismNet
that consists of two main parts: the Qubism map that visualizes the ground
states (or the purified reduced density matrices) as images, and a CNN that
maps the images to the target physical parameters. By assuming certain
constraints on the training set for the sake of balance, QubismNet exhibits
impressive powers of learning and generalization on several quantum spin
models. While the training samples are restricted to the states from certain
ranges of the parameters, QubismNet can accurately estimate the parameters of
the states beyond such training regions. For instance, our results show that
QubismNet can estimate the magnetic fields near the critical point by learning
from the states away from the critical vicinity. Our work illuminates a
data-driven way to infer the Hamiltonians that give the designed ground states,
and therefore would benefit the existing and future generalizations of quantum
technologies such as Hamiltonian-based quantum simulations and state
tomography.",2012.03019v2
2021-01-25,Degenerated Liouvillians and Steady-State Reduced Density Matrices,"Symmetries in an open quantum system lead to degenerated Liouvillian that
physically implies the existence of multiple steady states. In such cases,
obtaining the initial condition independent stead states is highly nontrivial
since any linear combination of the \emph{true} asymptotic states, which may
not necessarily be a density matrix, is also a valid asymptote for the
Liouvillian. Thus, in this work we consider different approaches to obtain the
\emph{true} steady states of a degenerated Liouvillian. In the ideal scenario,
when the open system symmetry operators are known we show how these can be used
to obtain the invariant subspaces of the Liouvillian and hence the steady
states. We then discuss two other approaches that do not require any knowledge
of the symmetry operators. These could be a powerful tool to deal with quantum
many-body complex open systems. The first approach which is based on
Gramm-Schmidt orthonormalization of density matrices allows us to obtain
\emph{all} the steady states, whereas the second one based on large deviations
allows us to obtain the non-degenerated maximum and minimum current-carrying
states. We discuss our method with the help of an open para-Benzene ring and
examine interesting scenarios such as the dynamical restoration of Hamiltonian
symmetries in the long-time limit and apply the method to study the
eigenspacing statistics of the nonequilibrium steady state.",2101.10236v1
2020-01-30,Accurate Ground State Electronic and Related Properties of Hexagonal Boron Nitride (h-BN),"We present an ab initio, self consistent density functional theory (DFT)
description of ground state electronic and related properties of hexagonal
boron nitride (hex-BN). We used a local density approximation (LDA) potential
and the linear combination of atomic orbitals (LCAO) formalism. We rigorously
implemented the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma
and Franklin (BZW-EF). The method ensures a generalized minimization of the
energy that is far beyond what can be obtained with self-consistency iterations
using a single basis set. The method leads to the ground state of the material,
in a verifiable manner, without employing over-complete basis sets.
Consequently, our results possess the full, physical content of DFT, as per the
second DFT theorem. We report the ground state band structure, band gap, total
and partial densities of states, and electron and hole effective masses. Our
calculated, indirect band gap of 4.37 eV,obtained with room temperature
experimental lattice constant, is in agreement with the measured value of 4.3
eV. The valence band maximum is slightly to the left of the K point, while the
conduction band minimum is at the M point. Our calculated total width of the
valence and total and partial densities of states are in agreement with
corresponding, experimental findings.",2001.11596v1
1996-03-04,Density-matrix renormalization-group method in momentum space,"A momentum-space approach of the density-matrix renormalization-group (DMRG)
method is developed. Ground state energies of the Hubbard model are evaluated
using this method and compared with exact diagonalization as well as quantum
Monte-Carlo results. It is shown that the momentum-space DMRG is a very useful
numerical tool for studying the Hubbard model and other fundamental models of
interacting electrons in two dimensions. For the Hubbard model in two
dimensions, the momentum-space DMRG method reproduces accurately the exact
diagonalization results of ground state energies on a $4\times 4$ lattice and
yields new upper bounds of ground state energies on an 8$\times$8 lattice.",9603020v1
2001-04-13,Quasiparticle excitation in and around the vortex core of underdoped YBa_2Cu_4O_8 studied by site-selective NMR,"We report a site-selective ^{17}O spin-lattice relaxation rate T_1^{-1} in
the vortex state of underdoped YBa_2Cu_4O_8. We found that T_1^{-1} at the
planar sites exhibits an unusual nonmonotonic NMR frequency dependence. In the
region well outside the vortex core, T_1^{-1} cannot be simply explained by the
density of states of the Doppler-shifted quasiparticles in the d-wave
superconductor. Based on T_1^{-1} in the vortex core region, we establish
strong evidence that the local density of states within the vortex core is
strongly reduced.",0104252v2
2005-09-26,Consistent particle-based algorithm with a non-ideal equation of state,"A thermodynamically consistent particle-based model for fluid dynamics with
continuous velocities and a non-ideal equation of state is presented. Excluded
volume interactions are modeled by means of biased stochastic multiparticle
collisions which depend on the local velocities and densities. Momentum and
energy are exactly conserved locally. The equation of state is derived and
compared to independent measurements of the pressure. Results for the kinematic
shear viscosity and self-diffusion constants are presented. A caging and
order/disorder transition is observed at high densities and large collision
frequency.",0509631v1
2004-09-27,Criteria of partial separability of multipartite qubit mixed-states,"In this paper, we discuss the partial separability and its criteria problems
of multipartite qubit mixed-states. First we strictly define what is the
partial separability of a multipartite qubit system. Next we give a reduction
way from N-partite qubit density matrixes to bipartite qubit density matrixes,
and prove a necessary condition that a N-partite qubit mixed-state to be
partially separable is its reduction to satisfy the PPT condition.
  PACC numbers: 03.67.Mn; 03.65.Ud; 03.67.Hk",0409182v2
2008-01-11,A Complete Set of Local Invariants for a Family of Multipartite Mixed States,"We study the equivalence of quantum states under local unitary
transformations by using the singular value decomposition. A complete set of
invariants under local unitary transformations is presented for several classes
of tripartite mixed states in KxMxN composite systems. Two density matrices in
the same class are equivalent under local unitary transformations if and only
if all these invariants have equal values for these density matrices.",0801.1706v1
2008-11-19,Out-of-equilibrium bosons on a one-dimensional optical random lattice,"We study the transport properties of a one-dimensional hard-core boson
lattice gas coupled to two particle reservoirs at different chemical potentials
generating a current flow through the system. In particular, the influence of
random fluctuations of the underlying lattice on the stationary state
properties is investigated. We show analytically that the steady-state density
presents a linear profile. The local steady-state current obeys the Fourier law
$j=-\kappa(\tau)\nabla \rho $ where $\tau$ is a typical timescale of the
lattice fluctuations and $\nabla \rho$ the density gradient imposed %on the
system by the reservoirs.",0811.3079v1
2011-06-22,Low temperature properties of the infinite-dimensional attractive Hubbard model,"We investigate the attractive Hubbard model in infinite spatial dimensions by
combining dynamical mean-field theory with a strong-coupling continuous-time
quantum Monte Carlo method. By calculating the superfluid order parameter and
the density of states, we discuss the stability of the superfluid state. In the
intermediate coupling region above the critical temperature, the density of
states exhibits a heavy fermion behavior with a quasi-particle peak in the
dense system, while a dip structure appears in the dilute system. The formation
of the superfluid gap is also addressed.",1106.4559v1
2013-11-28,Topological Lifshitz phase transition in effective model of QCD with chiral symmetry non-restoration,"The topological Lifshitz phase transition is studied systematically within an
effective model of QCD, in which the chiral symmetry, broken at zero
temperature, is not restored at high temperature and/or baryon chemical
potential. It is found that during phase transition the quark system undergoes
a first-order transition from low density fully-gapped state to high density
state with Fermi sphere which is protected by momentum-space topology. The
Lifshitz phase diagram in the plane of temperature and baryon chemical
potential is established. The critical behaviors of various equations of state
are determined.",1311.7354v1
2014-11-14,Two-leg fermionic Hubbard ladder system in the presence of state-dependent hopping,"We study a two-leg fermionic Hubbard ladder model with a state-dependent
hopping. We find that, contrary to the case without a state-dependent hopping,
for which the system has a superfluid nature regardless of the sign of the
interaction at incommensurate filling, in the presence of such a hopping a
spin-triplet superfluid, spin- density wave and charge-density wave phases
emerge. We examine our results in the light of recent experiments on
periodically-driven optical lattices in cold atoms. We give protocols allowing
us to realize the spin-triplet superfluid elusive in the cold atoms.",1411.3905v2
2015-05-08,Universal structure of two and three dimensional self-gravitating systems in the quasi-equilibrium state,"We study a universal structure of two and three dimensional self-gravitating
systems in the quasi-equilibrium state. It is shown numerically that the two
dimensional self-gravitating system in the quasi-equilibrium state has the same
kind of density profile as the three dimensional one. We develop a
phenomenological model to describe this universal structure by using a special
Langevin equation with a distinctive random noise to self-gravitating systems.
We find that the density profile derived theoretically is consistent well with
results of observations and simulations.",1505.02014v1
2014-05-04,FRW cosmology with the extended Chaplygin gas,"In this paper, we propose extended Chaplygin gas equation of state for which
it recovers barotropic fluid with quadratic equation of state. We use numerical
method to investigate the behavior of some cosmological parameters such as
scale factor, Hubble expansion parameter, energy density and deceleration
parameter. We also discuss about the resulting effective equation of state
parameter. Using density perturbations we investigate the stability of the
theory.",1405.0667v2
2014-06-02,Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring,"We consider a one-dimensional totally asymmetric exclusion process on a ring
with extended inhomogeneities, consisting of several segments with different
hopping rates. Depending upon the underlying inhomogeneity configurations and
for moderate densities, our model displays both localised (LDW) and delocalised
(DDW) domain walls and delocalisation transitions of LDWs in the steady states.
Our results allow us to construct the possible steady state density profiles
for an arbitrary number of segments with unequal hopping rates. We explore the
scaling properties of the fluctuations of LDWs and DDWs.",1406.0251v2
2017-11-08,On orbital stability of ground states for finite crystals in fermionic Schrödinger--Poisson model,"We consider the Schr\""odinger--Poisson--Newton equations for finite crystals
under periodic boundary conditions with one ion per cell of a lattice. The
electron field is described by the $N$-particle Schr\""odinger equation with
antisymmetric wave function.
  Our main results are i) the global dynamics with moving ions, and ii) the
orbital stability of periodic ground state under a novel Jellium and
Wiener-type conditions on the ion charge density. Under Jellium condition both
ionic and electronic charge densities of the ground state are uniform.",1711.02938v1
2019-07-04,Generalized Anti-Wick Quantum States,"The purpose of this Note is to study a simple class of mixed states and the
corresponding density operators (matrices). These operators, which we call
quite Toeplitz density operators correspond to states obtained from a fixed
function (""window"") by position-momentum translations, and reduce in the
simplest case to the anti-Wick operators considered long ago by Berezin. The
rigorous study of Toeplitz operators requires the use of classes of functional
spaces defined by Feichtinger.",1907.02471v1
2020-10-30,Analysis of doorway states in a graphene structure,"Doorway states, which are related to the strength function phenomenon and
giant resonances, arise when two systems interact, one with a high density
eigenvalue spectrum and the other with a comparatively low density. These
concepts, first studied in nuclear physics in the 40's, are here analyzed from
a theoretical point of view in special and simple graphene structures, obtained
after applying appropriate voltages to a graphene sheet. The influence of the
doorway states on the electronic transport in these systems is also studied. To
analyze these effects we consider a two-dimensional model of two potential
barriers of equal height but very different widths separated by a well.",2010.16057v1
2022-09-11,On genuine entanglement for tripartite systems,"We investigate the genuine entanglement in tripartite systems based on
partial transposition and the norm of correlation tensors of the density
matrices. We first derive an analytical sufficient criterion to detect genuine
entanglement of tripartite qubit quantum states combining with the partial
transposition of the density matrices. Then we use the norm of correlation
tensors to study genuine entanglement for tripartite qudit quantum states and
obtain a genuine entanglement criterion by constructing certain matrices. With
detailed examples our results are seen to be able to detect more genuine
tripartite entangled states than previous studies.",2209.04768v1
2024-01-25,Exact surface energy of the Hubbard model with unparallel boundary magnetic fields,"In this paper, we study the exact physical quantities in the thermodynamic
limit of the one-dimensional Hubbard model with unparallel boundary magnetic
fields based on the off-diagonal Bethe ansatz solution. At the half-filling, we
obtain the different patterns of Bethe roots of the reduced Bethe ansatz
equations for the different boundary parameters. According to them, we obtain
the densities of states, ground state energy density and surface energy. Our
results show that the system has the stable boundary bound states when the
boundary magnetic fields satisfy some constraints.",2401.14356v1
1994-06-17,Disorder effect in low dimensional superconductors,"The quasiparticle density of states (DOS), the energy gap, the superfluid
density $\rho_s$, and the localization effect in the s- and d-wave
superconductors with non-magnetic impurity in two dimensions (2D) are studied
numerically. For strong (unitary) scatters, we find that it is the range of the
scattering potential rather than the symmetry of the superconducting pairing
which is more important in explaining the impurity dependences of the specific
heat and the superconducting transition temperature in Zn doped YBCO. The
localization length is longer in the d-wave superconducting state than in the
normal state, even in the vicinity of the Fermi energy.",9406075v1
2002-09-19,Indirect Mn-Mn pair interaction induces pseudogap in density of states of Al(Si)-Mn approximants,"The effect on the electronic structure of an indirect Mn-Mn interaction
mediated by the valence states and the sp-d hybridisation is presented. In
Al(rich)-Mn phases related to quasicrystals (Al12Mn, o-Al6Mn, alpha-Al9Mn2Si),
this indirect interaction creates a Hume-Rothery pseudogap in the density of
states together with a minimisation of the band energy. It is shown that Mn-Mn
interaction up to distances around 1.0-2.0 nm plays an essential role in
stabilizing related quasicrystal structures.",0209458v1
2006-06-06,On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors,"We discuss a scheme for reconstructing experimentally the diagonal elements
of the density matrix of quantum optical states. Applications to PDC heralded
photons, multi-thermal and attenuated coherent states are illustrated and
discussed in some details.",0606046v1
2013-05-04,Negative Conditional Entropy of Post-Selected States,"We define a quantum entropy conditioned on post-selection which has the von
Neumann entropy of pure states as a special case. This conditional entropy can
take negative values which is consistent with part of a quantum system
containing less information than the whole which can be in a pure state. The
definition is based on generalised density operators for postselected
ensembles. The corresponding density operators are consistent with the quantum
generalisation of classical conditional probabilities following Dirac s
formalism of quasiprobability distributions.",1305.0932v2
2016-01-28,Discrete Density of States,"By considering the quantum-mechanically minimum allowable energy interval, we
exactly count number of states (NOS) and introduce discrete density of states
(DOS) concept for a particle in a box for various dimensions. Expressions for
bounded and unbounded continua are analytically recovered from discrete ones.
Even though substantial fluctuations prevail in discrete DOS, they're almost
completely flatten out after summation or integration operation. It's seen that
relative errors of analytical expressions of bounded/unbounded continua rapidly
decrease for high NOS values (weak confinement or high energy conditions),
while the proposed analytical expressions based on Weyl's conjecture always
preserve their lower error characteristic.",1602.05219v1
2020-09-11,Quantum Dot in a Hybrid Structure with Dipolar Excitons,"Electron states in a quantum dot (QD) located near a 2D system of dipolar
excitons are perturbed by fluctuations of the exciton density caused by the
electron-exciton interaction. This results in the frequency changes of electron
transitions in a QD. The frequency depends on the exciton density, as well as
on the exciton gas phase state. In the present work, the shifts of the two
lowest QD energy levels are found both in the normal state of the exciton
system and for the Bose-Einstein condensation (BEC) regime.",2009.05500v2
2020-03-17,Biexciton State Energies from Many-Body Perturbation Theory Based on Density Functional Theory Simulation,"We develop a method for computing self-energy of a biexciton state in a
semiconductor nanostructure using many-body perturbation theory (MBPT) based on
the density functional theory (DFT) simulation. We compute energies of
low-energy biexciton states composed of singlet excitons in the chiral
single-wall carbon nanotubes (SWCNT), such as (6,2), (6,5) and (10,5). In all
cases we find a small decrease in the biexciton gap: -0.045 $eV$ in (6,2),
which is 4.59\% of the non-interacting biexciton gap; -0.041 $eV$ in (6,5),
which is 4.47\% of the non-interacting gap and -0.036 $eV$ in (10,5), which is
4.31\%.",2003.07986v1
2022-02-13,Detection of tripartite entanglement based on principal basis matrix representations,"We study the entanglement in tripartite quantum systems by using the
principal basis matrix representations of density matrices. Using the Schmidt
decomposition and local unitary transformation, we first convert the general
states to simpler forms and then construct some special matrices from the
correlation tensors of the simplified density matrices. Based on the different
linear combinations of these matrices, necessary conditions are presented to
detect entanglement of tripartite states. Detailed examples show that our
method can detect more entangled states than previous ones.",2202.06176v2
2022-08-09,Zero-energy states in graphene quantum dot with wedge disclination,"We investigate the effects of wedge disclination on charge carriers in
circular graphene quantum dots subjected to a magnetic flux. Using the
asymptotic solutions of the energy spectrum for large arguments, we approximate
the scattering matrix elements, and then study the density of states. It is
found that the density of states shows several resonance peaks under various
conditions. In particular, it is shown that the wedge disclination is able to
change the amplitude, width, and positions of resonance peaks.",2208.04920v1
2012-07-16,A Spectral Approach to the Relativistic Inverse Stellar Structure Problem,"A new method for solving the relativistic inverse stellar structure problem
is presented. This method determines a spectral representation of the unknown
high density portion of the stellar equation of state from a knowledge of the
total masses M and radii R of the stars. Spectral representations of the
equation of state are very efficient, generally requiring only a few spectral
parameters to achieve good accuracy. This new method is able, therefore, to
determine the high density equation of state quite accurately from only a few
accurately measured [M,R] data points. This method is tested here by
determining the equations of state from mock [M,R] data computed from tabulated
""realistic"" neutron-star equations of state. The spectral equations of state
obtained from these mock data are shown to agree on average with the originals
to within a few percent (over the entire high density range of the neutron-star
interior) using only two [M,R] data points. Higher accuracies are achieved when
more data are used. The accuracies of the equations of state determined in
these examples are shown to be nearly optimal, in the sense that their errors
are comparable to the errors of the best-fit spectral representations of these
realistic equations of state.",1207.3744v2
2005-04-22,Evolution of the density of states at EF of Bi2-yPbySr2-xLaxCuO6+d and Bi2Sr2-xLaxCuO6+d cuprates with hole doping,"Bi2Sr2-xLaxCuO6+d and Bi2-yPbySr2-xLaxCuO6+d high-Tc superconductors in a
wide doping range from overdoped to heavily underdoped were studied by X-ray
absorption and photo-emission spectroscopy. The hole concentration p was
determined by an analysis of the Cu L3-absorption edge. Besides the occupied
density of states derived from photoemission, the un-occupied density of states
was determined from the prepeak of the O K-absorption edge. Both, the occupied
as well as the unoccupied density of states reveal the same dependence on hole
doping, i.e. a continuous increase with increasing doping in the hole
underdoped region and a constant density in the hole overdoped region. By
comparing these results of single-layer BSLCO with previous results on
single-layer LSCO it could be argued that besides the localized holes on Cu
sites the CuO2-planes consist of two types of doped holes, from which the
so-called mobile holes determine the intensity of the prepeak of the O 1s
absorption edge.",0504590v2
2023-04-27,Nonzero angular momentum density wave phases in SU($N$) fermions with singlet-bond and triplet-current interactions,"We employ the sign-problem-free projector determinant quantum Monte Carlo
method to study a microscopic model of SU($N$) fermions with singlet-bond and
triplet-current interactions on the square lattice. We find the gapped singlet
$p_x$ and gapless triplet $d_{x^2-y^2}$ density wave states in the half-filled
$N=4$ model. Specifically, the triplet $d_{x^2-y^2}$ density wave order is
observed in the weak triplet-current interaction regime. As the triplet-current
interaction strength is further increased, our simulations demonstrate a
transition to the singlet $p_x$ density wave state, accompanied by a gapped
mixed-ordered area where the two orders coexist. With increasing singlet-bond
interaction strength, the triplet $d_{x^2-y^2}$-wave order persists up to a
critical point after which the singlet $p_x$ density wave state is stabilized,
while the ground state is disordered in between the two ordered phases. The
analytical continuation is then performed to derive the single-particle
spectrum. In the spectra of triplet $d_{x^2-y^2}$ and singlet $p_x$ density
waves, the anisotropic Dirac cone and the parabolic shape around the Dirac
point are observed, respectively. As for the mixed-ordered area, a
single-particle gap opens and the velocities remain anisotropic at the Dirac
point.",2304.14033v1
2011-01-17,Phase diagram of hard-core bosons on a frustrated zig-zag ladder,"We study hard-core bosons with unfrustrated nearest-neighbor hopping $t$ and
repulsive interaction $V$ on a zig-zag ladder. As a function of the boson
density $\rho$ and $V/t$, the ground state displays different quantum phases. A
standard one-component Tomonaga-Luttinger liquid is stable for $\rho<1/3$ (and
$\rho>2/3$) at any value of $V/t$. At commensurate densities $\rho=1/3$, $1/2$,
and $2/3$ insulating (crystalline) phases are stabilized for a sufficiently
large interaction $V$. For intermediate densities $1/3<\rho<2/3$ and large
$V/t$, the ground state shows a clear evidence of a bound state of two bosons,
implying gapped single-particle excitations but gapless excitations of boson
pairs. Here, the low-energy properties may be described by a two-component
Tomonaga-Luttinger liquid with a finite gap in the antisymmetric sector.
Finally, for the same range of boson densities and weak interactions, the
system is again a one-component Tomonaga-Luttinger liquid with no evidence of
any breaking of discrete symmetries, in contrast to the frustrated case, where
a ${\cal Z}_2$ symmetry breaking has been predicted.",1101.3217v1
2012-12-18,Inelastic neutron scattering study of phonon density of states in nanostructured Si1xGex thermoelectrics,"Inelastic neutron scattering measurements are utilized to explore relative
changes in the generalized phonon density of states of nanocrystalline Si1xGex
thermoelectric materials prepared via ball milling and hot-pressing techniques.
Dynamic signatures of Ge clustering can be inferred from the data by
referencing the resulting spectra to a density functional theoretical model
assuming homogeneous alloying via the virtual-crystal approximation.
Comparisons are also presented between as-milled Si nanopowder and bulk,
polycrystalline Si where a preferential low-energy enhancement and lifetime
broadening of the phonon density of states appear in the nanopowder. Negligible
differences are however observed between the phonon spectra of bulk Si and hot
pressed, nanostructured Si samples suggesting that changes to the single phonon
dynamics above 4 meV play only a secondary role in the modified heat conduction
of this compound.",1212.4431v1
2016-01-29,Why state of quantum system is fully defined by density matrix,"We show that probabilities of results of all possible measurements performing
on a quantum system depend on the system's state only through its density
matrix. Therefore all experimentally available information about the state
contains in the density matrix. In this study, we do not postulate that
measurements obey some given formalism (such as observables, positive-operator
valued measures, etc.), and do not use Born rule. The process of measurement is
considered in a fully operational manner---as an interaction of a measured
system with some black-box apparatus. The key point of our approach is the
proof that, for improper mixtures, the expected value of any measurement
depends linearly on the reduced density function. Such a proof is achieved by
considering appropriate thought experiments. We demonstrate that Born rule can
be derived as a natural consequence of our results.",1601.08205v1
2011-11-25,Soft nuclear equation-of-state from heavy-ion data and implications for compact stars,"Measurements of kaon production at subthreshold energies in heavy-ion
collisions point to a soft nuclear equation-of-state for densities up to 2-3
times nuclear matter saturation density. We apply these results to study the
implications on compact star properties, especially in the context of the
recent measurement of the two solar mass pulsar PSR J1614-2230. The
implications are two-fold: Firstly, the heavy-ion results constrain nuclear
matter at densities relevant to light neutron stars. Hence, a radius
measurement could provide information about the density dependence of the
symmetry energy which is a crucial quantity in nuclear physics. Secondly, the
information on the nucleon potential obtained from the analysis of the
heavy-ion data can be combined with restrictions from causality on the nuclear
equation-of-state. From this we can derive a limit for the highest allowed
compact star mass of three solar masses.",1111.6058v2
2021-11-18,Density of states approach for lattice field theory with topological terms,"We discuss a new density of states (DoS) approach to solve the complex action
problem that is caused by topological terms. The key ingredient is to use open
boundary conditions for (at least) one of the directions, such that the
quantization of the topological charge is lifted and the density becomes a
regular function. We employ the DoS FFA method and compute the density of
states as a function of the topological charge. Subsequent integration with
suitable factors gives rise to the observables we are interested in. We here
explore two test cases: U(1) lattice gauge theory in two dimensions, and SU(2)
lattice gauge theory in four dimensions. Since the 2-d case has an exact
solution we may use it to assess the method, in particular to establish the
equivalence of the open boundary results with the usual choice of periodic
boundary conditions. The SU(2) case is a first step of developing the
techniques towards their eventual application in full QCD.",2111.09535v1
2023-09-25,Non-equilibrium steady states of electrolyte interfaces,"The non-equilibrium steady states of a semi-infinite quasi-one-dimensional
univalent binary electrolyte solution, characterised by non-vanishing electric
currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory.
Exact analytical expressions of the electric field, the charge density and the
number density are derived, which depend on the electric current density as a
parameter. From a non-equilibrium version of the Grahame equation, which
relates the total space charge per cross-sectional area and the corresponding
contribution of the electric potential drop, the current-dependent differential
capacitance of the diffuse layer is derived. In the limit of vanishing electric
current these results reduce to those within Gouy-Chapman theory. It is shown
that improperly chosen boundary conditions lead to non-equilibrium steady state
solutions of the PNP equations with negative ion number densities. A necessary
and sufficient criterion on surface conductivity constitutive relations is
formulated which allows one to detect such unphysical solutions.",2309.14126v2
2019-12-02,Phase behavior of a cell fluid model with modified morse potential,"The present manuscript gives a theoretical description of the first-order
phase transition in a cell fluid model with a modified Morse potential and
additional repulsive interaction. In the framework of the grand canonical
ensemble, the equation of state of the system in terms of chemical
potential-temperature and terms of density-temperature is calculated for a wide
range of density and temperature. The behavior of the chemical potential as a
function of temperature and density is investigated. The maximum and minimum
admissible values of the chemical potential, which approach each other with
decreasing temperature, are exhibited. The existence of a liquid-gas phase
transition in a limited temperature range below the critical $T_c$ is
established.",1912.00769v1
2001-10-12,From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states,"The self-consistent propagation of generalized $D_{1}$ [coherent-product]
states and of a class of gaussian density matrix generalizations is examined,
at both zero and finite-temperature, for arbitrary interactions between the
localized lattice (electronic or vibronic) excitations and the phonon modes. It
is shown that in all legitimate cases, the evolution of $D_{1}$ states reduces
to the disentangled evolution of the component $D_{2}$ states. The
self-consistency conditions for the latter amount to conditions for
decoherence-free propagation, which complement the $D_{2}$ Davydov soliton
equations in such a way as to lift the nonlinearity of the evolution for the
on-site degrees of freedom. Although it cannot support Davydov solitons, the
coherent-product ansatz does provide a wide class of exact density-matrix
solutions for the joint evolution of the lattice and phonon bath in compatible
systems. Included are solutions for initial states given as a product of a
[largely arbitrary] lattice state and a thermal equilibrium state of the
phonons. It is also shown that external pumping can produce self-consistent
Frohlich-like effects. A few sample cases of coherent, albeit not solitonic,
propagation are briefly discussed.",0110084v1
2014-11-28,Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix,"We describe a direct method to determine the negativity of an arbitrary
two-qubit state in experiments. The method is derived by analyzing the relation
between the purity, negativity, and a universal entanglement witness for
two-qubit entanglement. We show how the negativity of a two-qubit state can be
calculated from just three experimentally accessible moments of the partially
transposed density matrix of a two-photon state. Moreover, we show that the
negativity can be given as a function of only six invariants, which are linear
combinations of nine invariants from the complete set of 21 fundamental and
independent two-qubit invariants. We analyze the relation between these moments
and the concurrence for some classes of two-qubit states (including the X
states, as well as pure states affected by the amplitude-damping and
phase-damping channels). We also discuss the possibility of using the universal
entanglement witness as an entanglement measure for various classes of
two-qubit states. Moreover, we analyze how noise affects the estimation of
entanglement via this witness.",1411.7977v2
2018-10-19,Electrical dipole on gapped graphene: Bound states and atomic collapse,"We investigate the energy spectrum, wave functions, and local density of
states of an electrical dipole placed on a sheet of gapped graphene as function
of the charge strength Z{\alpha} for different sizes of the dipole and for
different regularization parameters. The dipole is modeled as consisting of a
positive and negative charge. Bound states are found within the gap region with
some energy levels that anticross and others that cross as function of the
impurity strength Z{\alpha}. The anticrossings are more pronounced and move to
higher charges Z{\alpha} when the length of the dipole decreases. These energy
levels turn into atomic collapse states when they enter the positive (or
negative) energy continuum. A smooth transition from the single-impurity
behavior to the dipole one is observed: The states diving towards the continuum
in the single-impurity case are gradually replaced by a series of anticrossings
that represent a continuation of the diving states in the single-impurity case.
By studying the local density of states at the edge of the dipole we show how
the series of anticrossings persist in the positive and negative continuum.",1810.08456v1
2009-03-31,Global Radiation-Magnetohydrodynamic Simulations of Black Hole Accretion Flow and Outflow: Unified Model of Three States,"Black-hole accretion systems are known to possess several distinct modes (or
spectral states), such as low/hard state, high/soft state, and so on. Since the
dynamics of the corresponding flows is distinct, theoretical models were
separately discussed for each state. We here propose a unified model based on
our new, global, two-dimensional radiation-magnetohydrodynamic simulations. By
controlling a density normalization we could for the first time reproduce three
distinct modes of accretion flow and outflow with one numerical code. When the
density is large (model A), a geometrically thick, very luminous disk forms, in
which photon trapping takes place. When the density is moderate (model B), the
accreting gas can effectively cool by emitting radiation, thus generating a
thin disk, i.e., the soft-state disk. When the density is too low for radiative
cooling to be important (model C), a disk becomes hot, thick, and faint; i.e.,
the hard-state disk. The magnetic energy is amplified within the disk up to
about twice, 30%, and 20% of the gas energy in models A, B, and C,
respectively. Notably, the disk outflows with helical magnetic fields, which
are driven either by radiation pressure force or magnetic pressure force, are
ubiquitous in any accretion modes. Finally, our simulations are consistent with
the phenomenological alpha-viscosity prescription, that is, the disk viscosity
is proportional to the pressure.",0903.5364v1
2014-03-20,A formal method for identifying distinct states of variability in time-varying sources: SgrA* as an example,"Continuously time variable sources are often characterized by their power
spectral density and flux distribution. These quantities can undergo dramatic
changes over time if the underlying physical processes change. However, some
changes can be subtle and not distinguishable using standard statistical
approaches. Here, we report a methodology that aims to identify distinct but
similar states of time variability. We apply this method to the Galactic
supermassive black hole, where 2.2 um flux is observed from a source associated
with SgrA*, and where two distinct states have recently been suggested. Our
approach is taken from mathematical finance and works with conditional flux
density distributions that depend on the previous flux value. The discrete,
unobserved (hidden) state variable is modeled as a stochastic process and the
transition probabilities are inferred from the flux density time series. Using
the most comprehensive data set to date, in which all Keck and a majority of
the publicly available VLT data have been merged, we show that SgrA* is
sufficiently described by a single intrinsic state. However the observed flux
densities exhibit two states: a noise-dominated and a source-dominated one. Our
methodology reported here will prove extremely useful to assess the effects of
the putative gas cloud G2 that is on its way toward the black hole and might
create a new state of variability.",1403.5289v1
2021-11-13,Global Stability and Non-Vanishing Vacuum States of 3D Compressible Navier-Stokes Equations,"We investigate the global stability and non-vanishing vacuum states of large
solutions to the compressible Navier-Stokes equations on the torus
$\mathbb{T}^3$, and the main novelty of this work is three-fold: First, under
the assumption that the density $\rho({\bf{x}}, t)$ verifies $\sup_{t\geq
0}\|\rho(t)\|_{L^\infty}\leq M$, it is shown that the solutions converge to
equilibrium state exponentially in $L^2$-norm. Second, by employing some new
thoughts, we also show that the density converges to its equilibrium state
exponentially in $L^\infty$-norm if additionally the initial density
$\rho_0({\bf{x}})$ satisfies
$\inf_{{\bf{x}}\in\mathbb{T}^3}\rho_0({\bf{x}})\geq c_0>0$. Finally, we prove
that the vacuum states will not vanish for any time provided that the vacuum
states are present initially. This phenomenon is totally new and somewhat
surprising, and particularly is in contrast to the previous work of [H. L. Li
et al., Commun. Math. Phys., 281 (2008), 401-444], where the authors showed
that the vacuum states must vanish within finite time for the 1D compressible
Navier-Stokes equations with density-dependent viscosity
$\mu(\rho)=\rho^\alpha$ with $\alpha>1/2$.",2111.07028v3
2023-06-28,Smectic Pair Density Wave Order in EuRbFe4As4,"The pair density wave (PDW) is a novel superconducting state in which Cooper
pairs carry center-of-mass momentum in equilibrium, leading to the breaking of
translational symmetry. Experimental evidence for such a state exists in high
magnetic field and in some materials that feature density wave orders that
explicitly break translational symmetry. However, evidence for a zero-field PDW
state that exists independent of other spatially ordered states has so far been
elusive. Here, we show that such a state exists in the iron pnictide
superconductor EuRbFe4As4 (Eu-1144), a material that features coexisting
superconductivity (Tc ~ 37K) and magnetism (Tm ~ 15 K). We show from the
Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) measurements that
the superconducting gap at low temperature has long-range, unidirectional
spatial modulations with an incommensurate period of ~8 unit cells. Upon
raising the temperature above Tm, the modulated superconductor disappears, but
a uniform superconducting gap survives to Tc. When an external magnetic field
is applied, gap modulations disappear inside the vortex halo. The SI-STM and
bulk measurements show the absence of other density wave orders, showing that
the PDW state is a primary, zero-field superconducting state in this compound.
Both four-fold rotational symmetry and translation symmetry are recovered above
Tm, indicating that the PDW is a smectic order.",2306.16570v1
2003-01-23,Revivals and entanglement from initially entangled mixed states of a damped Jaynes-Cummings model,"An exact density matrix of a phase-damped Jaynes - Cummings model (JCM) with
entangled Bell-like initial states formed from a model two-state atom and sets
of adjacent photon number states of a single mode radiation field is presented.
The entanglement of the initial states and the subsequent time evolution is
assured by finding a positive lower bound on the concurrence of local 2x2
projections of the full 2xinfinity JCM density matrix. It is found that the
time evolution of the lower bound of the concurrence systematically captures
the corresponding collapse and revival features in atomic inversion, relative
entropies of atomic and radiation, mutual entropy, and quantum deficit. The
atom and radiation subsystems exhibit alternating sets of collapses and
revivals in a complementary fashion due to the initially mixed states of the
atom and radiation employed here. This is in contrast with the result obtained
when the initial state of the dissipationless system is a factored pure state
of atom and radiation, where the atomic and radiation entropies are necessarily
the same. The magnitudes of the entanglement lower bound and the atomic and
radiation revivals become larger as both magnitude and phase of the Bell-like
initial state contribution increases. The time evolution of the entropy
difference of the total system and that of the radiation subsystem exhibits
negative regions called ""supercorrelated"" states which do not appear in the
atomic subsystem. Entangled initial states are found to enhance this
supercorrelated feature. Finally, the effect of phase damping is to randomize
both the subsystems for asymptotically long times .",0301126v1
2009-01-14,Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points,"We study the effects of interference on the quenching dynamics of a
one-dimensional spin 1/2 $XY$ model in the presence of a transverse field
($h(t)$) which varies sinusoidally with time as $h = h_0\cos{\omega t}$, with
$|t| \leq t_f = \pi/\omega$. We also consider the situation where the magnetic
field consists of an oscillatory as well as a linearly varying component, i.e.,
$h(t) = h_0\cos{\omega t} + t/\tau$. Our purpose is to estimate the defect
density and the local entropy density in the final state if the system is
initially prepared in its ground state. For a single crossing through the
quantum critical point with $h = h_0\cos{\omega t}$, the density of defects in
the final state is calculated by mapping the dynamics to an equivalent Landau
Zener problem by linearizing near the crossing point, and is found to vary as
$\sqrt{\omega}$ in the limit of small $\omega$. On the other hand, the local
entropy density is found to attain a maximum as a function of $\omega$ near a
characteristic scale $\omega_0$. Extending to the situation of multiple
crossings, we show that the non-trivial interference effects of certain
resonance modes solely contribute to the production of defects. Kink density as
well as the diagonal entropy density show oscillatory dependence on the number
of full cycles of oscillation. Finally, the inclusion of a linear term in the
transverse field on top of the oscillatory component, results to a kink density
which decreases continuously with $\tau$ and $\omega$. The entropy density
shows monotonous growth with both $\tau$ and $\omega$, in sharp contrast to the
situations studied earlier. We do also propose appropriate scaling relations
for the defect density in above situations and compare the results with the
numerical results obtained by integrating the Schrodinger equations.",0901.1933v2
2021-10-15,Charge instability of topological Fermi arcs in chiral crystal CoSi,"Topological boundary states, emerged at the spatial boundary between
topological non-trivial and trivial phases, are usually gapless, or commonly
referred as metallic states. For example, the surface state of a topological
insulator is a gapless Dirac state. These metallic topological boundary states
are typically well described by non-interacting fermions. However, the behavior
of topological boundary states with significant electron-electron interactions,
which could turn the gapless boundary states into gapped ordered states, e.g.,
density wave states or superconducting states, is of great interest
theoretically, but is still lacking evidence experimentally. Here, we report
the observation of incommensurable charge density wave (CDW) formed on the
topological boundary states driven by the electron-electron interactions on the
(001) surface of CoSi. The wavevector of CDW varies as the temperature changes,
which coincides with the evolution of topological surface Fermi arcs with
temperature. The orientation of CDW phase is determined by the chirality of the
Fermi arcs, which indicates direct association between CDW and Fermi arcs. Our
finding will stimulate the search of more interactions-driven ordered states,
such as superconductivity and magnetism, on the boundaries of topological
materials.",2110.07815v1
2022-12-20,Entanglement phase diagrams from partial transpose moments,"We present experimentally and numerically accessible quantities that can be
used to differentiate among various families of random entangled states. To
this end, we analyze the entanglement properties of bipartite reduced states of
a tripartite pure state. We introduce a ratio of simple polynomials of
low-order moments of the partially transposed reduced density matrix and show
that this ratio takes well-defined values in the thermodynamic limit for
various families of entangled states. This allows to sharply distinguish
entanglement phases, in a way that can be understood from a quantum information
perspective based on the spectrum of the partially transposed density matrix.
We analyze in particular the entanglement phase diagram of Haar random states,
states resulting form the evolution of chaotic Hamiltonians, stabilizer states,
which are outputs of Clifford circuits, Matrix Product States, and fermionic
Gaussian states. We show that for Haar random states the resulting phase
diagram resembles the one obtained via the negativity and that for all the
cases mentioned above a very distinctive behaviour is observed. Our results can
be used to experimentally test necessary conditions for different types of
mixed-state randomness, in quantum states formed in quantum computers and
programmable quantum simulators.",2212.10181v1
2021-05-13,Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase,"An unidentified quantum fluid designated as the pseudogap (PG) phase is
produced by electron-density depletion in the CuO$_2$ antiferromagnetic
insulator. Current theories suggest that the PG phase may be a pair density
wave (PDW) state characterized by a spatially modulating density of electron
pairs. Such a state should exhibit a periodically modulating energy gap
$\Delta_P(\pmb r)$ in real-space, and a characteristic quasiparticle scattering
interference (QPI) signature $\Lambda_P(\pmb q)$ in wavevector space. By
studying strongly underdoped Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ at hole-density ~0.08
in the superconductive phase, we detect the $8a_0$-periodic $\Delta_P(\pmb r)$
modulations signifying a PDW coexisting with superconductivity. Then, by
visualizing the temperature dependence of this electronic structure from the
superconducting into the pseudogap phase, we find evolution of the scattering
interference signature $\Lambda(\pmb q)$ that is predicted specifically for the
temperature dependence of an $8a_0$-periodic PDW. These observations are
consistent with theory for the transition from a PDW state coexisting with
d-wave superconductivity to a pure PDW state in the Bi$_2$Sr$_2$CaDyCu$_2$O$_8$
pseudogap phase.",2105.06518v2
2009-10-17,Probing the 5f Electrons in Am-I by Hybrid Density Functional Theory,"The ground states of the actinides and their compounds continue to be matters
of considerable controversies. Experimentally, Americium-I (Am-I) is a
non-magnetic dhcp metal whereas theoretically an anti-ferromagnetic ground
state is predicted. We show that hybrid density functional theory, which
admixes a fraction of exact Hartree-Fock (HF) exchange with approximate DFT
exchange, can correctly reproduce the ground state properties of Am. In
particular, for a 0.40 fraction of HF exchange we obtain a non-magnetic ground
state with equilibrium atomic volume, bulk modulus, 5f electron population, and
the density of electronic states all in good agreement with experimental data.
We argue that the exact HF exchange corrects the overestimation of the
approximate DFT exchange interaction.",0910.3340v1
2009-11-13,Electrically driven magnetism on a Pd thin film,"Using first-principles density functional calculations we demonstrate that
ferromagnetism can be induced and modulated on an otherwise paramagnetic Pd
metal thin-film surface through application of an external electric field. As
free charges are either accumulated or depleted at the Pd surface to screen the
applied electric field there is a corresponding change in the surface density
of states. This change can be made sufficient for the Fermi-level density of
states to satisfy the Stoner criterion, driving a transition locally at the
surface from a paramagnetic state to an itinerant ferromagnetic state above a
critical applied electric field, Ec. Furthermore, due to the second-order
nature of this transition, the surface magnetization of the ferromagnetic state
just above the transition exhibits a substantial dependence on electric field,
as the result of an enhanced magnetoelectric susceptibility. Using a linearized
Stoner model we explain the occurrence of the itinerant ferromagnetism and
demonstrate that the magnetic moment on the Pd surface follows a square-root
variation with electric field consistent with our first-principles
calculations.",0911.2678v1
2015-10-09,Informational completeness in bounded-rank quantum-state tomography,"We consider the problem of quantum-state tomography under the assumption that
the state is pure, and more generally that its rank is bounded by a given
value. In this scenario, new notions of informationally complete POVMs emerge,
which allow for high-fidelity state estimation with fewer measurement outcomes
than are required for an arbitrary rank state. We study this in the context of
matrix completion, where the POVM outcomes determine only a few of the density
matrix elements. We give an analytic solution that fully characterizes
informational completeness and elucidates the important role that the
positive-semidefinite property of density matrices plays in tomography. We show
how positivity can impose a stricter notion of information completeness and
allow us to use convex optimization programs to robustly estimate bounded-rank
density matrices in the presence of statistical noise.",1510.02736v2
2020-01-09,Dynamics of the linear-chain alpha cluster in microscopic time-dependent relativistic density functional theory,"The time-dependent covariant density functional theory in 3D lattice space
has been developed and applied to investigate the microscopic dynamics of the
linear-chain cluster states for carbon isotopes in the reactions $^4$He$+^8$Be
and $^4$He$+^{10}$Be without any symmetry assumptions. By examining the density
distribution and its time evolutions, the structure and dynamics of the
linear-chain states are analyzed, and the quasiperiodic oscillations of the
clusters are revealed. For $^4$He$+^8$Be, the linear-chain states evolve to a
triangular configuration and then to a more compact shape. In contrast, for
$^4$He$+^{10}$Be, the lifetime of the linear-chain states is much more
prolonged due to the dynamical isospin effects by the valence neutrons which
slow down the longitudinal oscillations of the clusters and persist the
linear-chain states. The dependence of the linear chain survival time and
dynamical isospin effects on impact parameters have been illustrated as well.",2001.02834v1
2020-11-23,The newly observed $ Z_{cs}(3985)^- $ state: in vacuum and a dense medium,"We report on some properties of the newly observed charged hidden-charmed
open strange $ Z_{cs}(3985)^- $ state by BESIII Collaboration. Assigning the
quantum numbers $ J^{P} = 1^{+}$ and the quark composition $ c \bar c s\bar u $
and considering it as the strange partner of the famous $ Z_c(3900) $ state, we
estimate the mass of the $ Z_{cs}(3985)^- $ resonance in vacuum and compare it
with the experimental data. We also investigate its mass, current coupling and
vector-self energy in a medium with finite density. Our result on the mass in
vacuum agrees well with the experimental data. We estimate the mass and current
coupling of the b-partner of this state, $ Z_{bs}$, in the vacuum as well. For
its mass we get $ m_{Z_{bs}}= 10732^{+97}_{-46}~\mbox{MeV}$, which may be
checked via other nonperturbative approaches as well as future experiments. We
present the dependence of the spectroscopic parameters of $ Z_{cs}(3985)^- $
state on density and observe that these parameters are linearly changed with
increasing in the density.",2011.11488v3
2000-06-19,Theory of Luminescence Spectra of High-Density Electron-Hole Systems: Crossover from Excitonic Bose-Einstein Condenstation to Electron-Hole BCS State,"We present a unified theory of luminescence spectra for highly excited
semiconductors, which is applicable both to the electron-hole BCS state and to
the exciton Bose-Einstein condensate. The crossover behavior between
electron-hole BCS state and exciton Bose-Einstein condensate clearly manifests
itself in the calculated luminescence spectra. The analysis is based on the
Bethe-Salpeter equation combined with the generalized
random-phase-approximation, which enables us to consider the multiple Coulomb
scattering and the quantum fluctuation associated with the center-of-mass
motion of electron-hole pairs. In the crossover regime, the calculated spectra
are essentially different from results obtained by the BCS-like mean-field
theory and the interacting Boson model. In particular, it is found that the
broad spectrum, arising from the recombination of electron-hole BCS state,
splits into the P- and P_2-luminescence bands with decreasing the particle
density. The dependence of these bands on the carrier density is in good
agreement with experiments for highly excited semiconductors.",0006277v1
2005-09-06,"Doping, density of states and conductivity in polypyrrole and poly(p-phenylene vinylene)","The evolution of the density of states (DOS) and conductivity as function of
well controlled doping levels in OC_1C_10-poly(p-phenylene vinylene)
[OC_1C_10-PPV] doped by FeCl_3 and PF_6, and PF_6 doped polypyrrole (PPy-PF_6
have been investigated. At a doping level as high as 0.2 holes per monomer, the
former one remains non-metallic, while the latter crosses the metal-insulator
transition. In both systems a similar almost linear increase in DOS as function
of charges per unit volume c* has been observed from the electrochemical gated
transistor data. In PPy-PF_6, when compared to doped OC_1C_10-PPV, the energy
states filled at low doping are closer to the vacuum level; by the higher c* at
high doping more energy states are available, which apparently enables the
conduction to change to metallic. Although both systems on the insulating side
show log(sigma) proportional to T^-1/4 as in variable range hopping, for highly
doped PPy-PF_6 the usual interpretation of the hopping parameters leads to
seemingly too high values for the density of states.",0509143v1
2005-11-15,Classical Phase Space Density for the Relativistic Hydrogen Atom,"Quantum mechanics is considered to arise from an underlying classical
structure (``hidden variable theory'', ``sub-quantum mechanics''), where
quantum fluctuations follow from a physical noise mechanism. The stability of
the hydrogen ground state can then arise from a balance between Lorentz damping
and energy absorption from the noise. Since the damping is weak, the ground
state phase space density should predominantly be a function of the conserved
quantities, energy and angular momentum.
  A candidate for this phase space density is constructed for ground state of
the relativistic hydrogen problem of a spinless particle. The first excited
states and their spherical harmonics are also considered in this framework. The
analytic expression of the ground state energy can be reproduced, provided
averages of certain products are replaced by products of averages. This
analysis puts forward that quantum mechanics may arise from an underlying
classical level as a slow variable theory, where each new quantum operator
relates to a new, well separated time interval.",0511144v1
2010-11-04,Spin polarization phenomena in dense neutron matter at a strong magnetic field,"Spin polarized states in neutron matter at strong magnetic fields up to
$10^{18}$ G are considered in the model with the Skyrme effective interaction.
Analyzing the self-consistent equations at zero temperature, it is shown that a
thermodynamically stable branch of solutions for the spin polarization
parameter as a function of density corresponds to the negative spin
polarization when the majority of neutron spins are oriented oppositely to the
direction of the magnetic field. Besides, it is found that in a strong magnetic
field the state with the positive spin polarization can be realized as a
metastable state at the high density region in neutron matter. At finite
temperature, the entropy of the thermodynamically stable branch demonstrates
the unusual behavior being larger than that for the nonpolarized state (at
vanishing magnetic field) above certain critical density which is caused by the
dependence of the entropy on the effective masses of neutrons in a spin
polarized state.",1011.1244v1
2013-04-02,Singular Density of States Measure for Subshift and Quasi-Periodic Schrödinger Operators,"Simon's subshift conjecture states that for every aperiodic minimal subshift
of Verblunsky coefficients, the common essential support of the associated
measures has zero Lebesgue measure. We disprove this conjecture in this paper,
both in the form stated and in the analogous formulation of it for discrete
Schr\""odinger operators. In addition we prove a weak version of the conjecture
in the Schr\""odinger setting. Namely, under some additional assumptions on the
subshift, we show that the density of states measure, a natural measure
associated with the operator family and whose topological support is equal to
the spectrum, is singular. We also consider one-frequency quasi-periodic
Schr\""odinger operators with continuous sampling functions and show that
generically, the density of states measure is singular as well.",1304.0519v2
2018-08-09,Amphoteric behavior of Hydrogen in Bimetallic Molecular like Hydrides,"Generally hydrogen will adopt the +1, 0 or -1 oxidation state in solids
depending upon the chemical environment it occupy. Typically, there are some
exceptional cases in which hydrogen exhibits both anionic and cationic behavior
in the same structural frame works. In this study we briefly explore an
amphoteric behavior of hydrogen present in ammine bimetallic borohydrides with
the chemical formula M1M2 (BH4)3 (NH3)2 (M1= Na; M2 = Zn, Mg) using the
state-of-the-art density functional calculations. In order to establish the
amphoteric behavior of hydrogen in M1M2 (BH4)3 (NH3)2, we have made detailed
chemical bonding analyses using partial density of states, charge density,
electron localization function, and Born effective charge. From these analyses
we found that the hydrogen closer to boron is in negative oxidation state
whereas the hydrogen closer to nitrogen is in positive oxidation state. The
establishment of the present of hydrogen with amphoteric behavior in solids has
large implication on hydrogen storage application.",1808.03020v1
2018-08-15,The Steady-State Behavior of Multivariate Exponentially Weighted Moving Average Control Charts,"Multivariate Exponentially Weighted Moving Average, MEWMA, charts are
popular, handy and effective procedures to detect distributional changes in a
stream of multivariate data. For doing appropriate performance analysis,
dealing with the steady-state behavior of the MEWMA statistic is essential.
Going beyond early papers, we derive quite accurate approximations of the
respective steady-state densities of the MEWMA statistic. It turns out that
these densities could be rewritten as the product of two functions depending on
one argument only which allows feasible calculation. For proving the related
statements, the presentation of the non-central chisquare density deploying the
confluent hypergeometric limit function is applied. Using the new methods it
was found that for large dimensions, the steady-state behavior becomes
different to what one might expect from the univariate monitoring field. Based
on the integral equation driven methods, steady-state and worst-case average
run lengths are calculated with higher accuracy than before. Eventually,
optimal MEWMA smoothing constants are derived for all considered measures.",1808.05069v1
2019-02-09,Symmetry Breaking in Density Functional Theory due to Dirac Exchange for a Hydrogen Molecule,"We study symmetry breaking in the mean field solutions to the 2 electron
hydrogen molecule within Kohn Sham (KS) local spin density function theory with
Dirac exchange (the XLDA model). This simplified model shows behavior related
to that of the (KS) spin density functional theory (SDFT) predictions in
condensed and molecular systems. The Kohn Sham solutions to the constrained
SDFT variation problem undergo spontaneous symmetry breaking as the relative
strength of the non-convex exchange term increases. This results in the change
of the molecular ground state from a paramagnetic state to an antiferromagnetic
ground states and a stationary symmetric delocalized 1st excited state. We
further characterize the limiting behavior of the minimizer when the strength
of the exchange term goes to infinity. This leads to further bifurcations and
highly localized states with varying character. The stability of the various
solution classes is demonstrated by Hessian analysis. Finite element numerical
results provide support for the formal conjectures.",1902.03497v2
2019-09-19,Asymptotic reduced density matrix of discrete-time quantum walks,"In this article we show that for any quantum walker with
\textit{m}-dimensional coin subspace, we have $m^2\times m^2$ specific constant
matrix $\mathcal{C}$ where it completely determines the asymptotic reduced
density matrix of the walker. We show that for any initial state with $P_0$
projector, reduced density matrix, can be obtained by $Tr_1\left(P_0\otimes
I\;\mathcal{C}\right)$ or equivalently $Tr_2\left(I\otimes
P_0\;\mathcal{C}\right)$. It is worth to mention that characteristic matrix
$\mathcal{C}$ is independent of the initial state and just depends on coin
operator, so by finding this matrix for specific type of QW the long-time
behavior of it, such as local state of the coin after a long time walking and
asymptotic entanglement between coin and position will be completely known for
any initial state. We have found the characteristic matrix $\mathcal{C}$ for
general coin operator, $U\left(2\right)$, as well as exact form of this matrix
for local initial state.",1909.09214v1
2005-08-31,Many-Body Density Matrices On a Two-Dimensional Square Lattice: Noninteracting and Strongly Interacting Spinless Fermions,"The reduced density matrix of an interacting system can be used as the basis
for a truncation scheme, or in an unbiased method to discover the strongest
kind of correlation in the ground state. In this paper, we investigate the
structure of the many-body fermion density matrix of a small cluster in a
square lattice. The cluster density matrix is evaluated numerically over a set
of finite systems, subject to non-square periodic boundary conditions given by
the lattice vectors $\bR_1 \equiv (R_{1x}, R_{1y})$ and $\bR_2 \equiv (R_{2x},
R_{2y})$. We then approximate the infinite-system cluster density-matrix
spectrum, by averaging the finite-system cluster density matrix (i) over
degeneracies in the ground state, and orientations of the system relative to
the cluster, to ensure it has the proper point-group symmetry; and (ii) over
various twist boundary conditions to reduce finite size effects. We then
compare the eigenvalue structure of the averaged cluster density matrix for
noninteracting and strongly-interacting spinless fermions, as a function of the
filling fraction $\nbar$, and discuss whether it can be approximated as being
built up from a truncated set of single-particle operators.",0508750v4
2017-03-02,Superfluid density and carrier concentration across a superconducting dome: the case of SrTi$_{1-x}$Nb$_{x}$O$_{3}$,"We present a study of the lower critical field, \hc1, of \STO as a function
of carrier concentration with the aim of quantifying the superfluid density. At
low carrier concentration (i.e. the underdoped side), superfluid density and
the carrier concentration in the normal state are equal within experimental
margin. A significant deviation between the two numbers starts at optimal
doping and gradually increases with doping. The inverse of the penetration
depth and the critical temperature follow parallel evolutions as in the case of
cuprate superconductors. In the overdoped regime, the zero-temperature
superfluid density becomes much lower than the normal-state carrier density
before vanishing all together. We show that the density mismatch and the
clean-to-dirty crossover are concomitant. Our results imply that the
discrepancy between normal and superconducting densities is expected whenever
the superconducting gap becomes small enough to put the system in the dirty
limit. A quantitative test of the dirty BCS theory is not straightforward, due
to he multiplicity of the bands in superconducting strontium titanate.",1703.00863v2
2021-06-17,Reduced density matrix approach to ultracold few-fermion systems in one dimension,"The variational determination of the two-fermion reduced density matrix is
described for harmonically trapped, ultracold few-fermion systems in one
dimension with equal spin populations. This is accomplished by formulating the
problem as a semi-definite program, with the two-fermion reduced density matrix
being subject to well-known $N$-representability conditions. The ground-state
energies, as well as the density, pair-correlation function, and lower-order
eigenvalues of the two-fermion reduced density matrix of various fermionic
systems are found by utilising an augmented Lagrangian method for semi-definite
programming. The ground-state energies are found to match well to those
determined by full-configuration interaction and coupled-cluster calculations
and the density, pair-correlation function, and eigenvalue results demonstrate
that the salient features of these systems are well-described by this method.
These results collectively demonstrate the utility of the reduced density
matrix method firstly in describing strong correlation arising from short-range
interactions, suggesting that the well-known N-representability conditions are
sufficient to model ultracold fermionic systems, and secondly in illustrating
the prospect of treating larger systems currently out of the reach of
established methods.",2106.09187v2
1995-01-26,Ground states of the infinite q-deformed Heisenberg ferromagnet,"We set up a general structure for the analysis of ``frustration-free ground
states'', or ``zero-energy states'', i.e., states minimizing each term in a
lattice interaction individually. The nesting of the finite volume ground state
spaces is described by a generalized inductive limit of observable algebras.
The limit space of this inductive system has a state space which is canonically
isomorphic (as a compact convex set) to the set of zero-energy states. We show
that for Heisenberg ferromagnets, and for generalized valence bond solid
states, the limit space is an abelian C*-algebra, and all zero-energy states
are translationally invariant or periodic. For the $q$-deformed spin-$1/2$
Heisenberg ferromagnet in one dimension (i.e., the XXZ-chain with
S$_q$U(2)-invariant boundary conditions) the limit space is an extension of the
non-commutative algebra of compact operators by two points, corresponding to
the ``all spins up'' and the ``all spins down'' states, respectively. These are
the only translationally invariant zero-energy states. The remaining ones are
parametrized by the density matrices on a Hilbert space, and converge weakly to
the ``all up'' (resp.\ ``all down'') state for shifts to $-\infty$ (resp.\
$+\infty$).",9501123v1
2000-02-14,Liouvillian Approach to the Integer Quantum Hall Effect Transition,"We present a novel approach to the localization-delocalization transition in
the integer quantum Hall effect. The Hamiltonian projected onto the lowest
Landau level can be written in terms of the projected density operators alone.
This and the closed set of commutation relations between the projected
densities leads to simple equations for the time evolution of the density
operators. These equations can be used to map the problem of calculating the
disorder averaged and energetically unconstrained density-density correlation
function to the problem of calculating the one-particle density of states of a
dynamical system with a novel action. At the self-consistent mean-field level,
this approach yields normal diffusion and a finite longitudinal conductivity.
While we have not been able to go beyond the saddle point approximation
analytically, we show numerically that the critical localization exponent can
be extracted from the energetically integrated correlation function yielding
$\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling
studies.",0002202v1
2001-02-14,Interacting particles at a metal-insulator transition,"We study the influence of many-particle interaction in a system which, in the
single particle case, exhibits a metal-insulator transition induced by a finite
amount of onsite pontential fluctuations. Thereby, we consider the problem of
interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain.
We employ the density-matrix renormalization scheme to investigate the finite
particle density situation. In the case of incommensurate densities, the
expected transition from the single-particle analysis is reproduced. Generally
speaking, interaction does not alter the incommensurate transition. For
commensurate densities, we map out the entire phase diagram and find that the
transition into a metallic state occurs for attractive interactions and
infinite small fluctuations -- in contrast to the case of incommensurate
densities. Our results for commensurate densities also show agreement with a
recent analytic renormalization group approach.",0102251v2
1997-05-28,Hartree Fock Calculations in the Density Matrix Expansion Approach,"The density matrix expansion is used to derive a local energy density
functional for finite range interactions with a realistic meson exchange
structure. Exchange contributions are treated in a local momentum
approximation. A generalized Slater approximation is used for the density
matrix where an effective local Fermi momentum is chosen such that the next to
leading order off-diagonal term is canceled. Hartree-Fock equations are derived
incorporating the momentum structure of the underlying finite range
interaction. For applications a density dependent effective interaction is
determined from a G-matrix which is renormalized such that the saturation
properties of symmetric nuclear matter are reproduced. Intending applications
to systems far off stability special attention is paid to the low density
regime and asymmetric nuclear matter. Results are compared to predictions
obtained from Skyrme interactions. The ground state properties of stable nuclei
are well reproduced without further adjustments of parameters. The potential of
the approach is further exemplified in calculations for A=100...140 tin
isotopes. Rather extended neutron skins are found beyond 130Sn corresponding to
solid layers of neutron matter surrounding a core of normal composition.",9705049v1
2014-12-10,Observation and Structural Control of Charge-Density-Waves resonating with Terahertz Frequencies in NdNiO3,"Formation of charge-density-waves in ordered electronic phases (such as
charge-order) is an emergent phenomenon in the perovskite class of correlated
oxides. This scenario is visualized to prevail in exotic RNiO3 (R=rare-earth)
nickelates in which the structure controls the incipient charge-order to form
in weak localization limit. However, any consequent effect demonstrating these
nickelates in rare category of charge-density-waves conductors with controlled
charge-lattice interactions has been a fundamental challenge so-far. Here, we
present first evidence of the charge-density-waves in a prototypical NdNiO3
system employing terahertz time-domain spectroscopy along selective crystal
axes. A finite peak structure at 5meV in the terahertz conductivity displays
all the characteristics of a charge-density-wave condensate. Contrasting
charge-dynamics of collective charge-density-waves mode and Drude conductivity
emerging, respectively, from orthorhombic and cubic symmetries disentangle
charge-ordering from the insulating state, establish a novel structure-property
cause-effect relationship, and present opportunities to harness these diverse
attributes in oxide electronics.",1412.3244v1
2014-12-17,Generalized Labeled Multi-Bernoulli Approximation of Multi-Object Densities,"In multi-object inference, the multi-object probability density captures the
uncertainty in the number and the states of the objects as well as the
statistical dependence between the objects. Exact computation of the
multi-object density is generally intractable and tractable implementations
usually require statistical independence assumptions between objects. In this
paper we propose a tractable multi-object density approximation that can
capture statistical dependence between objects. In particular, we derive a
tractable Generalized Labeled Multi-Bernoulli (GLMB) density that matches the
cardinality distribution and the first moment of the labeled multi-object
distribution of interest. It is also shown that the proposed approximation
minimizes the Kullback-Leibler divergence over a special tractable class of
GLMB densities. Based on the proposed GLMB approximation we further demonstrate
a tractable multi-object tracking algorithm for generic measurement models.
Simulation results for a multi-object Track-Before-Detect example using radar
measurements in low signal-to-noise ratio (SNR) scenarios verify the
applicability of the proposed approach.",1412.5294v3
2016-03-10,Encircling the dark: constraining dark energy via cosmic density in spheres,"The recently published analytic probability density function for the mildly
non-linear cosmic density field within spherical cells is used to build a
simple but accurate maximum likelihood estimate for the redshift evolution of
the variance of the density, which, as expected, is shown to have smaller
relative error than the sample variance. This estimator provides a competitive
probe for the equation of state of dark energy, reaching a few percent accuracy
on wp and wa for a Euclid-like survey. The corresponding likelihood function
can take into account the configuration of the cells via their relative
separations. A code to compute one-cell density probability density functions
for arbitrary initial power spectrum, top-hat smoothing and various spherical
collapse dynamics is made available online so as to provide straightforward
means of testing the effect of alternative dark energy models and initial
power-spectra on the low-redshift matter distribution.",1603.03347v2
2016-06-28,A Local Density-Based Approach for Local Outlier Detection,"This paper presents a simple but effective density-based outlier detection
approach with the local kernel density estimation (KDE). A Relative
Density-based Outlier Score (RDOS) is introduced to measure the local
outlierness of objects, in which the density distribution at the location of an
object is estimated with a local KDE method based on extended nearest neighbors
of the object. Instead of using only $k$ nearest neighbors, we further consider
reverse nearest neighbors and shared nearest neighbors of an object for density
distribution estimation. Some theoretical properties of the proposed RDOS
including its expected value and false alarm probability are derived. A
comprehensive experimental study on both synthetic and real-life data sets
demonstrates that our approach is more effective than state-of-the-art outlier
detection methods.",1606.08538v1
2017-03-02,Travelling waves of density for a fourth-gradient model of fluids,"In mean-field theory, the non-local state of fluid molecules can be taken
into account using a statistical method. The molecular model combined with a
density expansion in Taylor series of the fourth order yields an internal
energy value relevant to the fourth-gradient model, and the equation of
isother-mal motions takes then density's spatial derivatives into account for
waves travelling in both liquid and vapour phases. At equilibrium, the equation
of the density profile across interfaces is more precise than the Cahn and
Hilliard equation, and near the fluid's critical-point, the density profile
verifies an Extended Fisher-Kolmogorov equation, allowing kinks, which
converges towards the Cahn-Hillard equation when approaching the critical
point. Nonetheless, we also get pulse waves oscillating and generating critical
opalescence.",1703.00689v1
2017-03-10,Limiting symmetry energy elements from empirical evidence,"In the framework of an equation of state (EoS) constructed from a momentum
and density-dependent finite-range two-body effective interaction, the
quantitative magnitudes of the different symmetry elements of infinite nuclear
matter are explored. The parameters of this interaction are determined from
well-accepted characteristic constants associated with homogeneous nuclear
matter. The symmetry energy coefficient $a_2$, its density slope $L_0$, the
symmetry incompressibility $K_\delta $ as well as the density dependent
incompressibility $K(\rho )$ evaluated with this EoS are seen to be in good
harmony with those obtained from other diverse perspectives. The higher order
symmetry energy coefficients $a_4,~a_6$ etc are seen to be not very significant
in the domain of densities relevant to finite nuclei, but gradually build up at
supra-normal densities. The analysis carried with a Skyrme-inspired energy
density functional obtained with the same input values for the empirical bulk
data associated with nuclear matter yields nearly the same results.",1703.03549v1
2018-02-05,Pair Density Waves in Superconducting Vortex Halos,"We analyze the interplay between a d-wave uniform superconducting and a
pair-density-wave (PDW) order parameter in the neighborhood of a vortex. We
develop a phenomenological nonlinear sigma-model, solve the saddle point
equation for the order parameter configuration, and compute the resulting local
density of states in the vortex halo. The intertwining of the two
superconducting orders leads to a charge density modulation with the same
periodicity as the PDW, which is twice the period of the charge-density-wave
that arises as a second-harmonic of the PDW itself. We discuss key features of
the charge density modulation that can be directly compared with recent results
from scanning tunneling microscopy and speculate on the role PDW order may play
in the global phase diagram of the hole-doped cuprates.",1802.01582v2
2019-12-09,On the fast rotation asymptotics of a non-homogeneous incompressible MHD system,"This paper is devoted to the analysis of a singular perturbation problem for
a $2$-D incompressible MHD system with density variations and Coriolis force,
in the limit of small Rossby numbers. Two regimes are considered. The first one
is the quasi-homogeneous regime, where the densities are small perturbations
around a constant state. The limit dynamics is identified as an incompressible
homogeneous MHD system, coupled with an additional transport equation for the
limit of the density variations. The second case is the fully non-homogeneous
regime, where the densities vary around a general non-constant profile. In this
case, in the limit, the equation for the magnetic field combines with an
underdetermined linear equation, which links the limit density variation
function with the limit velocity field. The proof is based on a compensated
compactness argument, which enables us to consider general ill-prepared initial
data. An application of Di Perna-Lions theory for transport equations allows to
treat the case of density-dependent viscosity and resistivity coefficients.",1912.04077v1
2020-04-21,Investigation of neutron density distribution of $^{208}$Pb nucleus when the proton density is constrained to its experimental distribution,"In this study, two novel improvements for the theoretical calculation of the
neutron distributions are presented. First, the available experimental proton
distributions are used as a constraint rather than inferred from the
calculation. Second, the recently proposed distribution formula, d3pF, is used
for the neutron density, which is more detailed than the usual shapes, for the
first time in nuclear structure calculation. A semi-microscopic approach for
binding energy calculation is considered in this study, however, the proposed
improvements can be introduced to any other approach. The ground state binding
energy and neutron density distribution of $^{208}$Pb nucleus are calculated by
optimizing the binding energy considering three different distribution
formulae. The implementation of the proposed improvements leads to a
qualitative and quantitative improvement in the calculation of the binding
energy and neutron density distribution. The calculated binding energy agrees
with the experimental value, and the calculated neutron density shows
fluctuations within the nuclear interior, which agrees with the predictions of
self-consistent approaches.",2004.09727v1
2023-05-26,Kernel Density Matrices for Probabilistic Deep Learning,"This paper introduces a novel approach to probabilistic deep learning, kernel
density matrices, which provide a simpler yet effective mechanism for
representing joint probability distributions of both continuous and discrete
random variables. In quantum mechanics, a density matrix is the most general
way to describe the state of a quantum system. This work extends the concept of
density matrices by allowing them to be defined in a reproducing kernel Hilbert
space. This abstraction allows the construction of differentiable models for
density estimation, inference, and sampling, and enables their integration into
end-to-end deep neural models. In doing so, we provide a versatile
representation of marginal and joint probability distributions that allows us
to develop a differentiable, compositional, and reversible inference procedure
that covers a wide range of machine learning tasks, including density
estimation, discriminative learning, and generative modeling. The broad
applicability of the framework is illustrated by two examples: an image
classification model that can be naturally transformed into a conditional
generative model, and a model for learning with label proportions that
demonstrates the framework's ability to deal with uncertainty in the training
samples.",2305.18204v2
2023-06-28,Frontiers to the learning of nonparametric hidden Markov models,"Hidden Markov models (HMMs) are flexible tools for clustering dependent data
coming from unknown populations, allowing nonparametric modelling of the
population densities. Identifiability fails when the data is in fact
independent, and we study the frontier between learnable and unlearnable
two-state nonparametric HMMs. Interesting new phenomena emerge when the cluster
distributions are modelled via density functions (the 'emission' densities)
belonging to standard smoothness classes compared to the multinomial setting.
Notably, in contrast to the multinomial setting previously considered, the
identification of a direction separating the two emission densities becomes a
critical, and challenging, issue. Surprisingly, it is possible to ""borrow
strength"" from estimators of the smoother density to improve estimation of the
other. We conduct precise analysis of minimax rates, showing a transition
depending on the relative smoothnesses of the emission densities.",2306.16293v1
2023-09-21,On the role of soft gluons in collinear parton densities,"The role of soft (non-perturbative) gluons in collinear parton densities is
investigated with the Parton Branching method as a solution of the DGLAP
evolution equations. It is found that soft gluons contribute significantly to
collinear parton densities.
  Within the Parton Branching frame, the Sudakov form factor can be split into
a perturbative and non-perturbative part. The non-perturbative part can be
calculated analytically under certain conditions. It is shown that the
inclusion of soft (non-perturbative) gluons to the parton density evolution is
essential for the proper cancellation of divergent terms.
  It is argued that the non-perturbative part of the Sudakov form factor has
its correspondence in Transverse Momentum Dependent parton distributions.
Within the Parton Branching approach, this non-perturbative Sudakov form factor
is constrained by fits of inclusive, collinear parton densities.
  We show that the non-perturbative Sudakov form factor and soft gluon
emissions are essential for inclusive distributions (collinear parton densities
and Drell-Yan transverse momentum spectra), while those soft gluons play
essentially no role in final state hadron spectra.",2309.11802v2
2014-03-24,Superdeformed $Λ$ hypernuclei from relativistic mean field models,"We study the superdeformed (SD) states and corresponding SD hypernuclei of Ar
isotopes with the multidimensionally-constrained relativistic mean field
(MDC-RMF) models which can accommodate various shape degree of freedom. %The
hyperon-nucleon $\sigma$-$\Lambda$ and $\omega$-$\Lambda $ interactions are
introduced %in the same covariant framework. We found that the density profiles
of SD states in Ar isotopes show a strong localization with a ring structure
near the surface, while the central part of the density is dilute showing a
hole structure. This localization of SD density induces an appreciable
deformation in the hyperon wave function and results in a large overlap between
the core and the hyperon in the SD hypernuclei of Ar isotopes. Then the
$\Lambda$ separation energy of SD state becomes larger than that of normally
deformed or spherical ground state. This feature is different from that found
in other nuclei such as $^{32}$S, $^{56}$Ni, and $^{60}$Zn in which the
$\Lambda$ separation energy of larger deformed state is smaller. In this
context, the measurement of the $\Lambda$ separation energy may provide an
important information on the localization of the density profile of SD states.",1403.5866v1
2018-07-09,Fractal aggregation of active particles,"We study active run-and-tumble particles with an additional two-state
internal variable characterizing their motile or non-motile state. Motile
particles change irreversibly into non-motile ones upon collision with a
non-motile particle. The system evolves towards an absorbing state where all
particles are non-motile. We initialize the system with one non-motile
particles in a bath of motile ones and study numerically the kinetics of
relaxation to absorbing state and its structure as function of the density of
the initial bath of motile particles and of their tumbling rate. We find a
crossover from fractal aggregates at low density to homogeneous ones at high
density. The persistence of single-particle dynamics as quantified by the
tumbling rate pushes this crossover to higher density and can be used to tune
the porosity of the aggregate. At the lowest density the fractal dimension of
the aggregate approaches that obtained in single-particle diffusion limited
aggregation. Our results could be exploited for the design of structures of
desired porosity. The model is a first step towards the study of the collective
dynamics of active particles that can exchange biological information.",1807.02928v4
2018-07-17,Constraining neutron-star equation of state using heavy-ion collisions,"The LIGO-Virgo collaboration ground-breaking detection of the binary
neutron-star merger event, GW170817, has intensified efforts towards the
understanding of the equation of state (EoS) of nuclear matter. In this letter,
we compare directly the density-pressure constraint on the EoS obtained from a
recent analysis of the neutron-star merger event to density-pressure
constraints obtained from nuclear physics experiments. To relate constraints
from nuclear physics to the radii and the tidal deformabilities of neutron
stars, we use a large collection of Skyrme density functionals that describe
properties of nuclei to calculate properties of 1.4 solar maass neutron stars.
We find that restricting this set of Skyrme equations of state to density
functionals that describe nuclear masses, isobaric analog states, and low
energy nuclear reactions does not sufficiently restrict the predicted
neutron-star radii and the tidal deformabilities. Including pressure
constraints on the EoS around twice saturation density, obtained from high
energy nucleus-nucleus collisions, does constrain predicted radii and tidal
deformabilities to be consistent with the results obtained from the analysis of
GW170817. We discuss how new measurements of nucleus-nucleus collisions can
improve these constraints on the EoS to be more restrictive than the current
constraints from the GW170817 merger event.",1807.06571v1
2007-04-14,Orbital-Free Density Functional Theory: Kinetic Potentials and Ab-Initio Local Pseudopotentials,"In the density functional (DF) theory of Kohn and Sham, the kinetic energy of
the ground state of a system of noninteracting electrons in a general external
field is calculated using a set of orbitals. Orbital free methods attempt to
calculate this directly from the electron density by approximating the
universal but unknown kinetic energy density functional. However simple local
approximations are inaccurate and it has proved very difficult to devise
generally accurate nonlocal approximations. We focus instead on the kinetic
potential, the functional derivative of the kinetic energy DF, which appears in
the Euler equation for the electron density. We argue that the kinetic
potential is more local and more amenable to simple physically motivated
approximations in many relevant cases, and describe two pathways by which the
value of the kinetic energy can be efficiently calculated. We propose two
nonlocal orbital free kinetic potentials that reduce to known exact forms for
both slowly varying and rapidly varying perturbations and also reproduce exact
results for the linear response of the density of the homogeneous system to
small perturbations. A simple and systematic approach for generating accurate
and weak ab-initio local pseudopotentials which produce a smooth slowly varying
valence component of the electron density is proposed for use in orbital free
DF calculations of molecules and solids. The use of these local
pseudopotentials further minimizes the possible errors from the kinetic
potentials. Our theory yields results for the total energies and ionization
energies of atoms, and for the shell structure in the atomic radial density
profiles that are in very good agreement with calculations using the full
Kohn-Sham theory.",0704.1878v1
2010-04-26,Impact of CIR Storms on Thermosphere Density Variability during the Solar Minimum of 2008,"The solar minimum of 2008 was exceptionally quiet, with sunspot numbers at
their lowest in 75 years. During this unique solar minimum epoch, however,
solar wind high - speed streams emanating from near-equatorial coronal holes
occurred frequently and were the primary contributor to the recurrent
geomagnetic activity at Earth. These conditions enabled the isolation of
forcing by geomagnetic activity on the preconditioned solar minimum state of
the upper atmosphere caused by Corotating Interaction Regions (CIRs).
Thermosphere density observations around 400 km from the CHAMP satellite are
used to study the thermosphere density response to solar wind high - speed
streams/CIRs. Superposed epoch results show that thermosphere density responds
to high - speed streams globally, and the density at 400 km changes by 75% on
average. The relative changes of neutral density are comparable at different
latitudes, although its variability is largest at high latitudes. In addition,
the response of thermosphere density to high - speed streams is larger at night
than in daytime, indicating the preconditioning effect of the thermosphere
response to storms. Finally, the thermosphere density variations at the periods
of 9 and 13.5 days associated with CIRs are linked to the spatial distribution
of low - middle latitude coronal holes on the basis of the EUVI observations
from the STEREO.",1004.4593v1
2014-11-21,Structures of simple liquids in contact with nanosculptured surfaces,"We present a density functional study of Lennard-Jones liquids in contact
with a nano-corrugated wall. The corresponding substrate potential is taken to
exhibit a repulsive hard core and a van der Waals attraction. The corrugation
is modeled by a periodic array of square nano-pits. We have used the modified
Rosenfeld density functional in order to study the interfacial structure of
these liquids which with respect to their thermodynamic bulk state are
considered to be deep inside their liquid phase. We find that already
considerably below the packing fraction of bulk freezing of these liquids,
inside the nanopits a three-dimensional-like density localization sets in. If
the sizes of the pits are commensurate with the packing requirements, we
observe high density spots separated from each other in all spatial directions
by liquid of comparatively very low density. The number, shape, size, and
density of these high density spots depend sensitively on the depth and width
of the pits. Outside the pits, only layering is observed; above the pit
openings these layers are distorted with the distortion reaching up to a few
molecular diameters. We discuss quantitatively how this density localization is
affected by the geometrical features of the pits and how it evolves upon
increasing the bulk packing fraction. Our results are transferable to colloidal
systems and pit dimensions corresponding to several diameters of the colloidal
particles. For such systems the predicted unfolding of these structural changes
can be studied experimentally on much larger length scales and more directly
(e.g., optically) than for molecular fluids which typically call for
sophisticated X-ray scattering.",1411.5920v1
2013-08-07,Chiral dynamics and peripheral transverse densities,"In the partonic (or light-front) description of relativistic systems the
electromagnetic form factors are expressed in terms of frame-independent charge
and magnetization densities in transverse space. This formulation allows one to
identify the chiral components of nucleon structure as the peripheral densities
at transverse distances b = O(M_pi^{-1}) and compute them in a parametrically
controlled manner. A dispersion relation connects the large-distance behavior
of the transverse charge and magnetization densities to the spectral functions
of the Dirac and Pauli form factors near the two-pion threshold at timelike t =
4 M_pi^2. Using relativistic chiral effective field theory in the leading-order
approximation, we (a) derive the asymptotic behavior (Yukawa tail) of the
isovector transverse densities in the ""chiral"" region b = O(M_pi^{-1}) and the
""molecular"" region b = O(M_N^2/M_pi^3); (b) perform the heavy-baryon expansion;
(c) explain the relative magnitude of the peripheral charge and magnetization
densities in a simple mechanical picture; (d) include Delta intermediate states
and study the densities in the large-N_c limit of QCD; (e) quantify the spatial
region where the chiral components are numerically dominant; (f) calculate the
chiral divergences of the b^2-weighted moments of the transverse densities
(charge and magnetic radii) and determine their spatial support. Our approach
provides a concise formulation of the spatial structure of the nucleon's chiral
component and offers new insights into basic properties of the chiral
expansion. It relates the information extracted from low-t elastic form factors
to the generalized parton distributions probed in peripheral high-energy
scattering processes.",1308.1634v1
2015-09-28,Anticoherence of spin states with point group symmetries,"We investigate multiqubit permutation-symmetric states with maximal entropy
of entanglement. Such states can be viewed as particular spin states, namely
anticoherent spin states. Using the Majorana representation of spin states in
terms of points on the unit sphere, we analyze the consequences of a
point-group symmetry in their arrangement on the quantum properties of the
corresponding state. We focus on the identification of anticoherent states (for
which all reduced density matrices in the symmetric subspace are maximally
mixed) associated with point-group symmetric sets of points. We provide three
different characterizations of anticoherence, and establish a link between
point symmetries, anticoherence and classes of states equivalent through
stochastic local operations with classical communication (SLOCC). We then
investigate in detail the case of small numbers of qubits, and construct
infinite families of anticoherent states with point-group symmetry of their
Majorana points, showing that anticoherent states do exist to arbitrary order.",1509.08300v2
2010-09-08,Duality Relations for the Classical Ground States of Soft-Matter Systems,"Bounded interactions are particularly important in soft-matter systems, such
as colloids, microemulsions, and polymers. We derive new duality relations for
a class of soft potentials, including three-body and higher-order functions,
that can be applied to ordered and disordered classical ground states. These
duality relations link the energy of configurations associated with a
real-space potential to the corresponding energy of the dual
(Fourier-transformed) potential. We apply the duality relations by
demonstrating how information about the classical ground states of short-ranged
potentials can be used to draw new conclusions about the ground states of
long-ranged potentials and vice versa. The duality relations also lead to
bounds on the T=0 system energies in density intervals of phase coexistence.
Additionally, we identify classes of ""self-similar"" potentials, for which one
can relate low- and high-density ground-state energies. We analyze the ground
state configurations and thermodynamic properties of a one-dimensional system
previously thought to exhibit an infinite number of structural phase
transitions and comment on the known ground states of purely repulsive
monotonic potentials in the context of our duality relations.",1009.1601v1
2016-11-23,An explicit formula for the polynomial entanglement measures of degree 2 of even-N qubits mixed states,"Characterization of the multipartite mixed state entanglement is still a
challenging problem. Since due to the fact that the entanglement for the mixed
states, in general, is defined by a convex-roof extension. That is the
entanglement measure of a mixed state \r{ho} of a quantum system can be defined
as the minimum average entanglement of an ensemble of pure states. In this
Letter, we give an explicit formula for the polynomial entanglement measures of
degree 2 of even-N qubits mixed states that is similar to Wooters formula in
[1]. Then we discuss our findings in the framework of X density matrices and
show that our formula for this type of density matrices is in the full
agreement with the genuine multipartite (GM) entanglement of these states.",1611.07958v2
2019-06-20,Finite-temperature Equations of State for Neutron Star Mergers,"The detection of gravitational waves from a neutron star merger has opened up
the possibility of detecting the presence or creation of deconfined quark
matter using the gravitational wave signal. To investigate this possibility, we
construct a family of neutron star matter equations of state at nonzero density
and temperature by combining state-of-the-art nuclear matter equations of state
with holographic equations of state for strongly interacting quark matter. The
emerging picture consistently points toward a strong first order deconfinement
transition, with a temperature-dependent critical density and latent heat that
we quantitatively examine. Recent neutron star mass measurements are further
used to discriminate between the different equations of state obtained, leaving
a tightly constrained family of preferred equations of state.",1906.08440v2
2015-08-20,Population imbalanced lattice fermions near the BCS-BEC crossover: II. The FFLO regime and its thermal signatures,"We study the effect of high population imbalance in the two dimensional
attractive Hubbard model, in the coupling regime corresponding to BCS-BEC
crossover, and focus on thermal effects on the Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state. Using a method that retains all the classical thermal
fluctuations on the FFLO state we estimate a very low $T_c$ and infer a
strongly first order normal state to FFLO transition. The $T_c$ is an order of
magnitude below the mean field estimate. We track the fermionic momentum
distribution, the density of states, and the pairing structure factor deep into
the normal state. The pairing structure factor retains weak signature of finite
momentum pairing to a high temperature despite the low $T_c$ itself, while the
spin resolved density of states changes from the `pseudogapped' FFLO character
to gapless and pseudogapped again with increasing temperature. These results
map out the rather narrow temperature window, and diverse physical indicators,
relevant to FFLO states on a cold atom optical lattice, and complements our
work on the lower field `breached pair' state.",1508.05036v2
2020-01-14,Ground State of the Fe(II)-porphyrin Model System Corresponds to the Quintet State: A DFT and DMRG-based Tailored CC Study,"Fe(II)-porphyrins (FeP) play an important role in many reactions relevant to
material science and biological processes, due to their closely lying spin
states. However, this small energetic separation also makes it challenging to
establish the correct spin state ordering. Although the prevalent opinion is
that these systems posses the triplet ground state, the recent experiment on
Fe(II)-phthalocyanine under conditions matching those of an isolated molecule
points toward the quintet ground state. We present a thorough study of FeP
model by means of the density functional theory and density matrix
renormalization group based tailored coupled clusters, in which we address all
previously discussed correlation effects. We examine the importance of
geometrical parameters, the Fe-N distances in particular, and conclude that the
system possesses the quintet ground state, which is in our calculations
well-separated from the triplet state.",2001.04903v2
1997-08-22,Theory of Photoemission from the Copper Oxide Material,"A mean-field theory which satisfying the electron on-site local constraint in
the relevant regime of density for the high temperature superconductors is
developed. Within this approach, the electron spectral function, the electron
dispersion, and the electron density of states of copper oxide materials are
discussed, and the results are qualitative consistent with the numerical
simulations.",9708177v1
1999-07-14,Two Definitions of Superfluid Density,"We point out that two different definitions of the superfluid density -
through statistical response to static gauge phase and through dynamic response
to altering gauge phase - yield, generally speaking, different quantities in
$d<3$. The physics leading to this difference is associated with the
equilibrium statistics of supercurrent states. Some experimentally observable
consequences of this fact are discussed.",9907203v1
1999-09-07,Asymptotic Distribution of Eigenvalues for a Self-Affine String,"We consider a string with fixed endpoints where the mass density and/or the
elastic coefficient vary in a self-affine way as function of position. It is
demonstrated how the eigenvalues in the asymptotic limit are distributed.
Scaling laws for the Weyl term of the asymptotic integrated density of states
is established and confirmed numerically.",9909094v1
1999-12-07,Impurity Scattering in f-wave Superconductor UPt_3,"We study theoretically the effect of impurity scattering in f-wave (or
E_{2u}) superconductors. The quasi-particle density of states of f-wave
superconductor is very similar to the one for d-wave superconductor as in
hole-doped high T_c cuprates. Also in spite of anisotropy in Delta(k), both the
normalized superfluid density and the thermal conductivity is completely
isotropic.",9912124v1
2001-09-27,Bosonic behavior of excitons and screening: a consistent calculation,"Excitons have recently been shown to deviate from pure bosons at densities a
hundred times smaller than the Mott density. The corresponding calculations
relied on the unscreened excitonic ground state wavefunction. A consistent
inclusion of screening, by use of the fundamental eigenfunction of the
Hulth\'{e}n potential, vindicates this approximation.",0109529v1
2002-03-21,Impurity scattering in unconventional density waves,"We have investigated the effect of nonmagnetic impurities on the
quasi-one-dimensional unconventional density wave (UDW) ground state. The
thermodynamics were found to be close to those of a d-wave superconductor in
the Born limit. Four different optical conductivity curves were found depending
on the direction of the applied electric field and on the wavevector dependence
of the gap.",0203434v1
1993-11-16,Monofractal Density Fluctuations and Scaling Laws for Count Probabilities and Combinants,"The relation of combinants to various statistics characterizing the
fluctuation pattern of multihadron final states is discussed. Scaling laws are
derived for count probabilities and combinants in the presence of homogeneous
and clustered monofractal density fluctuations. It is argued that both types of
scaling rules are well suited to signal Quark-Gluon Plasma formation in a
second-order QCD phase transition.",9311301v1
2001-12-21,The path from chemical to thermal freeze-out,"The evolution of a hadronic system after its chemical decomposition is
described through a model that conserves the hadronic multiplicities to their
values at chemical freeze-out. The state of the system is found as function of
temperature and the corresponding baryon density is evaluated. The baryon
density at thermal decoupling is also computed.",0112311v2
2001-08-02,An efficient k.p method for calculation of total energy and electronic density of states,"An efficient method for calculating the electronic structure in large systems
with a fully converged BZ sampling is presented. The method is based on a
k.p-like approximation developed in the framework of the density functional
perturbation theory. The reliability and efficiency of the method are
demostrated in test calculations on Ar and Si supercells.",0108004v1
2006-05-09,Mathematical Theory of the Duality Computer in the Density Matrix Formalism,"We give the mathematical theory of duality computer in the density matrix
formalism. This result complements the mathematical theory of duality computer
of Gudder in the pure state formalism.",0605087v4
2008-11-20,Weizsacker energy of unitary Fermi gas in a harmonic trap,"The universal method of construction of the rigorous lower bounds to the
Weizsacker energy is presented. We study a few-fermion systemat the unitarity.
Upper and lower bounds to the density functional theory(DFT) ground state
energy within the local density approximation (LDA) aregiven. Therigorous lower
bounds to the accuracy of the method are derived.",0811.3352v1
2008-12-15,About density functional theory interpretation,"Two forms of relativistic density functional are derived from Dirac equation.
Based on their structure analysis model of split electron is proposed. In this
model electric charge and mass of electron behave like two point-like
particles. It is shown that two electrons obeying this model cannot occupy the
same quantum state. Empirical verification of the model is discussed.",0812.2919v3
2009-10-14,Electronic properties of novel 6K superconductor LiFeP,"Very recently, the new 6K superconductor (SC) LiFeP, the first arsenic-free
analogue of the family of the so-called ""111"" FeAs SCs, was discovered. Here,
based on first-principle FLAPW-GGA calculations, the band structure, density of
states, Fermi surface topology, electron density distribution and effective
atomic charges for the new SC LiFeP are investigated and discussed in
comparison with isostructural and isoelectronic LiFeAs.",0910.2550v1
2011-05-05,Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs,"We consider the low density limit of a Fermi gas in the BCS approximation. We
show that if the interaction potential allows for a two-particle bound state,
the system at zero temperature is well approximated by the Gross-Pitaevskii
functional, describing a Bose-Einstein condensate of fermion pairs.",1105.1100v1
2011-07-17,A note on the cosmological constant problem,"An speculative solution for the cosmological constant problem is proposed. It
is argued that while the true quantum vacuum energy density is of the order of
$M_P^4$, the observed classical vacuum energy density may be much smaller due
to the huge amount of scattering process in the vacuum state of quantum
gravity.",1107.3307v1
2013-03-28,Finite size corrections to the large deviation function of the density in the one dimensional symmetric simple exclusion process,"The symmetric simple exclusion process is one of the simplest
out-of-equilibrium systems for which the steady state is known. Its large
deviation functional of the density has been computed in the past both by
microscopic and macroscopic approaches. Here we obtain the leading finite size
correction to this large deviation functional. The result is compared to the
similar corrections for equilibrium systems.",1303.7135v1
2015-09-23,Copulas in Hilbert spaces,"In this article, the concept of copulas is generalised to infinite
dimensional Hilbert spaces. We show one direction of Sklar's theorem and
explain that the other direction fails in infinite dimensional Hilbert spaces.
We derive a necessary and sufficient condition which allows to state this
direction of Sklar's theorem in Hilbert spaces. We consider copulas with
densities and specifically construct copulas in a Hilbert space by a family of
pairwise copulas with densities.",1509.06941v1
2016-07-26,Maxwell equation violation by density dependent magnetic fields in neutron stars,"We show that the widely used density dependent magnetic field prescriptions,
necessary to account for the variation of the field intensity from the crust to
the core of neutron stars violate one of the Maxwell equations. We estimate how
strong the violation is when different equations of state are used and check
for which cases the pathological problem can be cured.",1607.07687v1
2018-11-21,N-vicinity method and 1D Ising Model,"For a 1D Ising model, we obtained an exact expression for the spectral
density in an n-vicinity of the ground state and explained why our n-vicinity
method with the Gaussian approximation of the spectral density did not
applicable in this case. We also found an analytical expression for the
distribution of magnetization at an arbitrary temperature. When the temperature
tends to zero the distribution of magnetization gradually flattens.",1811.08703v1
2017-01-06,Quantum theory of a strongly-dissipative scalar field,"The properties of a quantum dissipative scalar field is analyzed by
Caldeira-Leggett model in strong-coupling regime. The Lagrangian of the total
system is canonically quantized and the full Hamiltonian is diagonalized using
Fano technique. A mode-dependent probability density is introduced. The steady
state energy and correlation functions at finite temperature are calculated in
terms of the probability density.",1701.01750v1
2012-04-17,X-matrices provide a lower bound of concurrence,"By focusing on the X-matrix part of a density matrix of two qubits we provide
an algebraic lower bound for the concurrence. The lower bound is generalized
for cases beyond two qubits and can serve as a sufficient condition for
non-separability for bipartite density matrices of arbitrary dimension.
Experimentally, our lower bound can be used to confirm non-separability without
performing a complete state tomography.",1204.3912v1
2017-11-26,The Hohenberg-Kohn Theorem for Schrodinger Semigroups,"At the basis of much of computational chemistry is density functional theory,
as initiated by the Hohenberg-Kohn theorem. The theorem states that, when
nuclei are fixed, nuclear potentials are determined by $1$-electron densities.
We recast and derive this result within the context of the principal eigenvalue
of Schrodinger semigroups.",1711.09463v1
2023-05-02,Electromagnetic and gravitational local spatial densities for spin-1 systems,"The matrix elements of the electromagnetic current and the energy-momentum
tensor for sharply localized states of spin-1 systems are considered. Their
interpretation as local spatial densities of various characteristics of the
considered system is discussed.",2305.01491v1
2023-09-01,Subsonic steady-states for bipolar hydrodynamic model for semiconductors,"In this paper, we study the well-posedness, ill-posedness and uniqueness of
the stationary 3-D radial solution to the bipolar isothermal hydrodynamic model
for semiconductors. The density of electron is imposed with sonic boundary and
interiorly subsonic case and the density of hole is fully subsonic case.",2309.00418v1
2013-05-27,Subgap states in disordered superconductors,"We revise the problem of the density of states in disordered superconductors.
Randomness of local sample characteristics translates to the quenched spatial
inhomogeneity of the spectral gap, smearing the BCS coherence peak. We show
that various microscopic models of potential and magnetic disorder can be
reduced to a universal phenomenological random order parameter model, whereas
the details of the microscopic description are encoded in the correlation
function of the order parameter fluctuations. The resulting form of the density
of states is generally described by two parameters: the width Gamma measuring
the broadening of the BCS peak, and the energy scale Gamma_{tail} which
controls the exponential decay of the density of the subgap states. We refine
the existing instanton approaches for determination of Gamma_{tail} and show
that they appear as limiting cases of a unified theory of optimal fluctuations
in a nonlinear system. Application to various types of disorder is discussed.",1305.6300v2
2023-03-08,Effects of a uniform magnetic field on twisted graphene nanoribbons,"In the present work, the relativistic quantum motion of massless fermions in
a helicoidal graphene nanoribbon under the influence of a uniform magnetic
field is investigated. Considering a uniform magnetic field ($B$) aligned along
the axis of helicoid, this problem is explored in the context of Dirac equation
in a curved space-time. As this system does not support exact solutions due to
considered background, the bound-state solutions and local density of state
(LDOS) are obtained numerically by means of the Numerov method. The combined
effects of width of the nanoribbon ($D$), length of ribbon ($L$), twist
parameter ($\omega$) and $B$ on the equations of motion and local density of
states (LDOS) are analyzed and discussed. It is verified that the presence of
$B$ produces a constant minimum value of local density of state on the axis of
helicoid, which is possible only for values large enough of $\omega$, in
contrast to the case for $B=0$ already studied in the literature.",2303.04645v1
2003-06-10,Local Density of States in a d-wave Superconductor with Stripe-Like Modulations and a Strong Impurity,"Using an effective Hamiltonian with d-wave superconductivity (dSC) and
competing antiferromagnetic (AF) interactions, we show that weak and
one-dimensionally modulated dSC, spin density wave (SDW) and charge density
wave (CDW) could coexist in the ground state configuration. With proper
parameters, the SDW order exhibits a period of 8a, while for dSC and CDW orders
the period is 4a. The local density of states (LDOS), which probing the
behavior of quasiparticle excitations, is found to have the identical
stripe-like structure as those in dSC and CDW orders. We point out that any
energy dependent modulations should come from the scatterings of the
quasiparticles from weak defects. The LDOS as a function of the bias voltage
are showing two small bumps within the superconducting coherence peaks, a
signature of presence of the stripes. When a strong impurity like Zn is placed
in such a system, the LDOS at its nearest neighboring sites are suppressed at
the zero bias by the local AF order and show a double-peak structure.",0306232v2
2005-10-03,Spin polarization of edge states and magnetosubband structure in quantum wires,"We provide a quantitative description of the structure of edge states in
split-gate quantum wires in the integer quantum Hall regime. We develop an
effective numerical approach based on the Green's function technique for the
self-consistent solution of Schrodinger equation where electron- and spin
interactions are included within the density functional theory in the local
spin density approximation. The major advantage of this technique is that it
can be directly incorporated into magnetotransport calculations, because it
provides the self-consistent eigenstates and wave vectors at a given energy,
not at a given wavevector (as conventional methods do). We use the developed
method to calculate the subband structure and propagating states in the quantum
wires in perpendicular magnetic field starting with a geometrical layout of the
wire. We discuss how the spin-resolved subband structure, the current
densities, the confining potentials, as well as the spin polarization of the
electron and current densities evolve when an applied magnetic field varies. We
demonstrate that the exchange and correlation interactions dramatically affect
the magnetosubbands in quantum wires bringing qualitatively new features in
comparison to a widely used model of spinless electrons in Hartree
approximation.",0510048v1
1998-12-10,Metastable quark-antiquark droplets within the Nambu-Jona-Lasinio model,"Chemically non-equilibrated quark-antiquark matter is studied within the
Nambu-Jona-Lasinio model. The equations of state of non-strange (q=u,d) and
strange (q=s) quark-antiquark systems are calculated in the mean-field
approximation. The existence of metastable bound states with zero pressure is
predicted at finite densities and temperatures less than about 50 MeV. It is
shown that the minimum energy per particle occurs for symmetric systems, with
equal densities of quarks and antiquarks. At T=0 these metastable states have
quark number densities of about 0.5 fm^-3 for q=u,d and of 1 fm^-3 for q=s. A
first order chiral phase transition is found at finite densities and
temperatures. The critical temperature for this phase transition is
approximately 75 MeV (90 MeV) for the non-strange (strange) baryon-free
quark-antiquark matter. For realistic choices of parameters, the model does not
predict the phase transition in chemically equilibrated systems. Possible decay
channels of the metastable quark-antiquark droplets and their signatures in
relativistic heavy-ion collisions are discussed.",9812319v1
2005-08-22,Behavior of shell-model configuration moments,"An important input into reaction theory is the density of states or the level
density. Spectral distribution theory (also known as nuclear statistical
spectroscopy) characterizes the secular behavior of the density of states
through moments of the Hamiltonian. One particular approach is to partition the
model space into subspaces and find the moments in those subspaces; a
convenient choice of subspaces are spherical shell-model configurations. We
revisit these configuration moments and find, for complete $0\hbar\omega$
many-body spaces, the following behaviors: (a) the configuration width is
nearly constant for all configurations; (b) the configuration asymmetry or
third moment is strongly correlated with the configuration centroid; (c) the
configuration fourth moment, or excess is linearly related to the square to the
configuration asymmetry. Such universal behavior may allow for more efficient
modeling of the density of states in a shell-model framework.",0508040v1
2008-02-21,Entanglement and Density Matrix of a Block of Spins in AKLT Model,"We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk
and $S/2$ at both ends. The unique ground state of this AKLT model is described
by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a
contiguous block of bulk spins in this ground state. It is shown that the
density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This
subspace is described by non-zero eigenvalues and corresponding eigenvectors of
the density matrix. We prove that for large block the von Neumann entropy
coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.",0802.3221v2
2009-07-22,Narrow depression in the density of states at the Dirac point in disordered graphene,"The electronic properties of non-interacting particles moving on a
two-dimensional bricklayer lattice are investigated numerically. In particular,
the influence of disorder in form of a spatially varying random magnetic flux
is studied. In addition, a strong perpendicular constant magnetic field $B$ is
considered. The density of states $\rho(E)$ goes to zero for $E\to 0$ as in the
ordered system, but with a much steeper slope. This happens for both cases: at
the Dirac point for B=0 and at the center of the central Landau band for finite
$B$. Close to the Dirac point, the dependence of $\rho(E)$ on the system size,
on the disorder strength, and on the constant magnetic flux density is analyzed
and fitted to an analytical expression proposed previously in connection with
the thermal quantum Hall effect. Additional short-range on-site disorder
completely replenishes the indentation in the density of states at the Dirac
point.",0907.3846v2
2009-09-08,Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models Part I: The Thomas-Fermi-von Weizacker model,"We provide {\it a priori} error estimates for the spectral and pseudospectral
Fourier (also called planewave) discretizations of the periodic
Thomas-Fermi-von Weizs\""acker (TFW) model and of the Kohn-Sham model, within
the local density approximation (LDA). These models allow to compute
approximations of the ground state energy and density of molecular systems in
the condensed phase. The TFW model is stricly convex with respect to the
electronic density, and allows for a comprehensive analysis (Part I). This is
not the case for the Kohn-Sham LDA model, for which the uniqueness of the
ground state electronic density is not guaranteed. Under a coercivity
assumption on the second order optimality condition, we prove in Part II that
for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a
minimizer in the vicinity of any Kohn-Sham ground state, and that this
minimizer is unique up to unitary transform. We then derive optimal {\it a
priori} error estimates for both the spectral and the pseudospectral
discretization methods.",0909.1464v1
2010-03-08,Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models,"We provide a priori error estimates for the spectral and pseudospectral
Fourier (also called planewave) discretizations of the periodic
Thomas-Fermi-von Weizs\""{a}cker (TFW) model and for the spectral discretization
of the Kohn-Sham model, within the local density approximation (LDA). These
models allow to compute approximations of the ground state energy and density
of molecular systems in the condensed phase. The TFW model is stricly convex
with respect to the electronic density, and allows for a comprehensive
analysis. This is not the case for the Kohn-Sham LDA model, for which the
uniqueness of the ground state electronic density is not guaranteed. Under a
coercivity assumption on the second order optimality condition, we prove that
for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a
minimizer in the vicinity of any Kohn-Sham ground state, and that this
minimizer is unique up to unitary transform. We then derive optimal a priori
error estimates for the spectral discretization method.",1003.1612v1
2012-06-22,Hadron Mass Spectrum and the Shear Viscosity to Entropy Density Ratio of Hot Hadronic Matter,"Lattice calculations of the QCD trace anomaly at temperatures $T<160$ MeV
have been shown to match hadron resonance gas model calculations, which include
an exponentially rising hadron mass spectrum. In this paper we perform a more
detailed comparison of the model calculations to lattice data that confirms the
need for an exponentially increasing density of hadronic states. Also, we find
that the lattice data is compatible with a hadron density of states that goes
as $\rho(m) \sim m^{-a}\exp(m/T_H) $ at large $m$ with $a> 5/2$ (where $T_H
\sim 167$ MeV). With this specific subleading contribution to the density of
states, heavy resonances are most likely undergo 2-body decay (instead of
multi-particle decay), which facilitates their inclusion into hadron transport
codes. Moreover, estimates for the shear viscosity and the shear relaxation
time coefficient of the hadron resonance model computed within the excluded
volume approximation suggest that these transport coefficients are sensitive to
the parameters that define the hadron mass spectrum.",1206.5138v1
2014-02-11,Density dependence of the Ionization Avalanche in ultracold Rydberg gases,"We report on the behaviour of the ionization avalanche in an ensemble of
ultracold 87Rb atoms coupled to a high lying Rydberg state and investigate
extensions to the current model by including the effects of three-body
recombination and plasma expansion. To separate the two effects we study the
time dependence of the plasma formation at various densities as well as for
different nS and nD states. At medium densities and low n we observe the onset
of the avalanche as has been reported in other experiments, as well as a
subsequent turn-off of the avalanche for longer excitation times, which we
associate with plasma expansion. At higher densities and for higher lying
Rydberg states we observe a disappearance of the avalanche signature, which we
attribute to three-body recombination.",1402.2400v1
2015-01-22,Dynamical properties of ordered Fe-Pt alloys,"The structure, magnetic properties, and lattice dynamics of ordered Fe-Pt
alloys with three stoichiometric compositions, Fe$_3$Pt, FePt and FePt$_3$,
have been investigated using the density functional theory. Additionally, the
existing experimental data have been complemented by new measurements of the Fe
projected phonon density of states performed for the Fe$_3$Pt and FePt$_3$ thin
films using the nuclear inelastic scattering technique. The calculated phonon
dispersion relations and phonon density of states have been compared with the
experimental data. The dispersion curves are very well reproduced by the
calculations, although, the softening of the transversal acoustic mode TA$_1$
leads to some discrepancy between the theory and experiment in Fe$_3$Pt. A very
goood agreement between the measured spectra and calculations performed for the
tetragonal structure derived from the soft mode may signal that the tetragonal
phase with the space group $P4/mbm$ plays an important role in the martensitic
transformation observed in Fe$_3$Pt. For FePt$_3$, the antiferromagnetic order
appearing with decreasing temperature has been also investigated. The studies
showed that the phonon density of states of FePt$_3$ very weakly depends on the
magnetic configuration.",1501.05550v1
2016-07-12,Hall-effect within the colossal magnetoresistive semi-metallic state of MoTe2,"Here, we report a systematic study on the Hall-effect of the semi-metallic
state of bulk MoTe$_2$, which was recently claimed to be a candidate for a
novel type of Weyl semi-metallic state. The temperature ($T$) dependence of the
carrier densities and of their mobilities, as estimated from a numerical
analysis based on the isotropic two-carrier model, indicates that its
exceedingly large and non-saturating magnetoresistance may be attributed to a
near perfect compensation between the densities of electrons and holes at low
temperatures. A sudden increase in hole density, with a concomitant rapid
increase in the electron mobility below $T \sim 40$ K, leads to comparable
densities of electrons and holes at low temperatures suggesting a possible
electronic phase-transition around this temperature.",1607.03330v1
2017-04-18,Electronic properties of disordered Weyl semimetals at charge neutrality,"Weyl semimetals have been intensely studied as a three dimensional
realization of a Dirac-like excitation spectrum where the conduction bands and
valence bands touch at isolated Weyl points in momentum space. Like in
graphene, this property entails various peculiar electronic properties.
However, recent theoretical studies have suggested that resonant scattering
from rare regions can give rise to a non-zero density of states even at charge
neutrality. Here, we give a detailed account of this effect and demonstrate how
the semimetallic nature is suppressed at the lowest scales. To this end, we
develop a self-consistent T-matrix approach to investigate the density of
states beyond the limit of weak disorder. Our results show a nonvanishing
density of states at the Weyl point which exhibits a non-analytic dependence on
the impurity density. This unusually strong effect of rare regions leads to a
revised estimate for the conductivity close to the Weyl point and emphasizes
possible deviations from semimetallic behavior in dirty Weyl semimetals at
charge neutrality even with very low impurity concentration.",1704.05481v1
2011-12-04,"Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy","We present a phenomenological theory of nuclei that incorporates clustering
at the nuclear surface in a general form. The theory explains the recently
extracted large symmetry energy by Natowitz et al. at low densities of nuclear
matter and is fully consistent with the static properties of nuclei. In
phenomenological way clusters of all sizes, shapes along with medium
modifications are included. Symmetric nuclear matter properties are discussed
in detail. Arguments are given that lead to an equation of state of nuclear
matter consistent with clustering in the low density region. We also discuss
properties of asymmetric nuclear matter. Because of clustering, an interesting
interpretation of the equation of state of asymmetric nuclear matter emerges.
As a framework, an extended version of Thomas Fermi theory is adopted for
nuclei which also contain phenomenological pairing and Wigner contributions.
This theory connects the nuclear matter equation of state, which incorporate
clustering at low densities, with clustering in nuclei at the nuclear surface.
Calculations are performed for various equation of state of nuclear matter. We
consider measured binding energies of 2149 nuclei for N, Z \geq 8. The
importance of quartic term in symmetry energy is demonstrated at and below the
saturation density of nuclear matter. It is shown that it is largely related to
the use of, ab initio, realistic equation of state of neutron matter,
particularly the contribution arising from the three neutron interaction and
somewhat to clustering. Reasons for these are discussed. Because of clustering
the neutron skin thickness in nuclei is found to reduce significantly. Theory
predicts new situations and regimes to be explored both theoretically and
experimentally.",1112.0718v1
2001-04-12,Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density,"We studied ferromagnetism in the one-dimensional Hubbard model with doubly
degenerate atomic orbitals by means of the density-matrix renormalization-group
method and obtained the ground-state phase diagrams. It was found that
ferromagnetism is stable from low to high (0< n < 1.75) electron density when
the interactions are sufficiently strong. Quasi-long-range order of triplet
superconductivity coexists with the ferromagnetic order for a strong Hund
coupling region, where the inter-orbital interaction U'-J is attractive. At
quarter-filling (n=1), the insulating ferromagnetic state appears accompanying
orbital quasi-long-range order. For low densities (n<1), ferromagnetism occurs
owing to the ferromagnetic exchange interaction caused by virtual hoppings of
electrons, the same as in the quarter-filled system. This comes from separation
of the charge and spin-orbital degrees of freedom in the strong coupling limit.
This ferromagnetism is fragile against variation of band structure. For high
densities (n>1), the phase diagram of the ferromagnetic phase is similar to
that obtained in infinite dimensions. In this case, the double exchange
mechanism is operative to stabilize the ferromagnetic order and this long-range
order is robust against variation of the band-dispersion. A partially polarized
state appears in the density region 1.68<n<1.75 and phase separation occurs for
n just below the half-filling (n=2).",0104223v2
2019-05-03,Correlated quantum dynamics of two quenched fermionic impurities immersed in a Bose-Einstein Condensate,"We unravel the nonequilibrium dynamics of two fermionic impurities immersed
in a one-dimensional bosonic gas following an interspecies interaction quench
from weak to strong repulsions. Monitoring the temporal evolution of the
single-particle density of each species we reveal the existence of four
distinct dynamical regimes. For weak interspecies repulsions both species
either perform a breathing motion or the impurity density splits into two parts
which interact and disperse within the bosonic cloud. Turning to strong
interactions we observe the formation of dark-bright states within the
mean-field approximation. However, the correlated dynamics shows that the
fermionic density splits into two repelling density peaks which either travel
towards the edges of the bosonic cloud where they equilibrate or they approach
an almost steady state propagating robustly within the bosonic gas which forms
density dips at the same location. For these strong interspecies interactions
an energy transfer process from the impurities to their environment occurs at
the many-body level, while a periodic energy exchange from the bright states
(impurities) to the bosonic species is identified in the absence of
correlations. Finally, inspecting the one-body coherence function for strong
interactions enables us to conclude on the spatial localization of the
quench-induced fermionic density humps.",1905.02624v2
2017-09-26,Renyi Entropy of Chaotic Eigenstates,"Using arguments built on ergodicity, we derive an analytical expression for
the Renyi entanglement entropies corresponding to the finite-energy density
eigenstates of chaotic many-body Hamiltonians. The expression is a universal
function of the density of states and is valid even when the subsystem is a
finite fraction of the total system - a regime in which the reduced density
matrix is not thermal. We find that in the thermodynamic limit, only the von
Neumann entropy density is independent of the subsystem to the total system
ratio $V_A/V$, while the Renyi entropy densities depend non-linearly on
$V_A/V$. Surprisingly, Renyi entropies $S_n$ for $n > 1$ are convex functions
of the subsystem size, with a volume law coefficient that depends on $V_A/V$,
and exceeds that of a thermal mixed state at the same energy density. We
provide two different arguments to support our results: the first one relies on
a many-body version of Berry's formula for chaotic quantum mechanical systems,
and is closely related to eigenstate thermalization hypothesis. The second
argument relies on the assumption that for a fixed energy in a subsystem, all
states in its complement allowed by the energy conservation are equally likely.
We perform Exact Diagonalization study on quantum spin-chain Hamiltonians to
test our analytical predictions, and find good agreement.",1709.08784v2
2022-07-18,Non-Gaussian Bayesian Filtering by Density Parametrization Using Power Moments,"Non-Gaussian Bayesian filtering is a core problem in stochastic filtering.
The difficulty of the problem lies in parameterizing the state estimates.
However the existing methods are not able to treat it well. We propose to use
power moments to obtain a parameterization. Unlike the existing parametric
estimation methods, our proposed algorithm does not require prior knowledge
about the state to be estimated, e.g. the number of modes and the feasible
classes of function. Moreover, the proposed algorithm is not required to store
massive parameters during filtering as the existing nonparametric Bayesian
filters, e.g. the particle filter. The parameters of the proposed
parametrization can also be determined by a convex optimization scheme with
moments constraints, to which the solution is proved to exist and be unique. A
necessary and sufficient condition for all the power moments of the density
estimate to exist and be finite is provided. The errors of power moments are
analyzed for the density estimate being either light-tailed or heavy-tailed.
Error upper bounds of the density estimate for the one-step prediction are
proposed. Simulation results on different types of density functions of the
state are given, including the heavy-tailed densities, to validate the proposed
algorithm.",2207.08519v3
2002-05-06,Itinerant Ferromagnetism and Quantum Criticality in Sc$_3$In,"The electronic structure and magnetic properties of hexagonal Sc$_3$In are
calculated within density functional theory. We find that the Fermi energy lies
in a region of flat Sc $d$ derived bands leading to a peak in the density of
states and Stoner ferromagnetism. The calculated local spin density and
generalized gradient approximation spin magnetizations are both enhanced with
respect to experiment, which is an indication of significant quantum critical
fluctuations, neglected in these approximations. We find, as expected, that the
ferromagnetism is initially enhanced under pressure, meaning that the critical
point cannot be reached with modest pressure. However, we find that the density
of states peak around the Fermi energy and the calculated density functional
magnetic properties are sensitive to the $c/a$ ratio, so that the quantum
critical point may be reached under uniaxial strain.",0205103v1
2002-11-05,Glass Transition of Hard Sphere Systems: Molecular Dynamics and Density Functional Theory,"The glass transition of a hard sphere system is investigated within the
framework of the density functional theory (DFT). Molecular dynamics (MD)
simulations are performed to study dynamical behavior of the system on the one
hand and to provide the data to produce the density field for the DFT on the
other hand. Energy landscape analysis based on the DFT shows that there appears
a metastable (local) free energy minimum representing an amorphous state as the
density is increased. This state turns out to become stable, compared with the
uniform liquid, at some density, around which we also observe sharp slowing
down of the $alpha$ relaxation in MD simulations.",0211091v3
2002-04-08,Chemical Freezeout in Heavy Ion Collisions,"We construct a hadronic equation of state consistent with chemical freezeout
and discuss how such an equation of state modifies the radial and elliptic flow
in a hydrodynamic + hadronic cascade model of relativistic heavy ion collisions
at the SPS. Incorporating chemical freezeout does not change the relation
between pressure and energy density. However, it does change the relation
between temperature and energy density. Consequently, when the hydrodynamic
solution and freezeout are expressed in terms of energy density, chemical
freezeout does not modify the hydrodynamic radial and elliptic flow velocities
studied previously. Finally, we examine chemical freezeout within the hadronic
cascade (RQMD). Once chemical freezeout is incorporated into the hydrodynamics,
the final spectra and fireball lifetimes are insensitive to the temperature at
which the switch from hydrodynamics to cascade is made. Closer inspection
indicates that the pion spectrum in chemically frozen hydrodynamics is
significantly cooler than in the hydro+cascade model. This difference is
reflected in $v_{2}(p_{T})$. We extract the freezeout hadron density in RQMD
and interpret it in thermal terms; the freezeout hadron density corresponds to
a freezeout temperature of $T_{f}\approx100 $ MeV and $\mu_{\pi} \approx 80 $
MeV.",0204023v1
2006-10-10,Intrinsic-Density Functionals,"The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to
functionals of the localized intrinsic density of a self-bound system such as a
nucleus. After defining the intrinsic-density functional, we modify the usual
Kohn-Sham procedure slightly to evaluate the mean-field approximation to the
functional, and carefully describe the construction of the leading corrections
for a system of fermions in one dimension with a spin-degeneracy equal to the
number of particles N. Despite the fact that the corrections are complicated
and nonlocal, we are able to construct a local Skyrme-like intrinsic-density
functional that, while different from the exact functional, shares with it a
minimum value equal to the exact ground-state energy at the exact ground-state
intrinsic density, to next-to-leading order in 1/N. We briefly discuss
implications for real Skyrme functionals.",0610043v1
2010-09-30,Holographic Charge Density Waves,"We discuss a gravity dual of a charge density wave consisting of a U(1) gauge
field and two scalar fields in the background of an AdS$_4$ Schwarzschild black
hole together with an antisymmetric field (probe limit). Interactions drive the
system to a phase transition below a critical temperature. We numerically
compute the ground states characterized by modulated solutions for the gauge
potential corresponding to a dynamically generated unidirectional charge
density wave in the conformal field theory. Signatures of the holographic
density waves are retrieved by studying the dynamical response to an external
electric field. We find that this novel holographic state shares many common
features with the standard condensed matter version of charge density wave
systems.",1009.6179v3
2012-07-12,On the alternatives for bath correlators and spectral densities from mixed quantum-classical simulations,"We investigate on the procedure of extracting a ""spectral density"" from mixed
QM/MM calculations and employing it in open quantum systems models. In
particular, we study the connection between the energy gap correlation function
extracted from ground state QM/MM and the bath spectral density used as input
in open quantum system approaches. We introduce a simple model which can give
intuition on when the ground state QM/MM propagation will give the correct
energy gap. We also discuss the role of higher order correlators of the
energy-gap fluctuations which can provide useful information on the bath.
Further, various semiclassical corrections to the spectral density, are applied
and investigated. Finally, we apply our considerations to the photosynthetic
Fenna-Matthews-Olson complex. For this system, our results suggest the use of
the Harmonic prefactor for the spectral density rather than the Standard one,
which was employed in the simulations of the system carried out to date.",1207.3087v3
2013-06-22,Defect recombination induced by density-activated carrier diffusion in nonpolar InGaN quantum wells,"We report on the observation of carrier-diffusion-induced defect emission at
high excitation density in a-plane InGaN single quantum wells. When increasing
excitation density in a relatively high regime, we observed the emergence of
defect-related emission together with a significant reduction in bandedge
emission efficiency. The experimental results can be well explained with the
density-activated carrier diffusion from localized states to defect states.
Such a scenario of density-activated defect recombination, as confirmed by the
dependences of photoluminescence on the excitation photon energy and
temperature, is a plausible origin of efficiency droop in a-plane InGaN
quantum-well light-emitting diodes.",1306.5292v1
2016-04-16,Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation,"Estimation of quantum states is one of the most important steps in any
quantum information processing experiment. A naive reconstruction of the
density matrix from experimental measurements can often give density matrices
which are not positive, and hence not physically acceptable. How do we ensure
that at all stages of reconstruction, we keep the density matrix positive and
normalized? Recently a method has been suggested based on maximum likelihood
estimation, wherein the density matrix is guaranteed to be positive definite.
We experimentally implement this protocol and demonstrate its utility on an NMR
quantum information processor. We discuss several examples where we undertake
such an estimation and compare it with the standard method of state estimation.",1604.04691v1
2016-06-11,Coupled Leidenfrost States as a Monodisperse Granular Clock,"Using an event-driven molecular dynamics simulation, we show that simple
monodisperse granular beads confined in coupled columns may oscillate as a new
type of granular clock. To trigger this oscillation, the system needs to be
driven against gravity into a density-inverted state, with a high-density
clustering phase supported from below by a gas-like low-density phase
(Leidenfrost effect) in each column. Our analysis reveals that the
density-inverted structure and the relaxation dynamics between the phases can
amplify any small asymmetry between the columns, and lead to a giant
oscillation. The oscillation occurs only for an intermediate range of the
coupling strength, and the corresponding phase diagram can be universally
described with a characteristic height of the density-inverted structure. A
minimal two-phase model is proposed and linear stability analysis shows that
the triggering mechanism of the oscillation can be explained as a switchable
two-parameter Hopf bifurcation. Numerical solutions of the model also reproduce
similar oscillatory dynamics to the simulation results.",1606.03559v1
2018-11-30,Ionization potential depression and Pauli blocking in degenerate plasmas at extreme densities,"New facilities explore warm dense matter (WDM) at extreme conditions where
the densities are very high (e.g., carbon up to density of 50 g cm$^{-3}$) so
that electrons are degenerate even at 100 eV temperature. Whereas in the
non-degenerate region correlation effects such as Debye screening and its
improvements are relevant for the ionization potential depression (IPD), new
effects have to be considered in degenerate plasmas. In addition to the Fock
shift of the self-energies, the bound-state Pauli blocking becomes important
with increasing density. Taking these degeneracy effects into account leads to
a reduction of the ionization potential and to a higher degree of ionization.
Standard approaches to IPD such as Stewart-Pyatt and widely used opacity tables
(e.g., OPAL) do not contain Pauli blocking effects for bound states so that
they fail to explain experiments with WDM in the high density region. As
example, results for the ionization degree of carbon plasmas are presented.",1811.12912v1
2019-08-08,Gravitational Waves from Holographic Neutron Star Mergers,"We simulate the merger of binary neutron stars and analyze the spectral
properties of their gravitational waveforms. For the stars we construct hybrid
equations of state (EoSs) with a standard nuclear matter EoS at low densities,
transitioning to a state-of-the-art holographic EoS in the otherwise
intractable high density regime. Depending on the transition density the
characteristic frequencies in the spectrum produced from the hybrid EoSs are
shifted to significantly lower values as compared to the pure nuclear matter
EoS. The highest rest-mass density reached outside a possible black hole
horizon is approximately $1.1 \cdot 10^{15}$ g/cm$^3$, which for the
holographic model is below the density of the deconfined quark matter phase.",1908.03213v1
2018-10-24,Exact Kohn-Sham Density Functional Theory on a Lattice,"We formulate a set of equations that facilitate an exact numerical solution
of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour
hopping and arbitrary site potentials. The approach relies on a mapping of the
non-interacting Kohn-Sham ground state wave function onto the exact interacting
system wavefunction and two interconnected self-consistent cycles. The
self-consistent cycles are performed within the framework of the Kohn-Sham
non-interacting system without any direct reference to the interacting system.
The first self-consistent cycle updates the mapping of the non-interacting
wavefunction onto the interacting wavefunction based on a trial input density,
while the second self-consistent cycle updates the Kohn-Sham potential to yield
the trial density. At the solution point, the exact density, the exact
Kohn-Sham potential, the density functional correlation energy and the exact
interacting system ground state energy are available.",1810.10442v1
2019-01-03,"Charge density functional plus $U$ calculation of lacunar spinel GaM$_4$Se$_8$ (M = Nb, Mo, Ta, and W)","Charge density functional plus $U$ calculations are carried out to examine
the validity of molecular $J_\text{eff}$=1/2 and 3/2 state in lacunar spinel
GaM$_4$X$_8$ (M = Nb, Mo, Ta, and W). With LDA (spin-unpolarized local density
approximation)$+U$, which has recently been suggested as the more desirable
choice than LSDA (local spin density approximation)$+U$, we examine the band
structure in comparison with the previous prediction based on the
spin-polarized version of functional and with the prototypical
$J_\text{eff}$=1/2 material Sr$_2$IrO$_4$. It is found that the previously
suggested $J_\text{eff}$=1/2 and 3/2 band characters remain valid still in
LDA$+U$ calculations while the use of charge-only density causes some minor
differences. Our result provides the further support for the novel molecular
$J_\text{eff}$ state in this series of materials, which can hopefully motivate
the future exploration toward its verification and the further search for new
functionalities.",1901.00647v1
2021-06-08,Revisiting the variational two-particle reduced density matrix for nuclear systems,"In most nuclear many-body methods, observables are calculated using many-body
wave functions explicitly. The variational two-particle reduced density matrix
method is one of the few exceptions to the rule. Ground-state energies of both
closed-shell and open-shell nuclear systems can indeed be evaluated by
minimizing a constrained linear functional of the two-particle reduced density
matrix. However, it has virtually never been used in nuclear theory, because
nuclear ground states were found to be well overbound, contrary to those of
atoms and molecules. Consequently, we introduced new constraints in the nuclear
variational two-particle reduced density matrix method, developed recently for
atomic and molecular systems. Our calculations then show that this approach can
provide a proper description of nuclear systems where only valence neutrons are
included. For the nuclear systems where both neutrons and protons are active,
however, the energies obtained with the variational two-particle reduced
density matrix method are still overbound. The possible reasons for the noticed
discrepancies and solutions to this problem will be discussed.",2106.04103v1
2021-08-30,Nuclear landscape in a mapped collective Hamiltonian from covariant density functional theory,"The nuclear landscape has been investigated within the triaxial relativistic
Hartree-Bogoliubov theory with the PC-PK1 density functional, and the
beyond-mean-field dynamical correlation energies are taken into account by a
microscopically mapped five-dimensional collective Hamiltonian without
additional free parameters. The effects of triaxial deformation and dynamical
correlations on the nuclear landscape are analyzed. The present results provide
the best description of the experimental binding energies, in particular for
medium and heavy mass regions, in comparison with the results obtained
previously with other state-of-the-art covariant density functionals. The
inclusion of the dynamical correlation energies plays an important role in the
PC-PK1 results. It is emphasized that the nuclear landscape is considerably
extended by the PC-PK1 functional in comparison with the previous results with
other density functionals, which may be due to the different isovector
properties in the density functionals.",2108.13057v2
2010-03-18,Effects of the density dependence of nuclear symmetry energy on properties of superheavy nuclei,"Effects of the density dependence of the nuclear symmetry energy on
ground-state properties of superheavy nuclei are studied in the relativistic
mean-field theory. It is found that the softening of the symmetry energy plays
an important role in the empirical shift [Phys. Rev. C 67, 024309 (2003)] of
spherical orbitals in superheavy nuclei. The calculation based on the
relativistic mean-field models NL3 and FSUGold supports the double shell
closure in $^{292}120$ with the softening of the symmetry energy. In addition,
the significant effect of the density dependence of the symmetry energy on the
neutron skin thickness in superheavy nuclei are investigated.",1003.3520v1
2006-05-12,Smoothness of Correlations in the Anderson Model at Strong Disorder,"We study the higher-order correlation functions of covariant families of
observables associated with random Schr\""odinger operators on the lattice in
the strong disorder regime. We prove that if the distribution of the random
variables has a density analytic in a strip about the real axis, then these
correlation functions are analytic functions of the energy outside of the
planes corresponding to coincident energies. In particular, this implies the
analyticity of the density of states, and of the current-current correlation
function outside of the diagonal. Consequently, this proves that the
current-current correlation function has an analytic density outside of the
diagonal at strong disorder.",0605042v1
2013-01-03,Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids,"I describe the Time-Dependent Superfluid Local Density Approximation, which
is an adiabatic extension of the Density Functional Theory to superfluid Fermi
systems and their real-time dynamics. This new theoretical framework has been
applied to describe a number of phenomena in cold atomic gases and nuclear
collective motion: excitation of the Higgs modes in strongly interacting Fermi
superfluids, generation of quantized vortices, crossing and reconnection of
vortices, excitation of the superflow at velocities above the critical
velocity, excitation of quantum shock waves and domain walls in the collisions
of superfluid atomic clouds, excitation of collective states in nuclei.",1301.0357v1
2023-03-13,Small Fermi pockets intertwined with charge stripes and pair density wave order in a kagome superconductor,"The kagome superconductor family AV3Sb5 (A=Cs, K, Rb) emerged as an exciting
platform to study exotic Fermi surface instabilities. Here we use
spectroscopic-imaging scanning tunneling microscopy (SI-STM) and angle-resolved
photoemission spectroscopy (ARPES) to reveal how the surprising cascade of
higher and lower-dimensional density waves in CsV3Sb5 is intimately tied to a
set of small reconstructed Fermi pockets. ARPES measurements visualize the
formation of these pockets generated by a 3D charge density wave transition.
The pockets are connected by dispersive q* wave vectors observed in Fourier
transforms of STM differential conductance maps. As the additional 1D charge
order emerges at a lower temperature, q* wave vectors become substantially
renormalized, signaling further reconstruction of the Fermi pockets.
Remarkably, in the superconducting state, the superconducting gap modulations
give rise to an in-plane Cooper pair-density-wave at the same q* wave vectors.
Our work demonstrates the intrinsic origin of the charge-stripes and the
pair-density-wave in CsV3Sb5 and their relationship to the Fermi pockets. These
experiments uncover a unique scenario of how Fermi pockets generated by a
parent charge density wave state can provide a favorable platform for the
emergence of additional density waves.",2303.07254v1
1999-10-25,Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground states,"A Hubbard model with a N_d-fold degenerate single-particle ground state has
ferromagnetic ground states if the number of electrons is less or equal to N_d.
It is shown rigorously that the local stability of ferromagnetism in such a
model implies global stability: The model has only ferromagnetic ground states,
if there are no single spin-flip ground states. If the number of electrons is
equal to N_d, it is well known that the ferromagnetic ground state is unique if
and only if the single-particle density matrix is irreducible. We present a
simplified proof for this result.",9910385v1
2003-05-07,Staggered-flux normal state in the weakly doped t-J model,"A normal (non-superconducting) ground state of the t-J model may be
variationally approximated by a Gutzwiller-projected wave function. Within this
approximation, at small hole doping near half-filling, the normal state favors
staggered-flux ordering. Such a staggered-flux state may occur in vortex cores
of underdoped high-temperature cuprate superconductors. From comparing the
energies of the staggered-flux state and of the superconducting state, we
numerically obtain the condensation energy. Extracting the superfluid density
directly from the projected superconducting wave function, we can also estimate
the coherence length at zero temperature.",0305143v1
1999-10-05,No-Concentrating Theorem of Pure Entangled States,"Suppose two distant observers Alice and Bob share a pure biparticle entangled
state secretly chosen from a set, it is shown that Alice (Bob) can
probabilistic concentrate the state to a maximally entangled state by applying
local operations and classical communication (LQCC) if and only if the states
in the set share the same marginal density operator for her (his) subsystem.
Applying this result, we present probabilistic superdense coding and show that
perfect purification of mixed state is impossible using only LQCC on individual
particles.",9910018v2
2003-12-17,Geometric phase for mixed states: a differential geometric approach,"A new definition and interpretation of geometric phase for mixed state cyclic
unitary evolution in quantum mechanics are presented. The pure state case is
formulated in a framework involving three selected Principal Fibre Bundles, and
the well known Kostant-Kirillov-Souriau symplectic structure on (co) adjoint
orbits associated with Lie groups. It is shown that this framework generalises
in a natural and simple manner to the mixed state case. For simplicity, only
the case of rank two mixed state density matrices is considered in detail. The
extensions of the ideas of Null Phase Curves and Pancharatnam lifts from pure
to mixed states are also presented.",0312146v1
2004-03-15,A note on continuous ensemble expansions of quantum states,"Generalizing the notion of relative entropy, the difference between a priori
and a posteriori relative entropy for quantum systems is drawn. The former,
known as quantum relative entropy, is associated with quantum states
recognition. The latter -- a posteriori relative quantum entropy is shown to be
related with state reconstruction due to the following property: given a
density operator $\rho$, ensembles of pure states with Gibbs distribution with
respect to the defined distance are proved to represent the initial state
$\rho$ up to an amount of white noise (completely mixed state) which can be
made arbitrary small.",0403105v1
2006-11-10,Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators,"We discuss some basic tools for an analysis of one-dimensionalquantum systems
defined on a cyclic coordinate space. The basic features of the generalized
coherent states, the complexifier coherent states are reviewed. These states
are then used to define the corresponding (quasi)densities in phase space. The
properties of these generalized Husimi distributions are discussed, in
particular their zeros.Furthermore, the use of the complexifier coherent states
for a semiclassical analysis is demonstrated by deriving a semiclassical
coherent state propagator in phase space.",0611116v2
2007-05-24,On circulant states with positive partial transpose,"We construct a large class of quantum ""d x d"" states which are positive under
partial transposition (so called PPT states). The construction is based on
certain direct sum decomposition of the total Hilbert space displaying
characteristic circular structure - that is way we call them circulant states.
It turns out that partial transposition maps any such decomposition into
another one and hence both original density matrix and its partially transposed
partner share similar cyclic properties. This class contains many well known
examples of PPT states from the literature and gives rise to a huge family of
completely new states.",0705.3534v3
2013-09-04,Partial Multipartite Entanglement in the Matrix Product State Formalism,"We present a method to apply the well-known matrix product state (MPS)
formalism to partially separable states in solid state systems. The
computational effort of our method is equal to the effort of the standard
density matrix renormalisation group (DMRG) algorithm. Consequently, it is
applicable to all usually considered condensed matter systems where the DMRG
algorithm is successful. We also show in exemplary cases, that polymerisation
properties of ground states are closely connected to properties of partial
separability, even if the ground state itself is not partially separable.",1309.1058v1
2007-10-10,Quantum states with strong positive partial transpose,"We construct a large class of bipartite M x N quantum states which defines a
proper subset of states with positive partial transposes (PPT). Any state from
this class is PPT but the positivity of its partial transposition is recognized
with respect to canonical factorization of the original density operator. We
propose to call elements from this class states with strong positive partial
transposes (SPPT). We conjecture that all SPPT states are separable.",0710.1934v1
2010-05-05,The Equation of State from Observed Masses and Radii of Neutron Stars,"We determine an empirical dense matter equation of state from a heterogeneous
dataset of six neutron stars: three type I X-ray bursters with photospheric
radius expansion, studied by Ozel et al., and three transient low-mass X-ray
binaries. We critically assess the mass and radius determinations from the
X-ray burst sources and show explicitly how systematic uncertainties, such as
the photospheric radius at touchdown, affect the most probable masses and
radii. We introduce a parameterized equation of state and use a Markov Chain
Monte Carlo algorithm within a Bayesian framework to determine nuclear
parameters such as the incompressibility and the density dependence of the bulk
symmetry energy. Using this framework we show, for the first time, that these
parameters, predicted solely on the basis of astrophysical observations, all
lie in ranges expected from nuclear systematics and laboratory experiments. We
find significant constraints on the mass-radius relation for neutron stars, and
hence on the pressure-density relation of dense matter. The predicted symmetry
energy and the equation of state near the saturation density are soft,
resulting in relatively small neutron star radii around 11-12 km for M=1.4
Msun. The predicted equation of state stiffens at higher densities, however,
and our preferred model for X-ray bursts suggests that the neutron star maximum
mass is relatively large, 1.9-2.2 Msun. Our results imply that several commonly
used equations of state are inconsistent with observations.",1005.0811v2
2012-04-17,Spin properties of 2D semiconductors probed by scanning tunneling microscopy,"The interrelation between spin and charge in semiconductors leads to
interesting effects, e.g., the Rashba-type spin-orbit splitting or the exchange
enhancement. These properties are proposed to be used in applications such as
spin transistors or spin qubits. Probing them on the local scale with the
ultimate spatial resolution of the scanning tunneling microscope addresses
their susceptibility to disorder directly. Here we review the results obtained
on two-dimensional semiconductor systems (2DES). We describe the preparation
and characterization of an adequate 2DES which can be probed by scanning
tunneling microscopy. It is shown how the electron density and the disorder
within the 2DES can be tuned and measured. The observed local density of states
of weakly and strongly disordered systems is discussed in detail. It is shown
that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field.
The corresponding local density of states across a quantum Hall transition is
mapped showing the development from localized states to extended states and
back to localized states in real space. Decoupling the 2DES from screening
electrons of the bulk of the III-V semiconductor leads to a measurable exchange
enhancement of up to 0.7 meV which depends on the local spin polarization of
the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba
spin splitting with $\alpha$ as large as $7\cdot 10^{-11}$eVm is observed as a
beating in the density of states in magnetic field. The Rashba spin splitting
varies with position by about $\pm 50$% being largest at potential hills.",1204.3815v1
2014-10-27,Taming the pion condensation in QCD at finite baryon density,"In the Monte Carlo study of QCD at finite baryon density based upon the phase
reweighting method, the pion condensation in the phase-quenched theory and
associated zero-mode prevent us to go to the low-temperature high-density
region. We propose a method to circumvent them by a simple modification of the
density of state method. We first argue that the standard version of the
density of state method, which is invented to solve the overlapping problem, is
effective only for a certain `good' class of observables. We then modify it so
as to solve the overlap problem for `bad' observables as well. While, in the
standard version of the density of state method, we usually constrain an
observable we are interested in, we fix a different observable in our new
method which has a sharp peak at some particular value characterizing the
correct vacuum of the target theory. In the finite-density QCD, such an
observable is the pion condensate. The average phase becomes vanishingly small
as the value of the pion condensate becomes large, hence it is enough to
consider configurations with small values of pion condensate, where the zero
mode does not appear. We demonstrate an effectiveness of our method by using a
toy model (the chiral random matrix theory) which captures the properties of
finite-density QCD qualitatively. We also argue how to apply our method to
other theories including finite-density QCD. Although the example we study
numerically is based on the phase reweighting method, the same idea can be
applied to more general reweighting methods and we show how this idea can be
applied to find a possible QCD critical point.",1410.7421v1
2022-09-22,Detection of a Pair Density Wave State in UTe$_2$,"Spin-triplet topological superconductors should exhibit many unprecedented
electronic properties including fractionalized electronic states relevant to
quantum information processing. Although UTe$_2$ may embody such bulk
topological superconductivity, its superconductive order-parameter
$\Delta(\mathbf{k})$ remains unknown. Many diverse forms for
$\Delta(\mathbf{k})$ are physically possible in such heavy fermion materials.
Moreover, intertwined density waves of spin (SDW), charge (CDW) and pairs (PDW)
may interpose, with the latter state exhibiting spatially modulating
superconductive order-parameter $\Delta(\mathbf{r})$, electron pair density and
pairing energy-gap. Hence, the newly discovered CDW state in UTe$_2$ motivates
the prospect that a PDW state may exist in this material. To search for it, we
visualize the pairing energy-gap with $\mu$$eV$-scale energy-resolution using
superconductive STM tips. We detect three PDWs, each with peak-peak gap
modulations circa 10 $\mu$$eV$ and at incommensurate wavevectors
$\mathbf{P}_{i=1,2,3}$ that are indistinguishable from the wavevectors
$\mathbf{Q}_{i=1,2,3}$ of the prevenient CDW. Concurrent visualization of the
UTe$_2$ superconductive PDWs and the non-superconductive CDWs reveals that
every $\mathbf{P}_i$ : $\mathbf{Q}_i$ pair exhibits a relative phase
$\delta\phi \approx \pi$. From these observations, and given UTe$_2$ as a
spin-triplet superconductor, this PDW state should be a spin-triplet pair
density wave. While such states do exist in superfluid $^{3}$He, for
superconductors they are unprecedented.",2209.10859v3
2022-12-05,Enhanced Negative Energy with a Massless Dirac Field,"Motivated by traversable wormhole constructions that require large amounts of
negative energy, we explore constraints on the amount of negative energy that
can be carried by a free Dirac field in a slab-shaped region between two
parallel spatial planes. Specifically, we ask what is the minimum possible
uniform energy density that can exist at some time, considering all possible
states and all possibilities for the physics outside the slab. The vacuum state
where we identify the two sides of the slab with antiperiodic boundary
conditions gives one possible state with uniform negative energy, but we argue
that states with more negative energy exist above 1+1 dimensions. Technically,
we reduce the problem to studying a massive Dirac field on an interval in 1+1
dimensions and numerically search for states with uniform energy density in a
lattice regulated model. We succeed in finding states with enhanced negative
energy (relative to the antiperiodic vacuum) which also appear to have a
sensible continuum limit. Our results for the mass-dependence of the minimum
uniform energy density in 1+1 dimensions suggest that for a 3+1 dimensional
massless Dirac fermion, it is possible to have states with arbitrarily large
uniform negative energy density in an arbitrarily wide slab.",2212.02609v3
2016-04-08,Transformation of bound states of relativistic hydrogen-l ike atom into two-component form,"A single-step Eriksen transformation of~$1S_{1/2}$,~$2P_{1/2}$ and~$2P_{3/2}$
states of the relativistic hydrogen-like atom is performed exactly by
expressing each transformed function (TF) as a linear combination of
eigenstates of the Dirac Hamiltonian. The transformed functions, which are
four-component spinors with vanishing two lower components, are calculated
numerically and have the same symmetries as the initial states. For all nuclear
charges~$Z \in [1\ldots 92]$ a contribution of the initial state to TFs exceeds
86\% of the total probability density. Next large contribution to TFs comes
from continuum states with negative energies close to~$-m_0c^2-E_b$,
where~$E_b$ is the binding energy of initial state. Contribution of other
states to TFs is less than~$0.1\%$ of the total probability density. Other
components of TFs are nearly zero which confirms both validity of the Eriksen
transformation and accuracy of the numerical calculations. The TFs
of~$1S_{1/2}$ and~$2P_{1/2}$ states are close to~$1s$ and~$2p$ states of the
nonrelativistic hydrogen-like atom, respectively, but the TF of~$2P_{3/2}$
state differs qualitatively from the~$2p$ state. Functions calculated with use
of a linearized Eriksen transformation, being equivalent to the second order
Foldy-Wouthuysen transformation, are compared with corresponding functions
obtained by Eriksen transformation. A very good agreement between both results
is obtained.",1604.02478v2
2000-09-28,"A Study of the Thermodynamical Properties of a Hot, Dense Hadron Gas Using an Event Generator - Hadro-Molecular-Dynamical Calculation -","We investigate the equilibration and the equation of state of a hot hadron
gas at finite baryon density using an event generator which is designed to
approximately satisfy detailed balance at finite temperatures and finite baryon
densities of the hadronic scale (80 MeV < T < 170 MeV and 0.157 fm^-3 < n_B <
0.315 fm^-3). Molecular-dynamical simulations were performed for a system of
hadrons in a box with periodic boundary conditions. Starting from an initial
state composed of only nucleons with a uniform phase-space distribution, the
evolution takes place through interactions such as collisions, productions and
absorptions. The system approaches a stationary state of baryons, mesons and
their resonances, which is characterized by the value of the exponent in the
energy distribution common to the different particles, i.e., the temperature.
After the equilibration, thermodynamic quantities, such as the energy density,
particle density, entropy and pressure are calculated. Above T - m_pi, the
obtained equation of state exhibits a significant deviation from the naive
mixed free gas model. Large values of the entropy per baryon are also notable.
In our system, the excitation of heavy baryon resonances and meson production
are enhanced simultaneously, and the increase of the temperature becomes
moderate, but a Hagedorn-type artificial temperature saturation does not occur.
The pressure exhibits a linear dependence on the energy density.",0009326v3
2017-09-28,Algebra of distributions of quantum-field densities and space-time properties,"In this paper we consider properties of the space-time manifold M caused by
the proposition that, according to the scheme theory, the manifold M is locally
isomorphic to the spectrum of the algebra A, M = Spec(A), where A is the
commutative algebra of distributions of quantum-field densities. In order to
determine the algebra A, it is necessary to define multiplication on densities
and to eliminate those densities, which cannot be multiplied. This leads to
essential restrictions imposed on densities and on space-time properties. It is
found that the only possible case, when the commutative algebra A exists, is
the case, when the quantum fields are in the spacetime manifold M with the
structure group SO(3,1) (Lorentz group). The algebra A consists of
distributions of densities with singularities in the closed future light cone
subset. On account of the local isomorphism M = Spec(A), the quantum fields
exist only in the space-time manifold with the one-dimensional arrow of time.
In the fermion sector the restrictions caused by the possibility to define the
multiplication on the densities of spinor fields can explain the chirality
violation. It is found that for bosons in the Higgs sector the charge
conjugation symmetry violation on the densities of states can be observed. This
symmetry violation can explain the matter-antimatter imbalance.",1709.10358v1
2023-04-03,Coherent States of Multilayer Lithiated Graphene utilizing an Electric Vector Potential,"The computational research that will be presented compares the coherent
states of multiple layer graphene versus the coherent states of lithium ions
diffused within this multilayer graphene. Unlike the prevailing research on
graphene coherent states that uses an external magnetic vector potential, this
research will utilize an electric vector potential that is inherent from the
electron current density that transverses the {\pi}-bonds on the graphene
surface. The results from this study will display that the electric vector
potential produces energies that can lead to coherent states for graphene and
lithiated graphene without the necessity of a strong applied magnetic vector
potential. Two excited states will be analyzed for each material. The first
excited state (n=1) the graphene coherent state energies lags behind the
energies of the lithiated graphene coherent state where as the second excited
state (n=2) the coherent state energies of graphene exceeds that of the
lithiated graphene coherent state.",2304.00823v3
2003-02-04,A Unified Approach to High Density: Pion Fluctuations in Skyrmion Matter,"As the first in a series of systematic work on dense hadronic matter, we
study the properties of the pion in dense medium using Skyrme's effective
Lagrangian as a unified theory of the hadronic interactions applicable in the
large $N_c$ limit. Dense baryonic matter is described as the ground state of a
skyrmion matter which appears in two differentiated phases as a function of
matter density: i) at high densities as a stable cubic-centered (CC)
half-skyrmion crystal; ii) at low densities as an unstable face-centered cubic
(FCC) skyrmion crystal. We substitute the latter by a stable inhomogeneous
phase of lumps of dense matter, which represents a naive Maxwell construction
of the phase transition. This baryonic dense medium serves as a background for
the pions whose effective {\em in-medium} Lagrangian we construct by allowing
time-dependent quantum fluctuations on the classical dense matter field. We
find that the same parameter which describes the phase transition for baryonic
matter, the expectation value of the $\sigma$ field, also describes the phase
transition for the dynamics of the {\em in-medium} pion. Thus, the structure of
the baryonic ground state $crucially$ determines the behavior of the pion in
the medium. As matter density increases, $<\sigma>$ decreases, a phenomenon
which we interpret to signal, in terms of the parameters of the effective pion
Lagrangian $f_\pi^*$ and $m_\pi^*$, the restoration of chiral symmetry at high
density. Our calculation shows also the important role played by the higher
powers in the density as it increases and chiral symmetry is being restored.
This feature is likely to be generic at high density although our ground state
may not be the true ground state.",0302019v1
1998-08-06,Anderson localization due to random magnetic field in two dimensions,"Results of large-scale numerical simulations are reported on the Anderson
localization in a two-dimensional square lattice tight-binding model with
random flux. Localization lengths, fluctuations of the conductance, and the
density of states are computed for quasi-one-dimensional geometry. Numerical
results indicate that the model exhibits the same critical behavior as the one
studied by Gade and Wegner. It is argued that all the states except a
zero-energy state are localized and the density of states has a singularity in
the center of the band. The energy scale below which the density of states
increases is found to be extremely small.",9808059v3
1999-02-09,Electronic states of metallic and semiconducting carbon nanotubes with bond and site disorder,"Disorder effects on the density of states in carbon nanotubes are analyzed by
a tight binding model with Gaussian bond or site disorder. Metallic armchair
and semiconducting zigzag nanotubes are investigated. In the strong disorder
limit, the conduction and valence band states merge, and a finite density of
states appears at the Fermi energy in both of metallic and semiconducting
carbon nanotubes. The bond disorder gives rise to a huge density of states at
the Fermi energy differently from that of the site disorder case. Consequences
for experiments are discussed.",9902109v2
2008-05-19,Shell States of Neutron Rich Matter,"The equation of state (EOS) for nuclear and neutron rich matter is
investigated in a Relativistic Mean Field (RMF) model. New shell states are
found that minimize the free energy per baryon, calculated in a spherical
Wigner-Seitz (WS) approximation, over a significant range of baryon densities.
These shell states, that have both inside and outside surfaces, minimize the
Coulomb energy of large proton number configurations at the expense of a larger
surface energy. This is related to a possible depression in the central density
of super heavy nuclei. As the baryon density increases, we find the system
changes from normal nuclei, to shell states, and then to uniform matter.",0805.2774v2
2010-09-20,Quenched dynamics in interacting one-dimensional systems: Appearance of current carrying steady states from initial domain wall density profiles,"We investigate dynamics arising after an interaction quench in the quantum
sine-Gordon model for a one-dimensional system initially prepared in a
spatially inhomogeneous domain wall state. We study the time-evolution of the
density, current and equal time correlation functions using the truncated
Wigner approximation (TWA) to which quantum corrections are added in order to
set the limits on its validity. For weak to moderate strengths of the
back-scattering interaction, the domain wall spreads out ballistically with the
system within the light cone reaching a nonequilibrium steady-state
characterized by a net current flow. A steady state current exists for a quench
at the exactly solvable Luther-Emery point. The magnitude of the current
decreases with increasing strength of the back-scattering interaction. The
two-point correlation function of the variable canonically conjugate to the
density reaches a spatially oscillating steady state at a wavelength inversely
related to the current.",1009.3918v2
2013-04-30,Generalized One-Particle Density Matrices and Quasifree States,"In the spirit of the generalized one-particle density matrix for fermions, we
introduce generalized one- and two-particle density matrices to state
representability conditions up to second order for boson systems without
assuming particle number-conservation. Furthermore, we show for both particle
species that, for a semibounded Hamiltonian, the in?mum of the variation of the
energy functional w.r.t quasifree states coincides with the one of a variation
over pure quasifree states. Moreover, it is proven for fermions that only pure
quasifree states have a generalized 1-pdm that is a projection, and a similar
statement for bosons.",1304.7995v1
2015-10-12,Global performance of multireference density functional theory for low-lying states in $sd$-shell nuclei,"We present a comprehensive study of low-lying states in even-even Ne, Mg, Si,
S, Ar isotopes with the multireference density functional theory (MR-DFT) based
on a relativistic point-coupling energy density functional (EDF). Beyond
mean-field (BMF) effects are taken into account by configuration mixing of both
particle-number and angular-momentum projected axially deformed states with
generator coordinate method (GCM). Global performance of the MR-DFT for the
properties of both ground state and of the first $2^+, 4^+$ states is examined,
in comparison with previous studies based on nonrelativistic EDFs and available
data. Our results indicate that an EDF parameterized at the BMF level is
demanded to achieve a quantitative description.",1510.03127v1
2018-04-25,Non-equilibrium absorbing state phase transitions in discrete-time quantum dynamics,"We introduce a discrete-time quantum dynamics on a two-dimensional lattice
that describes the evolution of a $1+1$-dimensional spin system. The underlying
quantum map is constructed such that the reduced state at each time step is
separable. We show that for long times this state becomes stationary and
displays a continuous phase transition in the density of excited spins. This
phenomenon can be understood through a connection to the so-called
Domany-Kinzel automaton, which implements a classical non-equilibrium process
that features a transition to an absorbing state. Near the transition
density-density correlations become long-ranged, but interestingly the same is
the case for quantum correlations despite the separability of the stationary
state. We quantify quantum correlations through the local quantum uncertainty
and show that in some cases they may be determined experimentally solely by
measuring expectation values of classical observables. This work is inspired by
recent experimental progress in the realization of Rydberg lattice quantum
simulators, which - in a rather natural way - permit the realization of
conditional quantum gates underlying the discrete-time dynamics discussed here.",1804.09794v1
2019-08-02,Real-Space Investigation of the Charge Density Wave in VTe2 Monolayer with Rotational and Mirror Symmetries Broken,"Recently the charge density wave (CDW) in vanadium dichalcogenides have
attracted increasing research interests, but a real-space investigation on the
symmetry breaking of the CDW state in VTe2 monolayer is still lacking. We have
investigated the CDW of VTe2 monolayer by low energy electron diffraction
(LEED) and scanning tunneling microscope (STM). While the LEED experiments
revealed a (4X4) CDW transition at 192+-2 K, our low-temperature STM
experiments resolved the (4X4) lattice distortions and charge-density
modulation in real space, and further unveiled a 1D modulation that breaks the
three-fold rotational and mirror symmetries in the CDW state. In accordance
with the CDW state at low temperature, a CDW gap of 12 meV was detected by
scanning tunneling spectroscopy (STS) at 4.9 K. Our work provides real-space
evidence on the symmetry breaking of the (4X4) CDW state in VTe2 monolayer, and
implies there is a certain mechanism, beyond the conventional Fermi surface
nesting or the q-dependent electron-phonon coupling, is responsible for the
formation of CDW state in VTe2 monolayer.",1908.00714v1
2017-11-21,Reentrant Quantum Spin Hall States in Charge Density Wave Phase of Doped Single-Layer Transition Metal Dichalcogenides,"Using first-principles calculation methods, we reveal a series of phase
transitions as a function of electron doping in single-layer 1T$'$-MoTe$_2$ and
1T$'$-WTe$_2$ exhibiting quantum spin Hall (QSH) edge states without doping. As
increasing doping, we show that a phonon mediated superconducting phase first
realizes and is followed by a charge density wave (CDW) phase with a
nonsymmorphic lattice symmetry. The newly found CDW phase exhibits Dirac or
Weyl energy bands with a spin-orbit coupling in case of a fractional band
filling and re-enters into topological insulating phase with fully filled
bands. The robust resurgence of QSH state coexisting with the CDW phase is
shown to originate from band inversions induced by the nonsymmorphic lattice
distortion through the strong electron-phonon interaction, thus suggesting a
realization of various interfacial states between superconducting, density wave
and topological states on a two-dimensional crystal only by doping.",1711.08073v1
2022-11-02,Equation of state of superfluid neutron matter with low-momentum interactions,"In this work, we calculate the ground state energy of pure neutron matter
using the renormalization group based low-momentum effective interaction
$V_{\text{low-}k}$ in Bogoliubov many-body perturbation theory (BMBPT), which
is a perturbative expansion around the Hartree-Fock-Bogoliubov (HFB) ground
state. In order to capture the low-density behavior of neutron matter, it turns
out to be better to use a density dependent cutoff in the $V_{\text{low-}k}$
interaction. Perturbative corrections to the HFB energy up to third order are
included. We find that at low densities corresponding to the inner crust of
neutron stars, the HFB state that includes pairing is a better starting point
for perturbation expansion. It is observed that including the higher order
perturbative corrections, the cutoff dependence of the ground state energy is
reduced.",2211.01308v2
2023-08-16,Pair density wave superconductivity: a microscopic model in two dimensions,"Pair-density-wave (PDW) superconductivity is a long-sought exotic state with
oscillating superconducting order parameter without the need of applying
external magnetic field. So far it has been rare in establishing a
two-dimensional (2D) microscopic model with such exotic long-range order in its
ground state. Here we propose to study PDW superconductivity in a minimal model
of spinless fermions on the honeycomb lattice with nearest-neighbor (NN) and
next-nearest-neighbor (NNN) interaction $V_1$ and $V_2$, respectively. By
performing a state-of-the-art density-matrix renormalization group (DMRG) study
of this $t$-$V_1$-$V_2$ model at finite doping on six-leg and eight-leg
honeycomb cylinders, we showed that the ground state exhibits PDW ordering
(namely quasi-long-range order with a divergent PDW susceptibility). Remarkably
this PDW state persists on the wider cylinder with 2D-like Fermi surfaces (FS).
To the best of our knowledge, this is probably the first controlled numerical
evidence of PDW in systems with 2D-like FS.",2308.08609v1
1995-02-03,The Structure of Fractional Edge States: A Composite Fermion Approach,"I study the structure of the two-dimensional electron gas edge in the quantum
Hall regime using the composite fermion approach. The electron density
distribution and the composite fermion energy spectrum are obtained numerically
in Hartree approximation for bulk filling factors $\nu=1,1/3,2/3,1/5$. For a
very sharp edge of the $\nu=1$ state the one-electron picture is valid. As the
edge width $a$ is increased the density distribution shows features related to
the fractional states and new fractional channels appear in pairs. For a very
smooth edge I find quasiclassically the number of channels $p\sim\sqrt{a/l_H}$,
where $l_H$ is the magnetic length.",9502014v1
2001-03-06,Staggered local density-of-states around the vortex in underdoped cuprates,"We have studied a single vortex with the staggered flux (SF) core based on
the SU(2) slave-boson theory of high $T_c$ superconductors. We find that
whereas the center in the vortex core is a SF state, as one moves away from the
core center, a correlated staggered modulation of the hopping amplitude $\chi$
and pairing amplitude $\Delta$ becomes predominant. We predict that in this
region, the local density-of-states (LDOS) exhibits staggered modulation when
measured on the bonds, which may be directly detected by STM experiments.",0103148v3
2002-06-11,Tail states in clean superconductors with magnetic impurities,"We analyse the behavior of the density of states in a singlet s-wave
superconductor with weak magnetic impurities in the clean limit. By using the
method of optimal fluctuation and treating the order parameter
self-consistently we show that the density of states is finite everywhere in
the superconducting gap, and that it varies as $\ln N(E)\propto
-|E-\Delta_0|^{(7-d)/4}$ near the mean field gap edge $\Delta_0$ in a
d-dimensional superconductor. In contrast to most studied cases the optimal
fluctuation is strongly anisotropic.",0206183v2
2004-06-18,Matrix Product Density Operators: Simulation of finite-T and dissipative systems,"We show how to simulate numerically both the evolution of 1D quantum systems
under dissipation as well as in thermal equilibrium. The method applies to both
finite and inhomogeneous systems and it is based on two ideas: (a) a
representation for density operators which extends that of matrix product
states to mixed states; (b) an algorithm to approximate the evolution (in real
or imaginary time) of such states which is variational (and thus optimal) in
nature.",0406426v2
2007-01-16,Optical properties of the Ce and La di-telluride charge density wave compounds,"The La and Ce di-tellurides LaTe$_2$ and CeTe$_2$ are deep in the
charge-density-wave (CDW) ground state even at 300 K. We have collected their
electrodynamic response over a broad spectral range from the far infrared up to
the ultraviolet. We establish the energy scale of the single particle
excitation across the CDW gap. Moreover, we find that the CDW collective state
gaps a very large portion of the Fermi surface. Similarly to the related rare
earth tri-tellurides, we envisage that interactions and Umklapp processes play
a role in the onset of the CDW broken symmetry ground state.",0701386v1
1999-03-26,A General Type of a Coherent States with Thermal Effects,"Within the framework of thermofield dynamics, we construct a thermalized
coherent thermal state, which is a general type of the coherent state with the
thermal effects and can be presumably produced experimentally. The wavefunction
and the density matrix element in the coordinate repersentation are calculated,
and furthermore we give the probability densities, average values and variances
of the position, momentum and particle number, which in special cases are
consistent with those in the literature. All calculations are performed in the
coordinate representation.",9903084v2
2007-08-23,Phase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement,"We study the ground-state phase diagram of a Bose-Fermi mixture loaded in a
one-dimensional optical lattice by computing the ground-state fidelity and
quantum entanglement. We find that the fidelity is able to signal quantum phase
transitions between the Luttinger liquid phase, the density-wave phase, and the
phase separation state of the system; and the concurrence can be used to signal
the transition between the density-wave phase and the Ising phase.",0708.3178v1
2009-07-07,Two-dimensional electron liquid state at LaAlO3-SrTiO3 interfaces,"Using tunneling spectroscopy we have measured the spectral density of states
of the mobile, two-dimensional electron system generated at the LaAlO3-SrTiO3
interface. As shown by the density of states the interface electron system
differs qualitatively, first, from the electron systems of the materials
defining the interface and, second, from the two-dimensional electron gases
formed at interfaces between conventional semiconductors.",0907.1176v2
2010-03-19,Fourier's law on a one-dimensional optical random lattice,"We study the transport properties of a one-dimensional hard-core bosonic
lattice gas coupled to two particle reservoirs at different chemical potentials
which generate a current flow through the system. In particular, the influence
of random fluctuations of the underlying lattice on the stationary-state
properties is investigated. We show analytically that the steady-state density
presents a linear profile. The local steady-state current obeys the Fourier law
$j=-\kappa(\tau)\nabla n $ where $\tau$ is a typical timescale of the lattice
fluctuations and $\nabla n$ the density gradient imposed by the reservoirs.",1003.3755v1
2011-04-14,Quantum Percolation Transition from Graphene to Graphane: Graph Theoretical Approach,"Graphane is obtained by perfectly hydrogenating graphene. There exists an
intermediate material, partially hydrogenated graphene (which we call
\textit{hydrographene}), interpolating from pure graphene to pure graphane. It
has various intriguing electronic and magnetic properties. We investigate a
metal-insulator transition, employing a quantum-site percolation model together
with a graph theoretical approach. Hydrographene is an exceptional case in
which electronic properties cannot be determined solely by the density of
states at the Fermi energy. Though there are plenty of zero energy state in
wide range of hydrogenation density, most of them are insulating states. We
also demonstrate that it shows a bulk ferromagnetic property based on the Lieb
theory.",1104.2646v1
2012-10-17,Topology and symmetry breaking in ABC trilayer graphene,"The effects of topology and electron-electron interactions on the phase
diagram of ABC stacked trilayer graphene (TLG) at the neutrality point are
investigated within a weak coupling renormalization group approach. We find
that the leading instability of TLG with only a forward scattering
density-density interaction is towards a mirror-breaking gapless state.
Addition of a small, but finite back scattering favors gapped phases, allowing
us to make connections to the existing experiments on TLG. We identify a
fundamental symmetry difference between TLG and bilayer graphene (BLG) which is
responsible for disfavoring nematic states in TLG under the same conditions
that favor nematic states in BLG.",1210.4923v1
2014-07-24,On Single Qubit Quantum State Tomography,"In this paper, we derive analytic expressions for the starting (initial)
values of the parameters of the T-matrix that is frequently employed in the
construction of a theoretical density matrix in a Maximum Likelihood Estimate
(MLE) procedure; this optimization procedure is used to fit the experimental
data pertaining to single qubit state tomography. Appropriate starting values
are critical in achieving a global minimum in the fitting process. We also
indicate an analytic way of making the experimentally determined density matrix
physical without resorting to the MLE process, if optimality in quantum state
tomography can be disregarded, since the ultimate goal is optimality in quantum
process tomography.",1407.6668v1
2014-09-14,Tunable Magnetism and Half-Metallicity in Hole-doped Monolayer GaSe,"We find, through first-principles calculations, that hole doping induces a
ferromagnetic phase transition in monolayer GaSe. Upon increasing hole density,
the average spin magnetic moment per carrier increases and reaches a plateau
near 1.0 $\mu_{\rm{B}}$/carrier in a range of $3\times
10^{13}$/cm$^{2}$-$1\times 10^{14}$/cm$^{2}$ with the system in a half-metal
state before the moment starts to descend abruptly. The predicted magnetism
originates from an exchange splitting of electronic states at the top of the
valence band where the density of states exhibits a sharp van Hove singularity
in this quasi-two-dimensional system.",1409.4112v1
2017-08-11,Polyatomic trilobite Rydberg molecules in a dense random gas,"Trilobites are exotic giant dimers with enormous dipole moments. They consist
of a Rydberg atom and a distant ground-state atom bound together by short-range
electron-neutral attraction. We show that highly polar, polyatomic trilobite
states unexpectedly persist and thrive in a dense ultracold gas of randomly
positioned atoms. This is caused by perturbation-induced quantum scarring and
the localization of electron density on randomly occurring atom clusters. At
certain densities these states also mix with a s-state, overcoming selection
rules that hinder the photoassociation of ordinary trilobites.",1708.03503v2
2017-08-23,Asymptotics of the ground state energy in the relativistic settings and with self-generated magnetic field,"The purpose of this paper is to derive sharp asymptotics of the ground state
energy for the heavy atoms and molecules in the relativistic settings, with the
self-generated magnetic field, and, in particular, to derive relativistic Scott
correction term and also Dirac, Schwinger and relativistic correction terms.
Also we will prove that Thomas-Fermi density approximates the actual density of
the ground state, which opens the way to estimate the excessive negative and
positive charges and the ionization energy.",1708.07737v1
2014-03-11,Long-range interaction induced phases in Weyl semimetals,"The interplay of spin orbit coupling and electron electron interaction
condensing new phases of matter is an important new phenomena in solid state
physics. In this paper we explore the nature of excitonic phases induced in
Weyl semimetals by long range Coulomb repulsion. Its has been previously shown
that short range repulsion leads to a ferromagnetic insulator while short range
attraction results in a charge density wave state. Here we show the the charge
density wave is the energetically favored state in the presence of long range
repulsion.",1403.2456v1
2018-08-24,On stability of ground states for finite crystals in the Schroedinger-Poisson model,"We consider the Schr\""odinger-Poisson-Newton equations for finite crystals
under periodic boundary conditions with one ion per cell of a lattice. The
electrons are described by one-particle Schr\""odinger equation. Our main
results are i) the global dynamics with moving ions; ii) the orbital stability
of periodic ground state under a novel Jellium and Wiener-type conditions on
the ion charge density. Under the Jellium condition both ionic and electronic
charge densities for the ground state are uniform.",1808.10385v1
2017-07-21,Asymptotics of the ground state energy in the relativistic settings,"The purpose of this paper is to derive sharp asymptotics of the ground state
energy for the heavy atoms and molecules in the relativistic settings, and, in
particular, to derive relativistic Scott correction term and also Dirac,
Schwinger and relativistic correction terms. Also we will prove that
Thomas-Fermi density approximates the actual density of the ground state, which
opens the way to estimate the excessive negative and positive charges and the
ionization energy.",1707.07014v3
2019-12-31,Exact Hyperuniformity Exponents and Entropy Cusps in Models of Active-Absorbing Transition,"Recent studies of nonequilibrium phase transitions have shown that in many
systems which have transitions involving an arrested phase, the arrested states
show suppressed density fluctuations and a cusp in the configurational entropy
at the transition point. We study quasistatic driving in the 1D fixed-energy
abelian sandpile model, and in conserved lattice gases with range $n$ in 1D,
and exactly determine the measure over the absorbing states for both cases,
along with the behaviour of density fluctuations and the configurational
entropy of absorbing states. We show that both models exhibit hyperuniformity
near the transition, and also that the configurational entropy shows a cusp at
the transition point in the conserved lattice gases.",1912.13420v1
2021-10-16,Protonium annihilation densities in a unitary coupled channel model,"We consider a unitary coupled channel model to describe the low energy
proton-antiproton scattering and the lower Coulomb-like protonium states. The
existence of deeper quasi-bound states of nuclear nature is found to be a
consequence of the experimental data. The properties of these states as well as
the protonium annihilation densities are described and the difference with
respect to the optical models description are manifested.",2110.08628v1
2021-10-25,Constructing k-local parent Lindbladians for matrix product density operators,"Matrix product density operators (MPDOs) are an important class of states
with interesting properties. Consequently, it is important to understand how to
prepare these states experimentally. One possible way to do this is to design
an open system that evolves only towards desired states. A Markovian evolution
of a quantum mechanical system can be generally described by a Lindbladian. In
this work we develop an algorithm that for a given (small) linear subspace of
MPDOs determines if this subspace can be the stable space for some frustration
free Lindbladian consisting of only local terms and, if so, outputs a suitable
Lindbladian.",2110.13134v1
2022-10-24,Evolution of topological end states in the one-dimensional Kondo-Heisenberg model with site modulation,"We investigate the interplay of the topological and Kondo effects in a
one-dimensional Kondo-Heisenberg model with nontrivial conduction band using
the density matrix renormalization group method. By analyzing the density
profile, the local hybridization, and the spin/charge gap, we find that the
Kondo effect can be destructed at the edges of the chain by the topological end
state below a finite critical Kondo coupling $J_{K}^{c}$. We construct a phase
diagram characterizing the transition of the end states.",2210.13090v1
2023-11-27,Symmetry breaking in vanadium trihalides,"In the light of new experimental evidence we study the insulating ground
state of the $3d^2$-transition metal trihalides VX$_3$ (X=Cl, I). Based on
Density Functional Theory with the Hubbard correction (DFT$+U$) we
systematically show how these systems host multiple metastable states
characterized by different orbital ordering and electronic behaviour. Our
calculations reveal the importance of imposing a precondition in the on site
$d$ density matrix and of considering a symmetry broken unit cell to correctly
take into account the correlation effects in a mean field framework.
Furthermore we ultimately found a ground state with the $a_{1g}$ orbital
occupied in a distorted VX$_6$ octahedra driven by an optical phonon mode.",2311.16068v1
2016-09-22,Incommensurate charge ordered states in the $\mathit{t-t^{\prime}-J}$ model,"We study the incommensurate charge ordered states in the
$\mathit{t-t^{\prime}-J}$ model using the Gutzwiller mean field theory on large
systems. In particular, we explore the properties of incommensurate charge
modulated states referred to as nodal pair density waves (nPDW) in the
literature. nPDW states intertwine site and bond charge order with modulated
$d$-wave pair order, and are characterized by a nonzero amplitude of uniform
pairing; they also manifest a dominant intra-unit cell $d$-density wave form
factor. To compare with a recent scanning tunneling microscopy (STM) study
[Hamidian \textit{et al.}, Nat. Phys. 3519 (2015)] of the cuprate
superconductor BSCCO-2212, we compute the continuum local density of states
(LDOS) at a typical STM tip height using the Wannier function based approach.
By Fourier transforming Cu and O sub-lattice LDOS we also obtain bias-dependent
intra-unit cell form factors and spatial phase difference. We find that in the
nPDW state the behavior of form factors and spatial phase difference as a
function of energy agrees remarkably well with the experiment. This is in
contrast to commensurate charge modulated states, which we show do not agree
with experiment. We propose that the nPDW states are good candidates for the
charge density wave phase observed in the superconducting state of underdoped
cuprates.",1609.07067v1
2016-01-22,Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model,"Using an efficient cluster approach, we study the physics of two-dimensional
lattice bosons in a strong magnetic field in the regime where the tunneling is
much weaker than the on-site interaction strength. We study both dilute, hard
core bosons at filling factors much smaller than unity occupation per site, and
the physics in the vicinity of the superfluid-Mott lobes as the density is
tuned away from unity. For hardcore bosons, we carry out extensive numerics for
a fixed flux per plaquette $\phi=1/5$ and $\phi = 1/3$. At large flux, the
lowest energy state is a strongly correlated superfluid, analogous to He-$4$,
in which the order parameter is dramatically suppressed, but non-zero. At
filling factors $\nu=1/2,1$, we find competing incompressible states which are
metastable. These appear to be commensurate density wave states. For small
flux, the situation is reversed, and the ground state at $\nu = 1/2$ is an
incompressible density-wave solid. Here, we find a metastable lattice
supersolid phase, where superfluidity and density-wave order coexist. We then
perform careful numerical studies of the physics near the vicinity of the Mott
lobes for $\phi = 1/2$ and $\phi = 1/4$. At $\phi = 1/2$, the superfluid ground
state has commensurate density-wave order. At $\phi = 1/4$, incompressible
phases appear outside the Mott lobes at densities $n = 1.125$ and $n = 1.25$,
corresponding to filling fractions $\nu = 1/2$ and $1$ respectively. These
phases, which are absent in single-site mean-field theory are metastable, and
have slightly higher energy than the superfluid, but the energy difference
between them shrinks rapidly with increasing cluster size, suggestive of an
incompressible ground state. We thus explore the interplay between Mott
physics, magnetic Landau levels, and superfluidity, finding a rich phase
diagram of competing compressible and incompressible states.",1601.06172v1
2010-08-24,Effective 3-Body Interaction for Mean-Field and Density-Functional Theory,"Density functionals for nuclei usually include an effective 3-body
interaction that depends on a fractional power of the density. Using insights
from the many-body theory of the low-density two-component Fermi gas, we
consider a new, nonlocal, form for the energy functional that is consistent
with the Fock space representation of interaction operators. In particular,
there is a unique spatially nonlocal generalization of the contact form of the
interaction that preserves the density-to-the-seven-thirds dependence required
by the many-body theory. We calculate the ground state energies for particles
in a harmonic trap using the nonlocal induced 3-body interaction, and compare
them to numerically accurate Green's Function Monte Carlo calculations. Using
no free parameters, we find that a nonlocality in the space domain provides a
better description of the weak-coupling regime than the local-density
approximation.",1008.4130v2
2013-01-24,A New Hole Density as a Stability Measure for Boron Fullerenes,"We investigate the stability of boron fullerene sets B76, B78 and B82. We
evaluate the ground state energies, nucleus-independent chemical shift (NICS),
the binding energies per atom and the band gap values by means of
first-principles methods. We construct our fullerene design by capping of
pentagons and hexagons of B60 cage in such a way that the total number of atoms
is preserved. In doing so, a new hole density definition is proposed such that
each member of a fullerene group has a different hole density which depends on
the capping process. Our analysis reveal that each boron fullerene set has its
lowest-energy configuration around the same normalized hole density and the
most stable cages are found in the fullerene groups which have relatively large
difference between the maximum and the minimum hole densities. The result is a
new stability measure relating the cage geometry characterized by the hole
density to the relative energy.",1301.6156v3
2015-06-17,Probing a quantum gas with single Rydberg atoms,"We present a novel spectroscopic method for probing the \insitu~density of
quantum gases. We exploit the density-dependent energy shift of highly excited
{Rydberg} states, which is of the order $10$\MHz\,/\,1E14\,cm$^{\text{-3}}$ for
\rubidium~for triplet s-wave scattering. The energy shift combined with a
density gradient can be used to localize Rydberg atoms in density shells with a
spatial resolution less than optical wavelengths, as demonstrated by scanning
the excitation laser spatially across the density distribution. We use this
Rydberg spectroscopy to measure the mean density addressed by the Rydberg
excitation lasers, and to monitor the phase transition from a thermal gas to a
Bose-Einstein condensate (BEC).",1506.05302v2
2015-12-07,Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models,"We consider several one-dimensional driven lattice gas models that show a
phase transition in the stationary state between a high-density fluid phase in
which the particles are homogeneously distributed and a low-density jammed
phase where a hole cluster of macroscopic length forms in front of a particle.
Using a hydrodynamic equation for an interface growth model obtained from the
driven lattice gas models of interest here, we find that in the fluid phase,
the roughness exponent and the dynamic exponent that, respectively,
characterise the scaling of the saturation width and the relaxation time of the
interface with the system size are given by the KPZ exponents. However, at the
critical point, we show analytically that when the equal time density-density
correlation function decays slower than inverse distance, the roughness
exponent varies continuously with a parameter in the hop rates but it is one
half otherwise. Using these results and numerical simulations for the
density-density autocorrelation function, we further find that the dynamic
exponent $z=3/2$ in all the cases.",1512.01929v2
2017-12-07,Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities,"We derive a microscopic optical potential for intermediate energies using ab
initio translationally invariant nonlocal one-body nuclear densities computed
within the no-core shell model (NCSM) approach utilizing two- and three-nucleon
chiral interactions as the only input. The optical potential is derived at
first-order within the spectator expansion of the non-relativistic multiple
scattering theory by adopting the impulse approximation and using the same
chiral nucleon-nucleon interaction as that used to compute densities. The
ground state local and nonlocal densities of 4,6,8He, 12C, and 16O are
calculated and applied to optical potential construction. The differential
cross sections and the analyzing powers for the elastic proton scattering off
of these nuclei are then calculated for different values of the incident proton
energy. The impact of nonlocality and the COM removal is discussed. The use of
nonlocal densities has a substantial impact on the differential cross sections
and improves agreement with experiment in comparison to results generated with
the local densities especially for light nuclei.",1712.02879v2
2019-09-25,Optimal Safe Controller Synthesis: A Density Function Approach,"This paper considers the synthesis of optimal safe controllers based on
density functions. We present an algorithm for robust constrained optimal
control synthesis using the duality relationship between the density function
and the value function. The density function follows the Liouville equation and
is the dual of the value function, which satisfies Bellman's optimality
principle. Thanks to density functions, constraints over the distribution of
states, such as safety constraints, can be posed straightforwardly in an
optimal control problem. The constrained optimal control problem is then solved
with a primal-dual algorithm. This formulation is extended to the case with
external disturbances, and we show that the robust constrained optimal control
can be solved with a modified primal-dual algorithm. We apply this formulation
to the problem of finding the optimal safe controller that minimizes the
cumulative intervention. An adaptive cruise control (ACC) example is used to
demonstrate the efficacy of the proposed, wherein we compare the result of the
density function approach with the conventional control barrier function (CBF)
method.",1909.11798v2
2020-04-12,Density Map Guided Object Detection in Aerial Images,"Object detection in high-resolution aerial images is a challenging task
because of 1) the large variation in object size, and 2) non-uniform
distribution of objects. A common solution is to divide the large aerial image
into small (uniform) crops and then apply object detection on each small crop.
In this paper, we investigate the image cropping strategy to address these
challenges. Specifically, we propose a Density-Map guided object detection
Network (DMNet), which is inspired from the observation that the object density
map of an image presents how objects distribute in terms of the pixel intensity
of the map. As pixel intensity varies, it is able to tell whether a region has
objects or not, which in turn provides guidance for cropping images
statistically. DMNet has three key components: a density map generation module,
an image cropping module and an object detector. DMNet generates a density map
and learns scale information based on density intensities to form cropping
regions. Extensive experiments show that DMNet achieves state-of-the-art
performance on two popular aerial image datasets, i.e. VisionDrone and UAVDT.",2004.05520v1
2022-07-19,The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms,"The constrained-search formulation of Levy and Lieb provides a concrete
mapping from N-representable densities to the space of N-particle wavefunctions
and explicitly defines the universal functional of density functional theory.
We numerically implement the Levy-Lieb procedure for a paradigmatic lattice
system, the Hubbard dimer, using a modified variational quantum eigensolver
approach. We demonstrate density variational minimization using the resulting
hybrid quantum-classical scheme featuring real-time computation of the
Levy-Lieb functional along the search trajectory. We further illustrate a
fidelity based quantum kernel associated with the density to pure-state
embedding implied by the Levy-Lieb procedure and employ the kernel for learning
observable functionals of the density. We study the kernel's ability to
generalize with high accuracy through numerical experiments on the Hubbard
dimer.",2207.08995v1
2022-07-28,Moment-functional based spectral density-functional theory,"We describe a density-functional method which aims at computing the ground
state electron density and the spectral function at the same time. One basic
ingredient of our method is the construction of the spectral function from the
first four spectral moment matrices. The second basic ingredient is the
construction of the spectral moment matrices from density functionals. We call
our method moment-functional based spectral density-functional theory
(MFbSDFT), because it is based on density-functionals for the spectral moments
and because it allows us to compute the spectral function. If it is implemented
in second variation our method consumes only a fraction more computer time than
a standard DFT calculation with the PBE functional. We show that MFbSDFT
captures correlation effects such as the valence-band satellite in Ni and the
formation of lower and upper Hubbard bands in SrVO$_3$. For the purpose of
constructing the spectral function from the first four $N\times N$ spectral
moment matrices we describe an efficient algorithm based on the diagonalization
of one hermitean $2N\times 2N$ matrix.",2207.13960v4
2023-01-31,Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations,"Kohn-Sham density functional theory (KS-DFT) is a powerful method to obtain
key materials' properties, but the iterative solution of the KS equations is a
numerically intensive task, which limits its application to complex systems. To
address this issue, machine learning (ML) models can be used as surrogates to
find the ground-state charge density and reduce the computational overheads. We
develop a grid-centred structural representation, based on Jacobi and Legendre
polynomials combined with a linear regression, to accurately learn the
converged DFT charge density. This integrates into a ML pipeline that can
return any density-dependent observable, including energy and forces, at the
quality of a converged DFT calculation, but at a fraction of the computational
cost. Fast scanning of energy landscapes and producing starting densities for
the DFT self-consistent cycle are among the applications of our scheme.",2301.13550v2
2006-04-22,Modulation of charge-density waves by superlattice structures,"We discuss the interplay between electronic correlations and an underlying
superlattice structure in determining the period of charge density waves
(CDW's), by considering a one-dimensional Hubbard model with a repeated
(non-random) pattern of repulsive (U>0) and free (U=0) sites. Density matrix
renormalization group diagonalization of finite systems (up to 120 sites) is
used to calculate the charge-density correlation function and structure factor
in the ground state. The modulation period can still be predicted through
effective Fermi wavevectors, k_F*, and densities, and we have found that it is
much more sensitive to electron (or hole) doping, both because of the narrow
range of densities needed to go from q*=0 to \pi, but also due to sharp
2k_F*-4k_F* transitions; these features render CDW's more versatile for actual
applications in heterostructures than in homogeneous systems.",0604523v1
1995-08-15,Towards a Linear-Scaling DFT Technique: The Density Matrix Approach,"A recently proposed linear-scaling scheme for density-functional
pseudopotential calculations is described in detail. The method is based on a
formulation of density functional theory in which the ground state energy is
determined by minimization with respect to the density matrix, subject to the
condition that the eigenvalues of the latter lie in the range [0,1].
Linear-scaling behavior is achieved by requiring that the density matrix should
vanish when the separation of its arguments exceeds a chosen cutoff. The
limitation on the eigenvalue range is imposed by the method of Li, Nunes and
Vanderbilt. The scheme is implemented by calculating all terms in the energy on
a uniform real-space grid, and minimization is performed using the
conjugate-gradient method. Tests on a 512-atom Si system show that the total
energy converges rapidly as the range of the density matrix is increased. A
discussion of the relation between the present method and other linear-scaling
methods is given, and some problems that still require solution are indicated.",9508008v1
2019-07-15,Atoms in molecules from alchemical perturbation density functional theory,"Based on thermodynamic integration we introduce atoms in molecules (AIM)
using the orbital-free framework of alchemical perturbation density functional
theory (APDFT). Within APDFT, atomic energies and electron densities in
molecules are arbitrary because any arbitrary reference system and integration
path can be selected as long as it meets the boundary conditions. We choose the
uniform electron gas as the most generic reference, and linearly scale up all
nuclear charges, situated at any query molecule's atomic coordinates. Within
the approximations made when calculating one-particle electron densities, this
choice affords exact and unambiguous definitions of energies and electron
densities of AIMs We illustrate the approach for neutral iso-electronic
diatomics (CO, N$_2$, BF), various small molecules with different electronic
hybridisation states of carbon (CH$_4$, C$_2$H$_6$, C$_2$H$_4$, C$_2$H$_2$,
HCN), and for all the possible BN doped mutants connecting benzene to borazine
(C$_{2n}$B$_{3-n}$N$_{3-n}$H$_6$, $0 \le n \le 3$). Analysis of the numerical
results obtained suggests that APDFT based AIMs enable meaningful and new
interpretations of molecular energies and electron densities.",1907.06677v1
2020-10-27,Nonparametric estimation of highest density regions for COVID-19,"Highest density regions refer to level sets containing points of relatively
high density. Their estimation from a random sample, generated from the
underlying density, allows to determine the clusters of the corresponding
distribution. This task can be accomplished considering different nonparametric
perspectives. From a practical point of view, reconstructing highest density
regions can be interpreted as a way of determining hot-spots, a crucial task
for understanding COVID-19 space-time evolution. In this work, we compare the
behavior of classical plug-in methods and a recently proposed hybrid algorithm
for highest density regions estimation through an extensive simulation study.
Both methodologies are applied to analyze a real data set about COVID-19 cases
in the United States.",2010.14340v3
2005-05-22,On the temperature dependence of the interaction-induced entanglement,"Both direct and indirect weak nonresonant interactions are shown to produce
entanglement between two initially disentangled systems prepared as a tensor
product of thermal states, provided the initial temperature is sufficiently
low. Entanglement is determined by the Peres-Horodeckii criterion, which
establishes that a composite state is entangled if its partial transpose is not
positive. If the initial temperature of the thermal states is higher than an
upper critical value $T_{uc}$ the minimal eigenvalue of the partially
transposed density matrix of the composite state remains positive in the course
of the evolution. If the initial temperature of the thermal states is lower
than a lower critical value $T_{lc}\leq T_{uc}$ the minimal eigenvalue of the
partially transposed density matrix of the composite state becomes negative
which means that entanglement develops. We calculate the lower bound $T_{lb}$
for $T_{lc}$ and show that the negativity of the composite state is negligibly
small in the interval $T_{lb}<T<T_{uc}$. Therefore the lower bound temperature
$T_{lb}$ can be considered as \textit{the} critical temperature for the
generation of entanglement.",0505161v1
2011-09-28,Electronic States and Local Density of States in Graphene with a Corner Edge Structure,"We study electronic states of semi-infinite graphene with a corner edge,
focusing on the stability of edge localized states at zero energy. The
60{\deg}, 90{\deg}, 120{\deg} and 150{\deg} corner edges are examined. The
60{\deg} and 120{\deg} corner edges consist of two zigzag edges, while 90{\deg}
and 150{\deg} corner edges consist of one zigzag edge and one armchair edge. We
numerically obtain the local density of states (LDOS) on the basis of a
nearest-neighbor tight-binding model by using Haydock's recursion method. We
show that edge localized states appear along a zigzag edge of each corner edge
structure except for the 120{\deg} case. To provide insight into this behavior,
we analyze electronic states at zero energy within the framework of an
effective mass equation. The result of this analysis is consistent with the
behavior of the LDOS.",1109.6142v1
1994-11-22,Ground states of integrable quantum liquids,"Based on a recently introduced operator algebra for the description of a
class of integrable quantum liquids we define the ground states for all
canonical ensembles of these systems. We consider the particular case of the
Hubbard chain in a magnetic field and chemical potential. The ground states of
all canonical ensembles of the model can be generated by acting onto the
electron vacuum (densities $n<1$) or hole vacuum (densities $n>1$), suitable
pseudoparticle creation operators. We also evaluate the energy gaps of the
non-lowest-weight states (non - LWS's) and non-highest-weight states (non -
HWS's) of the eta-spin and spin algebras relative to the corresponding ground
states. For all sectors of parameter space and symmetries the {\it exact ground
state} of the many-electron problem is in the pseudoparticle basis the
non-interacting pseudoparticle ground state. This plays a central role in the
pseudoparticle perturbation theory.",9411096v1
2022-03-10,Point Density-Aware Voxels for LiDAR 3D Object Detection,"LiDAR has become one of the primary 3D object detection sensors in autonomous
driving. However, LiDAR's diverging point pattern with increasing distance
results in a non-uniform sampled point cloud ill-suited to discretized
volumetric feature extraction. Current methods either rely on voxelized point
clouds or use inefficient farthest point sampling to mitigate detrimental
effects caused by density variation but largely ignore point density as a
feature and its predictable relationship with distance from the LiDAR sensor.
Our proposed solution, Point Density-Aware Voxel network (PDV), is an
end-to-end two stage LiDAR 3D object detection architecture that is designed to
account for these point density variations. PDV efficiently localizes voxel
features from the 3D sparse convolution backbone through voxel point centroids.
The spatially localized voxel features are then aggregated through a
density-aware RoI grid pooling module using kernel density estimation (KDE) and
self-attention with point density positional encoding. Finally, we exploit
LiDAR's point density to distance relationship to refine our final bounding box
confidences. PDV outperforms all state-of-the-art methods on the Waymo Open
Dataset and achieves competitive results on the KITTI dataset. We provide a
code release for PDV which is available at https://github.com/TRAILab/PDV.",2203.05662v2
2013-07-12,Singular Behavior At The Edge of Laughlin States,"A distinguishing feature of fractional quantum Hall (FQH) states is a
singular behavior of equilibrium densities at boundaries. In contrast to states
at integer filling fraction, such quantum liquids posses an additional dipole
moment localized near edges. It enters observable quantities such as universal
dispersion of edge states and Lorentz shear stress. For a Laughlin state, this
behavior is seen as a peak, or overshoot, in the single particle density near
the edge, reflecting a general tendency of electrons in FQH states to cluster
near edges. We compute the singular edge behavior of the one particle density
by a perturbative expansion carried out around a completely filled Landau
level. This correction is shown to fully capture the dipole moment and the
major features of the overshoot observed numerically. Furthermore, it exhibits
the Stokes phenomenon with the Stokes line at the boundary of the droplet,
decaying like a Gaussian inside and outside the liquid with different decay
lengths. In the limit of vanishing magnetic length the shape the overshoot is a
singular double layer with a capacity that is a universal function of the
filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH
states. The result suggests an explicit connection between the magnitude of the
dipole moment and the bulk odd viscosity.",1307.3334v2
2014-07-15,"States that ""look the same"" with respect to every basis in a mutually unbiased set","A complete set of mutually unbiased bases in a Hilbert space of dimension $d$
defines a set of $d+1$ orthogonal measurements. Relative to such a set, we
define a ""MUB-balanced state"" to be a pure state for which the list of
probabilities of the $d$ outcomes of one of these measurements is independent
of the choice of measurement, up to permutations. In this paper we explicitly
construct a MUB-balanced state for each prime power dimension $d$ for which $d
= 3$ (mod 4). These states have already been constructed by Appleby in
unpublished notes, but our presentation here is different in that both the
expression for the states themselves and the proof of MUB-balancedness are
given in terms of the discrete Wigner function, rather than the density matrix
or state vector. The discrete Wigner functions of these states are
""rotationally symmetric"" in a sense roughly analogous to the rotational
symmetry of the energy eigenstates of a harmonic oscillator in the continuous
two-dimensional phase space. Upon converting the Wigner function to a density
matrix, we find that the states are expressible as real state vectors in the
standard basis. We observe numerically that when $d$ is large (and not a power
of 3), a histogram of the components of such a state vector appears to form a
semicircular distribution.",1407.4074v3
2002-04-08,Dynamical state of superclusters of galaxies: do superclusters expand or have they started to collapse?,"We investigate the dynamical state of superclusters in Lambda cold dark
matter ($\Lambda$CDM) cosmological models, where the density parameter
$\Omega_0=0.2-0.4$ and $\sigma_8$ (the rms fluctuation on the $8h^{-1}$Mpc
scale) is $0.7-0.9$. To study the nonlinear regime, we use N-body simulations.
We define superclusters as maxima of the density field smoothed on the scale
$R=10h^{-1}$Mpc. Smaller superclusters defined by the density field smoothed on
the scale $R=5h^{-1}$Mpc are also investigated. We find the relations between
the radially averaged peculiar velocity and the density contrast in the
superclusters for different cosmological models. These relations can be used to
estimate the dynamical state of a supercluster on the basis of its density
contrast. In the simulations studied, all the superclusters defined with the
$10h^{-1}$Mpc smoothing are expanding by the present epoch. Only a small
fraction of the superclusters defined with $R=5h^{-1}$Mpc has already reached
their turnaround radius and these superclusters have started to collapse. In
the model with $\Omega_0=0.3$ and $\sigma_8=0.9$, the number density of objects
which have started to collapse is $5 \times 10^{-6}h^3$Mpc$^{-3}$. The results
for superclusters in the N-body simulations are compared with the spherical
collapse model. We find that the radial peculiar velocities in N-body
simulations are systematically smaller than those predicted by the spherical
collapse model ($\sim 25$% for the $R=5h^{-1}$Mpc superclusters).",0204121v2
2015-08-15,Making a soft relativistic mean-field equation of state stiffer at high density,"We study relativistic mean-field (RMF) models including nucleons interacting
with scalar, vector and iso-vector mean fields and self- and cross- mean-field
interaction terms. Usually, in such a models the magnitude of the scalar field
increases monotonically with the nucleon density, and the nucleon effective
mass decreases. We demonstrate that the latter quantity stops to decrease and
the equation of state stiffens, provided the mean-field self-interaction
potential rises sharply in a narrow vicinity of the values of mean fields
corresponding to nucleon densities $n> n_{*}>n_0$, where $n_0$ is the nuclear
saturation density. As the result the limiting neutron star mass increases.
This procedure offers a simple way to stiffen the equation of state at
densities above $n_{*}$ without altering it at densities $n\le n_{0}$. The
developed scheme allows an application to neutron stars of the RMF models,
which are well fitted to finite nuclei but do not fulfill the experimental
constraint on the limiting neutron star mass. The exemplary application of the
method to the well-known FSUGold model allows us to increase the limiting
neutron star mass from $1.72~M_\odot$ to $M \geq 2.01~M_\odot$.",1508.03771v2
2016-01-18,The importance of finite-temperature exchange-correlation for warm dense matter calculations,"Effects of explicit temperature dependence in the exchange-correlation (XC)
free-energy functional upon calculated properties of matter in the warm dense
regime are investigated. The comparison is between the KSDT finite-temperature
local density approximation (TLDA) XC functional [Phys.\ Rev.\ Lett.\
\textbf{112}, 076403 (2014)] parametrized from restricted path integral Monte
Carlo data on the homogeneous electron gas (HEG) and the conventional Monte
Carlo parametrization ground-state LDA XC functional (Perdew-Zunger, ""PZ"")
evaluated with $T$-dependent densities. Both Kohn-Sham (KS) and orbital-free
density functional theory (OFDFT) are used, depending upon computational
resource demands. Compared to the PZ functional, the KSDT functional generally
lowers the direct-current (DC) electrical conductivity of low density Al,
yielding improved agreement with experiment. The greatest lowering is about
15\% for T= 15 kK. Correspondingly, the KS band structure of low-density fcc Al
from KSDT exhibits a clear increase in inter-band separation above the Fermi
level compared to the PZ bands. In some density-temperature regimes, the
Deuterium equations of state obtained from the two XC functionals exhibit
pressure differences as large as 4\% and a 6\% range of differences. However,
the Hydrogen principal Hugoniot is insensitive to explicit XC $T$-dependence
because of cancellation between the energy and pressure-volume work difference
terms in the Rankine-Hugoniot equation. Finally, the temperature at which the
HEG becomes unstable is $T\geq$ 7200 K for $T$-dependent XC, a result that the
ground-state XC underestimates by about 1000 K.",1601.04543v2
2020-02-20,Dispersion without many-body density distortion: Assessment on atoms and small molecules,"We have implemented and tested the method we have recently proposed [J. Phys.
Chem. Lett. 10, 1537 (2019)] to treat dispersion interactions, which is derived
from a supramolecular wavefunction constrained to leave the diagonal of the
many-body density matrix of each monomer unchanged. The corresponding
variational optimization leads to expressions for the dispersion coefficients
in terms of the ground-state pair densities of the isolated monomers only,
which provides a framework to build new approximations without the need for
polarizabilities or virtual orbitals. The question we want to answer here is
how accurate this ``fixed diagonal matrices'' (FDM) method can be for isotropic
and anisotropic $C_6$ dispersion coefficients when using monomer pair densities
from different levels of theory, namely Hartree-Fock, MP2 and CCSD. For
closed-shell systems, FDM with CCSD monomer pair densities yields the best
results, with a mean average percent error for isotropic $C_6$ dispersion
coefficients of about 7\% and a maximum absolute error within 18\%. The
accuracy for anisotropic dispersion coefficients with FDM on top of CCSD ground
states is found to be similar. The performance for open shell systems is less
satisfactory, with CCSD pair densities not always providing the best result. In
the present implementation, the computational cost on top of the monomer's
ground-state calculations is $\mathcal{O}(N^4)$.",2002.08708v2
2017-05-29,"Beyond Counting: Comparisons of Density Maps for Crowd Analysis Tasks - Counting, Detection, and Tracking","For crowded scenes, the accuracy of object-based computer vision methods
declines when the images are low-resolution and objects have severe occlusions.
Taking counting methods for example, almost all the recent state-of-the-art
counting methods bypass explicit detection and adopt regression-based methods
to directly count the objects of interest. Among regression-based methods,
density map estimation, where the number of objects inside a subregion is the
integral of the density map over that subregion, is especially promising
because it preserves spatial information, which makes it useful for both
counting and localization (detection and tracking). With the power of deep
convolutional neural networks (CNNs) the counting performance has improved
steadily. The goal of this paper is to evaluate density maps generated by
density estimation methods on a variety of crowd analysis tasks, including
counting, detection, and tracking. Most existing CNN methods produce density
maps with resolution that is smaller than the original images, due to the
downsample strides in the convolution/pooling operations. To produce an
original-resolution density map, we also evaluate a classical CNN that uses a
sliding window regressor to predict the density for every pixel in the image.
We also consider a fully convolutional (FCNN) adaptation, with skip connections
from lower convolutional layers to compensate for loss in spatial information
during upsampling. In our experiments, we found that the lower-resolution
density maps sometimes have better counting performance. In contrast, the
original-resolution density maps improved localization tasks, such as detection
and tracking, compared to bilinear upsampling the lower-resolution density
maps. Finally, we also propose several metrics for measuring the quality of a
density map, and relate them to experiment results on counting and
localization.",1705.10118v2
2009-08-14,Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling,"We have completed a numerical investigation of the Anderson-Hubbard model for
three-dimensional simple cubic lattices using a real-space self-consistent
Hartree-Fock decoupling approximation for the Hubbard interaction. In this
formulation we treat the spatial disorder exactly, and therefore we account for
effects arising from localization physics. We have examined the model for
electronic densities well away 1/2 filling, thereby avoiding the physics of a
Mott insulator. Several recent studies have made clear that the combined
effects of electronic interactions and spatial disorder can give rise to a
suppression of the electronic density of states, and a subsequent
metal-insulator transition can occur. We augment such studies by calculating
the ac conductivity for such systems. Our numerical results show that weak
interactions enhance the density of states at the Fermi level and the
low-frequency conductivity, there are no local magnetic moments, and the ac
conductivity is Drude-like. However, with a large enough disorder strength and
larger interactions the density of states at the Fermi level and the
low-frequency conductivity are both suppressed, the conductivity becomes
non-Drude-like, and these phenomena are accompanied by the presence of local
magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc
omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in
the nonmetallic regime. Our numerical results show that the formation of
magnetic moments is essential to the suppression of the density of states at
the Fermi level, and therefore essential to the metal-insulator transition.",0908.2139v1
2010-01-27,"Ground and excited states of Li$^-$, Be$^-$ through a density-based approach","Density functional calculations are performed for ground [He]2s$^2$
$^1$S$^e$, and three metastable bound excited states, 1s2s2p$^2$ $^5$P$^e$,
1s2p$^3$ $^5$S$^o$, 1s2s2p3p $^5$P$^e$ of Li$^-$ and [He]2s2p$^2$ $^4$P$^e$,
[He]2p$^3$ $^4$S$^o$, 1s2s2p$^3$ $^6$S$^o$ of Be$^-$ each. The
work-function-based exchange potential is used, while the correlation effects
are included by employing the Lee-Yang-Parr potential. The relevant
nonrelativistic KS equation is solved by means of a generalized pseudospectral
discretization scheme offering nonuniform and optimal spatial grid. Computed
total energies, radial densities, selected density moments, as well as two
transition wavelengths (1s2s2p$^2$ $^5$P$^e \to$1s2p$^3$ $^5$S$^o$ of Li$^-$,
[He]2s2p$^2$ $^4$P$^e \to$ [He]2p$^3$ $^4$S$^o$ of Be$^-$) show reasonably good
agreement with the available theoretical and experimental data. The term
energies show an absolute deviation of 0.007--0.171% with the largest deviation
being observed for the even-parity $^5$P state of Li$^-$. The transition
wavelengths of Li$^-$, Be$^-$ are calculated within 0.891 and 0.438% of the
experimental values. This offers a simple practical route towards accurate
reliable calculation of excited states of anions within density functional
theory.",1001.4869v1
2014-02-19,Exactly solvable tight-binding model on the RAN: fractal energy spectrum and Bose-Einstein condensation,"We initially consider a single-particle tight-binding model on the
Regularized Apollonian Network (RAN). The RAN is defined starting from a
tetrahedral structure with four nodes all connected (generation 0). At any
successive generations, new nodes are added and connected with the surrounding
three nodes. As a result, a power-law cumulative distribution of connectivity
$P(k)\propto {1}/{k^{\eta}}$ with $\eta=\ln(3)/\ln(2) \approx 1.585$ is
obtained.
  The eigenvalues of the Hamiltonian are exactly computed by a recursive
approach for any size of the network. In the infinite size limit, the density
of states and the cumulative distribution of states (integrated density of
states) are also exactly determined. The relevant scaling behavior of the
cumulative distribution close to the band bottom is shown to be power law with
an exponent depending on the spectral dimension and not on the embedding
dimension.
  We then consider a gas made by an infinite number of non-interacting bosons
each of them described by the tight-binding Hamiltonian on the RAN and we prove
that, for sufficiently large bosonic density and sufficiently small
temperature, a macroscopic fraction of the particles occupy the lowest
single-particle energy state forming the Bose-Einstein condensate. We determine
no only the transition temperature as a function of the bosonic density, but
also the fraction of condensed particle, the fugacity, the energy and the
specific heat for any temperature and bosonic density.",1402.4661v1
1998-12-08,Bound States in the Vortex Core,"The quasiparticle excitation spectrum of isolated vortices in clean layered
d-wave superconductors is calculated. A large peak in the density of states in
the ""pancake"" vortex core is found, in an agreement with the recent
experimental data for high-temperature superconductors.",9812131v1
2007-03-30,Exact many-electron ground states on the diamond Hubbard chain,"Exact ground states of interacting electrons on the diamond Hubbard chain in
a magnetic field are constructed which exhibit a wide range of properties such
as flat-band ferromagnetism and correlation induced metallic, half-metallic or
insulating behavior. The properties of these ground states can be tuned by
changing the magnetic flux, local potentials, or electron density.",0703818v1
2002-01-08,Spectral cross correlations of magnetic edge states,"We observe strong, non-trivial cross-correlations between the edge states
found in the interior and the exterior of magnetic quantum billiards. Our
analysis is based on a novel definition of the edge state spectral density
which is rigorous, practical and semiclassically accessible.",0201010v1
1997-10-14,Quantum State Reconstruction of a Bose-Einstein Condensate,"We propose a tomographic scheme to reconstruct the quantum state of a
Bose-Einstein condensate, exploiting the radiation field as a probe and
considering the atomic internal degrees of freedom. The density matrix in the
number state basis can be directly retrieved from the atom counting
probabilities.",9710038v1
2004-05-22,A simple entanglement measure for multipartite pure states,"A simple entanglement measure for multipartite pure states is formulated
based on the partial entropy of a series of reduced density matrices. Use of
the proposed new measure to distinguish disentangled, partially entangled, and
maximally entangled multipartite pure states is illustrated.",0405133v2
2007-10-10,Purity distribution for bipartite random pure states,"Analytic expressions for the probability density distribution of the linear
entropy and the purity are derived for bipartite pure random quantum states.
The explicit distributions for a state belonging to a product of Hilbert spaces
of dimensions p and q are given for p=3 and any q>=3, as well as for p=q=4.",0710.2045v1
2011-03-10,Irreversibility and Entropy Production in Transport Phenomena I,"*First-principles derivation of the entropy production in erectric static
conduction. *The second-order (symmetric) density matrix contributes to the
entropy production. *New schemes of steady states formulated using a
relaxation-type von Neumann equation. *Stationary temperature is introduced to
characterize steady states. *The mechanism of the entropy production in steady
states is also clarified.",1103.1954v2
2015-04-27,Spontaneous Appearance of Low-dimensional Magnetic Electron System on Semiconductor Nanostructures,"We find that spin-polarized ground states emerge in nanofacets which are
self-organized on SiC (0001) surfaces. Our large-scale density-functional
calculations reveal that the nanofacet formed by bunching of single bilayer
steps generates peculiar carbon dangling bond states localized at but extended
along step edges. The flat-band characteristics of those C states cause either
ferromagnetic or anti-ferromagnetic chains on covalent semiconductors.",1504.06934v1
2021-09-22,State-space representation of Matérn and Damped Simple Harmonic Oscillator Gaussian processes,"Gaussian processes (GPs) are used widely in the analysis of astronomical time
series. GPs with rational spectral densities have state-space representations
which allow O(n) evaluation of the likelihood. We calculate analytic state
space representations for the damped simple harmonic oscillator and the
Mat\'ern 1/2, 3/2 and 5/2 processes.",2109.10685v1
2005-04-20,Covalent bonding and hybridization effects in the corundum-type transition-metal oxides V2O3 and Ti2O3,"The electronic structure of the corundum-type transition-metal oxides V2O3
and Ti2O3 is studied by means of the augmented spherical wave method, based on
density-functional theory and the local density approximation. Comparing the
results for the vanadate and the titanate allows us to understand the peculiar
shape of the metal 3d a_{1g} density of states, which is present in both
compounds. The a_{1g} states are subject to pronounced bonding-antibonding
splitting due to metal-metal overlap along the c-axis of the corundum
structure. However, the corresponding partial density of states is strongly
asymmetric with considerably more weight on the high energy branch. We argue
that this asymmetry is due to an unexpected broadening of the bonding a_{1g}
states, which is caused by hybridization with the e_g^{pi} bands. In contrast,
the antibonding a_{1g} states display no such hybridization and form a sharp
peak. Our results shed new light on the role of the a_{1g} orbitals for the
metal-insulator transitions of V2O3. In particular, due to a_{1g} - e_g^{pi}
hybridization, an interpretation in terms of molecular orbital singlet states
on the metal-metal pairs along the c-axis is not an adequate description.",0504524v1
2005-06-16,"Ground-state energies, densities and momentum distributions in closed-shell nuclei calculated within a cluster expansion approach and realistic interactions","A linked cluster expansion suitable for the treatment of ground-state
properties of complex nuclei, as well as of various particle-nucleus scattering
processes, has been used to calculate the ground-state energy, density and
momentum distribution of 16-O and 40-Ca using realistic interactions. First of
all, a benchmark calculation for the ground-state energy has been performed
using the truncated V8' potential, and consisting in the comparison of our
results with the ones obtained by the Fermi Hypernetted Chain approach,
adopting in both cases the same mean field wave functions and the same
correlation functions. The results exhibited a nice agreement between the two
methods. Therefore, the approach has been applied to the calculation of the
ground-state energy, density and momentum distributions of 16-O and 40-Ca using
the full V8' potential, finding again a satisfactory agreement with the results
based on more advanced approaches where higher order cluster contributions are
taken into account. It appears therefore that the cluster expansion approach
can provide accurate approximations for various diagonal and non diagonal
density matrices, so that it could be used for a reliable evaluation of nuclear
effects in various medium and high energy scattering processes off nuclear
targets. The developed approach can be readily generalized to the treatment of
Glauber type final state interaction effects in inclusive, semi-inclusive and
exclusive processes off nuclei at medium and high energies.",0506054v2
2017-09-18,The Majorana spin in magnetic atomic chain systems,"In this paper, we establish that Majorana zero modes emerging from a
topological band structure of a chain of magnetic atoms embedded in a
superconductor can be distinguished from trivial localized zero energy states
that may accidentally form in this system using spin resolved measurements. To
demonstrate this key Majorana diagnostics, we study the spin composition of
magnetic impurity induced in-gap Shiba states in a superconductor using a
quantum impurity model (at the mean-field level). By examining the spin and
spectral densities in the context of the Bogoliubov-de Gennes (BdG)
particle-hole symmetry, we derive a sum rule that relates the spin densities of
localized Shiba states with those in the normal state without
superconductivity. Extending our investigations to ferromagnetic chain of
magnetic impurities, we identify key features of the spin properties of the
extended Shiba state bands, as well as those associated with a localized
Majorana end mode when the effect of spin-orbit interaction is included. We
then formulate a phenomenological theory for the measurement of the local spin
densities with spin-polarized scanning tunneling microscopy (STM) techniques.
By combining the calculated spin densities and the measurement theory, we show
that spin-polarized STM measurements can reveal a sharp contrast in spin
polarization between an accidentally-zero-energy trivial Shiba state and a
Majorana zero mode in a topological superconducting phase in atomic chains. We
further confirm our results with numerical simulations that address generic
parameter settings.",1709.05967v3
2000-10-19,Dehydrogenation of polycyclic aromatic hydrocarbons in the diffuse interstellar medium,"We present a model for the hydrogenation states of Polycyclic Aromatic
Hydrocarbons (PAHs) in the diffuse interstellar medium. First, we study the
abundance of hydrogenation and charge states of PAHs due to photo-ionization,
photo-dissociation in the interstellar UV field, electron recombination and
chemical reactions between PAH cations and H or H_2. For PAH cations, we find
that the dehydrogenation effects are dominant. The hydrogenation state of PAHs
depends strongly on the H density, the size of the molecule and UV field. In
diffuse clouds with low H density and normal UV radiation, PAHs containing less
than 40 C are completely or strongly dehydrogenated whereas at high H density,
they are normally hydrogenated. The partially dehydrogenated species dominate
in intermediate density clouds. PAHs above 40 C are quite stable and are fully
hydrogenated, which would favor their spectroscopic search in near IR surveys
of Diffuse Interstellar Bands (DIBs).",0010385v1
2005-01-13,Lattice QCD Constraints on Hybrid and Quark Stars,"A QCD-motivated dynamical-quasiparticle model with parameters adjusted to
reproduce the lattice-QCD equation of state is extrapolated from region of high
temperatures and moderate baryonic densities to the domain of high baryonic
densities and zero temperature. The resulting equation of state matched with
realistic hadronic equations of state predicts a phase transition into the
quark phase at higher densities than those reachable in neutron star interiors.
This excludes the possibility of the existence of hybrid (hadron-quark) stars.
Pure quark stars are possible and have low masses, small radii and very high
central densities. Similar results are obtained for a simple bag model with
massive quarks, fitted to reproduce the same lattice results. Self-bound quark
matter is also excluded within these models. Uncertainties in the present
extrapolation re discussed. Comparison with standard bag models is made.",0501254v2
1995-11-23,Spin density wave selection in the one-dimensional Hubbard model,"The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard
model is calculated, constrained to uniform phases, which have no charge
density modulation. The allowed solutions are saturated ferromagnetism (FM), a
spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The
DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices.
FM occurs for small filling, SSDW in most of the remainder of the phase
diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling.
Itinerant electrons lift the degeneracy with respect to canting angle in the
DSDW. The Hartree-Fock states are metallic except at multiples of a quarter
filling. Near half filling the uniform SSDW phase is unstable against phase
separation into a half-filled antiferromagnetic phase and a hole-rich SSDW
phase. The dependence of the ground state wave number on chemical potential is
conjectured to be a staircase. Comparison is made with higher dimensional
Hubbard models and the $J_{1}-J_{2}$ Heisenberg model.",9511116v1
2000-01-12,Excitation energies from time-dependent density functional theory using exact and approximate functionals,"The role of the exchange-correlation potential and the exchange-correlation
kernel in the calculation of excitation energues from time-dependent density
functional theory is studied. Excitation energies of the He and Be atoms are
calculated, both from the exact ground-state Kohn-Sham potential, and from two
orbital-dependent approximations. These are exact exchange and self-interaction
corrected local density approximation (SIC-LDA), both calculated using the
Krieger-Li-Iafrate (KLI) approximation. For the exchange-correlation kernela,
three adiabatic approximations were tested: The local density approximation,
exact exchange, and SIC-LDA. The choice of the ground-state
exchange-correlation potential has the largest impact on the absolute position
of most excitation energies. In particular, orbital-dependent approximate
potentials result in a uniform shift of the transition energies to the Rydberg
states.",0001154v1
2003-09-22,Shear Viscosity Coefficient from Microscopic Models,"The transport coefficient of shear viscosity is studied for a hadron matter
through microscopic transport model, the Ultra--relativistic Quantum Molecular
Dynamics (UrQMD), using the Green--Kubo formulas. Molecular--dynamical
simulations are performed for a system of light mesons in a box with periodic
boundary conditions. Starting from an initial state composed of $\pi, \eta
,\omega ,\rho ,\phi$ with a uniform phase--space distribution, the evolution
takes place through elastic collisions, production and annihilation. The system
approaches a stationary state of mesons and their resonances, which is
characterized by common temperature. After equilibration, thermodynamic
quantities such as the energy density, particle density, and pressure are
calculated. From such an equilibrated state the shear viscosity coefficient is
calculated from the fluctuations of stress tensor around equilibrium using
Green--Kubo relations. We do our simulations here at zero net baryon density so
that the equilibration times depend on the energy density. We do not include
hadron strings as degrees of freedom so as to maintain detailed balance. Hence
we do not get the saturation of temperature but this leads to longer
equilibration times.",0309056v2
2004-05-31,Development of Novel Density Functionals for Thermochemical Kinetics,"A new density functional theory (DFT) exchange-correlation functional for the
exploration of reaction mechanisms is proposed. This new functional, denoted
BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for
transition state barriers but, unlike previous attempts at such a functional,
this improved accuracy does not come at the expense of equilibrium properties.
This makes it a general-purpose functional whose domain of applicability has
been extended to transition states, rather than a specialized functional for
kinetics. The improvement in BMK rests on the inclusion of the kinetic energy
density together with a large value of the exact exchange mixing coefficient.
For this functional, the kinetic energy density appears to correct `back' the
excess exact exchange mixing for ground-state properties, possibly simulating
variable exchange.",0405158v1
2007-08-21,Optical and dc transport properties of a strongly correlated charge density wave system: exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory,"We derive the dynamical mean-field theory equations for transport in an
ordered charge-density-wave phase on a bipartite lattice. The formalism is
applied to the spinless Falicov-Kimball model on a hypercubic lattice at half
filling. We determine the many-body density of states, the dc charge and heat
conductivities, and the optical conductivity. Vertex corrections continue to
vanish within the ordered phase, but the density of states and the transport
coefficients show anomalous behavior due to the rapid development of thermally
activated subgap states. We also examine the optical sum rule and sum rules for
the first three moments of the Green's functions within the ordered phase and
see that the total optical spectral weight in the ordered phase either
decreases or increases depending on the strength of the interactions.",0708.2748v1
2010-07-20,Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice with in-situ density imaging,"We analyze quantitatively how imaging techniques with single-site resolution
allow to measure thermodynamical properties that cannot be inferred from
time-of-light images for the trapped Bose-Hubbard model. If the normal state
extends over a sufficiently large range, the chemical potential and the
temperature can be extracted from a single shot, provided the sample is in
thermodynamic equilibrium. When the normal state is too narrow, temperature is
low but can still be extracted using the fluctuation-dissipation theorem over
the entire trap range as long as the local density approximation remains valid,
as was recently suggested by Qi Zhou and Tin-Lun Ho [arXiv:0908.3015]. However,
for typical present-day experiments, the number of samples needed is of the
order of 1000 in order to get the temperature at least $10 \%$ accurate, but it
is possible to reduce the variance by 2 orders of magnitude if the
density-density correlation length is short, which is the case for the
Bose-Hubbard model. Our results provide further evidence that cold gases in an
optical lattices can be viewed as quantum analog computers.",1007.3529v1
2013-01-21,Density Matrix Topological Insulators,"Thermal noise can destroy topological insulators (TI). However we demonstrate
how TIs can be made stable in dissipative systems. To that aim, we introduce
the notion of band Liouvillian as the dissipative counterpart of band
Hamiltonian, and show a method to evaluate the topological order of its steady
state. This is based on a generalization of the Chern number valid for general
mixed states (referred to as density matrix Chern value), which witnesses
topological order in a system coupled to external noise. Additionally, we study
its relation with the electrical conductivity at finite temperature, which is
not a topological property. Nonetheless, the density matrix Chern value
represents the part of the conductivity which is topological due to the
presence of quantum mixed edge states at finite temperature. To make our
formalism concrete, we apply these concepts to the two-dimensional Haldane
model in the presence of thermal dissipation, but our results hold for
arbitrary dimensions and density matrices.",1301.4872v2
2014-04-24,Density of states in a two-dimensional chiral metal with vacancies,"We study quantum interference effects in a two-dimensional chiral metal
(bipartite lattice) with vacancies. We demonstrate that randomly distributed
vacancies constitute a peculiar type of chiral disorder leading to strong
modifications of critical properties at zero energy as compared to conventional
chiral metals. In particular, the average density of states diverges as $\rho
\propto E^{-1} |\ln E|^{-3/2}$ and the correlation length $L_c \propto
\sqrt{|\ln E|}$ in the limit $E \to 0$. When the average density of vacancies
is different in the two sublattices, a finite concentration of zero modes
emerges and a gap in the quasiclassical density of states opens around zero
energy. Interference effects smear this gap resulting in exponentially small
tails at low energies.",1404.6139v2
2015-02-04,Optimal transport over a linear dynamical system,"We consider the problem of steering an initial probability density for the
state vector of a linear system to a final one, in finite time, using minimum
energy control. In the case where the dynamics correspond to an integrator
($\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport
(OMT) problem. In general, we show that the problem can again be reduced to
solving an OMT problem and that it has a unique solution. In parallel, we study
the optimal steering of the state-density of a linear stochastic system with
white noise disturbance; this is known to correspond to a Schr\""odinger bridge.
As the white noise intensity tends to zero, the flow of densities converges to
that of the deterministic dynamics and can serve as a way to compute the
solution of its deterministic counterpart. The solution can be expressed in
closed-form for Gaussian initial and final state densities in both cases.",1502.01265v1
2015-04-30,Tunneling in graphene-topological insulator hybrid devices,"Hybrid graphene-topological insulator (TI) devices were fabricated using a
mechanical transfer method and studied via electronic transport. Devices
consisting of bilayer graphene (BLG) under the TI Bi$_2$Se$_3$ exhibit
differential conductance characteristics which appear to be dominated by
tunneling, roughly reproducing the Bi$_2$Se$_3$ density of states. Similar
results were obtained for BLG on top of Bi$_2$Se$_3$, with 10-fold greater
conductance consistent with a larger contact area due to better surface
conformity. The devices further show evidence of inelastic phonon-assisted
tunneling processes involving both Bi$_2$Se$_3$ and graphene phonons. These
processes favor phonons which compensate for momentum mismatch between the TI
$\Gamma$ and graphene $K, K'$ points. Finally, the utility of these tunnel
junctions is demonstrated on a density-tunable BLG device, where the
charge-neutrality point is traced along the energy-density trajectory. This
trajectory is used as a measure of the ground-state density of states.",1504.08311v1
2015-07-04,Halos in medium-heavy and heavy nuclei with covariant density functional theory in continuum,"The covariant density functional theory with a few number of parameters has
been widely used to describe the ground-state and excited-state properties for
the nuclei all over the nuclear chart. In order to describe exotic properties
of unstable nuclei, the contribution of the continuum and its coupling with
bound states should be treated properly. In this Topical Review, the
development of the covariant density functional theory in continuum will be
introduced, including the relativistic continuum Hartree-Bogoliubov theory, the
relativistic Hartree-Fock-Bogoliubov theory in continuum, and the deformed
relativistic Hartree-Bogoliubov theory in continuum. Then the descriptions and
predictions of the neutron halo phenomena in both spherical and deformed nuclei
will be reviewed. The diffuseness of the nuclear potentials, nuclear shapes and
density distributions, and the impact of the pairing correlations on nuclear
size will be discussed.",1507.01079v1
2015-11-23,The difference between two random mixed quantum states: exact and asymptotic spectral analysis,"We investigate the spectral statistics of the difference of two density
matrices, each of which is independently obtained by partially tracing a random
bipartite pure quantum state. We first show how a closed-form expression for
the exact joint eigenvalue probability density function for arbitrary
dimensions can be obtained from the joint probability density function of the
diagonal elements of the difference matrix, which is straightforward to
compute. Subsequently, we use standard results from free probability theory to
derive a relatively simple analytic expression for the asymptotic eigenvalue
density (AED) of the difference matrix ensemble, and using Carlson's theorem,
we obtain an expression for its absolute moments. These results allow us to
quantify the typical asymptotic distance between the two random mixed states
using various distance measures; in particular, we obtain the almost sure
asymptotic behavior of the operator norm distance and the trace distance.",1511.07278v3
2017-07-20,String percolation threshold for elliptically bounded systems,"It has been shown that a hot and dense deconfined nuclear matter state
produced in ultra-relativistic heavy-ion collisions, can be quantitatively
described by the String Percolation phenomenological model. The model address
the phase transition in terms of the two-dimensional continuum percolation
theory over strings, which are schematic representations of the fundamental
interactions among the partons of the colliding nuclei in the initial state. In
this work, we present an extension of the critical string density results
including the eccentricity dependence on the initial state geometry focus on
small string number with different density profile, small deviations from the
different profile densities are found. The percolation threshold shows
consistency with the thermodynamic limit for the uniform density profile with a
large number of strings in the case of circular boundary system. A significant
dependence on the eccentricity for a small number of strings compared to high
occupancy systems is exhibited, the implications may become relevant in
hadron-hadron or hadron-nucleus collision systems.",1707.06395v1
2020-08-24,Universal Density of Low Frequency States in Amorphous Solids at Finite Temperatures,"It has been established that the low frequency quasi-localized modes of
amorphous solids at zero temperature exhibit universal density of states,
depending on the frequencies as $D(\omega) \sim \omega^4$. It remains an open
question whether this universal law extends to finite temperatures. In this
Letter we show that well quenched model glasses at temperatures as high as
$T_g/3$ possess the same universal density of states. The only condition
required is that {\em average} particle positions stabilize before thermal
diffusion destroys the cage structure of the material. The universal density of
quasi-localized low frequency modes refers then to vibrations around the
thermally averaged configuration of the material.",2008.10259v1
2021-12-14,In-plane magnetic field induced density wave states near quantum spin Hall phase transitions,"We study the influence of an in-plane magnetic field and Coulomb interactions
on the physics of quantum spin Hall insulators, like those in InAs/GaSb and
HgTe/CdTe quantum wells. Using a Hartree-Fock mean-field theory approximation,
we calculate phase diagrams as functions of the band gap, band hybridization,
and magnetic field strength. We show that when the band hybridization is weak,
the system is unstable against the formation of density wave states. As the
strength of the in-plane magnetic field increases, the density-wave region of
the phase diagram expands and distinct density-wave states appear. We discuss
possible experimental implications of our results.",2112.07523v1
2022-10-29,Tunable valley filtering in dynamically strained $α$-$\mathcal{T}_3$ lattices,"Mechanical deformations in $\alpha$-$\mathcal{T}_3$ lattices induce local
pseudomagnetic fields of opposite directionality for different valleys. When
this strain is equipped with a dynamical drive, it generates a complementary
valley-asymmetric pseudoelectric field which is expected to accelerate
electrons. We propose that by combining these effects by a time-dependent
nonuniform strain, tunable valley filtering devices can be engineered that
extend beyond the static capabilities. We demonstrate this by implementing an
oscillating Gaussian bump centered in a four-terminal Hall bar
$\alpha$-$\mathcal{T}_3$ setup and calculating the induced
pseudoelectromagnetic fields analytically. Within a recursive Floquet
Green-function scheme, we determine the time-averaged transmission and valley
polarization, as well as the spatial distributions of the local density of
states and current density. As a result of the periodic drive, we detect novel
energy regimes with highly valley-polarized transmission, depending on
$\alpha$. Analyzing the spatial profiles of the time-averaged local density of
states and current density we can relate these regimes to the
pseudoelectromagnetic fields in the setup.By means of the driving frequency, we
can manipulate the valley-polarized states, which might be advantageous for
future device applications.",2210.16522v2
2023-05-30,Density Dependence of the Symmetry Energy in the Post PREX-CREX Era,"The recently published CREX results suggest a rather peculiar picture for the
density dependence of the symmetry energy. Whereas PREX favors a large neutron
skin thickness in $^{208}$Pb, thereby suggesting a stiff equation of state,
CREX suggests instead a much softer equation of state. This discrepancy has
caused a large spur in the theoretical community since no model has been able
to simultaneously reproduce within $1\sigma$ the PREX and CREX results.
Motivated by a novel correlation between a CREX observable and a combination of
bulk symmetry energy parameters, we calibrate three new covariant energy
density functionals that reproduce binding energies and charge radii of
spherical nuclei - and also accommodate the constraints imposed by PREX and
CREX. Given that these models suggest a stiff equation of state at high
densities, predictions for neutron star properties are also discussed.",2305.19376v4
2023-08-31,On the Role of Non-Localities in Fundamental Diagram Estimation,"We consider the role of non-localities in speed-density data used to fit
fundamental diagrams from vehicle trajectories. We demonstrate that the use of
anticipated densities results in a clear classification of speed-density data
into stationary and non-stationary points, namely, acceleration and
deceleration regimes and their separating boundary. The separating boundary
represents a locus of stationary traffic states, i.e., the fundamental diagram.
To fit fundamental diagrams, we develop an enhanced cross entropy minimization
method that honors equilibrium traffic physics. We illustrate the effectiveness
of our proposed approach by comparing it with the traditional approach that
uses local speed-density states and least squares estimation. Our experiments
show that the separating boundary in our approach is invariant to varying
trajectory samples within the same spatio-temporal region, providing further
evidence that the separating boundary is indeed a locus of stationary traffic
states.",2308.16878v1
2024-02-22,Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals,"The presence of spin-orbit coupling or non-collinear magnetic spin states can
have dramatic effects on the ground-state and spectral properties of materials,
in particular on the band structure. Here, we develop non-collinear
Koopmans-compliant functionals based on Wannier functions and
density-functional perturbation theory, targeting accurate spectral properties
in the quasiparticle approximation. Our non-collinear Koopmans-compliant theory
involves functionals of four-component orbitals densities, that can be obtained
from the charge and spin-vector densities of Wannier functions. We validate our
approach on three emblematic and diverse semiconductors where the effect of
spin-orbit coupling goes from small to very large: the III-IV semiconductor
GaAs, the transition-metal dichalcogenide WSe$_2$, and the cubic perovskite
CsPbBr$_3$. The predicted band gaps are comparable in accuracy to
state-of-the-art many-body perturbation theory and include spin-dependent
interactions and screening effects that are missing in standard diagrammatic
approaches based on the random phase approximation. While the inclusion of
orbital- and spin-dependent interactions in many-body perturbation theory
requires self-screening or vertex corrections, that emerges naturally in the
Koopmans-functionals framework.",2402.14575v1
2021-01-16,Reflection Modeling of the Black Hole Binary 4U~1630$-$47: the Disk Density and Returning Radiation,"We present the analysis of X-ray observations of the black hole binary
4U~1630$-$47 using relativistic reflection spectroscopy. We use archival data
from the RXTE, Swift, and NuSTAR observatories, taken during different
outbursts of the source between $1998$ and $2015$. Our modeling includes two
relatively new advances in modern reflection codes: high-density disks, and
returning thermal disk radiation. Accretion disks around stellar-mass black
holes are expected to have densities well above the standard value assumed in
traditional reflection models (i.e., $n_{\rm e}\sim10^{15}~{\rm cm^{-3}}$). New
high-density reflection models have important implications in the determination
of disk truncation (i.e., the disk inner radius). This is because one must
retain self-consistency in the irradiating flux and corresponding disk
ionization state, which is a function of disk density and system geometry. We
find the disk density is $n_{\rm e}\ge10^{20}~{\rm cm^{-3}}$ across all
spectral states. This density, combined with our constraints on the ionization
state of the material, implies an irradiating flux impinging on the disk that
is consistent with the expected theoretical estimates. Returning thermal disk
radiation -- the fraction of disk photons which bend back to the disk producing
additional reflection components -- is expected predominantly in the soft
state. We show that returning radiation models indeed provide a better fit to
the soft state data, reinforcing previous results which show that in the soft
state the irradiating continuum may be blackbody emission from the disk itself.",2101.06343v1
2022-01-14,$n$-qubit states with maximum entanglement across all bipartitions: A graph state approach,"We discuss the construction of $n$-qubit pure states with maximum bipartite
entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which
implies that the Von Neumann entropy of every $k$-qubit reduced density matrix
corresponding to this state should be $k \ln 2 $. Such states have been
referred to as $k$-uniform, $k$-MM states. We show that a subset of the 'graph
states' satisfy this condition, hence providing a recipe for constructing
$k$-uniform states. Finding recipes for construction of $k$-uniform states
using graph states is useful since every graph state can be constructed
starting from a product state using only controlled-$Z$ gates. Though, a priori
it is not clear how to construct a graph which corresponds to an arbitrary
$k$-uniform state, but in particular, we show that graphs with no isolated
vertices are $1$-uniform. Graphs organized as a circular linear chain
corresponds to the case of $2$-uniform state, where we show that the minimum
number of qubits required to host such a state is $n=5$. $3$-uniform states can
be constructed by forming bi-layer graphs with $n/2$ qubits ($n=2\mathbb{Z}$)
in each layer, such that each layer forms a fully connected graph while
inter-layer connections are such that the vertices in one layer has a one to
one connectivity to the other layer. $4$-uniform states can be formed by taking
2D lattice graphs( also referred elsewhere as a 2D cluster Ising state ) with
periodic boundary conditions along both dimensions and both dimensions having
at least $5$ vertices.",2201.05622v2
1995-07-28,Density Dependent Hadron Field Theory,"A fully covariant approach to a density dependent hadron field theory is
presented. The relation between in--medium NN interactions and
field--theoretical meson--nucleon vertices is discussed. The medium dependence
of nuclear interactions is described by a functional dependence of the
meson--nucleon vertices on the baryon field operators. As a consequence, the
Euler--Lagrange equations lead to baryon rearrangement self--energies which are
not obtained when only a parametric dependence of the vertices on the density
is assumed. It is shown that the approach is energy--momentum conserving and
thermodynamically consistent. Solutions of the field equations are studied in
the mean--field approximation. Descriptions of the medium dependence in terms
of the baryon scalar and vector density are investigated. Applications to
infinite nuclear matter and finite nuclei are discussed. Density dependent
coupling constants obtained from Dirac--Brueckner calculations with the Bonn
NN-potentials are used. Results from Hartree calculations for energy spectra,
binding energies and charge density distributions of $^{16}O$, $^{40,48}Ca$ and
$^{208}Pb$ are presented. Comparisons to data strongly support the importance
of rearrangement in a relativistic density dependent field theory. Most
striking is the simultanuous improvement of charge radii, charge densities and
binding energies. The results indicate the appearance of a new ""Coester line""
in the nuclear matter equation of state.",9507044v1
2006-11-09,Cold uniform matter and neutron stars in the quark-mesons-coupling model,"A new density dependent effective baryon-baryon interaction has been recently
derived from the quark-meson-coupling (QMC) model, offering impressive results
in application to finite nuclei and dense baryon matter. This self-consistent,
relativistic quark-level approach is used to construct the Equation of State
(EoS) and to calculate key properties of high density matter and cold, slowly
rotating neutron stars. The results include predictions for the maximum mass of
neutron star models, together with the corresponding radius and central
density, as well the properties of neutron stars with mass of order 1.4
$M_\odot$. The cooling mechanism allowed by the QMC EoS is explored and the
parameters relevant to slow rotation, namely the moment of inertia and the
period of rotation investigated. The results of the calculation, which are
found to be in good agreement with available observational data, are compared
with the predictions of more traditional EoS. The QMC EoS provides cold neutron
star models with maximum mass 1.9--2.1 M$_\odot$, with central density less
than 6 times nuclear saturation density ($n_{0}= 0.16 {\rm fm}^{-3}$) and
offers a consistent description of the stellar mass up to this density limit.
In contrast with other models, QMC predicts no hyperon contribution at
densities lower than $3n_0$, for matter in $\beta$-equilibrium. At higher
densities, $\Xi^{-,0}$ and $\Lambda$ hyperons are present.",0611030v1
2015-09-08,Screened-exchange density functional theory description of the electronic structure and phase stability of the chalcopyrite materials AgInSe$_2$ and AuInSe$_2$,"We present a systematic assessment of the structural properties, the
electronic density of states, the charge densities, and the phase stabilities
of AgInSe$_2$ and AuInSe$_2$ using screened exchange hybrid density functional
theory, and compare their properties to those of CuInSe$_2$. For AgInSe$_2$,
hybrid density functional theory properly captures several experimentally
measured properties, including the increase in the band gap and the change in
the direction of the lattice distortion parameter $u$ in comparison to
CuInSe$_2$. While the electronic properties of AuInSe$_2$ have not yet been
experimentally characterized, we predict it to be a small gap ($\approx 0.15$
eV) semiconductor. We also present the phase stability of AgInSe$_2$ and
AuInSe$_2$ according to screened-exchange density functional theory, and
compare the results to predictions from conventional density functional theory,
results tabulated from several online materials data repositories, and
experiment (when available). In comparison to conventional density functional
theory, the hybrid functional predicts phase stabilities of AgInSe$_2$ in
better agreement with experiment: discrepancies in the calculated formation
enthalpies are reduced by approximately a factor of three, from $\approx$ 0.20
eV/atom to $\approx$ 0.07 eV/atom, similar to the improvement observed for
CuInSe$_2$. We further predict that AuInSe$_2$ is not a stable phase, and can
only be present under non-equilibrium conditions.",1509.02306v2
2022-12-06,Enhancing Low-Density EEG-Based Brain-Computer Interfaces with Similarity-Keeping Knowledge Distillation,"Electroencephalogram (EEG) has been one of the common neuromonitoring
modalities for real-world brain-computer interfaces (BCIs) because of its
non-invasiveness, low cost, and high temporal resolution. Recently,
light-weight and portable EEG wearable devices based on low-density montages
have increased the convenience and usability of BCI applications. However, loss
of EEG decoding performance is often inevitable due to reduced number of
electrodes and coverage of scalp regions of a low-density EEG montage. To
address this issue, we introduce knowledge distillation (KD), a learning
mechanism developed for transferring knowledge/information between neural
network models, to enhance the performance of low-density EEG decoding. Our
framework includes a newly proposed similarity-keeping (SK) teacher-student KD
scheme that encourages a low-density EEG student model to acquire the
inter-sample similarity as in a pre-trained teacher model trained on
high-density EEG data. The experimental results validate that our SK-KD
framework consistently improves motor-imagery EEG decoding accuracy when number
of electrodes deceases for the input EEG data. For both common low-density
headphone-like and headband-like montages, our method outperforms
state-of-the-art KD methods across various EEG decoding model architectures. As
the first KD scheme developed for enhancing EEG decoding, we foresee the
proposed SK-KD framework to facilitate the practicality of low-density
EEG-based BCI in real-world applications.",2212.03329v1
2001-05-07,Characteristic features of d pairing in bilayer cuprates under conditions of Peierls instability of the normal phase,"A system of self-consistent integral equations for the superconducting gap is
formulated and solved taking account of the instability of the normal phase of
bilayered cuprates against charge-density waves. The critical parameters are
calculated as a function of the wave vector, temperature, and doping index. It
is found that the region in which superconductivity coexists with d-type
charge-density waves depends strongly on the doping index. The effective
energy-gap parameter, determined as the interval between the peaks of the
density of states, can have a local minimum at temperatures T$<$T$_C$.",0105136v1
2005-12-17,Spin polarization of light atoms in jellium: Detailed electronic structures,"We revisit the problem of the spontaneous magnetization of an {\em sp}
impurity atom in a simple metal host. The main features of interest are: (i)
Formation of the spherical spin density/charge density wave around the
impurity; (ii) Considerable decrease in the size of the pseudoatom in the
spin-polarized state as compared with the paramagnetic one, and (iii) Relevance
of the electron affinity of the isolated atom to this spin polarization, which
is clarified by tracing the transformation of the pseudoatom into an isolated
negative ion in the low-density limit of the enveloping electron gas.",0512417v1
2009-11-19,Reduced density matrix of permutational invariant many-body systems,"We consider density matrices which are sums of projectors on states spanning
irreducible representations of the permutation group of L sites (eigenstates of
permutational invariant quantum system with L sites) and construct the reduced
density matrix (RDM) for blocks of size n<L by tracing out L-n sites, viewed as
environment. Explicit analytic expressions of the elements of the RDM are given
in the natural basis and the corresponding spectrum is derived. Results apply
to all quantum many-body systems with permutational symmetry for which the mean
field theory is exact.",0911.3777v1
2012-11-02,Markov chain approximations for transition densities of Lévy processes,"We consider the convergence of a continuous-time Markov chain approximation
X^h, h>0, to an R^d-valued Levy process X. The state space of X^h is an
equidistant lattice and its Q-matrix is chosen to approximate the generator of
X. In dimension one (d=1), and then under a general sufficient condition for
the existence of transition densities of X, we establish sharp convergence
rates of the normalised probability mass function of X^h to the probability
density function of X. In higher dimensions (d>1), rates of convergence are
obtained under a technical condition, which is satisfied when the diffusion
matrix is non-degenerate.",1211.0476v2
2014-09-30,Green's function method for single-particle resonant states in relativistic mean field theory,"Relativistic mean field theory is formulated with the Green's function method
in coordinate space to investigate the single-particle bound states and
resonant states on the same footing. Taking the density of states for free
particle as a reference, the energies and widths of single-particle resonant
states are extracted from the density of states without any ambiguity. As an
example, the energies and widths for single-neutron resonant states in
$^{120}$Sn are compared with those obtained by the scattering phase-shift
method, the analytic continuation in the coupling constant approach, the real
stabilization method and the complex scaling method. Excellent agreements are
found for the energies and widths of single-neutron resonant states.",1409.8412v1
2022-08-01,Interaction Driven Topological Phase Transition in Monolayer CrCl$_2$(pyrazine)$_2$,"The quadratic band crossing points (QBCPs) at Fermi level in two-dimension
have been proposed to be unstable under electron-electron interaction. The
possible interaction driven states include quantum anomalous Hall (QAH) state
and various nematic ordered states. In this work, motivated by the discovery of
ferromagnetic van der Waals layered metal-organic framework
CrCl$_2$(pyrazine)$_2$, we theoretically propose that the single layer of
CrCl$_2$(pyrazine)$_2$ might realize one or some of these interaction driven
states based on the QBCP protected by $C_4$ symmetry. By introducing the
short-range density-density type repulsion interactions into this system, we
have found the phase diagram depending on different interaction range and
strength. The exotic phases include the staggered chiral flux state manifesting
QAH effect, the site-nematic insulator and the site-nematic Dirac semimetal
state. The QAH state is robust against perturbations breaking the QBCP but it
is weakened by increasing temperature. The metal-organic framework is tunable
by changing the transition-metal elements, which might improve the gap size and
stability of this interaction induced QAH state.",2208.00942v1
2005-11-30,Coulomb drag between two spin incoherent Luttinger liquids,"In a one dimensional electron gas at low enough density, the magnetic (spin)
exchange energy $J$ between neighboring electrons is exponentially suppressed
relative to the characteristic charge energy, the Fermi energy $E_F$. At
non-zero temperature $T$, the energy hierarchy $J \ll T \ll E_F$ can be
reached, and we refer to this as the spin incoherent Lutinger liquid state. We
discuss the Coulomb drag between two parallel quantum wires in the spin
incoherent regime, as well as the crossover to this state from the low
temperature regime by using a model of a fluctuating Wigner solid. As the
temperature increases from zero to above $J$ for a fixed electron density, the
$2k_F$ oscillations in the density-density correlations are lost. As a result,
the temperature dependence of the Coulomb drag is dramatically altered and
non-monotonic dependence may result. Drag between wires of equal and unequal
density are discussed, as well as the effects of weak disorder in the wires. We
speculate that weak disorder may play an important role in extracting
information about quantum wires in real drag experiments.",0511715v1
2011-03-16,Gutzwiller study of extended Hubbard models with fixed boson densities,"We studied all possible ground states, including supersolid (SS) phases and
phase separations of hard-core- and soft-core-extended Bose--Hubbard models
with fixed boson densities by using the Gutzwiller variational wave function
and the linear programming method. We found that the phase diagram of the
soft-core model depends strongly on its transfer integral. Furthermore, for a
large transfer integral, we showed that an SS phase can be the ground state
even below or at half filling against the phase separation. We also found that
the density difference between nearest-neighbor sites, which indicates the
density order of the SS phase, depends strongly on the boson density and
transfer integral.",1103.3106v4
2019-09-30,Transition densities and form factors in the triangular $α$-cluster model of $^{12}$C with application to $^{12}$C+$α$ scattering,"Densities and transition densities are computed in an equilateral triangular
alpha-cluster model for $^{12}$C, in which each $\alpha$ particle is taken as a
gaussian density distribution. The ground-state, the symmetric vibration (Hoyle
state) and the asymmetric bend vibration are analyzed in a molecular approach
and dissected into their components in a series of harmonic functions,
revealing their intrinsic structures. The transition densities in the
laboratory frame are then used to construct form-factors and to compute DWBA
inelastic cross-sections for the $^{12}$C$(\alpha, \alpha')$ reaction. The
comparison with experimental data indicates that the simple geometrical model
with rotations and vibrations gives a reliable description of reactions where
$\alpha$-cluster degrees of freedom are involved.",1909.13571v1
2021-02-22,"The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field","We compare the ground-state features of alternating ferrimagnetic chains
$(1/2, S)$ with $S=1,3/2,2,5/2$ in a magnetic field and the corresponding
Holstein-Primakoff bosonic models up to order $\sqrt{s/S}$, with $s=1/2$,
considering the fully polarized magnetization as the boson vacuum. {The
single-particle Hamiltonian is a Rice-Mele model with uniform hopping and
modified boundaries, while the interactions have a correlated
(density-dependent) hopping term and magnon-magnon repulsion.} The
magnon-magnon repulsion increases the many-magnon energy and the
density-dependent hopping decreases the kinetic energy. We use density matrix
renormalization group calculations to investigate the effects of these two
interaction terms in the bosonic model{, and display the quantitative agreement
between the results from the spin model and the full bosonic approximation. In
particular, we verify the good accordance in the behavior of the edge states,
associated with the ferrimagnetic plateau, from the spin and from the bosonic
models. Furthermore, we show that the boundary magnon density strongly depends
on the interactions and particle statistics.",2102.11143v1
1998-05-29,Properties of the energy landscape of network models for covalent glasses,"We investigate the energy landscape of two dimensional network models for
covalent glasses by means of the lid algorithm. For three different particle
densities and for a range of network sizes, we exhaustively analyse many
configuration space regions enclosing deep-lying energy minima. We extract the
local densities of states and of minima, and the number of states and minima
accessible below a certain energy barrier, the 'lid'. These quantities show on
average a close to exponential growth as a function of their respective
arguments. We calculate the configurational entropy for these pockets of states
and find that the excess specific heat exhibits a peak at a critical
temperature associated with the exponential growth in the local density of
states, a feature of the specific heat also observed in real glasses at the
glass transition.",9805396v1
2005-07-29,Local density approximation for a perturbative equation of state,"The knowledge of a series expansion of the equation of state provides a deep
insight into the physical nature of a quantum system. Starting from a generic
``perturbative'' equation of state of a homogeneous ultracold gas we make
predictions for the properties of the gas in the presence of harmonic
confinement. The local density approximation is used to obtain the chemical
potential, total and release energies, Thomas-Fermi size and density profile of
a trapped system in three-, two-, and one- dimensional geometries. The
frequencies of the lowest breathing modes are calculated using scaling and
sum-rule approaches and could be used in an experiment as a high precision tool
for obtaining the expansion terms of the equation of state. The derived
formalism is applied to dilute Bose and Fermi gases in different dimensions and
to integrable one-dimensional models. Physical meaning of expansion terms in a
number of systems is discussed.",0507711v1
2012-10-21,A geometrical approach to the mean density of states in many-body quantum systems,"We present a novel analytical approach for the calculation of the mean
density of states in many-body systems made of confined indistinguishable and
non-interacting particles. Our method makes explicit the intrinsic geometry
inherent in the symmetrization postulate and, in the spirit of the usual Weyl
expansion for the smooth part of the density of states in single-particle
confined systems, our results take the form of a sum over clusters of particles
moving freely around manifolds in configuration space invariant under elements
of the group of permutations. Being asymptotic, our approximation gives
increasingly better results for large excitation energies and we formally
confirm that it coincides with the celebrated Bethe estimate in the appropriate
region. Moreover, our construction gives the correct high energy asymptotics
expected from general considerations, and shows that the emergence of the
fermionic ground state is actually a consequence of an extremely delicate large
cancellation effect. Remarkably, our expansion in cluster zones is naturally
incorporated for systems of interacting particles, opening the road to address
the fundamental problem about the interplay between confinement and
interactions in many-body systems of identical particles.",1210.5748v1
2014-05-29,Quantum Monte Carlo study of a vortex in superfluid $^4$He and search for a vortex state in the solid,"We have performed a microscopic study of a straight quantized vortex line in
three dimensions in condensed $^4$He at zero temperature using the Shadow Path
Integral Ground State method and the fixed-phase approximation. We have
characterized the energy and the local density profile around the vortex axis
in superfluid $^4$He at several densities, ranging from below the equilibrium
density up to the overpressurized regime. For the Onsager-Feynman (OF) phase
our results are exact and represent a benchmark for other theories. The
inclusion of backflow correlations in the phase improves the description of the
vortex with respect to the OF phase by a large reduction of the core energy of
the topological excitation. At all densities the phase with backflow induces a
partial filling of the vortex core and this filling slightly increases with
density. The core size slightly decreases for increasing density and the
density profile has well defined density dependent oscillations whose wave
vector is closer to the wave vector of the main peak in the static density
response function rather than to the roton wave vector. Our results can be
applied to vortex rings of large radius $R$ and we find good agreement with the
experimental value of the energy as function of $R$ without any free parameter.
We have studied also $^4$He above the melting density in the solid phase using
the same functional form for the phase as in the liquid. We found that
off-diagonal properties of the solid are not qualitatively affected by the
velocity field induced by the vortex phase, both with and without backflow
correlations. Therefore we find evidence that a perfect $^4$He crystal is not a
marginally stable quantum solid in which rotation would be able to induce
off-diagonal long-range coherence.",1405.7589v2
2009-02-03,Magnetic field induced pattern of coexisting condensates in the superconducting state of CeCoIn$_5$,"In usual superconductors the carriers form Cooper pairs that have zero total
momentum meaning that the superfluid density is homogeneous. We know for
decades that it is a priori possible to observe at high fields the
Fulde-Ferrel-Larkin-Ovchinikov (FFLO) state in which the superfluid density
exhibits a field dependent modulation. The search for such inhomogeneous
condensates in materials is the subject of tremendous excitement especially
after the discovery of a promising high-field superconducting (HFSC) phase in
CeCoIn$_5$. However, subsequent neutron and NMR experiments contradicted the
FFLO picture in CeCoIn$_5$ establishing a puzzling coupling of the distinct
HFSC state with a magnetic modulation. Here we show that, a novel type of
exotic state is observed at high fields in CeCoIn$_5$ in which a pattern of
coexisting condensates manifests. The specific pattern includes the d-wave
singlet SC state, the staggered $\pi$-triplet SC state and Spin Density Waves
(SDW). Because of particle-hole asymmetry these three condensates may either
appear separately or all three together providing a new perspective on
antiferromagnetic superconductors that may include high-$T_c$ cuprates and
pniktides. The field induced transition to the pattern state in CeCoIn$_5$ is
only a paradigm of a generic mechanism that prevents the elimination of the
dominating condensate by the field via the formation of a pattern of
condensates. This opens new avenues for the search of exotic states not only in
electronic systems, but also in other systems where inhomogeneous condensates
are actively discussed like trapped atomic fermi gases and dense quark matter.",0902.0553v1
2017-12-21,"Conservation of energy, density of states and spin lattice relaxation","The starting point of all NMR experiments is a spin polarization which
develops when we place the sample in static magnetic field $B_0$. There are
excess of spins aligned along $B_0$ (spin up with lower energy) than spins
aligned opposite (spin down with higher energy) to the field $B_0$. A natural
question is what is the source of this excess spin polarization because
relaxation mechanisms can flip a up spin to a down spin and vice-versa. The
answer lies in the density of states. When a molecule with spin down flips to
spin up it loses energy. This energy goes into increasing the kinetic energy of
the molecule in the gas/solution phase. At this increased kinetic energy, there
are more rotational-translational states accessible to the molecule than at
lower energy. This increases the probability the molecule will spend in spin up
state (higher kinetic energy state). This is the source of excess polarization.
In this paper, we use an argument based on equipartition of energy to
explicitly count the excess states that become accessible to the molecule when
its spin is flipped from down to up. Using this counting, we derive the
familiar Boltzmann distribution of the ratio of up vs down spins. Although
prima facie, there is nothing new in this paper, we find the mode counting
argument for excess states interesting. Furthermore, the paper stresses the
fact that spin polarization arises from higher density of states at increased
kinetic energy of molecules.",1712.07859v1
2022-04-21,Density Functional Theory for Electronic Excited States,"This chapter provides a basic introduction to excited-state extensions of
density functional theory (DFT), including time-dependent (TD-)DFT in both its
linear-response and its explicitly time-dependent formulations. As applied to
the Kohn-Sham DFT ground state, linear-response theory affords an
eigenvalue-type problem for the excitation energies in a basis of
singly-excited Slater determinants, and is widely known simply as ""TDDFT""
despite its frequency-domain formulation. This form of TDDFT is the mostly
widely-used quantum-chemical method for excited states, due to a favorable
combination of low cost and reasonable accuracy. The chapter surveys the
accuracy of linear-response TDDFT, which is generally more sensitive to the
details of the exchange-correlation functional as compared to ground-state DFT,
and also describes some known systemic problems exhibited by this approach.
Some of those problems can be corrected on a case-by-case basis using
orbital-optimized, excited-state self-consistent field (SCF) calculations, in
what is known as excited-state Kohn-Sham theory or a ""Delta-SCF"" procedure, a
class of methods that includes restricted open-shell Kohn-Sham theory. Recent
successes of these approaches are highlighted, including double excitations and
core-level excitations. Finally, explicitly time-dependent (or ""real-time"")
TDDFT involves propagation of the molecular orbitals in time following an
external perturbation, according to the Kohn-Sham analogue of the
time-dependent Schroedinger equation. The time-dependent approach has been used
to model strong-field electron dynamics, and in the weak-field limit it
provides a route to broadband spectra based on the time evolution of the dipole
moment function. This is useful for describing high-energy excitations (as in
x-ray spectroscopy) and in systems where the density of states is high, as
demonstrated by a few examples.",2204.10135v1
2002-02-25,Non-conservation of Density of States in Bi$_2$Sr$_2$CaCu$_2$O$_y$: Coexistence of Pseudogap and Superconducting gap,"The tunneling spectra obtained within the ab-plane of
Bi$_2$Sr$_2$CaCu$_2$O$_y$ (Bi2212) for temperatures below and above the
critical temperature (T$_c$) are analyzed. We find that the tunneling
conductance spectra for the underdoped compound in the superconducting state do
not follow the conservation of states rule. There is a consistent loss of
states for the underdoped BI2212 implying an underlying depression in the
density of states (DOS) and hence the pseudogap near the Fermi energy (E$_F$).
Such an underlying depression can also explain the peak-dip-hump structure
observed in the spectra. Furthermore, the conservation of states is recovered
and the dip-hump structure disappears after normalizing the low temperature
spectra with that of the normal state. We argue that this is a direct evidence
for the coexistence of a pseudogap with the superconducting gap.",0202450v1
2007-03-01,Stochastic particle annihilation: a model of state reduction in relativistic quantum field theory,"A model of state reduction in relativistic quantum field theory involving a
nonlinear stochastic extension of Schr\""odinger's equation is outlined. The
eigenstates of the annihilation operator are chosen as the preferred basis onto
which reduction occurs. These are the coherent states which saturate the bound
of the Heisenberg uncertainty relation, exhibiting classical-like behavior. The
quantum harmonic oscillator is studied in detail before generalizing to
relativistic scalar quantum field theory. The infinite rates of increase in
energy density which have plagued recent relativistic proposals of dynamical
state reduction are absent in this model. This is because the state evolution
equation does not drive particle creation from the vacuum. The model requires
the specification of a preferred sequence of space-like hyper-surfaces
supporting the time-like state evolution. However, it is shown that the choice
of preferred surfaces has no effect on perturbative results to second order in
the coupling parameter. It is demonstrated how state reduction to a charge
density basis can be induced in fermionic matter via an appropriate coupling to
a bosonic field undergoing this mechanism.",0703011v2
2010-09-21,The ground states of the two-component order parameter superconductor,"We show that in presence of an applied external field the two-component order
parameter superconductor falls in two categories of ground states, namely, in
the traditional Abrikosov ground state or in a new ground state fitted to
describe a superconducting layer with texture, that is, patched regions
separated by a phase difference of $\pi$. The existence of these two kinds of
ground states follows from the sole assumption that the total supercurrent is
the sum of the two individual supercurrents and is independent of any
consideration about the free energy expansion. Uniquely defined relations
between the current density and the superfluid density hold for these two
ground states, which also determine the magnetization in terms of average
values of the order parameters. Because these ground state conditions are also
Bogomolny equations we construct the free energy for the two-component
superconductor which admits the Bogomolny solution at a special coupling value.",1009.4155v1
2016-06-02,Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories,"We consider the tensors generating matrix product states and density
operators in a spin chain. For pure states, we revise the renormalization
procedure introduced by F. Verstraete et al. in 2005 and characterize the
tensors corresponding to the fixed points. We relate them to the states
possessing zero correlation length, saturation of the area law, as well as to
those which generate ground states of local and commuting Hamiltonians. For
mixed states, we introduce the concept of renormalization fixed points and
characterize the corresponding tensors. We also relate them to concepts like
finite correlation length, saturation of the area law, as well as to those
which generate Gibbs states of local and commuting Hamiltonians. One of the
main result of this work is that the resulting fixed points can be associated
to the boundary theories of two-dimensional topological states, through the
bulk-boundary correspondence introduced by Cirac et al. in 2011.",1606.00608v3
2020-06-02,Variational optimization of continuous matrix product states,"Just as matrix product states represent ground states of one-dimensional
quantum spin systems faithfully, continuous matrix product states (cMPS)
provide faithful representations of the vacuum of interacting field theories in
one spatial dimension. Unlike the quantum spin case however, for which the
density matrix renormalization group and related matrix product state
algorithms provide robust algorithms for optimizing the variational states, the
optimization of cMPS for systems with inhomogeneous external potentials has
been problematic. We resolve this problem by constructing a piecewise linear
parameterization of the underlying matrix-valued functions, which enables the
calculation of the exact reduced density matrices everywhere in the system by
high-order Taylor expansions. This turns the variational cMPS problem into a
variational algorithm from which both the energy and its backwards derivative
can be calculated exactly and at a cost that scales as the cube of the bond
dimension. We illustrate this by finding ground states of interacting bosons in
external potentials, and by calculating boundary or Casimir energy corrections
of continuous many-body systems with open boundary conditions.",2006.01801v2
2010-10-05,Maximally Random Jamming of Two-Dimensional One-Component and Binary Hard Disc Fluids,"We report calculations of the density of maximally random jamming (aka random
close packing) of one-component and binary hard disc fluids. The theoretical
structure used provides a common framework for description of the hard disc
liquid to hexatic, the liquid to hexagonal crystal and the liquid-to-maximally
random jammed state transitions. Our analysis is based on locating a particular
bifurcation of the solutions of the integral equation for the inhomogeneous
single particle density at the transition between different spatial structures.
The bifurcation of solutions we study is initiated from the dense metastable
fluid, and we associate it with the limit of stability of the fluid, which we
identify with the transition from the metastable fluid to a maximally random
jammed state. For the one-component hard disc fluid the predicted packing
fraction at which the metastable fluid to maximally random jammed state
transition occurs is 0.84, in excellent agreement with the experimental value
0.84 \pm 0.02. The corresponding analysis of the limit of stability of a binary
hard disc fluid with specified disc diameter ratio and disc composition
requires extra approximations in the representations of the direct correlation
function, the equation of state, and the number of order parameters accounted
for. Keeping only the order parameter identified with the largest peak in the
structure factor of the highest density regular lattice with the same disc
diameter ratio and disc composition as the binary fluid, the predicted density
of maximally random jamming is found to be 0.84 to 0.87, depending on the
equation of state used, and very weakly dependent on the ratio of disc
diameters and the fluid composition, in agreement with both experimental data
and computer simulation data.",1010.0885v1
2021-06-16,Defects in Conformal Crystals: Discrete vs. Continuous Disclination Models,"We study the relationship between topological defect formation and
ground-state packings in a model of repulsions in external confining
potentials. Specifically we consider screened 2D Coulombic repulsions, which
conveniently parameterizes the effects of interaction range, but also serves as
simple physical model of confined, parallel arrays of polyelectrolyte filaments
or vortices in type-II superconductors. The countervailing tendencies of
repulsions and confinement to, respectively, spread and concentrate particle
density leads to an energetic preference for non-uniform densities in the
clusters. Ground states in such systems have previously been modeled as {\it
conformal crystals}, which are composed of locally equitriangular packings
whose local areal densities exhibit long range gradients. Here, we assess two
theoretical models that connect the preference for non-uniform density to the
formation of disclination defects, one of which assumes a continuum
distributions of defect, while the second considers the quantized and localized
nature of disclinations in hexagonal conformal crystals. Comparing both models
to numerical simulations of discrete particles clusters, we study the influence
of interaction range and confining potential on defects in ground states. We
show that treating disclinations as continuously distributable well-captures
the number of topological defects in the ground state in the regime of
long-range interactions, while as interactions become shorter range, it
dramatically overpredicts the to growth in total defect charge. Analysis of the
discretized defect theory suggests that limitations of the continuous defect
theory can be attributed to the asymmetry in the placement of positive vs.
negative disclinations in the conformal crystal ground states, as well as a
strongly asymmetric dependence of self-energy of disclinations on sign of
topological charge.",2106.08520v1
1997-07-28,Lattice dependence of saturated ferromagnetism in the Hubbard model,"We investigate the instability of the saturated ferromagnetic ground state
(Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and
d=3. A variational resolvent approach is developed for the Nagaoka instability
both for U = infinity and for U < infinity which can easily be evaluated in the
thermodynamic limit on all common lattices. Our results significantly improve
former variational bounds for a possible Nagaoka regime in the ground state
phase diagram of the Hubbard model. We show that a pronounced particle-hole
asymmetry in the density of states and a diverging density of states at the
lower band edge are the most important features in order to stabilize Nagaoka
ferromagnetism, particularly in the low density limit.",9707286v2
2002-02-11,In-plane Tunneling Spectrum into a [110]-Oriented High-$T_c$ Superconductor in the Pseudogap Regime,"Both the differential tunneling conductance and the surface local density of
states (LDOS) of a [110]-oriented high-temperature superconductor in the
pseudogap (PG) regime are studied theoretically. As a competing candidate for
the mechanism of PG state, the charge-density wave (CDW), spin-density wave
(SDW), $d$-density wave (DDW), and d-wave superconducting (DSC) orderings show
distinct features in the tunneling conductance. For the CDW, SDW, and DSC
orderings, the tunneling conductance approaches the surface LDOS as the barrier
potential is increased. For the DDW ordering, we show for the first time that
there exist midgap states at the [110] surface, manifesting themselves as a
sharp zero-energy peak in the LDOS, as in the case of DSC ordering. However,
due to the particle-hole pair nature of the DDW state, these states do not
carry current, and consequently the one-to-one correspondence between the
tunneling conductance and the surface LDOS is absent.",0202187v1
2003-07-08,Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator,"We investigate the quasiparticle density of states in disordered d-wave
superconductors. By constructing a quantum map describing the quasiparticle
dynamics in such a medium, we explore deviations of the density of states from
its universal form ($\propto E$), and show that additional low-energy
quasiparticle states exist provided (i) the range of the impurity potential is
much larger than the Fermi wavelength [allowing to use recently developed
semiclassical methods]; (ii) classical trajectories exist along which the
pair-potential changes sign; and (iii) the diffractive scattering length is
longer than the superconducting coherence length. In the classically chaotic
regime, universal random matrix theory behavior is restored by quantum
dynamical diffraction which shifts the low energy states away from zero energy,
and the quasiparticle density of states exhibits a linear pseudogap below an
energy threshold $E^* \ll \Delta_0$.",0307159v1
2006-02-21,Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap,"We investigate the ground state of the system of N bosons enclosed in a
hard-wall trap interacting via a repulsive or attractive $\delta$-function
potential. Based on the Bethe ansatz method, the explicit ground state wave
function is derived and the corresponding Bethe ansatz equations are solved
numerically for the full physical regime from the Tonks limit to the strongly
attractive limit. It is shown that the solution takes different form in
different regime. We also evaluate the one body density matrix and second-order
correlation function of the ground state for finite systems. In the Tonks limit
the density profiles display the Fermi-like behavior, while in the strongly
attractive limit the Bosons form a bound state of N atoms corresponding to the
N-string solution. The density profiles show the continuous crossover behavior
in the entire regime. Further the correlation function indicates that the Bose
atoms bunch closer as the interaction constant decreases.",0602483v4
2000-12-07,A quantum-copying machine for equatorial qubits,"Bu\v{z}ek and Hillery proposed a universal quantum-copying machine (UQCM)
(i.e., transformation) to analyze the possibility of cloning arbitrary states.
The UQCM copies quantum-mechanical states with the quality of its output does
not depend on the input. We propose a slightly different transformation to
analyze a restricted set of input states. We impose the conditions (I) the
density matrices of the two output states are the same, and that (II) the
distance between input density operator and the output density operators is
input state independent. Using Hilbert-Schmidt norm and Bures fidelity, we show
that our transformation can achieves the bound of the fidelity.",0012033v3
2008-10-10,Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials,"We investigate the possibility of a strongly correlated Fractional Quantum
Hall (FQH) state in bulk three dimensional isotropic (not layered) materials.
We find that a FQH state can exist at low densities only if it is accompanied
by a staging transition in which the electrons re-organize themselves in
layers, perpendicular to the magnetic field, at distances of order the magnetic
length apart. The Hartree energy associated to the staging transition is
off-set by the correlation Fock energy of the 3D FQH state. We obtain the phase
diagram of bulk electrons in a magnetic field subject to Coulomb interactions
as a function of carrier density and lattice constant. At very low densities,
the 3D FQH state exhibits a transition to a 3D Wigner crystal state stabilized
by phonon correlations.",0810.1757v1
2018-03-15,Thickness-dependent phase transition in graphite under high magnetic field,"Various electronic phases emerge when applying high magnetic fields in
graphite. However, the origin of a semimetal-insulator transition at $B \simeq
30\; \textrm{T}$ is still not clear, while an exotic density-wave state is
theoretically proposed. In order to identify the electronic state of the
insulator phase, we investigate the phase transition in thin-film graphite
samples that were fabricated on silicon substrate by a mechanical exfoliation
method. The critical magnetic fields of the semimetal-insulator transition in
thin-film graphite shift to higher magnetic fields, accompanied by a reduction
in temperature dependence. These results can be qualitatively reproduced by a
density-wave model by introducing a quantum size effect. Our findings establish
the electronic state of the insulator phase as a density-wave state standing
along the out-of-plane direction, and help determine the electronic states in
other high-magnetic-field phases.",1803.05625v1
2016-12-04,M/g/c/c state dependent queueing model for road traffic simulation,"In this paper, we present a stochastic queuing model for the road traffic,
which captures the stationary density-flow relationships in both uncongested
and congestion conditions. The proposed model is based on the $M/g/c/c$ state
dependent queuing model of Jain and Smith, and is inspired from the
deterministic Godunov scheme for the road traffic simulation. We first propose
a reformulation of the $M/g/c/c$ state dependent model that works with
density-flow fundamental diagrams rather than density-speed relationships. We
then extend this model in order to consider upstream traffic demand as well as
downstream traffic supply. Finally, we calculate the speed and travel time
distributions for the $M/g/c/c$ state dependent queuing model and for the
proposed model, and derive stationary performance measures (expected number of
cars, blocking probability, expected travel time, and throughput). A comparison
with results predicted by the $M/g/c/c$ state dependent queuing model shows
that the proposed model correctly represents the dynamics of traffic and gives
good performances measures. The results illustrate the good accuracy of the
proposed model.",1612.09532v1
2020-11-20,Density matrix renormalization group study of the $ν=1/3$ edge states in fractional quantum Hall systems,"The edge states in the fractional quantum Hall systems at filling factor
$\nu=1/3$ are studied by the density matrix renormalization group method. It is
shown that the density oscillation induced by the local boundary condition at
the edge is characterized by the wave number of the minimum magnetoroton
excitation, and this structure is partially reconstructed with the change in
the confinement potential shape. In particular, the $\nu=1$ counterpropagating
edge channel appears with the change in the chemical potential, which is
consistent with recent experiments on heat transport. The stability of the bulk
states against the change in the number of electrons confirms that the bulk
part of the fractional quantum Hall state is incompressible, while the edge
state is compressible.",2011.10338v2
2023-06-01,Ultrafast Switching from the Charge Density Wave Phase to a Metastable Metallic State in 1T-TiSe$_2$,"The ultrafast electronic structures of the charge density wave material
1T-TiSe$_2$ were investigated by high-resolution time- and angle-resolved
photoemission spectroscopy. We found that the quasiparticle populations drove
ultrafast electronic phase transitions in 1T-TiSe$_2$ within 100 fs after
photoexcitation, and a metastable metallic state, which was significantly
different from the equilibrium normal phase, was evidenced far below the charge
density wave transition temperature. Detailed time- and pump-fluence-dependent
experiments revealed that the photoinduced metastable metallic state was a
result of the halted motion of the atoms through the coherent electron-phonon
coupling process, and the lifetime of this state was prolonged to picoseconds
with the highest pump fluence used in this study. Ultrafast electronic dynamics
were well captured by the time-dependent Ginzburg-Landau model. Our work
demonstrates a mechanism for realizing novel electronic states by photoinducing
coherent motion of atoms in the lattice.",2306.00311v1
2009-01-13,The Equation of State of the Intergalactic Medium After Hydrogen Reionization,"We use an analytic model to study how inhomogeneous hydrogen reionization
affects the temperature distribution of the intergalactic medium (IGM). During
this process, the residual energy of each ionizing photon is deposited in the
IGM as heat, increasing its temperature to 20,000-30,000 K; subsequent
expansion of the Universe then cools the gas. Because reionization most likely
proceeds from high to low densities, underdense voids are ionized last, have
less time to cool, and are (on average) warmer than mean-density gas
immediately after reionization is complete (an ""inverted"" equation of state).
  From this initial configuration, the low-density gas cools quickly and
eventually returns to a more normal equation of state. The rapidly evolving
temperature introduces systematic uncertainties in measurements of the ionizing
background at z~6. For example, late reionization implies rapid cooling, so
that the ionizing background would have to evolve even more rapidly at z ~5-6
than typically claimed. This degeneracy is difficult to disentangle, because
the Lyman-alpha forest probes only a narrow range in densities (over which the
gas is nearly isothermal). However, higher Lyman-series transitions probe wider
density ranges, sampling different effective temperatures, and offer a new way
to measure the IGM equation of state that should work where nearly saturated
absorption precludes other methods. This will help to separate evolution in
temperature from that in the ionizing background. While more detailed study
with hydrodynamic simulations is needed, we show that such measurements could
potentially distinguish early and late reionization using only a handful of
lines of sight.",0901.1888v1
2021-07-22,Quantum oscillations in 2D insulators induced by graphite gates,"We demonstrate a mechanism for magnetoresistance oscillations in insulating
states of two-dimensional (2D) materials arising from the interaction of the 2D
layer and proximal graphite gates. We study a series of devices based on
different two-dimensional systems, including mono- and bilayer Td-WTe2,
angle-aligned MoTe2/WSe2 heterobilayers and Bernal-stacked bilayer graphene,
which all share a similar graphite-gated geometry. We find that the resistivity
of the 2D system generically shows quantum oscillations as a function of
magnetic field corresponding to a high-density Fermi surface when they are
tuned near an insulating state, in contravention of na\""ive band theory.
Simultaneous measurement of the resistivity of the graphite gates show that
these oscillations are precisely correlated with quantum oscillations in the
resistivity of the graphite gates themselves. Further supporting this
connection, the oscillations are quenched when the graphite gate is replaced by
TaSe2, a high-density metal that does not show quantum oscillations. The
observed phenomenon arises from the oscillatory behavior of graphite density of
states, which modulates the device capacitance and, as a consequence, the
carrier density in the sample layer even when a constant electrochemical
potential is maintained between the sample and the gate electrode. Oscillations
are most pronounced near insulating states where the resistivity is strongly
density dependent. Our study suggests a unified mechanism for quantum
oscillations in graphite-gated 2D insulators based on sample-gate coupling.",2107.10430v2
2022-10-07,Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods,"Density functional theory (DFT) provides convenient electronic structure
methods for the study of molecular systems and materials. Regular Kohn-Sham DFT
calculations rely on unitary transformations to determine the ground-state
electronic density, ground state energy, and related properties. However, for
dissociation of molecular systems into open-shell fragments, due to the
self-interaction error present in a large number of density functional
approximations, the self-consistent procedure based on the this type of
transformation gives rise to the well-known charge delocalization problem. To
avoid this issue, we showed previously that the cluster operator of
coupled-cluster theory can be utilized within the context of DFT to solve in an
alternative and approximate fashion the ground-state self-consistent problem.
This work further examines the application of the singles cluster operator to
molecular ground state calculations. Two approximations are derived and
explored: i), A linearized scheme of the quadratic equation used to determine
the cluster amplitudes, and, ii), the effect of carrying the calculations in a
non-self-consistent field fashion. These approaches are found to be capable of
improving the energy and density of the system and are quite stable in either
case. The theoretical framework discussed in this work could be used to
describe, with an added flexibility, quantum systems that display challenging
features and require expanded theoretical methods.",2210.03694v1
2008-01-11,The local electronic structure of alpha-Li3N,"New theoretical and experimental investigation of the occupied and unoccupied
local electronic density of states (DOS) are reported for alpha-Li3N. Band
structure and density functional theory calculations confirm the absence of
covalent bonding character. However, real-space full-multiple-scattering
(RSFMS) calculations of the occupied local DOS finds less extreme nominal
valences than have previously been proposed. Nonresonant inelastic x-ray
scattering (NRIXS), RSFMS calculations, and calculations based on the
Bethe-Salpeter equation are used to characterize the unoccupied electronic
final states local to both the Li and N sites. There is good agreement between
experiment and theory. Throughout the Li 1s near-edge region, both experiment
and theory find strong similarities in the s- and p-type components of the
unoccupied local final density of states projected onto an orbital angular
momentum basis (l-DOS). An unexpected, significant correspondence exists
between the near-edge spectra for the Li 1s and N 1s initial states. We argue
that both spectra are sampling essentially the same final density of states due
to the combination of long core-hole lifetimes, long photoelectron lifetimes,
and the fact that orbital angular momentum is the same for all relevant initial
states. Such considerations may be generically applicable for low atomic number
compounds.",0801.1848v1
2010-04-29,Density of states and quantum phase transition in the thermodynamic limit of the Mermin central-spin model,"We apply a spin-coherent states formalism to study the central-spin model
with monochromatic bath and symmetric coupling (the Mermin model); in
particular, we derive analytic expressions for the density of states in the
thermodynamic limit when the number of bath spins is taken to infinity. From
the thermodynamic limit spectra we show the phase diagram for the system can be
divided into four regions, partitioned on the one hand into a symmetric
(non-degenerate) phase or a broken symmetry (degenerate) phase, and on the
other hand by the case of overlapping or non-overlapping energy surfaces. The
nature and position of singularities appearing in the energy surfaces change as
one moves from region to region. Our spin-coherent states formalism naturally
leads us to the Majorana representation, which is useful to transform the
Schr\""odinger equation into a Ricatti-like form that can be solved in the
thermodynamic limit to obtain closed-form expressions for the density of
states. The energy surface singularities correspond with critical points in the
density of states. We then use our results to compute expectation values for
the system that help to characterize the nature of the quantum phase transition
between the symmetric and broken phases.",1004.5422v2
2020-03-25,Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems,"Ground state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced
spin-1/2 one-dimensional Fermi systems that are spatially confined by either a
harmonic or a hard-wall trapping potential. It has been hoped that such
systems, which can be realized using ultracold atomic gases, would exhibit the
long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The
HFB formalism generalizes the standard Bogoliubov quasi-particle
transformation, by allowing for Cooper pairing to exist between all possible
single-particle states, and accounts for the effects of the inhomogeneous
trapping potential as well as the mean-field Hartree potential. This provides
an unbiased framework to describe inhomgenous densities and pairing
correlations in the FFLO state of a confined 1D gas. In a harmonic trap,
numerical minimization of the HFB ground state energy yields a spatially
oscillating order parameter reminiscent of the FFLO state. However, we find
that this state has almost no imprint in the local fermion densities
(consistent with experiments that found no evidence of the FFLO phase). In
contrast, for a hard-wall geometry, we find a strong signature of the spatial
oscillations of the FFLO pairing amplitude reflected in the local in situ
densities. In the hard wall case, the excess spins are strongly localized near
regions where there is a node in the pairing amplitude, creating an
unmistakeable crystalline modulation of the density.",2003.11659v1
2023-11-20,Multi-flavor quantum criticality,"In a quantum critical metal, the electronic density of states, or
quasiparticle mass on the Fermi surface, is strongly enhanced through
electronic correlations. The density of states in the quantum critical
unconventional superconductor CeCoIn$_5$, can be readily accessed in the normal
state because all energy scales are small. However, the experimental challenges
associated with large nuclear specific heat and long nuclear spin-lattice
relaxation times have impeded unveiling a more detailed physical picture. Here
we report an extensive thermal impedance spectroscopy study of CeCoIn$_5$ that
assesses the density of states in two independent ways, via the nuclear
spin-lattice relaxation rate and via the specific heat. We establish that the
temperature- and magnetic field dependence of the nuclear spin-lattice
relaxation rate is determined entirely by the energy-scale competition near the
quantum critical point. In particular, mass enhancement is cut off at finite
magnetic fields. However, the specific heat measurements reveal excess entropy
in addition to that associated with the density of states on the Fermi surface.
This excess entropy is direct thermodynamic evidence for a ""second flavor"" of
fluctuating boson in CeCoIn$_5$. The electronic nature of this excess entropy
is evidenced by its suppression in the superconducting state. We suggest such a
multi-flavour character for a broader class of quantum critical metals.",2311.11914v1
1999-06-14,Characteristic distributions of finite-time Lyapunov exponents,"We study the probability densities of finite-time or \local Lyapunov
exponents (LLEs) in low-dimensional chaotic systems. While the multifractal
formalism describes how these densities behave in the asymptotic or long-time
limit, there are significant finite-size corrections which are coordinate
dependent. Depending on the nature of the dynamical state, the distribution of
local Lyapunov exponents has a characteristic shape. For intermittent dynamics,
and at crises, dynamical correlations lead to distributions with stretched
exponential tails, while for fully-developed chaos the probability density has
a cusp. Exact results are presented for the logistic map, $x \to 4x(1-x)$. At
intermittency the density is markedly asymmetric, while for `typical' chaos, it
is known that the central limit theorem obtains and a Gaussian density results.
Local analysis provides information on the variation of predictability on
dynamical attractors. These densities, which are used to characterize the {\sl
nonuniform} spatial organization on chaotic attractors are robust to noise and
can therefore be measured from experimental data.",9906022v1
1996-04-16,Spin Instabilities in Coupled Semiconductor Quantum Wells,"We study the magnetic phases of two coupled two-dimensional electron gases in
order to determine under what circumstances these phases may occur in real
semiconductor quantum wells and what the experimental properties of the
broken-symmetry ground states may be. Within the local-density-approximation to
time-dependent density functional theory (DFT), we find a phase transition
signaled by the vanishing of the intersubband spin-density excitations at low
but accessible (\sim 10^10-10^11 cm^{-2}) electron densities. Through a
self-consistent Hartree-Fock calculation, we associate this transition with an
antiferromagnetic phase and study the phase diagram, thermodynamics, and
collective modes in it. The collective modes are in principle observable in
inelastic light scattering experiments, and we discuss the implications of our
calculations for these measurements. We also examine the ferromagnetic
transition in both single and double quantum wells within the
local-spin-density approximation to DFT and obtain a critical density which
depends on the well width and which is far below that of the antiferromagnetic
transition.",9604099v1
2005-02-02,Momentum space properties from coordinate space electron density,"Electron density and electron momentum density, while independently tractable
experimentally, bear no direct connection without going through the
many-electron wave function. However, invoking a variant of the
constrained-search formulation of density functional theory, we develop a
general scheme (valid for arbitrary external potentials) yielding decent
momentum space properties, starting exclusively from the coordinate space
electron density. Numerical illustration of the scheme is provided for the
closed-shell atomic systems He, Be and Ne and for $1s^1~2s^1$ singlet
electronic excited state for Helium by calculating the Compton profiles and the
$<p^n>$ expectation values derived from given coordinate space electron
densities.",0502010v1
2011-05-20,On the formulation of functional theory for pairing with particle number restoration,"The restoration of particle number within Energy Density Functional theory is
analyzed. It is shown that the standard method based on configuration mixing
leads to a functional of both the projected and non-projected densities. As an
alternative that might be advantageous for mass models, nuclear dynamics and
thermodynamics, we propose to formulate the functional in terms directly of the
one-body and two-body density matrices of the state with good particle number.
Our approach does not contain the pathologies recently observed when restoring
the particle number in an Energy Density Functional framework based on
transition density matrices and can eventually be applied with functionals
having arbitrary density dependencies.",1105.4084v1
2012-11-01,Laplace approximation for logistic Gaussian process density estimation and regression,"Logistic Gaussian process (LGP) priors provide a flexible alternative for
modelling unknown densities. The smoothness properties of the density estimates
can be controlled through the prior covariance structure of the LGP, but the
challenge is the analytically intractable inference. In this paper, we present
approximate Bayesian inference for LGP density estimation in a grid using
Laplace's method to integrate over the non-Gaussian posterior distribution of
latent function values and to determine the covariance function parameters with
type-II maximum a posteriori (MAP) estimation. We demonstrate that Laplace's
method with MAP is sufficiently fast for practical interactive visualisation of
1D and 2D densities. Our experiments with simulated and real 1D data sets show
that the estimation accuracy is close to a Markov chain Monte Carlo
approximation and state-of-the-art hierarchical infinite Gaussian mixture
models. We also construct a reduced-rank approximation to speed up the
computations for dense 2D grids, and demonstrate density regression with the
proposed Laplace approach.",1211.0174v3
2013-07-01,Two-colour QCD with heavy quarks at finite densities,"We extend the density-of-states approach to gauge systems (LLR method) to QCD
at finite temperature and density with heavy quarks. The approach features an
exponential error suppression and yields the Polyakov loop probability
distribution function over a range of more than hundred orders of magnitude.
SU(2) gauge theory is considered in the confinement and the high-temperature
phase, and at finite densities of heavy quarks. In the latter case, a smooth
rise of the density with the chemical potential is observed, and no critical
phenomenon associated with deconfinement due to finite densities is found.",1307.0455v1
2014-09-17,Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory,"We investigate fundamental properties of meta-generalized-gradient
approximations (meta-GGAs) to the exchange-correlation energy functional, which
have an implicit density dependence via the Kohn-Sham kinetic-energy density.
To this purpose, we construct the most simple meta-GGA by expressing the local
exchange-correlation energy per particle as a function of a fictitious density,
which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This
simple functional considerably improves the total energy of atoms as compared
to the standard local density approximation. The corresponding
exchange-correlation potentials are then determined exactly through a solution
of the optimized effective potential equation. These potentials support an
additional bound state and exhibit a derivative discontinuity at integer
particle numbers. We further demonstrate that through the kinetic-energy
density any meta-GGA incorporates a derivative discontinuity. However, we also
find that for commonly used meta-GGAs the discontinuity is largely
underestimated and in some cases even negative.",1409.5065v2
2016-03-13,Near-locality of exchange and correlation density functionals for 1- and 2-electron systems,"The uniform electron gas and the hydrogen atom play fundamental roles in
condensed matter physics and quantum chemistry. The former has an infinite
number of electrons uniformly distributed over the neutralizing
positively-charged background, and the latter only one electron bound to the
proton. The uniform electron gas was used to derive the local spin density
approximation (LSDA) to the exchange-correlation functional that undergirds the
development of the Kohn-Sham density functional theory. We show here that the
ground-state exchange-correlation energies of the hydrogen atom and many other
1- and 2-electron systems are modeled surprisingly well by a different local
spin density approximation (LSDA0). Our LSDA0 is constructed to satisfy exact
constraints, but agrees surprisingly well with the exact results for a uniform
two-electron density in a finite, curved three-dimensional space. We also apply
LSDA0 to excited or noded 1-electron densities. Furthermore, we show that the
locality of an orbital can be measured by the ratio between the exact exchange
energy and its optimal lower bound.",1603.04062v1
2017-03-21,Temperature profile in a liquid-vapor interface near the critical point,"Thanks to an expansion with respect to densities of energy, mass and entropy,
we discuss the concept of thermocapillary fluid for inhomogeneous fluids. The
non-convex state law valid for homogeneous fluids is modified by adding terms
taking into account the gradients of these densities. This seems more realistic
than Cahn and Hilliard's model which uses a density expansion in mass-density
gradient only. Indeed, through liquid-vapor interfaces, realistic potentials in
molecular theories show that entropy density and temperature do not vary with
the mass density as it would do in bulk phases. In this paper, we prove using a
rescaling process near the critical point that liquid-vapor interfaces behave
essentially in the same way as in Cahn and Hilliard's model.",1703.07302v2
2017-06-15,Reversible control of interface-water induced carrier density in graphene-on-SiO$_2$ by thermal cycling under gate-voltage,"A reversible handle on graphene carrier density, other than the gate electric
field, is desirable for memory applications of graphene. Our experiments show
that the commonly observed carrier density hysteresis in graphene on SiO$_2$
due to interface water/oxygen vanishes at temperatures below 250 K. The state
of these species, which affects the graphene carrier density, at low
temperatures can be reversibly controlled by thermal cycling to room
temperature at different gate voltages. Further, devices prepared with
relatively dry interface, and thus showing negligible hysteresis at room
temperature, show a marked increase in hysteresis on heating above room
temperature. Thus thermal-cycling, to high temperatures and under gate-voltage,
provides a reversible handle on carrier density. These results are discussed in
terms of temperature and interface-water density dependence of redox-reaction
kinetics.",1706.04899v1
2020-03-11,A weight-dependent local correlation density-functional approximation for ensembles,"We report a local, weight-dependent correlation density-functional
approximation that incorporates information about both ground and excited
states in the context of density-functional theory for ensembles (eDFT). This
density-functional approximation for ensembles is specially designed for the
computation of single and double excitations within Gross--Oliveira--Kohn (GOK)
DFT (i.e., eDFT for neutral excitations), and can be seen as a natural
extension of the ubiquitous local-density approximation in the context of
ensembles. The resulting density-functional approximation, based on both finite
and infinite uniform electron gas models, automatically incorporates the
infamous derivative discontinuity contributions to the excitation energies
through its explicit ensemble weight dependence. Its accuracy is illustrated by
computing single and double excitations in one-dimensional many-electron
systems in the weak, intermediate and strong correlation regimes. Although the
present weight-dependent functional has been specifically designed for
one-dimensional systems, the methodology proposed here is general, i.e.,
directly applicable to the construction of weight-dependent functionals for
realistic three-dimensional systems, such as molecules and solids.",2003.05553v2
2021-02-02,Forces within hadrons on the light front,"In this work, we find the light front densities for momentum and forces,
including pressure and shear forces, within hadrons. This is achieved by
deriving relativistically correct expressions relating these densities to the
gravitational form factors $A(t)$ and $D(t)$ associated with the energy
momentum tensor. The derivation begins from the fundamental definition of
density in a quantum field theory, namely the expectation value of a local
operator within a spatially-localized state. We find that it is necessary to
use the light front formalism to define a density that corresponds to internal
hadron structure. When using the instant form formalism, it is impossible to
remove the spatial extent of the hadron wave function from any density, and --
even within instant form dynamics -- one does not obtain a Breit frame Fourier
transform for a properly defined density. Within the front formalism, we derive
new expressions for various mechanical properties of hadrons, including the
mechanical radius, as well as for stability conditions. The multipole ansatz
for the form factors is used as an example to illustrate all of these findings.",2102.01683v2
2021-06-24,OCDE: Odds Conditional Density Estimator,"Conditional density estimation (CDE) models can be useful for many
statistical applications, especially because the full conditional density is
estimated instead of traditional regression point estimates, revealing more
information about the uncertainty of the random variable of interest. In this
paper, we propose a new methodology called Odds Conditional Density Estimator
(OCDE) to estimate conditional densities in a supervised learning scheme. The
main idea is that it is very difficult to estimate $p_{x,y}$ and $p_{x}$ in
order to estimate the conditional density $p_{y|x}$, but by introducing an
instrumental distribution, we transform the CDE problem into a problem of odds
estimation, or similarly, training a binary probabilistic classifier. We
demonstrate how OCDE works using simulated data and then test its performance
against other known state-of-the-art CDE methods in real data. Overall, OCDE is
competitive compared with these methods in real datasets.",2107.04118v1
2021-07-29,Cascaded Residual Density Network for Crowd Counting,"Crowd counting is a challenging task due to the issues such as scale
variation and perspective variation in real crowd scenes. In this paper, we
propose a novel Cascaded Residual Density Network (CRDNet) in a coarse-to-fine
approach to generate the high-quality density map for crowd counting more
accurately. (1) We estimate the residual density maps by multi-scale pyramidal
features through cascaded residual density modules. It can improve the quality
of density map layer by layer effectively. (2) A novel additional local count
loss is presented to refine the accuracy of crowd counting, which reduces the
errors of pixel-wise Euclidean loss by restricting the number of people in the
local crowd areas. Experiments on two public benchmark datasets show that the
proposed method achieves effective improvement compared with the
state-of-the-art methods.",2107.13718v1
2022-11-26,ResNeRF: Geometry-Guided Residual Neural Radiance Field for Indoor Scene Novel View Synthesis,"We represent the ResNeRF, a novel geometry-guided two-stage framework for
indoor scene novel view synthesis. Be aware of that a good geometry would
greatly boost the performance of novel view synthesis, and to avoid the
geometry ambiguity issue, we propose to characterize the density distribution
of the scene based on a base density estimated from scene geometry and a
residual density parameterized by the geometry. In the first stage, we focus on
geometry reconstruction based on SDF representation, which would lead to a good
geometry surface of the scene and also a sharp density. In the second stage,
the residual density is learned based on the SDF learned in the first stage for
encoding more details about the appearance. In this way, our method can better
learn the density distribution with the geometry prior for high-fidelity novel
view synthesis while preserving the 3D structures. Experiments on large-scale
indoor scenes with many less-observed and textureless areas show that with the
good 3D surface, our method achieves state-of-the-art performance for novel
view synthesis.",2211.16211v3
2022-12-28,Bayesian statistical learning using density operators,"This short study reformulates the statistical Bayesian learning problem using
a quantum mechanics framework. Density operators representing ensembles of pure
states of sample wave functions are used in place probability densities. We
show that such representation allows to formulate the statistical Bayesian
learning problem in different coordinate systems on the sample space. We
further show that such representation allows to learn projections of density
operators using a kernel trick. In particular, the study highlights that
decomposing wave functions rather than probability densities, as it is done in
kernel embedding, allows to preserve the nature of probability operators.
Results are illustrated with a simple example using discrete orthogonal wavelet
transform of density operators.",2212.14715v2
2017-10-27,Efficient treatment of local meta-generalized gradient density functionals via auxiliary density expansion: the density fitting (DF) J+X approximation,"We report an efficient technique to treat density functionals of the
meta-generalized gradient approximation (mGGA) class in conjunction with
density fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X).
While the kinetic energy density $\tau$ cannot be computed in the context of a
DF-JX calculation, we show that the Laplacian of the density $\upsilon$ can be
computed with almost no extra cost. With this technique, $\upsilon$-form mGGAs
become only slightly more expensive (10%--20%) than GGAs in DF-JX
treatment---and several times faster than regular $\tau$-based mGGA
calculations with DF-J and regular treatment of the density functional. We
investigate the translation of $\upsilon$-form mGGAs into $\tau$-form mGGAs by
employing a kinetic energy functional, but find this insufficiently reliable at
this moment. However, $\upsilon$ and $\tau$ are believed to carry essentially
equivalent information beyond $\rho$ and $\Vert\vec\nabla\rho\Vert$ [Phys. Rev.
B 2007, 75, 155109], so a reparametrization of accurate mGGAs from the
$\tau$-form into the $\upsilon$-form should be possible. Once such functionals
become available, we expect the presented technique to become a powerful tool
in the computation of reaction paths, intermediates, and transition states of
medium sized molecules.",1710.10049v2
2020-01-07,Uncertainty Quantification for Materials Properties in Density Functional Theory with k-Point Density,"Many computational databases emerged over the last five years that report
material properties calculated with density functional theory. The properties
in these databases are commonly calculated to a precision that is set by choice
of the basis set and the k-point density for the Brillouin zone integration. We
determine how the precision of properties obtained from the Birch equation of
state for 29 transition metals and aluminum in the three common structures --
fcc, bcc, and hcp -- correlate with the k-point density and the precision of
the energy. We show that the precision of the equilibrium volume, bulk modulus,
and the pressure derivative of the bulk modulus correlate comparably well with
the k-point density and the precision of the energy, following an approximate
power law. We recommend the k-point density as the convergence parameter
because it is computationally efficient, easy to use as a direct input
parameter, and correlates with property precision at least as well as the
energy precision. We predict that common k-point density choices in high
throughput DFT databases result in precision for the volume of 0.1%, the bulk
modulus of 1%, and the pressure derivative of 10%.",2001.01851v1
2015-06-14,Bosons with long range interactions on two-leg ladders in artificial magnetic fields,"Motivated by experiments exploring the physics of neutral atoms in artificial
magnetic fields, we study the ground state of bosons interacting with long
range dipolar interactions on a two-leg ladder. Using two complimentary
variational approaches, valid for weak interactions, we find rich physics
driven by the long range forces. Generically, long range interactions tend to
destroy the Meissner phase in favor of modulated density wave phases. Nearest
neighbor interactions produce a novel interleg charge density wave phase, where
the total density remains uniform, but the density on each leg of the ladder is
modulating in space, out-of-phase with one another. At weak magnetic fields,
next nearest neighbor interactions lead to a fully modulated biased ladder
phase, where all the particles are on one leg of the ladder, and the density is
modulating in space. This state simultaneously breaks $Z_{2}$ reflection
symmetry and $U(1)$ symmetry associated with translation in real space. For
values of the flux near $\phi = \pi$, we find that a switching effect occurs
for arbitrarily weak interactions, where the density modulates in space, but
the chiral current changes sign on every plaquette. Arbitrarily weak attractive
interactions along the rungs destroy the Meissner phase completely, in favor of
a modulated density wave phase. Varying magnetic field produces a cascade of
first order transitions between modulated density wave states with different
wave-vectors, which manifests itself as discrete jumps in the chiral current.
Polarizing the dipoles along the ladder direction yields a region of phase
space where a stable biased ladder phase occurs even at arbitrarily weak
magnetic fields. We discuss the experimental consequences of our work, in
particular, how the interleg charge density wave can manifest itself in recent
experiments on bosons in synthetic dimensions.",1506.04346v2
2022-09-28,Quasi-bound States and Resonant Skew Scattering in Two-Dimensional Materials with a Mexican-Hat Dispersion,"Mexican-hat dispersion of band electrons in two-dimensional materials
attracts a lot of interest, mainly due to the Van Hove singularity of the
density of states near the band edge. In this paper, we show that there is one
more feature of such a dispersion, which also leads to nontrivial effects. It
consists in the fact that the sign of the effective mass in the momentum space
near the central extremum is opposite to the sign of the mass outside this
region. For this reason, any localized potential that repels quasiparticles in
the outer region attracts quasiparticles in the central region and thereby
creates quasi-bound states. We study these states in the case when the
Mexican-hat dispersion is formed due to the hybridization of the inverted
electron and hole bands, and the potential is created by a point defect. The
energy and width of the resonance of the local density of states corresponding
to a quasi-bound state are found, and it is shown that, under certain
conditions, a quasi-bound state can transform into a bound state in a continuum
of band states. The presence of quasi-bound states leads to nontrivial effects
in the spin-dependent scattering of electrons. Due to the quasi-bound state,
the skew scattering is strongly enhanced for electrons with energy near the
resonance, and the skewness angle varies over a wide range depending on the
energy. In addition, in a certain energy range, a nontrivial effect of
scattering suppression appears in the direction opposite to the skewness angle.",2209.14112v1
2007-08-30,Equation of state at high densities and modern compact star observations,"Recently, observations of compact stars have provided new data of high
accuracy which put strong constraints on the high-density behaviour of the
equation of state of strongly interacting matter otherwise not accessible in
terrestrial laboratories. The evidence for neutron stars with high mass (M =2.1
+/- 0.2 M_sun for PSR J0751+1807) and large radii (R > 12 km for RX J1856-3754)
rules out soft equations of state and has provoked a debate whether the
occurence of quark matter in compact stars can be excluded as well. In this
contribution it is shown that modern quantum field theoretical approaches to
quark matter including color superconductivity and a vector meanfield allow a
microscopic description of hybrid stars which fulfill the new, strong
constraints. The deconfinement transition in the resulting stiff hybrid
equation of state is weakly first order so that signals of it have to be
expected due to specific changes in transport properties governing the
rotational and cooling evolution caused by the color superconductivity of quark
matter. A similar conclusion holds for the investigation of quark deconfinement
in future generations of nucleus-nucleus collision experiments at low
temperatures and high baryon densities such as CBM @ FAIR.",0708.4216v1
2020-08-09,Spherical collapse in a dark energy model with reconstructed effective equation of state,"The present work deals with the study of spherical collapse of matter density
contrast in a latetime cosmological model with a reconstructed effective
equation of state. The linear and nonlinear evolution of matter density
contrast are studied. The variation of the critical density at collapse of the
spherical overdense region along redshift are also investigate. Further the
number count of collapsed object or the dark matter halos, equivalent to the
number count of galaxy clusters, are also studied. Two different halo mass
function formulations, namely the Press-Schechter mass function and the
Sheth-Tormen mass function, are adopetd to study the cluster number count along
the redshift. Similar analysis is also carried out for wCDM dark energy model
to have a direct comparison with the reconstructed effective equation of state
model. These two models are highly degenerate at the background and linear
level of matter perturbation. But the nonlinear evolution of matter overdensity
breaks the degeneracy. The reconstructed effective equation of state model
shows a substantial suppression in the cluster number count compared to wCDM
for redshift z > 0.5, and for z < 0.5, the number count is slightly higher than
that of wCDM.",2008.03792v1
2021-07-08,Optical reconstruction of collective density matrix of qutrit,"Reconstruction of a quantum state is of prime importance for
quantum-information science. Specifically, means of efficient determination of
a state of atoms of room-temperature vapor may enable applications in quantum
computations and cryptography. To step toward such applications, here we
present a method of reconstruction of a collective density matrix of an atomic
ensemble, consisting of atoms with an $F=1$ ground state. Such a long-lived
state is often encountered in real systems (e.g., potassium, sodium, rubidium)
and hence may be practically utilized. Our theoretical treatment enables
derivation of explicit formulas relating optical signals (polarization rotation
and ellipticity change) with specific density-matrix elements. The analysis are
supported with numerical simulations, which allows to evaluate fidelity and
robustness of the algorithm. The tests show that our algorithm allows to obtain
the fidelity exceeded 0.95 even at noisy environment and/or significant atomic
manipulation imperfections.",2107.03923v3
2023-12-12,Quantum topological data analysis via the estimation of the density of states,"We develop a quantum topological data analysis (QTDA) protocol based on the
estimation of the density of states (DOS) of the combinatorial Laplacian.
Computing topological features of graphs and simplicial complexes is crucial
for analyzing datasets and building explainable AI solutions. This task becomes
computationally hard for simplicial complexes with over sixty vertices and
high-degree topological features due to a combinatorial scaling. We propose to
approach the task by embedding underlying hypergraphs as effective quantum
Hamiltonians and evaluating their density of states from the time evolution.
Specifically, we compose propagators as quantum circuits using the Cartan
decomposition of effective Hamiltonians and sample overlaps of time-evolved
states using multi-fidelity protocols. Next, we develop various post-processing
routines and implement a Fourier-like transform to recover the rank (and
kernel) of Hamiltonians. This enables us to estimate the Betti numbers,
revealing the topological features of simplicial complexes. We test our
protocol on noiseless and noisy quantum simulators and run examples on IBM
quantum processors. We observe the resilience of the proposed QTDA approach to
real-hardware noise even in the absence of error mitigation, showing the
promise to near-term device implementations and highlighting the utility of
global DOS-based estimators.",2312.07115v1
2016-10-04,"Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U","Approximate density functional theory (DFT) suffers from many-electron self-
interaction error, otherwise known as delocalization error, that may be
diagnosed and then corrected through elimination of the deviation from exact
piecewise linear behavior between integer electron numbers. Although paths to
correction of energetic delocalization error are well- established, the impact
of these corrections on the electron density is less well-studied. Here, we
compare the effect on density delocalization of DFT+U, global hybrid tuning,
and range- separated hybrid tuning on a diverse test set of 32 transition metal
complexes and observe the three methods to have qualitatively equivalent
effects on the ground state density. Regardless of valence orbital diffuseness
(i.e., from 2p to 5p), ligand electronegativity (i.e., from Al to O), basis set
(i.e., plane wave versus localized basis set), metal (i.e., Ti, Fe, Ni) and
spin state, or tuning method, we consistently observe substantial charge loss
at the metal and gain at ligand atoms (ca. 0.3-0.5 e or more). This charge loss
at the metal is preferentially from the minority spin, leading to increasing
magnetic moment as well. Using accurate wavefunction theory references, we
observe that a minimum error in partial charges and magnetic moments occur at
higher tuning parameters than typically employed to eliminate energetic
delocalization error. These observations motivate the need to develop
multi-faceted approximate-DFT error correction approaches that separately treat
density delocalization and energetic errors in order to recover both correct
density and magnetization properties.",1610.01222v1
2000-06-13,Density Functional Theory of Magnetic Systems Revisited,"The Hohenberg-Kohn theorem of density functional theory (DFT) for the case of
electrons interacting with an external magnetic field (that couples to spin
only) is examined in more detail than previously. A unexpected generalization
is obtained: in certain cases (which include half metallic ferromagnets and
magnetic insulators) the ground state, and hence the spin density matrix, is
invariant for some non-zero range of a shift in uniform magnetic field. In such
cases the ground state energy is not a functional of the spin density matrix
alone. The energy gap in an insulator or a half metal is shown to be a ground
state property of the N-electron system in magnetic DFT.",0006200v3
2008-04-10,Block Spin Density Matrix of the Inhomogeneous AKLT Model,"We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain
model. Spins at each lattice site could be different. Under certain conditions,
the ground state of this AKLT model is unique and is described by the
Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous
block of bulk spins in this ground state. The density matrix is independent of
spins outside the block. It is diagonalized and shown to be a projector onto a
subspace. We prove that for large block the density matrix behaves as the
identity in the subspace. The von Neumann entropy coincides with Renyi entropy
and is equal to the saturated value.",0804.1741v1
2011-06-16,Nonequilibrium density matrix description of steady state quantum transport,"With this work we investigate the stationary nonequilibrium density matrix of
current carrying nonequilibrium steady states of in-between quantum systems
that are connected to reservoirs. We describe the analytical procedure to
obtain the explicit result for the reduced density matrix of quantum transport
when the system, the connecting reservoirs and, as well, the system-reservoir
interactions are described by quadratic Hamiltonians. Our procedure is detailed
for both, electronic transport described by the tight-binding Hamiltonian and
for phonon transport described by harmonic Hamiltonians. For the special case
of weak system-reservoir couplings, a more detailed description of the
steady-state density matrix is obtained. Several paradigm transport setups for
inter-electrode electron transport and low-dimensional phonon heat flux are
elucidated.",1106.3207v2
2015-11-24,Machine Learning Exciton Dynamics,"Obtaining the exciton dynamics of large photosynthetic complexes by using
mixed quantum mechanics/molecular mechanics (QM/MM) is computationally
demanding. We propose a machine learning technique, multi-layer perceptrons, as
a tool to reduce the time required to compute excited state energies. With this
approach we predict time-dependent density functional theory (TDDFT) excited
state energies of bacteriochlorophylls in the Fenna-Matthews-Olson (FMO)
complex. Additionally we compute spectral densities and exciton populations
from the predictions. Different methods to determine multi-layer perceptron
training sets are introduced, leading to several initial data selections. In
addition, we compute spectral densities and exciton populations. Once
multi-layer perceptrons are trained, predicting excited state energies was
found to be significantly faster than the corresponding QM/MM calculations. We
showed that multi-layer perceptrons can successfully reproduce the energies of
QM/MM calculations to a high degree of accuracy with prediction errors
contained within 0.01 eV (0.5%). Spectral densities and exciton dynamics are
also in agreement with the TDDFT results. The acceleration and accurate
prediction of dynamics strongly encourage the combination of machine learning
techniques with ab-initio methods.",1511.07883v1
2016-04-05,Ising tricriticality in the extended Hubbard model with bond dimerization,"We explore the quantum phase transition between Peierls and
charge-density-wave insulating states in the one-dimensional, half-filled,
extended Hubbard model with explicit bond dimerization. We show that the
critical line of the continuous Ising transition terminates at a tricritical
point, belonging to the universality class of the tricritical Ising model with
central charge $c=7/10$. Above this point, the quantum phase transition becomes
first order. Employing a numerical matrix-product-state based (infinite)
density-matrix renormalization group method we determine the ground-state phase
diagram, the spin and two-particle charge excitations gaps, and the
entanglement properties of the model with high precision. Performing a
bosonization analysis we can derive a field description of the transition
region in terms of a triple sine-Gordon model. This allows us to derive field
theory predictions for the power-law (exponential) decay of the density-density
(spin-spin) and bond-order-wave correlation functions, which are found to be in
excellent agreement with our numerical results.",1604.01228v2
2020-09-16,Native Defects in Antiferromagnetic Topological Insulator MnBi$_2$Te$_4$,"Using scanning tunneling microscopy and spectroscopy, we visualized the
native defects in antiferromagnetic topological insulator
$\mathrm{MnBi_2Te_4}$. Two native defects $\mathrm{Mn_{Bi}}$ and
$\mathrm{Bi_{Te}}$ antisites can be well resolved in the topographic images.
$\mathrm{Mn_{Bi}}$ tend to suppress the density of states at conduction band
edge. Spectroscopy imaging reveals a localized peak-like local density of state
at $\sim80$~meV below the Fermi energy. A careful inspection of topographic and
spectroscopic images, combined with density functional theory calculation,
suggests this results from $\mathrm{Bi_{Mn}}$ antisites at Mn sites. The random
distribution of $\mathrm{Mn_{Bi}}$ and $\mathrm{Bi_{Mn}}$ antisites results in
spatial fluctuation of local density of states near the Fermi level in
$\mathrm{MnBi_2Te_4}$.",2009.07437v1
2013-09-26,The Transition to the Metallic State in Low Density Hydrogen,"Solid atomic hydrogen is one of the simplest systems to undergo a
metal-insulator transition. Near the transition, the electronic degrees of
freedom become strongly correlated and their description provides a difficult
challenge for theoretical methods. As a result, the order and density of the
phase transition are still subject to debate. In this work we use diffusion
quantum Monte Carlo to benchmark the transition between paramagnetic and
anti-ferromagnetic body centered cubic atomic hydrogen in its ground state. We
locate the density of the transition by computing the equation of state for
these two phases and identify the phase transition order by computing the band
gap near the phase transition. These benchmark results show that the phase
transition is continuous and occurs at a Wigner-Seitz radius of $r_s=2.27(3)
a_0$. We compare our results to previously reported density functional theory,
Hedin's GW approximation, and dynamical mean field theory results.",1309.7051v1
2019-10-16,Modeling Sequences with Quantum States: A Look Under the Hood,"Classical probability distributions on sets of sequences can be modeled using
quantum states. Here, we do so with a quantum state that is pure and entangled.
Because it is entangled, the reduced densities that describe subsystems also
carry information about the complementary subsystem. This is in contrast to the
classical marginal distributions on a subsystem in which information about the
complementary system has been integrated out and lost. A training algorithm
based on the density matrix renormalization group (DMRG) procedure uses the
extra information contained in the reduced densities and organizes it into a
tensor network model. An understanding of the extra information contained in
the reduced densities allow us to examine the mechanics of this DMRG algorithm
and study the generalization error of the resulting model. As an illustration,
we work with the even-parity dataset and produce an estimate for the
generalization error as a function of the fraction of the dataset used in
training.",1910.07425v1
2021-04-18,Multiband superconductivity with sign-preserving order parameter in kagome superconductor CsV3Sb5,"The superconductivity of a kagome superconductor CsV3Sb5 is studied by
scanning tunneling microscopy / spectroscopy at an ultralow temperature with
high resolution. Two kinds of superconducting gaps with multiple sets of
coherent peaks and residual zero-energy density of states are observed on both
half-Cs and Sb surfaces, implying multiband superconductivity with gap nodes.
Sixfold star-shaped magnetic vortex is observed with conventional Caroli-de
Gennes-Matricon bound states inside. Magnetic impurities suppress the
superconductivity, while nonmagnetic impurities do not, suggesting the absence
of sign-change in the superconducting order parameter. Moreover, the interplay
between charge density waves and superconductivity differs on various bands,
resulting in different density of state distributions. Our study provides
critical clues for further understanding the superconductivity and its relation
to charge density waves in CsV3Sb5.",2104.08810v1
2021-06-12,Circular swimming motility and disordered hyperuniform state in an algae system,"Active matter comprises individually driven units that convert locally stored
energy into mechanical motion. Interactions between driven units lead to a
variety of non-equilibrium collective phenomena in active matter. One of such
phenomena is anomalously large density fluctuations, which have been observed
in both experiments and theories. Here we show that, on the contrary, density
fluctuations in active matter can also be greatly suppressed. Our experiments
are carried out with marine algae ($\it{Effrenium\ voratum}$) which swim in
circles at the air-liquid interfaces with two different eukaryotic flagella.
Cell swimming generates fluid flow which leads to effective repulsions between
cells in the far field. Long-range nature of such repulsive interactions
suppresses density fluctuations and generates disordered hyperuniform states
under a wide range of density conditions. Emergence of hyperuniformity and
associated scaling exponent are quantitatively reproduced in a numerical model
whose main ingredients are effective hydrodynamic interactions and uncorrelated
random cell motion. Our results demonstrate a new form of collective state in
active matter and suggest the possibility to use hydrodynamic flow for
self-assembly in active matter.",2106.06754v1
2022-07-05,Covariant Density Functional Theory with Localized Exchange Terms,"A new density-dependent point-coupling covariant density functional PCF-PK1
is proposed, where the exchange terms of the four-fermion terms are local and
are taken into account with the Fierz transformation. The coupling constants of
the PCF-PK1 functional are determined by empirical saturation properties and ab
initio equation of state and proton-neutron Dirac mass splittings for nuclear
matter as well as the ground-state properties of selected spherical nuclei. The
success of the PCF-PK1 is illustrated with properties of the infinite nuclear
matter and finite nuclei including the ground-state properties and the
Gamow-Teller resonances. In particular, the PCFPK1 eliminates the spurious
shell closures at Z = 58 and Z = 92, which exist commonly in many covariant
density functionals without exchange terms. Moreover, the Gamow-Teller
resonances are nicely reproduced without any adjustable parameters, and this
demonstrates that a self-consistent description for the Gamow-Teller resonances
can be achieved with the localized exchange terms in the PCF-PK1. ?",2207.01764v1
2005-11-07,Properties of hadron and quark matter studied with a molecular dynamics,"We study the hadron-quark phase transition in a molecular dynamics (MD) of
quark degrees of freedom. The hadron state at low density and temperature, and
the deconfined quark state at high density and temperature are observed in our
model. We investigate the equations of state and draw the phase-diagram at wide
baryon density and temperature range. We also discuss the transport property,
e.g. viscosity, of $q\bar{q}$ matter. It is found that the ratio of the shear
viscosity to the entropy density is less than one for quark matter.",0511019v5
2005-08-11,Assumptions that imply quantum dynamics is linear,"A basic linearity of quantum dynamics, that density matrices are mapped
linearly to density matrices, is proved very simply for a system that does not
interact with anything else. It is assumed that at each time the physical
quantities and states are described by the usual linear structures of quantum
mechanics. Beyond that, the proof assumes only that the dynamics does not
depend on anything outside the system but must allow the system to be described
as part of a larger system. The basic linearity is linked with previously
established results to complete a simple derivation of the linear Schrodinger
equation. For this it is assumed that density matrices are mapped one-to-one
onto density matrices. An alternative is to assume that pure states are mapped
one-to-one onto pure states and that entropy does not decrease.",0508092v4
2020-12-25,Quantum Origins of the Density Operator,"Students in quantum mechanics class are taught that the wave function
contains all knowable information about an isolated system. Later in the
course, this view seems to be contradicted by the mysterious density matrix,
which introduces a new set of probabilities in addition to those that are built
into the wave function. This paper brings attention to the fact that the
density matrix can be reconciled with the underlying quantum-mechanical
description using a two-particle entangled state with a one-particle subsystem
as the simplest illustration of the basic principle. The extra-quantum
probabilities are traced to the coefficients of superposition of the quantum
state vector and the seemingly irreversible exponential population decay is
shown to be compatible with the unitary time evolution of a pure state when the
two particles interact. The two-particle universe thus provides the student
with a tool for understanding how the density operator, with all its richness,
emerges from quantum mechanics.",2104.07465v1
2002-01-09,Fulde-Ferrell-Larkin-Ovchinnikov state in d-wave superconductors,"The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be found in layered
d-wave superconductors such as high $T_c$ cuprates and $\kappa$-(ET)$_2$ salts
in a planar magnetic field. We show the superconducting order parameter forms
two dimensional crystalline lattice in the FFLO state for d-wave
superconductors. Also the quasiparticle density of states and the
thermodynamics of FFLO state are constructed. Therefore STM or NMR will provide
a definitive test for the existence of the FFLO state.",0201124v1
2007-02-13,Triplet absorption in carbon nanotubes: a TD-DFT study,"We predict properties of triplet excited states in single-walled carbon
nanotubes (CNTs) using a time-dependent density-functional theory (TD-DFT). We
show that the lowest triplet state energy in CNTs to be about 0.2-0.3 eV lower
than the lowest singlet states. Like in $\pi$-conjugated polymers, the lowest
CNT triplets are spatially localized. These states show strong optical
absorption at about 0.5-0.6 eV to the higher lying delocalized triplet states.
These results demonstrate striking similarity of the electronic features
between CNTs and $\pi$-conjugated polymers and provide explicit guidelines for
spectroscopic detection of CNT triplet states.",0702321v1
1999-08-15,Higher-Power Coherent and Squeezed States,"A closed form expression for the higher-power coherent states (eigenstates of
$a^{j}$) is given. The cases j=3,4 are discussed in detail, including the
time-evolution of the probability densities. These are compared to the case
j=2, the even- and odd-coherent states. We give the extensions to the
""effective"" displacement-operator, higher-power squeezed states and to the
ladder-operator/minimum-uncertainty, higher-power squeezed states. The
properties of all these states are discussed.",9908048v1
2007-12-19,Disentanglement of Source and Target and the Laser Quantum State,"Disentanglement of a laser source from its target qubit is proposed as a
criterion establishing the laser quantum state as a coherent state. It is shown
that the source-target density operator has a unique factorization in coherent
states when the environmental record monitoring laser pump quanta is ignored.
The source-target state conditioned upon the complete environmental record is
entangled, though, as a state of known total quanta number (source plus
target).",0712.3271v1
2016-11-17,Hund's metallicity and orbital-selective Mott localization of CrO$_{2}$ in the paramagnetic state,"We present electronic structure calculations of a CrO$_{2}$ compound in the
paramagnetic state within the computational scheme of density-functional theory
combined with dynamical mean-field theory. We find that CrO$_{2}$ in the
paramagnetic state is a strongly-correlated Hund's metal with mixed-valent Cr
ions. At high temperatures, CrO$_{2}$ shows an orbital-selective Mott phase, in
which the Cr $d_{xy}$ orbital is Mott-localized while the other Cr $t_{2g}$ $d$
orbitals remain itinerant. When the temperature is lowered, the
orbital-selective Mott state is found to evolve into a Kondo-like heavy-fermion
state with a small pseudo gap at the Fermi level if the system remains in the
paramagnetic state.",1611.05568v1
2017-04-16,Notes on steady state current through a noninteracting quantum dot,"A pedagogical introduction to matrix Green's function, focusing on its
application to steady state transport through discrete-level quantum systems.
Topics covered in the notes: 1. Retarded Green's function, spectral function
and density of states 2. LCR system 3. Green's function and spectral function
of LCR systems 4. Landauer formula and transmission coefficient 5.
Semi-infinite tight-binding leads and wide-band limit 6. Linear conductance at
zero temperature 7. Steady state current in a quantum dot: resonance and
coherence 8. Steady state current across a tight-binding chain: metal-insulator
transitions 9. Steady state current along the edge of a two-dimensional
lattice: topologically quantized transport",1704.04733v3
2021-06-16,Topological-chiral magnetic interactions in ultrathin films at surfaces,"We demonstrate that topological-chiral magnetic interactions can play a key
role for magnetic ground states in ultrathin films at surfaces. Based on
density functional theory we show that significant chiral-chiral interactions
occur in hexagonal Mn monolayers due to large topological orbital moments which
interact with the emergent magnetic field. Due to the competition with
higher-order exchange interactions superposition states of spin spirals such as
the 2Q state or a distorted 3Q state arise. Simulations of spin-polarized
scanning tunneling microscopy images suggest that the distorted 3Q state could
be the magnetic ground state of a Mn monolayer on Re(0001).",2106.08622v1
2020-03-30,Partial Traces and the Geometry of Entanglement; Sufficient Conditions for the Separability of Gaussian States,"The notion of partial trace of a density operator is essential for the
understanding of the entanglement and separability properties of quantum
states. In this paper we investigate these notions putting an emphasis on the
geometrical properties of the covariance ellipsoids of the reduced states. We
thereafter focus on Gaussian states and we give new and easily numerically
implementable sufficient conditions for the separability of all Gaussian
states. Unlike the positive partial transposition criterion, none of these
conditions is however necessary.",2003.13190v1
2006-06-08,Andreev bound states in rounded corners of d-wave superconductors,"Andreev bound states at boundaries of d-wave superconductors are strongly
influenced by the boundary geometry itself. In this work, the zero-energy
spectral weight of the local quasiparticle density of states is presented for
the case of wedge-shaped boundaries with rounded corners. Generally, both
orientation of the d-wave and the specific local reflection properties of the
rounded wedges determine, whether Andreev bound states exist or not. For the
bisecting line of the wedge being parallel to the nodal direction of the d-wave
gap function, strong zero-energy Andreev bound states are expected at the round
part of the boundary.",0606208v1
1993-10-04,Experimental Nuclear Masses and the Ground State of Cold Dense Matter,"We study the consequences of recent progress in the experimental
determination of masses of neutron rich nuclei for our knowledge of the ground
state of cold dense matter. The most recent experimental data determine the
ground state of cold dense matter up to $ \rho \simeq 10^{11}~{\rm g~cm^{-3}}
$. The composition and the equation of state of the ground state of matter, in
this density interval, are calculated.",9310003v1
2000-10-06,On the Ginzburg-Landau Free Energy of Charge Density Waves with a Three-Dimensional Order,"The effective free energy of a charge density wave (CDW) with a
three-dimensional order is derived from a microscopic model (Fr\""olich model)
based on the path integral method. Electron hoping and Coulomb interaction
between chains are taken into account perturbatively, leading to an elastic
interchain coupling of the CDW ordered state.",0010102v1
2004-03-29,Correlation effects in Co/Cu and Fe/Cr magnetic multilayers,"The electronic structure of Co/Cu(001) and Fe/Cr(001) magnetic multilayers
has been investigated within the local density approximation combined with
dynamical mean field theory. Our calculation shows enhanced density of states
at the Fermi level, suggesting that electronic correlations might play an
important role in the transport properties of multilayers.",0403685v1
2005-05-27,Optical response of many-polaron systems,"Exact results for the density of states and the ac conductivity of the
spinless Holstein model at finite carrier density are obtained combining
Lanczos and kernel polynomial methods.",0505664v1
1994-05-02,Dynamical correlation functions in the Calogero-Sutherland model,"We compute the dynamical Green function and density-density correlation in
the Calogero-Sutherland model for all integer values of the coupling constant.
An interpretation of the intermediate states in terms of quasi-particles is
found.",9405008v3
2002-04-03,In medium T matrix for neutron matter,"We calculate the equation of state of pure neutron matter, comparing the
G-matrix calculation with the in-medium T-matrix result. At low densities, we
obtain similar energies per nucleon, however some differences appear at higher
densities. We use the self-consistent spectral functions from the T-matrix
approach to calculate the 1S0 superfluid gap including self-energy effects. We
find a reduction of the superfluid gap by 30%.",0204012v2
2001-09-28,Asymptotic behaviour of the probability density in one dimension,"We demonstrate that the probability density of a quantum state moving freely
in one dimension may decay faster than 1/t. Inverse quadratic and cubic
dependences are illustrated with analytically solvable examples. Decays faster
than 1/t allow the existence of dwell times and delay times.",0109151v1
2002-09-04,Energy density and localization of particles,"We consider the use of the energy density for describing a localization of
relativistic particles. This method is consistent with the causality
requirements. The related positive operator valued measure is presented. The
probability distributions for one particle states are given explicitly.",0209034v1
2007-07-23,Gutzwiller density functional theory for correlated electron systems,"We develop a new density functional theory (DFT) and formalism for correlated
electron systems by taking as reference an interacting electron system that has
a ground state wavefunction which obeys exactly the Gutzwiller approximation
for all one particle operators. The solution of the many electron problem is
mapped onto the self-consistent solution of a set of single particle
Schroedinger equations analogous to standard DFT-LDA calculations.",0707.3459v1
2008-12-19,Convergent finite element methods for compressible barotropic Stokes systems,"We propose finite element methods for compressible barotropic Stokes systems.
We state convergence results for these methods and outline their proofs. The
principal tools of the proofs are higher integrability estimates for the
discrete density, equations for the discrete effective viscous flux, and
renormalized formulations of the numerical method for the density equation.",0812.3851v1
2009-02-14,Electronic structure of BaCu$_2$As$_2$ and SrCu$_2$As$_2$: sp-band metals,"The electronic structures of ThCr$_2$Si$_2$ structure BaCu$_2$As$_2$ and
SrCu$_2$As$_2$ are investigated using density functional calculations. The Cu
$d$ orbitals are located at 3 eV and higher binding energy, and are therefore
chemically inert with little contribution near the Fermi energy. These
materials are moderate density of states, sp-band metals with large Fermi
surfaces and low anisotropy.",0902.2502v1
2014-12-01,Logical Entropy for Quantum States,"The novel concept of quantum logical entropy is presented and analyzed. We
prove several basic properties of this entropy with regard to density matrices.
We hereby motivate a different approach for the assignment of quantum entropy
to density matrices.",1412.0616v2
2017-02-17,Renormalization group analysis for an asymmetric simple exclusion process,"A perturbative renormalization group method is used to obtain steady-state
density profiles of a particle non-conserving asymmetric simple exclusion
process. This method allows us to obtain a globally valid solution for the
density profile without the asymptotic matching of bulk and boundary layer
solutions. In addition, we show a nontrivial scaling of the boundary layer
width with the system size close to specific phase boundaries.",1702.05225v1
2017-05-02,Baryon susceptibilities from a holographic equation of state,"A black hole holographic model is used to mimic the behavior of the quark
gluon plasma at finite temperature and density. This model reproduces lattice
data at $\mu_B\!=\!0$ and displays critical behavior at large densities. High
order baryon susceptibilities are used to extract freeze-out points by
comparing those susceptibilities with the corresponding net-protons
distribution measured by STAR. Possible experimental signatures of the critical
end point are discussed.",1705.01021v1
2018-08-31,The Limiting Behavior of the FTASEP with Product Bernoulli Initial Distribution,"We study the facilitated totally asymmetric exclusion process on the one
dimensional integer lattice. We investigate the invariant measures and the
limiting behavior of the process. We mainly derive the limiting distribution of
the process when the initial distribution is the Bernoulli product measure with
density $1/2$. We also prove that in the low density regime, the system finally
converges to an absorbing state.",1808.10612v1
2021-03-29,Spectral density of interacting pairs in low-dimensional finite lattices,"The spectral density of bound pairs in ideal 1D, 2D and Bethe lattices is
computed for weak and strong interactions. The computations are performed with
Green's functions by an efficient recursion method in real space. For the range
of interaction strengths within which bound states are predominantly single
pairs, the spectral profiles guide to the energy bandwidths where the bound
pairs can be maximized.",2103.15496v1
2006-01-11,Inelastic form factors to alpha particle condensate states in 12C and 16O: what can we learn ?,"In order to discuss the spatial extention of the second 0+ state of 12C
(Hoyle state), we analyze the inelastic form factor of electron scattering to
the Hoyle state, which our 3 alpha condensate wave function reproduces very
well like previous 3 alpha RGM/GCM models. The analysis is made by varying the
size of the Hoyle state artificially. As a result, we find that only the
maximum value of the form factor sensitively depends on its size, while the
positions of maximum and minimum are almost unchanged. This size dependence is
found to come from a characteristic feature of the transition density from the
ground state to the Hoyle state. We further show the theoretical predictions of
the inelastic form factor to the second 2+ state of 12C, which was recently
observed above the Hoyle state, and of the inelastic form factor to the
calculated third 0+ state of 16O, which was conjectured to correspond to the 4
alpha condensed state in previous theoretical work by the present authors.",0601035v1
2004-12-20,Negative Quantum Capacitance of Carbon Nanotube Field-Effect Transistors,"Atomistic density functional theory (DFT) calculations of the capacitance
between a metallic cylindric gate and a carbon nanotube (CNT) are reported.
Results stressing the predominant effect of quantum capacitance in limiting or
even enhancing screening properties of the CNT are shown. Other contributions
to the quantum capacitance beyond the electronic density of state (DOS) are
pointed out. Negative values of the quantum capacitance are obtained for
low-density systems, which correspondingly over-screen the gate field. This
unconventional behavior of the quantum capacitance is related to the
predominance of the exchange contribution in the total electronic energy of the
CNT.",0412540v1
2005-09-26,"A new method for computation of QCD thermodynamics: EOS, specific heat and speed of sound","We propose a new variant of the operator method for the computation of the
equation of state of QCD, which yields positive pressure for all temperatures
and all values of temporal lattice spacings. Using this new method, we
calculate the continuum limit of pressure, energy density, entropy density,
specific heat, and the speed of sound, in quenched QCD, for 0.9 \le T/T_c \le
3.",0509127v1
2012-05-11,Elliptic flow and the symmetry energy at supra-saturation density,"The elliptic flow in collisions of neutron-rich heavy-ion systems at
intermediate energies emerges as an observable sensitive to the strength of the
symmetry energy at supra-saturation densities. First results obtained by
comparing ratios or differences of neutron and hydrogen flows with predictions
of transport models favor a moderately soft to linear density dependence,
consistent with ab-initio nuclear-matter theories. Comprehensive data sets of
high accuracy can be expected to improve our knowledge of the equation of state
of asymmetric nuclear matter.",1205.2585v2
2018-12-16,"On the geometric and magnetic properties of the monomer, dimer and trimer of NiFe2O4","In this work, by employing Density Functional Theory, we compute and discuss
some geometric and magnetic properties of the monomer, dimer and trimer of
NiFe2 O4 . The calculations are performed at the UDFT/ B3LYP level of
calculation, by employing the LANL2DZ effective pseudo potential. The results
of the Mulliken spin densities and the spin polarization will be presented.
Finally the outcome of the system density of states is considered.",1812.09126v1
2017-06-29,Non-demolition measurements of observables with general spectra,"It has recently been established that, in a non-demolition measurement of an
observable $\mathcal{N}$ with a finite point spectrum, the density matrix of
the system approaches an eigenstate of $\mathcal{N}$, i.e., it ""purifies"" over
the spectrum of $\mathcal{N}$. We extend this result to observables with
general spectra. It is shown that the spectral density of the state of the
system converges to a delta function exponentially fast, in an appropriate
sense. Furthermore, for observables with absolutely continuous spectra, we show
that the spectral density approaches a Gaussian distribution over the spectrum
of $\mathcal{N}$. Our methods highlight the connection between the theory of
non-demolition measurements and classical estimation theory.",1706.09584v1
2019-09-30,Entropy-type inequalities for generalized Gamma densities,"We investigate the relaxation to equilibrium of the solution of a class of
one-dimensional linear Fokker--Planck type equations that have been recently
considered in connection with the study of addiction phenomena in a system of
individuals. The steady states of these equations belong to the class of
generalized Gamma densities. As a by-product of the relaxation analysis, we
prove new weighted Poincar\'e and logarithmic Sobolev type inequalities for
this class of densities.",1909.13658v1
2022-11-19,Density-tuned effective metal-insulator transitions in 2D semiconductor layers: Anderson localization or Wigner crystallization,"Electrons (or holes) confined in 2D semiconductor layers have served as model
systems for studying disorder and interaction effects for almost 50 years. In
particular, strong disorder drives the metallic 2D carriers into a strongly
localized Anderson insulator (AI) at low densities whereas pristine 2D
electrons in the presence of no (or little) disorder should solidify into a
Wigner crystal at low carrier densities. Since the disorder in 2D
semiconductors is mostly Coulomb disorder arising from random charged
impurities, the applicable physics is complex as the carriers interact with
each other as well as with the random charged impurities through the same
long-range Coulomb coupling. By critically theoretically analyzing the
experimental transport data in depth using a realistic transport theory to
calculate the low-temperature 2D resistivity as a function of carrier density
in 11 different experimental samples covering 9 different materials, we
establish, utilizing the Ioffe-Regel-Mott criterion for strong localization, a
direct connection between the critical localization density for the 2D
metal-insulator transition (MIT) and the sample mobility deep into the metallic
state, which for clean samples could lead to a localization density low enough
to make the transition appear to be a Wigner crystallization. We believe that
the insulating phase is always an effective Coulomb disorder-induced localized
AI, which may have short-range WC-like correlations at low carrier densities.
Our theoretically calculated disorder-driven critical MIT density agrees with
experimental findings in all 2D samples, even for the ultra-clean samples. In
particular, the extrapolated critical density for the 2D MIT seems to vanish
when the high-density mobility goes to infinity, indicating that transport
probes a disorder-localized insulating ground state independent of how low the
carrier density might be.",2211.10673v2
1995-10-16,Ground-state properties of the One-dimensional Kondo Lattice at partial Band-filling,"We compute the magnetic structure factor, the singlet correlation function
and the momentum distribution of the one-dimensional Kondo lattice model at the
density $\rho =0.7$. The density matrix-renormalization group method is used.
We show that in the weak-coupling regime, the ground state is paramagnetic. We
argue that a Luttinger liquid description of the model in this region is
consistent with our calculations . In the strong-coupling regime, the ground
state becomes ferromagnetic. The conduction electrons show a spinless-fermion
like behavior.",9510087v1
1996-05-13,Size-effects in the Density of States in NS and SNS junctions,"The quasiparticle local density of states (LDOS) is studied in clean NS and
SNS junctions with increasing transverse size, from quasi-one-dimensional to
three-dimensional. It is shown that finite transverse dimensions are related to
pronounced effects in the LDOS, such as fast oscillations superimposed on the
quasiparticle interference oscillations (for NS) and additional peaks in the
bound state spectrum in the subgap region (for SNS). Also, the validity of the
Andreev approximation is discussed. It turns out to be an acceptable
approximation in all situations tested.",9605078v1
1998-01-16,Low-lying Quasiparticle Excitations around a Vortex Core in Quantum Limit,"Focusing on a quantum-limit behavior, we study a single vortex in a clean
s-wave type-II superconductor by self-consistently solving the Bogoliubov-de
Gennes equation. The discrete energy levels of the vortex bound states in the
quantum limit is discussed. The vortex core radius shrinks monotonically up to
an atomic-scale length on lowering the temperature T, and the shrinkage stops
to saturate at a lower T. The pair potential, supercurrent, and local density
of states around the vortex exhibit Friedel-like oscillations. The local
density of states has particle-hole asymmetry induced by the vortex. These are
potentially observed directly by STM.",9801166v1
2000-06-02,Constraints on the Quasiparticle Density of States in High-$T_c$ Superconductors,"In this Letter we present new tunneling data on YBa$_2$Cu$_3$O$_7$ thin films
by low temperature scanning tunneling spectroscopy. Unusual peak-dip-hump
features, previously reported in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, are also
found in YBa$_2$Cu$_3$O$_7$. To analyse these common signatures we propose a
new heuristic model in which, in addition to the d-wave symmetry, the gap
function is energy dependent. A simple expression for the quasiparticle density
of states is derived, giving an excellent agreement with the experiment. The
dynamics of the quasiparticle states and the energy scales involved in the
superconducting transition are discussed.",0006044v1
2005-05-03,Semiclassical quantisation of space-times with apparent horizons,"Coherent or semiclassical states in canonical quantum gravity describe the
classical Schwarzschild space-time. By tracing over the coherent state
wavefunction inside the horizon, a density matrix is derived.
Bekenstein-Hawking entropy is obtained from the density matrix, modulo the
Immirzi parameter. The expectation value of the area and curvature operator is
evaluated in these states. The behaviour near the singularity of the curvature
operator shows that the singularity is resolved. We then generalise the results
to space-times with spherically symmetric apparent horizons.",0505017v2
2007-05-03,Orthogonality catastrophe and Kondo effect in graphene,"Anderson's orthogonality catastrophe in graphene, at energies close to the
Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality
catastrophe is suppressed, due to the vanishing density of states at the Dirac
point. In the presence of preexisting localized states at the Dirac energy, the
orthogonality catastrophe shows similar features to those found in normal
metals with a finite density of states at the Fermi level. The implications for
the Kondo effect induced by magnetic impurities, and for the Fermi edge
singularities in tunneling processes are also discussed.",0705.0522v1
2007-06-13,Excitonic Mott transition in type-II quantum dots,"Photoluminescence spectra measured on a type-II GaSb/GaAs quantum dot
ensemble at high excitation power indicate a Mott transition from the low
density state comprising of spatially-indirect excitons to a high density
electron-plasma state. Under the influence of a very high magnetic field, the
electron-plasma that is formed at high excitation powers is `frozen-out' into a
state of optically inactive magneto-excitons.",0706.1972v1
2008-11-07,The ground state energy of the weakly interacting Bose gas at high density,"We prove the Lee-Huang-Yang formula for the ground state energy of the 3D
Bose gas with repulsive interactions described by the exponential function, in
a simultaneous limit of weak coupling and high density. In particular, we show
that the Bogoliubov approximation is exact in an appropriate parameter regime,
as far as the ground state energy is concerned.",0811.1166v1
2009-07-07,Multiband Superconductivity in Spin Density Wave Metals,"We study the emergence of multiband superconductivity with $s$- and $d-$wave
symmetry on the background of spin density wave (SDW). We show that the SDW
coherence factors renormalize the momentum dependence of the superconducting
(SC) gap, yielding a SC state with an \emph{unconventional} s-wave symmetry.
Interband Cooper pair scattering stabilizes superconductivity in both
symmetries. With increasing SDW order, the s-wave state is more strongly
suppressed than the d-wave state. Our results are universally applicable to
two-dimensional systems with a commensurate SDW.",0907.1296v1
2016-07-21,Energy Continuity in Degenerate Density Functional Perturbation Theory,"Fractional occupation numbers can produce open-shell degeneracy in density
functional theory. We develop the corresponding perturbation theory by
requiring that a differentiable map connects the initial and perturbed states.
The degenerate state connects to a single perturbed state which extremizes, but
does not necessarily minimize or maximize, the energy with respect to
occupation numbers. Using a system of three electrons in a harmonic oscillator
potential, we relate the counterintuitive sign of first-order occupation
numbers to eigenvalues of the electron-electron interaction Hessian.",1607.06404v1
2019-11-15,Two-component asymmetric dark matter via bound states and freeze-in decay,"We propose a novel mechanism to realize two-component asymmetric dark matter
of very different mass scales through bound state formation and late freeze-in
decay. Assuming a particle-antiparticle asymmetry is initially shared by SM
baryons and two dark matter components, we demonstrate that the existence of
bound states formed by the heavy component can efficiently transfer the
asymmetry from the heavy to the light component via late decay. In this case,
the energy densities of the two components can be comparable, and the correct
relic density is reproduced.",1911.06788v2
2014-03-05,Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks,"Generic inhomogeneous steady states in an asymmetric exclusion process on a
ring with a pair of point bottlenecks are studied. We show that, due to an
underlying universal feature, measurements of coarse-grained steady-state
densities in this model resolve the bottleneck structures only partially.
Unexpectedly, it displays localization-delocalization transitions and
confinement of delocalized domain walls, controlled by the interplay between
particle number conservation and bottleneck competition for moderate particle
densities.",1403.1018v3
2008-07-31,Separability of Multi-Partite Quantum States,"We give a direct tensor decomposition for any density matrix into Hermitian
operators. Based upon the decomposition we study when the mixed states are
separable and generalize the separability indicators to multi-partite states
and show that a density operator is separable if and only if the separable
indicator is non-negative. We then derive two bounds for the separable
indicator in terms of the spectrum of the factor operators in the tensor
summands.",0807.5003v1
2009-12-22,Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications,"Isospin symmetry of atomic nuclei is explicitly broken by the
charge-dependent interactions, primarily the Coulomb force. Within the nuclear
density functional theory, isospin is also broken spontaneously. We propose a
projection scheme rooted in a mean field theory, that allows the consistent
treatment of isospin breaking in both ground and exited nuclear states. We
demonstrate that this scheme is essentially free from spurious divergences
plaguing particle-number and angular-momentum restoration approaches.
Applications of the new technique include excited high-spin states in
medium-mass N=Z nuclei, such as superdeformed bands and many-particle-many-hole
terminating states.",0912.4381v1
2022-06-21,Density matrix of electrons coupled to phonons and the electron-phonon entanglement content of excited states,"We derive the exact reduced density matrix for the electrons in an
analytically solvable electron-phonon model. Here, the electrons are described
as a Luttinger liquid that is coupled to Einstein phonons. We further derive
analytical expressions for the electron-phonon entanglement, its spectrum and
mutual information at finite and zero temperature as well as for excited
states. The entanglement entropy is additive in momentum for the quasi-particle
excited states, but not in the electron-phonon coupled eigenmodes of the
system.",2206.10408v1
2004-10-04,Self-field effects upon the critical current density of flat superconducting strips,"We develop a general theory to account self-consistently for self-field
effects upon the average transport critical current density Jc of a flat
type-II superconducting strip in the mixed state when the bulk pinning is
characterized by a field-dependent depinning critical current density Jp(B),
where B is the local magnetic flux density. We first consider the possibility
of both bulk and edge-pinning contributions but conclude that bulk pinning
dominates over geometrical edge-barrier effects in state-of-the-art YBCO films
and prototype second-generation coated conductors. We apply our theory using
the Kim model, JpK(B) = JpK(0)/(1+|B|/B0), as an example. We calculate Jc(Ba)
as a function of a perpendicular applied magnetic induction Ba and show how
Jc(Ba) is related to JpK(B). We find that Jc(Ba) is very nearly equal to
JpK(Ba) when Ba > Ba*, where Ba* is the value of Ba that makes the net flux
density zero at the strip's edge. However, Jc(Ba) is suppressed relative to
JpK(Ba) at low fields when Ba < Ba*, with the largest suppression occurring
when Ba*/B0 is of order unity or larger.",0410093v3
2006-04-18,Non-BCS superfluidity in trapped ultracold Fermi gases,"Superconductivity and superfluidity of fermions require, within the BCS
theory, matching of the Fermi energies of the two interacting Fermion species.
Difference in the number densities of the two species leads either to a normal
state, to phase separation, or - potentially - to exotic forms of superfluidity
such as FFLO-state, Sarma state or breached pair state. We consider ultracold
Fermi gases with polarization, i.e. spin-density imbalance. We show that, due
to the gases being trapped and isolated from the environment in terms of
particle exchange, exotic forms of superfluidity appear as a shell around the
BCS-superfluid core of the gas and, for large density imbalance, in the core as
well. We obtain these results by describing the effect of the trapping
potential by using the Bogoliubov-de Gennes equations. For comparison to
experiments, we calculate also the condensate fraction, and show that, in the
center of the trap, a polarized superfluid leads to a small dip in the central
density difference. We compare the results to those given by local density
approximation and find qualitatively different behavior.",0604424v4
2023-11-17,Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices,"We analyse the ground-state quantum phase diagram of hardcore Bosons
interacting with repulsive dipolar potentials. The bosons dynamics is described
by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The
ground state results from the interplay between the lattice geometry and the
long-range interactions, which we account for by means of a classical spin
mean-field approach limited by the size of the considered unit cells. This
extended classical spin mean-field theory accounts for the long-range
density-density interaction without truncation. We consider three different
lattice geometries: square, honeycomb, and triangular. In the limit of zero
hopping the ground state is always a devil's staircase of solid (gapped)
phases. Such crystalline phases with broken translational symmetry are robust
with respect to finite hopping amplitudes. At intermediate hopping amplitudes,
these gapped phases melt, giving rise to various lattice supersolid phases,
which can have exotic features with multiple sublattice densities. At
sufficiently large hoppings the ground state is a superfluid. The stability of
phases predicted by our approach is gauged by comparison to the known quantum
phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as
well as quantum Monte Carlo simulations for the dipolar case on the square
lattice. Our results are of immediate relevance for experimental realisations
of self-organised crystalline ordering patterns in analogue quantum simulators,
e.g., with ultracold dipolar atoms in an optical lattice.",2311.10632v1
2002-07-25,Band- and k-dependent Self-Energy Effects in the Unoccupied and Occupied Quasiparticle Band Structure of Cu,"Excited-state self-energy effects in the electronic structure of Cu, a
prototype weakly correlated system containing states with different degrees of
localization, are investigated with emphasis on the unoccupied states up to 40
eV above the Fermi level. The analysis employs the experimental quasiparticle
states mapped under full control of the 3-dimensional wavevector k using
very-low energy electron diffraction for the unoccupied states and
photoemission for the occupied states. The self-energy corrections to the
density-functional theory show a distinct band- and k-dependence. This is
supported by quasiparticle GW calculations performed within the framework of
linearized muffin-tin orbitals. Our results suggest however that the GW
approximation may be less accurate in the localized d-bands of Cu with their
short-range charge fluctuations. We identify a connection of the self-energy
behavior with the spatial localization of the one-electron wavefunctions in the
unit cell and with their behavior in the core region. Mechanisms of this
connection are discussed based on the local-density picture and on the
non-local exchange interaction with the valence states.",0207604v2
2018-11-15,Superconductivity in systems exhibiting the Altshuler-Aronov anomaly,"Making use of generalized Eliashberg equations, we describe the
Altshuler-Aronov (AA) effect and superconductivity on equal footing. We derive
explicit expressions for the Coulomb pseudopotential in 3D, taking into account
also the anomalous diffusion. We present a full numerical solution for two
normal-state and two anomalous self-energies. In the normal state, we amend the
known results for the purely electronic AA effect; with electron-phonon
coupling turned on, we find additional anomalies in the density of states close
to the phonon energy. We study how the critical temperature and density of
states of strongly disordered 3D superconductors change with normal-state
resistivity. We find that the type of transition from the superconducting to
the insulating state depends on the strength of electron-phonon coupling: at
weak coupling there exists an intermediate normal state, whereas at strong
coupling the transition is direct.",1811.06467v1
2018-10-22,Mottness collapse without metallisation in the domain walls of triangular-lattice Mott insulator 1T-TaS$_2$,"1T-TaS$_2$ is a charge-density-wave (CDW) compound with a Mott-insulating
ground state. The metallic state obtained by doping, substitution or pulsed
charge injection is characterized by an emergent CDW domain wall network, while
single domain walls can be found in the pristine Mott state. Here we study
whether and how the single walls become metallic. Tunneling spectroscopy
reveals partial suppression of the Mott gap and the presence of in-gap states
strongly localized at the domain-wall sites. Using the real-space dynamical
mean field theory description of the strongly correlated quantum-paramagnet
ground state we show that the local gap suppression follows from the increased
hopping along the connected zig-zag chain of lattice sites forming the domain
wall, and that full metallisation is preempted by the splitting of the
quasiparticle band into bonding and antibonding sub-bands due to the structural
dimerization of the wall, explaining the presence of the in-gap states and the
low density of states at the Fermi level.",1810.09557v1
2020-07-16,Majorana end states in an interacting quantum wire,"We propose and investigate a simple one-dimensional model for a
single-channel quantum wire hosting electrons that interact repulsively and are
subject to a significant spin-orbit interaction. We show that an external
Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit
axis, drives the wire into a correlated spin-density wave state with gapped
spin and gapless charge excitations. By computing the ground-state degeneracies
of the model with either (anti-)periodic or open boundary conditions, we
conclude that the correlated spin-density state realizes a gapless
symmetry-protected topological phase, as the ground state is unique in the ring
geometry while it is two-fold degenerate in the wire with open boundaries.
Microscopically the two-fold degeneracy is found to be protected by the
conservation of the magnetization parity. Open boundaries induce localized
zero-energy (midgap) states which are described, at the special Luther-Emery
point of the model, by Majorana fermions. We find that spin densities at the
open ends of the wire exhibit unusual long-ranged correlations despite the fact
that all correlations in the bulk of the wire decay in a power-law or
exponential fashion. Our study exposes the crucial importance of the
long-ranged string operator needed to implement the correct commutation
relations between spin densities at different points in the wire. Along the way
we rederive the low-energy theory of Galilean-invariant electron systems in
terms of current operators.",2007.08482v3
2020-02-26,Atomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity,"The defining characteristic of hole-doped cuprates is $d$-wave high
temperature superconductivity. However, intense theoretical interest is now
focused on whether a pair density wave state (PDW) could coexist with cuprate
superconductivity (D. F. Agterberg et al., Annual Review of Condensed Matter
Physics 11, 231 (2020)). Here, we use a strong-coupling mean-field theory of
cuprates, to model the atomic-scale electronic structure of an eight-unit-cell
periodic, $d$-symmetry form factor, pair density wave (PDW) state coexisting
with $d$-wave superconductivity (DSC). From this PDW+DSC model, the
atomically-resolved density of Bogoliubov quasiparticle states N(r,E) is
predicted at the terminal BiO surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ and compared
with high-precision electronic visualization experiments using spectroscopic
imaging STM. The PDW+DSC model predictions include the intra-unit-cell
structure and periodic modulations of N(r,E), the modulations of the coherence
peak energy $\Delta_p$ (r), and the characteristics of Bogoliubov quasiparticle
interference in scattering-wavevector space (q-space). Consistency between all
these predictions and the corresponding experiments indicates that lightly
hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_8$ does contain a PDW+DSC state. Moreover, in
the model the PDW+DSC state becomes unstable to a pure DSC state at a critical
hole density p*, with empirically equivalent phenomena occurring in the
experiments. All these results are consistent with a picture in which the
cuprate translational symmetry breaking state is a PDW, the observed charge
modulations are its consequence, the antinodal pseudogap is that of the PDW
state, and the cuprate critical point at p* ~ 19% occurs due to disappearance
of this PDW.",2002.11654v2
2013-06-07,Spin and the Thermal Equilibrium Distribution of Wave Functions,"Consider a quantum system $S$ weakly interacting with a very large but finite
system $B$ called the heat bath, and suppose that the composite $S\cup B$ is in
a pure state $\Psi$ with participating energies between $E$ and $E+\delta$ with
small $\delta$. Then, it is known that for most $\Psi$ the reduced density
matrix of $S$ is (approximately) equal to the canonical density matrix. That
is, the reduced density matrix is universal in the sense that it depends only
on $S$'s Hamiltonian and the temperature but not on $B$'s Hamiltonian, on the
interaction Hamiltonian, or on the details of $\Psi$. It has also been pointed
out that $S$ can also be attributed a random wave function $\psi$ whose
probability distribution is universal in the same sense. This distribution is
known as the ""Scrooge measure"" or ""Gaussian adjusted projected (GAP) measure"";
we regard it as the thermal equilibrium distribution of wave functions. The
relevant concept of the wave function of a subsystem is known as the
""conditional wave function"". In this paper, we develop analogous considerations
for particles with spin. One can either use some kind of conditional wave
function or, more naturally, the ""conditional density matrix"", which is in
general different from the reduced density matrix. We ask what the thermal
equilibrium distribution of the conditional density matrix is, and find the
answer that for most $\Psi$ the conditional density matrix is (approximately)
deterministic, in fact (approximately) equal to the canonical density matrix.",1306.1659v2
2023-10-09,Influence of a Realistic Multiorbital Band Structure on Conducting Domain Walls in Perovskite Ferroelectrics,"Domain wall morphologies in ferroelectrics are believed to be largely shaped
by electrostatic forces. Here, we show that for conducting domain walls, the
morphology also depends on the details of the charge-carrier band structure.
For concreteness, we focus on transition-metal perovskites like BaTiO$_3$ and
SrTiO$_3$. These have a triplet of $t_{2g}$ orbitals attached to the Ti atoms
that form the conduction bands when electron doped. We solve a set of coupled
equations -- Landau-Ginzburg-Devonshire (LGD) equations for the polarization,
tight-binding Schr\""odinger equations for the electron bands, and Gauss' law
for the electric potential -- to obtain polarization and electron density
profiles as a function of electron density. We find that at low electron
densities, the electron gas is pinned to the surfaces of the ferroelectric by a
Kittel-like domain structure. As the electron density increases, the domain
wall evolves smoothly through a zigzag head-to-head structure, eventually
becoming a flat head-to-head domain wall at high density. We find that the
Kittel-like morphology is protected by orbital asymmetry at low electron
densities, while at large electron densities the high density of states of the
multiorbital band structure provides effective screening of depolarizing fields
and flattens the domain wall relative to single-orbital models. Finally, we
show that in the zigzag phase, the electron gas develops tails that extend away
from the domain wall, in contrast to na\""{i}ve expectations.",2310.06043v2
2004-08-24,"Contravariant Densities, Complete Distances and Relative Fidelities for Quantum Channels","Introducing contravariant trace-densities for quantum states, we restore one
to one correspondence between quantum operations described by normal CP maps
and their trace densities as Hermitian positive operator-valued contravariant
kernels. The CB-norm distance between two quantum operations with type one
input algebras is explicitly expressed in terms of these densities, and this
formula is also extended to a generalized CB-distances between quantum
operations with type two inputs. A larger C-distance is given as the natural
norm-distance for the channel densities, and another, Helinger type distance,
related to minimax mean square optimization problem for purification of quantum
channels, is also introduced and evaluated in terms of their contravariant
trace-densities. It is proved that the Helinger type complete fidelity distance
between two channels is equivalent to the CB distance at least for type one
inputs, and this equivalence is also extended to type two for the generalized
CB distance. An operational meaning for these distances and relative complete
fidelity for quantum channels is given in terms of quantum encodings as
generalized entanglements of quantum states opposite to the inputs and the
output states.",0408035v2
2021-06-10,Perturbation Theory for Quantum Information,"We report lowest-order series expansions for primary matrix functions of
quantum states based on a perturbation theory for functions of linear
operators. Our theory enables efficient computation of functions of perturbed
quantum states that assume only knowledge of the eigenspectrum of the zeroth
order state and the density matrix elements of a zero-trace, Hermitian
perturbation operator, not requiring analysis of the full state or the
perturbation term. We develop theories for two classes of quantum state
perturbations, perturbations that preserve the vector support of the original
state and perturbations that extend the support beyond the support of the
original state. We highlight relevant features of the two situations, in
particular the fact that functions and measures of perturbed quantum states
with preserved support can be elegantly and efficiently represented using
Fr\'echet derivatives. We apply our perturbation theories to find simple
expressions for four of the most important quantities in quantum information
theory that are commonly computed from density matrices: the Von Neumann
entropy, the quantum relative entropy, the quantum Chernoff bound, and the
quantum fidelity.",2106.05533v3
2009-06-20,First-Principles Calculation of Born Effective Charges and Spontaneous Polarization of Ferroelectric Bismuth Titanate,"In this study, we present the results of our first-principles calculations of
the band structure, density of states and the Born effective charge tensors for
the ferroelectric (ground state B1a1) and paraelectric (I4/mmm) phases of
bismuth titanate. The calculations are done using the generalized gradient
approximation (GGA) as well as the local density approximation (LDA) of the
density functional theory. In contrast to the literature, our calculations on
B1a1 structure using GGA and LDA yield smaller indirect band gaps as compared
to the direct band gaps, in agreement with the experimental data. The density
of states shows considerable hybridization among Ti 3d, Bi 6p and O 2p states
indicating covalent nature of the bonds leading to the ferroelectric
instability. The Born effective charge tensors of the constituent ions for the
ground state (B1a1) and paraelectric (I4/mmm) structures were calculated using
the Berry phase method. This is followed by the calculation of the spontaneous
polarization for the ferroelectric B1a1 phase using the Born effective charge
tensors of the individual ions. The calculated value for the spontaneous
polarization of ferroelectric bismuth titanate using different Born effective
charges was found to be in the range of 55+/-13 $\mu$C/cm2 in comparison to the
reported experimental value of (50+/-10 $\mu$C/cm2) for single crystals. The
origin of ferroelectricity is attributed to the relatively large displacements
of those oxygen ions in the TiO6 octahedra that lie along the a-axis of the
bismuth titanate crystal.",0906.3803v2
2016-12-20,Possible excited spin density wave states in zigzag graphene nanoribbons,"We theoretically examine the possible spin ordered states in zigzag graphene
nanoribbon in a large supercell by the self-consistent mean field method as
well as the first principle calculation. In addition to the well-known
anti-ferromagnetic (AF) and ferromagnetic (FM) edge states, we find that there
are also some excited spin density wave (ESDW) states, the energy of which are
close to the AF edge state (ground state). We thus argue that these ESDW states
may coexist in experiment when the temperature is not too low. Our numerical
results indicate that the allowed ESDW are commensurate; and their dispersion
curve is plotted. This interesting feature results from the fact the there is a
flat edge band near the Fermi surface in the graphene zigzag ribbon. Finally we
use the non-equilibrium Green function theory combined with the Hubbard model
to calculate some possible spin polarization states localized in the middle and
terminal parts of graphene nanoribbons.",1612.06762v1
2024-03-23,A systematic framework to construct unconventional superconducting pairing scar states using multi-body interactions,"We present a systematic framework to construct model Hamiltonians that have
unconventional superconducting pairing states as exact energy eigenstates, by
incorporating multi-body interactions (i.e., interactions among more than two
particles). The multi-body interactions are introduced in a form of the local
density-density coupling in such a way that any pair configuration in real
space has the same interaction energy by cancelling the two-body and multi-body
interactions. Our approach is applicable to both spinless and spinful models in
any spatial dimensions and on any bipartite lattices, facilitating an
exhaustive extension of Yang's $s$-wave $\eta$-pairing state to various other
unconventional pairing symmetries ($p$-wave, $d$-wave, $f$-wave, etc.). We
verify that the two-dimensional spinful Hubbard model on a square lattice with
the multi-body interactions has the $d$-wave pairing state as an energy
eigenstate, which can be regarded as a quantum many-body scar state as
evidenced from the numerical analysis of the pair correlation function, the
entanglement entropy, and the level statistics. We also discuss other examples,
including $f$-wave pairing states on a honeycomb lattice, $s$-wave pairing
states in a nearest-neighbor interacting system, and spinless $p$-wave pairing
states in one dimension.",2404.02914v1
2001-02-23,Charge superselection rule does not rule out pure states of subsystems to be coherent superpositions of states with different charges,"We consider a huge quantum system that is subject to the charge
superselection rule, which requires that any pure state must be an eigenstate
of the total charge. We regard some parts of the system as ""subsystems,"" and
the rest as an environment E. We assume that one does not measure anything of
E, i.e., one is only interested in observables of the subsystems. We show that
there exist states with the following properties: (i) Its reduced density
operator is completely equivalent to a vector state of the subsystems for any
gauge-invariant observable of the subsystems. (ii) The vector state is a simple
product of vector states of individual subsystems, each of which is not an
eigenstate of the charge of each subsystem. Furthermore, one can associate to
each subsystem its vector state, which is a pure state, and observables which
are not necessarily gauge invariant in each subsystem. These results justify
taking (a) superpositions of states with different charges, and (b)
non-gauge-invariant operators, such as the order parameter of the breaking of
the gauge symmetry, as observables, for subsystems.",0102429v2
2015-09-04,Ground-State Quantum-Electrodynamical Density-Functional Theory,"In this work we establish a density-functional reformulation of coupled
matter-photon problems subject to general external electromagnetic fields and
charge currents. We first show that for static minimally-coupled matter-photon
systems an external electromagnetic field is equivalent to an external charge
current. We employ this to show that scalar external potentials and transversal
external charge currents are in a one-to-one correspondence to the expectation
values of the charge density and the vector-potential of the correlated
matter-photon ground state. This allows to establish a Maxwell-Kohn-Sham
approach, where in conjunction with the usual single-particle Kohn-Sham
equations a classical Maxwell equation has to be solved. In the magnetic
mean-field limit this reduces to a current-density-functional theory that does
not suffer from non-uniqueness problems and if furthermore the magnetic field
is zero recovers standard density-functional theory.",1509.01417v2
2016-06-13,Form the density-of-states method to finite density quantum field theory,"During the last 40 years, Monte Carlo calculations based upon Importance
Sampling have matured into the most widely employed method for determinig first
principle results in QCD. Nevertheless, Importance Sampling leads to
spectacular failures in situations in which certain rare configurations play a
non-secondary role as it is the case for Yang-Mills theories near a first order
phase transition or quantum field theories at finite matter density when
studied with the re-weighting method. The density-of-states method in its LLR
formulation has the potential to solve such overlap or sign problems by means
of an exponential error suppression. We here introduce the LLR approach and its
generalisation to complex action systems. Applications include U(1), SU(2) and
SU(3) gauge theories as well as the Z3 spin model at finite densities and
heavy-dense QCD.",1606.03879v2
2018-01-21,Isomorph theory of physical aging,"This paper derives and discusses the configuration-space Langevin equation
describing a physically aging R-simple system and the corresponding
Smoluchowski equation. Externally controlled thermodynamic variables like
temperature, density, pressure enter the description via the single parameter
${T}_{\rm s}/T$ in which $T$ is the bath temperature and ${T}_{\rm s}$ is the
""systemic"" temperature defined at any time $t$ as the thermodynamic equilibrium
temperature of the state point with density $\rho(t)$ and potential energy
$U(t)$. In equilibrium ${T}_{\rm s}\cong T$ with fluctuations that vanish in
the thermodynamic limit. In contrast to Tool's fictive temperature and other
effective temperatures in glass science, the systemic temperature is defined
for any configuration with a well-defined density, even if it is not in any
sense close to equilibrium. Density and systemic temperature define an aging
phase diagram in which the aging system traces out a curve. Predictions are
discussed for aging following various density-temperature and
pressure-temperature jumps from one equilibrium state to another, as well as
for a few other scenarios. The proposed theory implies that R-simple
glass-forming liquids are characterized by a dynamic Prigogine-Defay ratio of
unity.",1801.06890v2
2020-08-19,Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory,"We study the charge-density-wave order and its competition with
superconductivity in the one-band Hubbard model for high-$T_c$ superconducting
cuprates. We use cluster dynamical mean field theory (CDMFT) at $T=0$. The
one-band Hubbard model only contains copper atoms, and a physical
charge-density-wave with charge excesses located on the oxygen atoms manifests
itself as a bond-density-wave (BDW) within this context. It arises purely out
of local correlation effects and also leads to a $s'$-wave pair-density-wave in
the presence of $d$-wave superconductivity. The $d$-wave BDW is suppressed on
increasing $U$ and is favored on increasing the magnitude of the
second-neighbor hopping $t'$. Further, the $d$-wave BDW order is weakened when
in competition with superconductivity, as seen in experiments. Additionally it
behaves quite differently on varying $U$ in the superconducting state compared
to the normal state.",2008.08661v2
2021-10-25,Microscopic mechanism for fluctuating pair density wave,"In weakly coupled BCS superconductors, only electrons within a tiny energy
window around the Fermi energy, $E_F$, form Cooper pairs. This may not be the
case in strong coupling superconductors such as cuprates, FeSe, SrTiO$_3$ or
cold atom condensates where the pairing scale, $E_B$, becomes comparable or
even larger than $E_F$. In cuprates, for example, a plausible candidate for the
pseudogap state at low doping is a fluctuating pair density wave, but no
microscopic model has yet been found which supports such a state. In this work,
we write an analytically solvable model to examine pairing phases in the
strongly coupled regime and in the presence of anisotropic interactions.
Already for moderate coupling we find an unusual finite temperature phase,
below an instability temperature $T_i$, where local pair correlations have
non-zero center-of-mass momentum but lack long-range order. At low temperature,
this fluctuating pair density wave can condense either to a uniform $d$-wave
superconductor or the widely postulated pair-density wave phase depending on
the interaction strength. Our minimal model offers a unified microscopic
framework to understand the emergence of both fluctuating and long range pair
density waves in realistic systems.",2110.13138v1
2006-06-10,Spinful bosons in an optical lattice,"We analyze the behavior of cold spin-1 particles with antiferromagnetic
interactions in a one-dimensional optical lattice using density matrix
renormalization group calculations. Correlation functions and the dimerization
are shown and we also present results for the energy gap between ground state
and the spin excited states. We confirm the anticipated phase diagram, with
Mott-insulating regions of alternating dimerized S=1 chains for odd particle
density versus on-site singlets for even density. We find no evidence for any
additional ordered phases in the physically accessible region, however for
sufficiently large spin interaction, on-site singlet pairs dominate leading,
for odd density, to a breakdown of the Mott insulator or, for even density, a
real-space singlet superfluid.",0606265v2
2005-11-28,Pair condensation and bound states in fermionic systems,"We study the finite temperature-density phase diagram of an attractive
fermionic system that supports two-body (dimer) and three-body (trimer) bound
states in free space. Using interactions characteristic for nuclear systems, we
obtain the critical temperature T_c2 for the superfluid phase transition and
the limiting temperature T_c3 for the extinction of trimers. The phase diagram
features a Cooper-pair condensate in the high-density, low-temperature domain
which, with decreasing density, crosses over to a Bose condensate of strongly
bound dimers. The high-temperature, low-density domain is populated by trimers
whose binding energy decreases toward the density-temperature domain occupied
by the superfluid and vanishes at a critical temperature T_c3 > T_c2.",0511076v2
2018-09-22,"Quantum and Coulomb repulsion effects on the bubble structures in $^{204, 206}$Hg","The decreasing proton and charge densities from around 5.0 fm towards the
center of $^{204, 206}$Hg are investigated by a covariant density functional
theory at the beyond mean-field level.The charge-density difference between
$^{208}$Pb and $^{204}$Hg is improved significantly and a central depression is
still visible in the ground-state density of $^{204, 206}$Hg when the dynamic
correlations associated with symmetry restoration and shape mixing are taken
into account. For the $0_2^+$ and $2_1^+$ excited states of $^{204, 206}$Hg,
their densities remain decreasing from 5.0 fm to around 2.0 fm, but become flat
in the interior region. The results show that the bubble structure in $^{204,
206}$Hg within 2.0 fm is mainly attributed to the quantum effect, while that
beyond 2.0 fm is formed by the Coulomb repulsion.",1809.08393v1
2003-07-05,Decoherence in a driven three-level system,"Dissipation and decoherence, and the evolution from pure to mixed states in
quantum physics are handled through master equations for the density matrix.
Master equations such as the Lindblad equation preserve the trace of this
matrix. Viewing them as first-order time-dependent operator equations for the
elements of the density matrix, a unitary integration procedure can be adapted
to solve for these matrix elements. A simple model for decoherence preserves
the hermiticity of the density matrix. A single, classical Riccati equation is
the only one requiring numerical handling to obtain a full solution of the
quantum evolution. The procedure is general, valid for any number of levels,
but is illustrated here for a three-level system with two driving fields. For
various choices of the initial state, we study the evolution of the system as a
function of the amplitudes, relative frequencies and phases of the driven
fields, and of the strength of the decoherence. The monotonic growth of the
entropy is followed as the system evolves from a pure to a mixed state. An
example is provided by the $n=3$ states of the hydrogen atom in a
time-dependent electric field, such degenerate manifolds affording an
analytical solution.",0307039v1
2007-10-12,First-principles prediction of coexistence of magnetism and ferroelectricity in rhombohedral Bi2FeTiO6,"First principles calculations based on the density functional theory within
the local spin density approximation plus U(LSDA+U)scheme, show rhombohedral
Bi$_2$FeTiO$_6$ is a potential multiferroic in which the magnetism and
ferroelectricity coexist . A ferromagnetic configuration with magnetic moment
of 4 $\mu_B$ per formula unit have been reported with respect to the minimum
total energy. Spontaneous polarization of 27.3 $\mu$ C/cm$^2$, caused mainly by
the ferroelectric distortions of Ti, was evaluated using the berry phase
approach in the modern theory of polarization. The Bi-6s stereochemical
activity of long-pair and the `d$^0$-ness' criterion in off-centring of Ti were
coexisting in the predicted new system. In view of the oxidation state of
Bi$^{3+}$,Fe$^{2+}$,Ti$^{4+}$, and O$^{2-}$ from the orbital-resolved density
of states of the Bi-6p, Fe-3d,Ti-3d, and O-2p states,the valence state of
Bi$_2$FeTiO$_6$ in the rhombohedral phase was found to be
Bi$_2$$^{3+}$Fe$^{2+}$Ti$^{4+}$O$_6$.",0710.2391v1
2022-05-22,New conserved integrals and invariants of radial compressible flow in $n>1$ dimensions,"Conserved integrals and invariants (advected scalars) are studied for the
equations of radial compressible fluid/gas flow in $n>1$ dimensions. Apart from
entropy, which is a well-know invariant, three additional invariants are found
from an explicit determination of invariants up to first-order. One holds for a
general equation of state, and the two others hold only for entropic equations
of state. A recursion operator on invariants is presented, which produces two
hierarchies of higher-order invariants. Each invariant yields a corresponding
integral invariant, describing an advected conserved integral on transported
radial domains. In addition, a direct determination of kinematic conserved
densities uncovers two ""hidden"" non-advected conserved integrals: one describes
enthalpy-flux, holding for barotropic equations of state; the other describes
entropy-weighted energy, holding for entropic equations of state. A further
explicit determination of a class of first-order conserved densities shows that
the corresponding non-kinematic conserved integrals on transported radial
domains are equivalent to integral invariants, modulo trivial densities.",2205.10950v2
1996-02-07,Proof of phase separation in the binary-alloy problem: the one-dimensional spinless Falicov-Kimball model,"The ground states of the one-dimensional Falicov-Kimball model are
investigated in the small-coupling limit, using nearly degenerate perturbation
theory. For rational electron and ion densities, respectively equal to
$\frac{p}{q}$, $\frac{p_i}{q}$, with $p$ relatively prime to $q$ and
$\frac{p_i}{q}$ close enough to $\frac{1}{2}$, we find that in the ground state
the ion configuration has period $q$. The situation is analogous to the Peierls
instability where the usual arguments predict a period-$q$ state that produces
a gap at the Fermi level and is insulating. However for $\frac{p_i}{q}$ far
enough from $\frac{1}{2}$, this phase becomes unstable against phase
separation. The ground state is a mixture of a period-$q$ ionic configuration
and an empty (or full) configuration, where both configurations have the same
electron density to leading order. Combining these new results with those
previously obtained for strong coupling, it follows that a phase transition
occurs in the ground state, as a function of the coupling, for ion densities
far enough from $\frac{1}{2}$.",9602042v1
2006-03-02,`Lazy' quantum ensembles,"We compare different strategies aimed to prepare an ensemble with a given
density matrix $\rho$. Preparing the ensemble of eigenstates of $\rho$ with
appropriate probabilities can be treated as `generous' strategy: it provides
maximal accessible information about the state. Another extremity is the
so-called `Scrooge' ensemble, which is mostly stingy to share the information.
We introduce `lazy' ensembles which require minimal efforts to prepare the
density matrix by selecting pure states with respect to completely random
choice.
  We consider two parties, Alice and Bob, playing a kind of game. Bob wishes to
guess which pure state is prepared by Alice. His null hypothesis, based on the
lack of any information about Alice's intention, is that Alice prepares any
pure state with equal probability. Then, the average quantum state measured by
Bob turns out to be $\rho$, and he has to make a new hypothesis about Alice's
intention solely based on the information that the observed density matrix is
$\rho$. The arising `lazy' ensemble is shown to be the alternative hypothesis
which minimizes the Type I error.",0603019v1
2022-04-29,An approximation of the Bayesian state observer with Markov chain Monte Carlo propagation stage,"The state estimation problem for nonlinear systems with stochastic
uncertainties can be formulated in the Bayesian framework, where the objective
is to replace the state completely by its probability density function. Without
the restriction to selected system classes and disturbance properties, the
Bayesian estimator is particularly interesting for highly nonlinear systems
with non-Gaussian noise. The main limitations of Bayesian filters are the
significant computational costs and the implementation problems for higher
dimensional systems. The present paper introduces a piecewise linear
approximation of the Bayesian state observer with Markov chain Monte Carlo
propagation stage and kernel density estimation. These methods are suitable for
the prediction of multivariate probability density functions. The piecewise
linear approximation and the proposed algorithms can increase the estimation
performance at reasonable computational cost. The estimation performance is
demonstrated in a benchmark comparing the Bayesian state observer with an
extended Kalman filter and a particle filter.",2204.14011v1
2022-10-13,Circuit depth versus energy in topologically ordered systems,"We prove a nontrivial circuit-depth lower bound for preparing a low-energy
state of a locally interacting quantum many-body system in two dimensions,
assuming the circuit is geometrically local. For preparing any state which has
an energy density of at most $\epsilon$ with respect to Kitaev's toric code
Hamiltonian on a two dimensional lattice $\Lambda$, we prove a lower bound of
$\Omega\left(\min\left(1/\epsilon^{\frac{1-\alpha}{2}},
\sqrt{|\Lambda|}\right)\right)$ for any $\alpha >0$. We discuss two
implications. First, our bound implies that the lowest energy density
obtainable from a large class of existing variational circuits (e.g.,
Hamiltonian variational ansatz) cannot, in general, decay exponentially with
the circuit depth. Second, if long-range entanglement is present in the ground
state, this can lead to a nontrivial circuit-depth lower bound even at nonzero
energy density. Unlike previous approaches to prove circuit-depth lower bounds
for preparing low energy states, our proof technique does not rely on the
ground state to be degenerate.",2210.06796v1
2023-12-29,Prediction of Magnetic State of UO2 within Hubbard-corrected Density-Functional Theory: A self-consistent approach,"The magnetic state of UO$_2$ was determined experimentally to be
anti-ferromagnetic. Starting from this experimental fact, researchers have
calculated other properties within the Hubbard-corrected density-functional
theory, DFT+U. Up to now, the Hubbard parameters for UO$_2$ were usually so
chosen that the calculations give good results for some experimental data.
Also, to our knowledge there exists no valid theoretical research report on the
energetically stable magnetic state of this system. In present work, employing
the new method which is based on density-functional perturbation theory, we
have determined self-consistently the Hubbard parameters and ground-state
energies for UO$_2$ crystal in both ferromagnetic and anti-ferromagnetic
configurations, and the calculated results show that UO$_2$ crystal
energetically favors an anti-ferromagnetic state with a small energy
difference. In all the calculations the PBE-sol approximation was used for the
exchange-correlation energy functional.",2401.00864v1
2024-02-13,On convertibility among bipartite 2x2 entangled states,"Some progress is reported on conditions for convertibility among bipartite
2x2 entangled states: An inconvertibility condition related to the rank of an
entangled state is given that it is impossible to convert to an entangled state
with lower rank under separable operations; a particular set of local
operations and classical communication (LOCC) is used to analyze convertibility
of three subclasses of states - Werner states, Bell diagonal states and
maximally entangled mixed states (MEMS). It is conjectured that MEMS may lie on
the bottom of entangled state ordering for given entanglement of formation. A
plausible way is suggested of systematically calculating convertibility in a
general subclass of bipartite states whose density matrices are defined to be
diagonal in a common basis. The set of LOCC adopted in this work is argued to
be generalizable to provide sufficient conditions for convertibility among a
large range of general 2x2 entangled states.",2402.08166v1
2008-08-18,"Faranoff-Riley type I jet deceleration at density discontinuities ""Relativistic hydrodynamics with realistic equation of state""","The deceleration mechanisms for relativistic jets in active galactic nuclei
remain an open question, and in this paper we propose a model which could
explain sudden jet deceleration, invoking density discontinuities. This is
particularly motivated by recent indications from HYMORS. Exploiting high
resolution, numerical simulations, we demonstrate that for both high and low
energy jets, always at high Lorentz factor, a transition to a higher density
environment can cause a significant fraction of the directed jet energy to be
lost on reflection. This can explain how one-sided jet deceleration and a
transition to FR I type can occur in HYMORS, which start as FR II (and remain
so on the other side). For that purpose, we implemented in the relativistic
hydrodynamic grid-adaptive AMRVAC code, the Synge-type equation of state
introduced in the general polytropic case by Meliani et al. (2004). We present
results for 10 model computations, varying the inlet Lorentz factor from 10 to
20, including uniform or decreasing density profiles, and allowing for
cylindrical versus conical jet models. As long as the jet propagates through
uniform media, we find that the density contrast sets most of the propagation
characteristics, fully consistent with previous modeling efforts. When the jet
runs into a denser medium, we find a clear distinction in the decelaration of
high energy jets depending on the encountered density jump. For fairly high
density contrast, the jet becomes destabilised and compressed, decelerates
strongly (up to subrelativistic speeds) and can form knots. We point out
differences that are found between cylindrical and conical jet models, together
with dynamical details like the Richtmyer-Meshkov instabilities developing at
the original contact interface.",0808.2492v1
2009-10-04,Color Superconductivity at Large N: A New Hope,"At zero density, the `t Hooft large N_c limit often provides some very useful
qualitative insights into the non-perturbative physics of QCD. However, it is
known that at high densities the `t Hooft large N_c world looks very different
from the N_c=3 world, which is believed to be in a color superconducting phase
at high densities. At large N_c, on the other hand, the DGR instability causes
a chiral-density wave phase to dominate over the color superconducting phase.
There is an alternative large N_c limit, with the quarks transforming in the
two-index antisymmetric representation of the gauge group, which at N_c=3
reduces to QCD but looks quite different at large N_c. We show that in this
alternative large N_c limit, the DGR instability does not occur, so that it may
be plausible that the ground state of high-density quark matter is a color
superconductor even when N_c is large. This revives the hope that a large N_c
approximation might be useful for getting some insights into the high-density
phenomenology of QCD.",0910.0470v1
2011-01-12,Unequal Layer Densities in Bilayer Wigner Crystal at High Magnetic Field,"We report studies of pinning mode resonances of magnetic field induced
bilayer Wigner crystals of bilayer hole samples with negligible interlayer
tunneling and different interlayer separations d, in states with varying layer
densities, including unequal layer densities. With unequal layer densities,
samples with large d relative to the in-plane carrier-carrier spacing a, two
pinning resonances are present, one for each layer. For small d/a samples, a
single resonance is observed even with significant density imbalance. These
samples, at balance, were shown to exhibit an enhanced pinning mode frequency
[Zhihai Wang et al., Phys. Rev. Lett. 136804 (2007)], which was ascribed to a
one-component, pseudospin ferromagnetic Wigner solid. The evolution of the
resonance frequency and line width indicates the quantum interlayer coherence
survives at moderate density imbalance, but disappears when imbalance is
sufficiently large.",1101.2436v1
2015-06-29,A new Phase Space Density for Quantum Expectations,"We introduce a new density for the representation of quantum states on phase
space. It is constructed as a weighted difference of two smooth probability
densities using the Husimi function and first-order Hermite spectrograms. In
contrast to the Wigner function, it is accessible by sampling strategies for
positive densities. In the semiclassical regime, the new density allows to
approximate expectation values to second order with respect to the high
frequency parameter and is thus more accurate than the uncorrected Husimi
function. As an application, we combine the new phase space density with
Egorov's theorem for the numerical simulation of time-evolved quantum
expectations by an ensemble of classical trajectories. We present supporting
numerical experiments in different settings and dimensions.",1506.08880v2
2018-05-01,One-dimensional electron fluid at high density,"We calculate the ground-state energy, pair correlation function, static
structure factor, and momentum density of the one-dimensional electron fluid at
high density using variational quantum Monte Carlo simulation. For an
infinitely thin cylindrical wire the predicted correlation energy is found to
fit nicely with a quadratic function of coupling parameter $r_s$. The extracted
exponent $\alpha$ of the momentum density for $k\sim k_F$ is used to determine
the Tomonaga-Luttinger parameter $K_\rho$ as a function of $r_s$ in the
high-density regime for the first time. We find that the simulated static
structure factor and pair correlation function for infinitely thin wires agree
with our recent high-density theory [K. Morawetz et al., Phys. Rev. B 97,
155147 (2018)].",1805.00344v2
2021-03-02,Quantum oscillations from a pair-density wave,"A pair-density wave state has been suggested to exist in underdoped cuprate
superconductors, with some supporting experimental evidence emerging over the
past few years from scanning tunneling spectroscopy. Several studies have also
linked the observed quantum oscillations in these systems to a reconstruction
of the Fermi surface by a pair-density wave. Here, we show, using semiclassical
analysis and numerical calculations, that a Fermi pocket created by first-order
scattering from a pair-density wave cannot induce such oscillations. In
contrast, pockets resulting from second-order scattering can cause
oscillations. We consider the effects of a finite pair-density wave correlation
length on the signal, and demonstrate that it is only weakly sensitive to
disorder in the form of $\pi$-phase slips. Finally, we discuss our results in
the context of the cuprates and show that a bidirectional pair-density wave may
produce observed oscillation frequencies.",2103.01892v1
2021-05-16,Variations of the Hartree-Fock fractional-spin error for one electron,"Fractional-spin errors are inherent in all current approximate density
functionals, including Hartree-Fock theory, and their origin has been related
to strong static correlation effects. The conventional way to encode
fractional-spin calculations is to construct an ensemble density that scales
between the high-spin and low-spin densities. In this article, we explore the
variation of the Hartree-Fock fractional-spin (or ghost-interaction) error in
one-electron systems using restricted and unrestricted ensemble densities, and
the exact generalized Hartree-Fock representation. By considering the hydrogen
atom and H$_2^+$ cation, we analyze how the unrestricted and generalized
Hartree-Fock schemes minimize this error by localizing the electrons or
rotating the spin coordinates. We also reveal a clear similarity between the
Coulomb hole of He-like ions and the density depletion near the nucleus induced
by the fractional-spin error in the unpolarized hydrogen atom. Finally, we
analyze the effect of the fractional-spin error on the M{\o}ller-Plesset
adiabatic connection, excited states, and functional- and density-driven
errors.",2105.07506v2
2022-06-24,Geometry of Degeneracy in Potential and Density Space,"In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found
counterexamples to the fundamental Hohenberg-Kohn theorem from
density-functional theory in finite-lattice systems represented by graphs.
Here, we demonstrate that this only occurs at very peculiar and rare densities,
those where density sets arising from degenerate ground states, called
degeneracy regions, touch each other or the boundary of the whole density
domain. Degeneracy regions are shown to generally be in the shape of the convex
hull of an algebraic variety, even in the continuum setting. The geometry
arising between density regions and the potentials that create them is analyzed
and explained with examples that, among other shapes, feature the Roman
surface.",2206.12366v3
2023-11-22,Orbital-Free Density Functional Theory with Continuous Normalizing Flows,"Orbital-free density functional theory (OF-DFT) provides an alternative
approach for calculating the molecular electronic energy, relying solely on the
electron density. In OF-DFT, both the ground-state density is optimized
variationally to minimize the total energy functional while satisfying the
normalization constraint. In this work, we introduce a novel approach by
parameterizing the electronic density with a normalizing flow ansatz, which is
also optimized by minimizing the total energy functional. Our model
successfully replicates the electronic density for a diverse range of chemical
systems, including a one-dimensional diatomic molecule, specifically Lithium
hydride with varying interatomic distances, as well as comprehensive
simulations of hydrogen and water molecules, all conducted in Cartesian space.",2311.13518v1
2019-03-15,Spinor bosons in optical superlattices: a numerical study,"The ground state of spin-1 ultracold bosons trapped in a periodic
one-dimensional optical superlattice is studied. The two sites of the unit cell
have an energy shift between them, whose competition with the spin-dependent
strength is the main focus of this paper. Charge density wave (CDW) phases
appear for semi-integer and integer densities, leading to rich phase diagrams
with Mott insulator, superfluid and CDW phases. The spin-dependent interaction
favors insulator phases for integer densities and disfavors CDW phases for
semi-integer densities, which tend to disappear. Also, quantum phase
transitions at finite values of the spin-dependent strength were observed. For
integer densities, Mott insulator-superfluid-CDW insulator transitions appear
for an energy shift lower (higher) than the local repulsion for the global
density $\rho=1$ ($\rho=2$).",1903.10320v2
2022-11-07,Introducing fluctuation-driven order into density functional theory using the quantum order-by-disorder framework,"Density functional theory in the local or semi-local density approximation is
a powerful tool for materials simulation, yet it struggles in many cases to
describe collective electronic order that is driven by electronic interactions.
In this work it is shown how arbitrary, fluctuation-driven electronic order may
be introduced into density functional theory using the quantum
order-by-disorder framework. This is a method of calculating the free energy
correction due to collective spin and charge fluctuations about a state that
hosts static order, in a self-consistent manner. In practical terms, the
quantum order-by-disorder method is applied to the Kohn-Sham auxiliary system
of density functional theory to give an order-dependent correction to the
exchange-correlation functional. Calculation of fluctuation propagators within
density functional theory renders the result fully first-principles. Two types
of order are considered as examples -- fluctuation-driven superconductivity and
spin nematic order -- and implementation schemes are presented in each case.",2211.03717v2
2023-03-08,DANet: Density Adaptive Convolutional Network with Interactive Attention for 3D Point Clouds,"Local features and contextual dependencies are crucial for 3D point cloud
analysis. Many works have been devoted to designing better local convolutional
kernels that exploit the contextual dependencies. However, current point
convolutions lack robustness to varying point cloud density. Moreover,
contextual modeling is dominated by non-local or self-attention models which
are computationally expensive. To solve these problems, we propose density
adaptive convolution, coined DAConv. The key idea is to adaptively learn the
convolutional weights from geometric connections obtained from the point
density and position. To extract precise context dependencies with fewer
computations, we propose an interactive attention module (IAM) that embeds
spatial information into channel attention along different spatial directions.
DAConv and IAM are integrated in a hierarchical network architecture to achieve
local density and contextual direction-aware learning for point cloud analysis.
Experiments show that DAConv is significantly more robust to point density
compared to existing methods and extensive comparisons on challenging 3D point
cloud datasets show that our network achieves state-of-the-art classification
results of 93.6% on ModelNet40, competitive semantic segmentation results of
68.71% mIoU on S3DIS and part segmentation results of 86.7% mIoU on ShapeNet.",2303.04473v1
2023-05-24,Exact and model exchange-correlation potentials for open-shell systems,"The conventional approaches to the inverse density functional theory problem
typically assume non-degeneracy of the Kohn-Sham (KS) eigenvalues, greatly
hindering their use in open-shell systems. We present a generalization of the
inverse density functional theory problem that can seamlessly admit degenerate
KS eigenvalues. Additionally, we allow for fractional occupancy of the
Kohn-Sham orbitals to also handle non-interacting ensemble-v-representable
densities, as opposed to just non-interacting pure-v-representable densities.
We present the exact exchange-correlation (XC) potentials for six open-shell
systems -- four atoms (Li, C, N, and O) and two molecules (CN and
$\text{CH}_2$) -- using accurate ground-state densities from configuration
interaction calculations. We compare these exact XC potentials with model XC
potentials obtained using non-local (B3LYP, SCAN0) and local/semi-local (SCAN,
PBE, PW92) XC functionals. Although the relative errors in the densities
obtained from these DFT functionals are of $\mathcal{O}(10^{-3}-10^{-2})$, the
relative errors in the model XC potentials remain substantially large --
$\mathcal{O}(10^{-1}-10^0)$.",2305.15620v2
2007-11-27,"A study of the breakdown of the quasi-static approximation at high densities and its effect on the helium-like K ALPHA complex of nickel, iron, and calcium","The General Spectral Modeling (GSM) code employs the quasi-static
approximation, a standard, low-density methodology that assumes the ionization
balance is separable from a determination of the excited-state populations that
give rise to the spectra. GSM also allows for some states to be treated only as
contributions to effective rates. While these two approximations are known to
be valid at low densities, this work investigates using such methods to model
high-density, non-LTE emission spectra and determines at what point the
approximations break down by comparing to spectra produced by the LANL code
ATOMIC which makes no such approximations. As both approximations are used by
other astrophysical and low-density modeling codes, the results should be of
broad interest. He-like K$\alpha$ emission spectra are presented for Ni, Fe,
and Ca, in order to gauge the effect of both approximations employed in GSM.
This work confirms that at and above the temperature of maximum abundance of
the He-like ionization stage, the range of validity for both approximations is
sufficient for modeling the low- and moderate-density regimes one typically
finds in astrophysical and magnetically confined fusion plasmas. However, a
breakdown does occur for high densities; we obtain quantitative limits that are
significantly higher than previous works. This work demonstrates that, while
the range of validity for both approximations is sufficient to predict the
density-dependent quenching of the z line, the approximations break down at
higher densities. Thus these approximations should be used with greater care
when modeling high-density plasmas such as those found in inertial confinement
fusion and electromagnetic pinch devices.",0711.4134v1
2014-06-14,Analytical and numerical studies of the one-dimensional sawtooth chain,"By using the analytical coupled cluster method, the numerical exact
diagonalization method, and the numerical density matrix renormalization group
method, we investigated the properties of the one-dimensional sawtooth chain.
The results of the coupled cluster method based on Neel state demonstrate that
the ground state is in the quasi-Neel-long-range order state when a<ac1. The
translational symmetry of the ground state varies and the ground state evolves
from the quasi-Neel-long-range order state to the dimerized state at the
critical point ac1. The dimerized state is stable in the intermediate parameter
regime and vanishes at another critical point ac2. The results drawn from the
exact diagonalization show that the precise critical point ac1 and ac2 can be
determined by using the spin stiffness fidelity susceptibility and spin gap
separately. We compared the results obtained by using the coupled cluster
method based on canted state with those obtained based on spiral state, and
found that the ground state of the sawtooth chain is in the quasi-canted state
if a>ac2. The results of the coupled cluster method and the density matrix
renormalization group method both disclose that the type of the quantum phase
transition occurring at ac2 belongs to the first-order transition.",1406.3686v2
2005-01-07,Centrally Condensed Collapse of Starless Cores,"Models of self-gravitating gas in the early stages of pressure-free collapse
are compared for initial states which are equilibrium layers, cylinders, and
Bonnor-Ebert spheres. For each geometrical case the density profile has an
inner region of shallow slope surrounded by an outer region of steep slope, and
the profile shape during early collapse remains similar to the profile shape of
the initial equilibrium. The two-slope density structure divides the spherical
collapse history into a starless infall phase and a protostellar accretion
phase. The similarity of density profiles implies that Bonnor-Ebert fits to
observed column density maps may not distinguish spherical cores from oblate or
prolate cores, and may not distinguish static cores from collapsing cores. The
velocity profiles discriminate better than the density profiles between initial
geometries and between collapse ages. The infall velocity generally has a
subsonic maximum value, which is approximately equal to the initial velocity
dispersion times the ratio of collapse age to central free-fall time.
  Observations of starless core line profiles constrain collapse models.
Collapse from initial states which are strongly condensed and slightly prolate
is consistent with infall asymmetry observed around starless cores, and is more
consistent than collapse from initial states which are weakly condensed, and/or
oblate. Spherical models match observed inward speeds 0.05-0.09 km/s over
0.1-0.2 pc, if the collapse has a typical age 0.3-0.5 free fall times, and if
it began from a centrally condensed state which was not in stable equilibrium.
In a collapsing core, optically thin line profiles should broaden and develop
two-peak structure as seen in L1544.",0501127v1
2015-07-23,"Emergence of a Kondo singlet state with the Kondo temperature well beyond 1,000K in the proton-embedded electron gas: Possible route to high-Tc superconductivity","Hydrogen in metals has attracted much attention for a long time from both
basic scientific and technological points of view. Its electronic state has
been investigated in terms of a proton embedded in the electron gas mostly by
the local density approximation (LDA) to the density functional theory. At high
electronic densities, it is well described by a bare proton H^+ screened by
metallic electrons (charge resonance), while at low densities two electrons are
localized at the proton site to form a closed-shell negative ion H^- protected
from surrounding metallic electrons by the Pauli exclusion principle. However,
no details are known about the transition from H^+ to H^- in the
intermediate-density region. Here, by accurately determining the ground-state
electron distribution n(r) by the combination of LDA and diffusion Monte Carlo
simulations with the total electron number up to 170, we obtain a complete
picture of the transition, in particular, a sharp transition from short-range
H^+ screening charge resonance to long-range Kondo-like spin-singlet resonance,
the emergence of which is confirmed by the presence of an anomalous Friedel
oscillation characteristic to the Kondo singlet state with the Kondo
temperature T_K well beyond 1,000K. This study not only reveals interesting
competition between charge and spin resonances, enriching the century-old
paradigm of metallic screening to a point charge, but also discovers a
long-sought novel high-T_K system, opening an unexpected route to
room-temperature superconductivity in a Kondo lattice made of protons.",1507.06432v2
2016-06-29,Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids,"We study the many-body phases of bosonic atoms with $N$ internal states
confined to a 1D optical lattice under the influence of a synthetic magnetic
field and strong repulsive interactions. The $N$ internal states of the atoms
are coupled via Raman transitions creating the synthetic magnetic field in the
space of internal spin states corresponding to recent experimental
realisations. We focus on the case of strong $\mbox{SU}(N)$ invariant local
density-density interactions in which each site of the 1D lattice is at most
singly occupied, and strong Raman coupling, in distinction to previous work
which has focused on the weak Raman coupling case. This allows us to keep only
a single state per site and derive a low energy effective spin $1/2$ model. The
effective model contains first-order nearest neighbour tunnelling terms, and
second-order nearest neighbour interactions and correlated next-nearest
neighbour tunnelling terms. By adjusting the flux $\phi$ one can tune the
relative importance of first-order and second-order terms in the effective
Hamiltonian. In particular, first-order terms can be set to zero, realising a
novel model with dominant second-order terms. We show that the resulting
competition between density-dependent tunnelling and repulsive density-density
interaction leads to an interesting phase diagram including a phase with
long-ranged pair-superfluid correlations. The method can be straightforwardly
extended to higher dimensions and lattices of arbitrary geometry including
geometrically frustrated lattices where the interplay of frustration,
interactions and kinetic terms is expected to lead to even richer physics.",1606.09089v2
2019-12-23,Origin of Aggregation-Induced Enhanced Emission: A Role of Pseudo-Degenerate Electronic States of Excimers Formed in Aggregation Phases,"Origin of aggregation-induced enhanced emission (AIEE) is investigated
considering cyano-substituted 1,2-bis(pyridylphenyl)ethene (CNPPE) as an
example. On the basis of ONIOM calculations using the time-dependent density
functional theory (TD-DFT), we found that pseudo-degeneracy of excimers formed
in solid phase plays an important role in the appearance of AIEE. The electron
density difference delocalized over molecules gives rise to small diagonal
vibronic coupling constants (VCCs), which suggests that the internal conversion
is more suppressed in solid phase than in solution phase. The reduction of the
off-diagonal VCCs owing to the packing effect is elucidated by vibronic
coupling density (VCD) analysis. The pseudo-degeneracy enables fluorescence
from the high singlet excited states against Kasha's rule because the electron
density difference and the overlap density between the excited states vanish. A
Hubbard model of a pseudo-degenerate electronic system is constructed to
explain the vanishing mechanism. We propose the following design principle for
AIEE: a candidate molecule for AIEE should have pseudo-degenerate adiabatic
electronic states in the aggregation phases originating from the excimer
formation.",1912.10677v3
2003-09-15,Impurity resonances in the mixed state of high-Tc superconductors,"We study the quasiparticle resonance states near strong impurities in the
mixed state of a d-wave superconductor. These states give rise to zero-bias
peaks in the local density of states, observed in scanning tunneling microscopy
experiments. The field dependence of the peaks is obtained by averaging with
respect to the spatially non-uniform Doppler shifts in the energy of
excitations. The hybridization of the magnetic field-induced nodal
quasiparticles with the impurity resonances results in the suppression and
broadening of the zero-bias peaks. The height of the peaks is found to scale as
\sqrt{Hc2/H}. The magnetic field response of the peaks is shown to be strongly
dependent on the field orientation.",0309355v1
1999-08-19,Induced Emission of Gamma Radiation from Isomeric Nuclei,"We study the possibility to influence the lifetime of nuclear isomeric states
with the aid of incident fluxes of photons. We assume that a nucleus initially
in an isomeric state |i> first absorbs an incident photon of energy E_{ni} to
reach a higher intermediate state |n>, then the state |n> decays to a lower
state |l>. In favorable cases the two-step induced emission rates become equal
to the natural isomeric decay rates for incident power densities of the order
of 10^{10} W cm^{-2}.",9908009v1
2000-02-24,Conditions for manipulation of a set of entangled pure states,"We derive a sufficient condition for a set of pure states, each entangled in
two remote $N$-dimensional systems, to be transformable to
$k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local
operations and classical communication. If $k=N$, the condition is also
necessary. This condition reveals the function of the relative marginal density
operators of the entangled states in the entanglement manipulation without
sufficient information of the initial states.",0002068v1
2001-01-03,Measuring the Quantum State of a Large Angular Momentum,"We demonstrate a general method to measure the quantum state of an angular
momentum of arbitrary magnitude. The (2F+1) x (2F+1) density matrix is
completely determined from a set of Stern-Gerlach measurements with (4F+1)
different orientations of the quantization axis. We implement the protocol for
laser cooled Cesium atoms in the 6S_{1/2}(F=4) hyperfine ground state and apply
it to a variety of test states prepared by optical pumping and Larmor
precession. A comparison of input and measured states shows typical
reconstruction fidelities of about 0.95.",0101017v1
2010-01-30,Gapped state in three-leg $S=1/2$ Heisenberg tube,"We study the ground state of three-leg $S=1/2$ Heisenberg tube using the
density-matrix renormalization group method. The dimerization order-parameter
and spin-excitation gap are calculated in a wide range of leg exchange
interactions. We confirm that a gapped state with the dimerization order is
realized even when the leg exchange interactions are ferromagnetic.
Furthermore, the topological configuration of spin-singlet pairs in the ordered
state is determined from the results of the Berry phase of each spin coupling
as well as the structure factor of singlet-singlet correlation functions. We
find that there exist three kinds of configurations of the valence-bond states
depending on the ratio of leg and rung exchange interactions.",1002.0096v1
2002-03-21,Mesoscopic fluctuations of the Density of States and Conductivity in the middle of the band of Disordered Lattices,"The mesoscopic fluctuations of the Density of electronic States (DoS) and of
the conductivity of two- and three- dimensional lattices with randomly
distributed substitutional impurities are studied. Correlations of the levels
lying above (or below) the Fermi surface, in addition to the correlations of
the levels lying on opposite sides of the Fermi surface, take place at half
filling due to nesting. The Bragg reflections mediate to increase static
fluctuations of the conductivity in the middle of the band which change the
distribution function of the conductivity at half- filling.",0203432v1
1996-03-21,Density Matrix Functional Calculations for Matter in Strong Magnetic Fields: I. Atomic Properties,"We report on a numerical study of the density matrix functional introduced by
Lieb, Solovej and Yngvason for the investigation of heavy atoms in high
magnetic fields. This functional describes {\em exactly} the quantum mechanical
ground state of atoms and ions in the limit when the nuclear charge $Z$ and the
electron number $N$ tend to infinity with $N/Z$ fixed, and the magnetic field
$B$ tends to infinity in such a way that $B/Z^{4/3}\to\infty$. We have
calculated electronic density profiles and ground state energies for values of
the parameters that prevail on neutron star surfaces and compared them with
results obtained by other methods. For iron at $B=10^{12}$ G the ground state
energy differs by less than 2 \% from the Hartree-Fock value. We have also
studied the maximal negative ionization of heavy atoms in this model at various
field strengths. In contrast to Thomas-Fermi type theories atoms can bind
excess negative charge in the density matrix model. For iron at $B=10^{12}$ G
the maximal excess charge in this model corresponds to about one electron.",9603005v1
2004-02-11,Pair Density Wave in the Pseudogap State of High Temperature Superconductors,"Recent scanning tunneling microscopy (STM) experiments of
Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ have shown evidence of real-space
organization of electronic states at low energies in the pseudogap state. We
argue based on symmetry considerations as well as model calculations that the
experimentally observed modulations are due to a density wave of d-wave
Cooper-pairs without global phase coherence. We show that STM measurements can
distinguish a pair-density-wave from more typical electronic modulations such
as those due to charge density wave ordering or scattering from an onsite
periodic potential.",0402323v4
2005-07-20,"Spin, charge, and orbital correlations in the one-dimensional t2g-orbital Hubbard model","We present the zero-temperature phase diagram of the one-dimensional
t2g-orbital Hubbard model, obtained using the density-matrix renormalization
group and Lanczos techniques. Emphasis is given to the case for the electron
density n=5 corresponding to five electrons per site, of relevance for some
Co-based compounds. However, several other cases for electron densities between
n=3 and 6 are also studied. At n=5, our results indicate a first-order
transition between a paramagnetic (PM) insulator phase and a fully-polarized
ferromagnetic (FM) state by tuning the Hund's coupling. The results also
suggest a transition from the n=5 PM insulator phase to a metallic regime by
changing the electron density, either via hole or electron doping. The behavior
of the spin, charge, and orbital correlation functions in the FM and PM states
are also described in the text and discussed. The robustness of these two
states varying parameters suggests that they may be of relevance in more
realistic higher dimensional systems as well.",0507472v1
2005-09-29,Superconductivity in the charge-density-wave state of the organic metal α-(BEDT-TTF)2KHg(SCN)4,"The superconducting transition in the layered organic compound
\alpha-(BEDT-TTF)_2KHg(SCN)_4 has been studied in the two hydrostatic pressure
regimes where a charge-density wave is either present or completely suppressed.
Within the charge-density-wave state the experimental results reveal a network
of weakly coupled superconducting regions. This is especially seen in a strong
enhancement of the measured critical field and the corresponding positive
curvature of its temperature dependence. Further, it is shown that on lowering
the pressure into the density-wave state traces of a superconducting phase
already start to appear at a much higher temperature.",0509769v1
2010-08-05,Preformed excitonic liquid route to a charge density wave in 2H-TaSe$_2$,"Recent experiments on 2H-TaSe$_2$ contradict the long-held view of the charge
density wave arising from a nested band structure. An intrinsically strong
coupling view, involving a charge density wave state arising as a Bose
condensation of preformed excitons emerges as an attractive, albeit scantily
investigated alternative. Using local density approximation plus multiorbital
dynamic mean-field theory, we show that this scenario agrees with a variety of
normal state data for 2H-TaSe$_{2}$. Based thereupon, the ordered states in a
subset of dichalcogenides should be viewed as instabilities of a correlated,
preformed excitonic liquid.",1008.0942v3
2012-12-06,Thermodynamic extension of density-functional theory. III. Zero-temperature limit of the ensemble spin-density functional theory,"In this work, the zero-temperature limit of the thermodynamic spin-density
functional theory is investigated. The coarse-grained approach to the
equilibrium density operator is used to describe the equilibrium state. The
characteristic functions of a macrostate are introduced and their
zero-temperature limits are investigated. A detailed discussion of the
spin-grand-canonical ensemble in the entropy and energy representations is
performed. The maps between the state function variables at 0K limit are
rigorously studied for both representations. In the spin-canonical ensemble,
the energy surface and the discontinuity pattern are investigated. Finally,
based on the maps between the state function variables at 0K limit, the
Hohenberg-Kohn theorem for the systems with non-integer electron and spin
numbers at zero-temperature limit is formulated.",1212.1367v2
2015-03-24,Gluino Coannihilation Revisited,"Some variants of the MSSM feature a strip in parameter space where the
lightest neutralino is identified as the lightest supersymmetric particle
(LSP), the gluino is the next-to-lightest supersymmetric particle (NLSP) and is
nearly degenerate with the LSP, and the relic cold dark matter density is
brought into the range allowed by astrophysics and cosmology by coannihilation
with the gluino NLSP. We calculate the relic density along this gluino
coannihilation strip in the MSSM, including the effects of gluino-gluino bound
states and initial-state Sommerfeld enhancement, and taking into account the
decoupling of the gluino and LSP densities that occurs for large values of the
squark mass. We find that bound-state effects can increase the maximum LSP mass
for which the relic cold dark matter density lies within the range favoured by
astrophysics and cosmology by as much as ~ 50% if the squark to gluino mass
ratio is 1.1, and that the LSP may weigh up to ~ 8 TeV for a wide range of the
squark to gluino mass ratio \lesssim 100.",1503.07142v2
2015-10-25,Explicit constructions of all separable two-qubits density matrices and related problems for three-qubits systems,"Explicitly separable density matrices are constructed for all separable
two-qubits states based on Hilbert-Schmidt (HS) decompositions. For density
matrices which include only two-qubits correlations the number of HS parameters
is reduced to 3 by using local rotations, and for two-qubits states which
include single qubit measurements, the number of parameters is reduced to 4 by
local Lorentz transformations. For both cases we related the absolute values of
the HS parameters to probabilities, and the outer products of various Pauli
matrices were transformed to pure states density matrices products. Simple
necessary and sufficient conditions for separability are derived. We discuss
related problems for three qubits. For n-qubits correlation systems the
sufficient condition for separability may be improved by local transformations,
related to high order singular value decompositions.",1510.07222v2
2017-03-22,Quantum spin Hall density wave insulator of correlated fermions,"We present the theory of a new type of topological quantum order which is
driven by the spin-orbit density wave order parameter, and distinguished by
$Z_2$ topological invariant. We show that when two oppositely polarized chiral
bands [resulting from the Rashba-type spin-orbit coupling $\alpha_k$, $k$ is
crystal momentum] are significantly nested by a special wavevector ${\bf
Q}\sim(\pi,0)/(0,\pi)$, it induces a spatially modulated inversion of the
chirality ($\alpha_{k+Q}=\alpha_k^*$) between different sublattices. The
resulting quantum order parameters break translational symmetry, but preserve
time-reversal symmetry. It is inherently associated with a $Z_2$-topological
invariant along each density wave propagation direction. Hence it gives a weak
topological insulator in two dimensions, with even number of spin-polarized
boundary states. This phase is analogous to the quantum spin-Hall state, except
here the time-reversal polarization is spatially modulated, and thus it is
dubbed quantum spin-Hall density wave (QSHDW) state. This order parameter can
be realized or engineered in quantum wires, or quasi-2D systems, by tuning the
spin-orbit couping strength and chemical potential to achieve the special
nesting condition.",1703.07629v1
2020-05-18,Construction and heat kernel estimates of general stable-like Markov processes,"A stable-like process is a Feller process $(X_t)_{t\geq 0}$ taking values in
$\mathbb{R}^d$ and whose generator behaves, locally, like an $\alpha$-stable
L\'evy process, but the index $\alpha$ and all other characteristics may depend
on the state space. More precisely, the jump measure need not to be symmetric
and it strongly depends on the current state of the process; moreover, we do
not require the gradient term to be dominated by the pure jump part. Our
approach is to understand the above phenomena as suitable microstructural
perturbations.
  We show that the corresponding martingale problem is well-posed, and its
solution is a strong Feller process which admits a transition density. For the
transition density we obtain a representation as a sum of an explicitly given
principal term -- this is essentially the density of an $\alpha$-stable random
variable whose parameters depend on the current state $x$ -- and a residual
term; the $L^\infty\otimes L^1$-norm of the residual term is negligible and so
is, under an additional structural assumption, the $L^\infty\otimes
L^\infty$-norm. Concrete examples illustrate the relation between the
assumptions and possible transition density estimates.",2005.08491v1
2021-01-01,Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of strained graphene,"We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT)
transition temperature for highly unconventional superconducting states with
the coexistence of chiral d-wave superconductivity, charge density waves and
pair density waves in the strained graphene. Our results show that the
strain-induced flat bands can promote the superconducting transition
temperature approximately $50\%$ compared to that of the original doped
graphene, which suggests that the flat-band superconductivity is a potential
route to get superconductivity with higher critical temperatures. In
particular, we obtain the superfluid weight for the pure superconducting
pair-density-wave states from which the deduced superconducting transition
temperature is shown to be much lower than the gap-opening temperature of the
pair density wave, which is helpful to understand the phenomenon of the
pseudogap state in high-$T_c$ cuprate superconductors. Finally, we show that
the BKT transition temperature versus doping for strained graphene exhibits a
dome-like shape and it depends linearly on the spin-spin interaction strength.",2101.00192v1
2021-12-22,Method for Generating Randomly Perturbed Density Operators Subject to Different Sets of Constraints,"This paper presents a general method for producing randomly perturbed density
operators subject to different sets of constraints. The perturbed density
operators are a specified ""distance"" away from the state described by the
original density operator. This approach is applied to a bipartite system of
qubits and used to examine the sensitivity of various entanglement measures on
the perturbation magnitude. The constraint sets used include constant energy,
constant entropy, and both constant energy and entropy. The method is then
applied to produce perturbed random quantum states that correspond with those
obtained experimentally for Bell states on the IBM quantum device ibmq_manila.
The results show that the methodology can be used to simulate the outcome of
real quantum devices where noise, which is important both in theory and
simulation, is present.",2112.12247v2
2022-09-09,"Excitonic density-waves, bi-excitons and orbital selective pairing in two-orbital correlated chains","We present a comprehensive study of a one-dimensional two-orbital model at
and below quarter-filling that realizes a number of unconventional phases. In
particular, we find an excitonic density wave in which excitons quasi-condense
with finite center of mass momentum and an order parameter that changes phase
with wave-vector $Q$. In this phase, excitons behave as hard-core bosons
without charge order. In addition, excitons can pair to form bi-excitons in a
state that is close to a charge density-wave instability. When pairing
dominates over the inter-orbital repulsion, we encounter a regime in which one
orbital is metallic, while the other forms a spin gapped superconductor, a
genuine orbital selective paired state. All these results are supported by
both, analytical and numerical calculations. By assuming a quasi-classical
approximation, we solve the three-body hole-electron-spinon problem and show
that excitons are held together by forming a bound state with spinons. In order
to preserve the antiferromagnetic background, excitons acquire a dispersion
that has a minimum away from $k=0$. The full characterization of the different
phases is obtained by means of extensive density matrix renormalization group
calculations.",2209.04094v1
2023-11-25,D-Wave and Pair-Density-Wave Superconductivity in the Square-Lattice t-J Model,"The Hubbard and closely related t-J models are exciting platforms for
unconventional superconductivity. Through state-of-the-art density matrix
renormalization group calculations using the grand canonical ensembles, we
address open issues regarding the ground-state phase diagram of the extended
t-J model on a square lattice in the parameter regime relevant to cuprate
superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J
model with only nearest-neighbor hoppings and superexchange interactions, for a
wide range of hole doping ($\delta = 0.1 - 0.2$), hosts an exotic SC state
where the d-wave and unidirectional pair density wave SC co-exist with spin and
charge bond orders. Furthermore, a small next nearest neighbor hopping $t_2$
suppresses the pair density wave and other co-coexisting orders, leading to a
d-wave SC phase in both electron- and hole-doped cuprate model systems. We
reveal a simple mechanism for SC in the t-J model, in which the nearest
neighbor hopping plays an essential role in driving the formation of Cooper
pairs with real-space sign oscillations balancing the competition between the
kinetic and exchange energies. Our work validates the t-J model as a proper
minimum model for describing fundamental physics of cuprate superconductors",2311.15092v2
2010-12-31,Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores,"Almost all time-dependent density-functional theory (TDDFT) calculations of
excited states make use of the adiabatic approximation, which implies a
frequency-independent exchange-correlation kernel that limits applications to
one-hole/one-particle states. To remedy this problem, Maitra et
al.[J.Chem.Phys. 120, 5932 (2004)] proposed dressed TDDFT (D-TDDFT), which
includes explicit two-hole/two-particle states by adding a frequency-dependent
term to adiabatic TDDFT. This paper offers the first extensive test of D-TDDFT,
and its ability to represent excitation energies in a general fashion. We
present D-TDDFT excited states for 28 chromophores and compare them with the
benchmark results of Schreiber et al.[J.Chem.Phys. 128, 134110 (2008).] We find
the choice of functional used for the A-TDDFT step to be critical for
positioning the 1h1p states with respect to the 2h2p states. We observe that
D-TDDFT without HF exchange increases the error in excitations already
underestimated by A-TDDFT. This problem is largely remedied by implementation
of D- TDDFT including Hartree-Fock exchange.",1101.0291v1
2016-03-16,Negativity in the Generalized Valence Bond Solid State,"Using a graphical presentation of the spin $S$ one dimensional Valence Bond
Solid (VBS) state, based on the representation theory of the $SU(2)$
Lie-algebra of spins, we compute the spectrum of a mixed state reduced density
matrix. This mixed state of two blocks of spins $A$ and $B$ is obtained by
tracing out the spins outside $A$ and $B$, in the pure VBS state density
matrix. We find in particular that the negativity of the mixed state is
non-zero only for adjacent subsystems. The method introduced here can be
generalized to the computation of entanglement properties in Levin-Wen models,
that possess a similar algebraic structure to the VBS state in the groundstate.",1603.05185v1
2020-03-27,Efficient description of many-body systems with Matrix Product Density Operators,"Matrix Product States form the basis of powerful simulation methods for
ground state problems in one dimension. Their power stems from the fact that
they faithfully approximate states with a low amount of entanglement, the ""area
law"". In this work, we establish the mixed state analogue of this result: We
show that one-dimensional mixed states with a low amount of entanglement,
quantified by the entanglement of purification, can be efficiently approximated
by Matrix Product Density Operators (MPDOs). In combination with results
establishing area laws for thermal states, this helps to put the use of MPDOs
in the simulation of thermal states on a formal footing.",2003.12418v1
2021-12-15,Inhomogeneous superconducting states in two weakly linked superconducting ultra thin films,"A sufficiently large parallel magnetic field will generate staggered
supercurrent loops and superfluid density wave in two weakly linked
superconducting (SC) ultrathin films, resulting in an inhomogeneous
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The SC order parameter of such
an FFLO state is characterized by Bloch wave functions, called the ""Bloch SC
state"". The staggered supercurrent loops form an array of Josephson
vortex-antivortex pairs, instead of the usual Josephson vortex lattice.
Enclosing a unit cell of the array, the London's fluxoid is quantized as
$\Phi^{\prime}=\Phi_0=hc/2e$, while the net orbital magnetization caused by the
staggered supercurrent is zero. Meanwhile, a small parallel magnetic field
gives rise to an Fulde-Ferrell (FF) state that has uniform superfluid density.
The phase transition between the Bloch SC state and the FF state belongs to the
universality class of two-dimensional commensurate-incommensurate transitions.
An analytical solution in terms of Jacobian elliptic functions is found to be
an excellent approximation to the Bloch SC order parameter.",2112.08190v2
2024-03-28,Quantum circuit design for mixture and preparation of arbitrary pure and mixed quantum states,"This paper addresses the challenge of preparing arbitrary mixed quantum
states, an area that has not been extensively studied compared to pure states.
Two circuit design methods are presented: one via a mixture of pure states and
the other via purification. A novel strategy utilizing the Cholesky
decomposition is proposed to improve both computational efficiency during
preprocessing and circuit efficiency in the resulting circuits, offering
significant advantages, especially when the targeted density matrix is
low-ranked or sparse. By leveraging the incomplete Cholesky decomposition with
threshold dropping, we also propose an appealing strategy for generating a
high-fidelity approximation of the targeted density matrix, enabling
substantial efficiency enhancement at the cost of mild fidelity loss.
Additionally, as a closely related issue, we prove the ""no-superposing
theorem"": given a certain number of arbitrary unknown pure states as input, it
is impossible to devise an operation that produces an output state as the
superposition of the input states with predefined coefficients unless all but
one of the coefficients vanish.",2403.19172v1
2000-02-18,Robustness of Wave Functions of Interacting Many Bosons in a Leaky Box,"We study the robustness, against the leakage of bosons, of wave functions of
interacting many bosons confined in a finite box, by deriving and analyzing a
general equation of motion for the reduced density operator. We identify a
robust wave function that remains a pure state, whereas other wave functions,
such as the Bogoliubov's ground state and the ground state with a fixed number
of bosons, evolve into mixed states. Although these states all have the
off-diagonal long-range order, and almost the same energy densities, we argue
that only the robust state is realized as a macroscopic quantum state.",0002052v3
2014-06-27,Stationary states in 2D systems driven by bi-variate Lévy noises,"Systems driven by $\alpha$-stable noises could be very different from their
Gaussian counterparts. Stationary states in single-well potentials can be
multimodal. Moreover, a potential well needs to be steep enough in order to
produce stationary states. Here, it is demonstrated that 2D systems driven by
bi-variate $\alpha$-stable noises are even more surprising than their 1D
analogs. In 2D systems, intriguing properties of stationary states originate
not only due to heavy tails of noise pulses, which are distributed according to
$\alpha$-stable densities, but also because of properties of spectral measures.
Consequently, 2D systems are described by a whole family of Langevin and
fractional diffusion equations. Solutions of these equations bear some common
properties but also can be very different. It is demonstrated that also for 2D
systems potential wells need to be steep enough in order to produce bounded
states. Moreover, stationary states can have local minima at the origin. The
shape of stationary states reflects symmetries of the underlying noise, i.e.
its spectral measure. Finally, marginal densities in power-law potentials also
have power-law asymptotics.",1406.7103v1
1998-09-30,Localization of spinwaves in the quantum Hall ferromagnet,"The quantum Hall ferromagnet at filling fraction $\nu = 1$ has some unusual
properties due to the remarkable identity between the topological density of a
spin distortion and the associated electrical charge density. We investigate
the localization of spinwaves by coupling to a scalar disorder potential via
their topological density. A low energy description of the system in terms of a
non-linear sigma model of unitary supermatrices is derived. All states of this
model are localized in two dimensions. A possible experimental signature of
these effects in photo-luminescence is suggested.",9809406v1
2003-12-05,Charge-density Waves Survive the Pauli Paramagnetic Limit,"Measurements of the resistance of single crystals of (Per)$_2$Au(mnt)$_2$
have been made at magnetic fields $B$ of up to 45 T, exceeding the Pauli
paramagnetic limit of $B_{\rm P}\approx 37$ T. The continued presence of
non-linear charge-density wave electrodynamics at $B \geq 37$ T unambiguously
establishes the survival of the charge-density wave state above the Pauli
paramagnetic limit, and the likely emergence of an inhomogeneous phase
analogous to that anticipated to occur in superconductors.",0312142v1
2005-09-07,Phases of QCD,"In these lectures we provide an introduction to the phase structure of QCD.
We begin with a brief discussion of QCD, the symmetries of QCD, and what we
mean by a ``phase of QCD''. In the main part of the lectures we discuss the
phase diagram of QCD as a function of the temperature and the baryon density.
We focus, in particular, on the high temperature plasma phase, the low
temperature and low density nuclear phase, and the high density color
superconducting phases.",0509068v1
2006-06-24,Superprocesses with Dependent Spatial Motion and General Branching Densities,"We construct a class of superprocesses by taking the high density limit of a
sequence of interacting-branching particle systems. The spatial motion of the
superprocess is determined by a system of interacting diffusions, the branching
density is given by an arbitrary bounded non-negative Borel function, and the
superprocess is characterized by a martingale problem as a diffusion process
with state space $M(\IR)$, improving and extending considerably the
construction of Wang (1997, 1998). It is then proved in a special case that a
suitable rescaled process of the superprocess converges to the usual super
Brownian motion. An extension to measure-valued branching catalysts is also
discussed.",0606615v1
2004-07-15,Operator-sum representation of time-dependent density operators and its applications,"We show that any arbitrary time-dependent density operator of an open system
can always be described in terms of an operator-sum representation regardless
of its initial condition and the path of its evolution in the state space, and
we provide a general expression of Kraus operators for arbitrary time-dependent
density operator of an $N$-dimensional system. Moreover, applications of our
result are illustrated through several examples.",0407111v1
2011-05-25,Nuclear matter within a dilatation-invariant parity doublet model: the role of the tetraquark at nonzero density,"We investigate the role of a scalar tetraquark state for the description of
nuclear matter within the parity doublet model in the mirror assignment. In the
dilatation-invariant version of the model a nucleon-nucleon interaction term
mediated by the lightest scalar tetraquark field naturally emerges. At nonzero
density one has, beyond the usual chiral condensate, also a tetraquark
condensate. The behavior of both condensates and the restoration of chiral
symmetry at high density are studied. It is shown that this additional scalar
degree of freedom affects non negligibly the properties of the medium.",1105.5003v1
2011-08-30,Effect of density dependent symmetry energy on Elliptical flow,"The effect of the density dependent symmetry energy on elliptical flow is
studied using isospin-dependent quantum molecular dynamics model(IQMD). We have
used the reduced isospin-dependent cross-section with soft equation of state to
study the sensitivity of elliptical flow towards symmetry energy. Aim of the
present study is to pin down the Elliptical flow for the various forms of the
density dependent symmetry energy.",1108.5836v1
2013-06-10,Magnetization and collective excitations of a magnetic dipole fermion gas,"The ground states and collective excitations of trapped Fermion gases
consisting of atoms with magnetic dipole moment are studied using a
time-dependent density-matrix approach. The advantages of the density-matrix
approach are that one-body and two-body observables are directly calculated
using one-body and two-body density matrices and that it has a clear relation
to the Hartree-Fock (HF) and time-dependent HF theory. The HF calculations show
the magnetization of the gases when the dipole-dipole interaction is strong. It
is shown that the tensor properties of the dipole-dipole interaction are
revealed in the excitation modes associated with spin degrees of freedom.",1306.2078v1
2015-03-09,Relativistic Modeling of Quark Stars with Tolman IV Type Potential,"In this paper, we studied the behavior of relativistic objects with
anisotropic matter distribution considering Tolman IV form for the
gravitational potential Z. The equation of state presents a quadratic relation
between the energy density and the radial pressure. New exact solutions of the
Einstein-Maxwell system are generated. A physical analysis of electromagnetic
field indicates that is regular in the origin and well behaved. We show as the
presence of an electrical field modifies the energy density, the radial
pressure and the mass of the stellar object and generates a singular charge
density.",1503.06678v1
2022-08-17,Brillouin propagation modes of cold atoms in dissipative optical lattices,"An exact series expansion of the average velocity of cold atoms in
dissipative optical lattices under probe driving, based on the amplitudes of
the excited atomic density waves, is derived from the semiclassical equations
for the phase space densities of the Zeeman ground-state sublevels. This
expansion permits the identification of the precise contribution to the current
of a propagating atomic wave for the specific driving, as well as providing the
general threshold for the transition into the regime of infinite density.",2208.08206v2
2002-12-11,Nuclear energy density functional from chiral pion-nucleon dynamics,"We calculate the nuclear energy density functional relevant for N=Z even-even
nuclei in the systematic framework of chiral perturbation theory. The
calculation includes the one-pion exchange Fock diagram and the iterated
one-pion exchange Hartree and Fock diagrams. From these few leading order
contributions in the small momentum expansion one obtains already a very good
equation of state of isospin symmetric nuclear matter. We find that in the
region below nuclear matter saturation density the effective nucleon mass
$\widetilde M^*(\rho)$ deviates by at most 15% from its free space value $M$,
with $0.89M<\widetilde M^*(\rho)<M$ for $\rho < 0.11 {\rm fm}^{-3}$ and
$\widetilde M^*(\rho)>M$ for higher densities. The parameterfree strength of
the $(\vec\nabla \rho)^2$-term, $F_\nabla(k_f)$, is at saturation density
comparable to that of phenomenological Skyrme forces. The magnitude of
$F_J(k_f)$ accompanying the squared spin-orbit density $\vec J ^2$ comes out
somewhat larger. The strength of the nuclear spin-orbit interaction,
$F_{so}(k_f)$, as given by iterated one-pion exchange is about half as large as
the corresponding empirical value, however, with the wrong negative sign. The
novel density dependencies of $\widetilde M^*(\rho)$ and $F_{\nabla,so,J}(k_f)$
as predicted by our parameterfree calculation should be examined in nuclear
structure calculations (after introducing an additional short range spin-orbit
contribution constant in density).",0212049v1
2015-09-24,Motor protein accumulation on antiparallel microtubule overlaps,"Biopolymers serve as one-dimensional tracks on which motor proteins move to
perform their biological roles. Motor protein phenomena have inspired
theoretical models of one-dimensional transport, crowding, and jamming.
Experiments studying the motion of Xklp1 motors on reconstituted antiparallel
microtubule overlaps demonstrated that motors recruited to the overlap walk
toward the plus end of individual microtubules and frequently switch between
filaments. We study a model of this system that couples the totally asymmetric
simple exclusion process (TASEP) for motor motion with switches between
antiparallel filaments and binding kinetics. We determine steady-state motor
density profiles for fixed-length overlaps using exact and approximate
solutions of the continuum differential equations and compare to kinetic Monte
Carlo simulations. Overlap motor density profiles and motor trajectories
resemble experimental measurements. The phase diagram of the model is similar
to the single-filament case for low switching rate, while for high switching
rate we find a new low density-high density-low density-high density phase. The
overlap center region, far from the overlap ends, has a constant motor density
as one would naively expect. However, rather than following a simple binding
equilibrium, the center motor density depends on total overlap length, motor
speed, and motor switching rate. The size of the crowded boundary layer near
the overlap ends is also dependent on the overlap length and switching rate in
addition to the motor speed and bulk concentration. The antiparallel
microtubule overlap geometry may offer a previously unrecognized mechanism for
biological regulation of protein concentration and consequent activity.",1509.07219v3
2019-04-06,Towards Locally Consistent Object Counting with Constrained Multi-stage Convolutional Neural Networks,"High-density object counting in surveillance scenes is challenging mainly due
to the drastic variation of object scales. The prevalence of deep learning has
largely boosted the object counting accuracy on several benchmark datasets.
However, does the global counts really count? Armed with this question we dive
into the predicted density map whose summation over the whole regions reports
the global counts for more in-depth analysis. We observe that the object
density map generated by most existing methods usually lacks of local
consistency, i.e., counting errors in local regions exist unexpectedly even
though the global count seems to well match with the ground-truth. Towards this
problem, in this paper we propose a constrained multi-stage Convolutional
Neural Networks (CNNs) to jointly pursue locally consistent density map from
two aspects. Different from most existing methods that mainly rely on the
multi-column architectures of plain CNNs, we exploit a stacking formulation of
plain CNNs. Benefited from the internal multi-stage learning process, the
feature map could be repeatedly refined, allowing the density map to approach
the ground-truth density distribution. For further refinement of the density
map, we also propose a grid loss function. With finer local-region-based
supervisions, the underlying model is constrained to generate locally
consistent density values to minimize the training errors considering both the
global and local counts accuracy. Experiments on two widely-tested object
counting benchmarks with overall significant results compared with
state-of-the-art methods demonstrate the effectiveness of our approach.",1904.03373v1
2020-11-09,Bayesian bandwidth estimation for local linear fitting in nonparametric regression models,"This paper presents a Bayesian sampling approach to bandwidth estimation for
the local linear estimator of the regression function in a nonparametric
regression model. In the Bayesian sampling approach, the error density is
approximated by a location-mixture density of Gaussian densities with means the
individual errors and variance a constant parameter. This mixture density has
the form of a kernel density estimator of errors and is referred to as the
kernel-form error density (c.f., Zhang et al., 2014). While Zhang et al. (2014)
use the local constant (also known as the Nadaraya- Watson) estimator to
estimate the regression function, we extend this to the local linear estimator,
which produces more accurate estimation. The proposed investigation is
motivated by the lack of data-driven methods for simultaneously choosing
bandwidths in the local linear estimator of the regression function and
kernel-form error density. Treating bandwidths as parameters, we derive an
approximate (pseudo) likelihood and a posterior. A simulation study shows that
the proposed bandwidth estimation outperforms the rule-of-thumb and
cross-validation methods under the criterion of integrated squared errors. The
proposed bandwidth estimation method is validated through a nonparametric
regression model involving firm ownership concentration, and a model involving
state-price density estimation.",2011.04155v1
2023-12-19,Domain Generalization in LiDAR Semantic Segmentation Leveraged by Density Discriminative Feature Embedding,"While significant progress has been achieved in LiDAR-based perception,
domain generalization continues to present challenges, often resulting in
reduced performance when encountering unfamiliar datasets due to domain
discrepancies. One of the primary hurdles stems from the variability of LiDAR
sensors, leading to inconsistencies in point cloud density distribution. Such
inconsistencies can undermine the effectiveness of perception models. We
address this challenge by introducing a new approach that acknowledges a
fundamental characteristic of LiDAR: the variation in point density due to the
distance from the LiDAR to the scene, and the number of beams relative to the
field of view. Understanding this, we view each LiDAR's point cloud at various
distances as having distinct density distributions, which can be consistent
across different LiDAR models. With this insight, we propose the Density
Discriminative Feature Embedding (DDFE) module, crafted to specifically extract
features related to density while ensuring domain invariance across different
LiDAR sensors. In addition, we introduce a straightforward but effective
density augmentation technique, designed to broaden the density spectrum and
enhance the capabilities of the DDFE. The proposed DDFE stands out as a
versatile and lightweight domain generalization module. It can be seamlessly
integrated into various 3D backbone networks, consistently outperforming
existing state-of-the-art domain generalization approaches. We commit to
releasing the source code publicly to foster community collaboration and
advancement.",2312.12098v1
2013-02-25,Periodicity of the time-dependent Kohn-Sham equation and the Floquet theorem,"The Floquet theorem allows to reformulate periodic time-dependent problems
such as the interaction of a many-body system with a laser field in terms of
time-independent, field-dressed states, also known as Floquet states. If this
was possible for density functional theory as well, one could reduce in such
cases time-dependent density functional theory to a time-independent Floquet
density functional theory. We analyze under which conditions the Floquet
theorem is applicable in a density-functional framework. By employing numerical
{\em ab initio} solutions of the interacting time-dependent Schr\""odinger
equation with time-periodic external potentials we show that the exact
effective potential in the corresponding Kohn-Sham equation is {\em not}
unconditionally periodic. Whenever several Floquet states in the interacting
system are involved in a physical process the corresponding
Hartree-exchange-correlation potential is not periodic with the external
frequency only. Using an analytically solvable example we demonstrate that, in
general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be
restored by choosing a different initial state. Only if the external periodic
potential is sufficiently weak such that the initial state of the interacting
system evolves adiabatically to a single, field-dressed state, the resulting
Kohn-Sham system admits the application of the Floquet theorem.",1302.6112v1
2015-09-30,Two-state Bogoliubov theory of a molecular Bose gas,"We present an analytic Bogoliubov description of a BEC of polar molecules
trapped in a quasi-2D geometry and interacting via internal state-dependent
dipole-dipole interactions. We derive the mean-field ground-state energy
functional, and we derive analytic expressions for the dispersion relations,
Bogoliubov amplitudes, and dynamic structure factors. This method can be
applied to any homogeneous, two-component system with linear coupling, and
direct, momentum-dependent interactions. The properties of the mean-field
ground state, including polarization and stability, are investigated, and we
identify three distinct instabilities: a density-wave rotonization that occurs
when the gas is fully polarized, a spin-wave rotonization that occurs near zero
polarization, and a mixed instability at intermediate fields. These
instabilities are clarified by means of the real-space density-density
correlation functions, which characterize the spontaneous fluctuations of the
ground state, and the momentum-space structure factors, which characterize the
response of the system to external perturbations. We find that the gas is
susceptible to both density-wave and spin-wave response in the polarized limit
but only a spin-wave response in the zero-polarization limit. These results are
relevant for experiments with rigid rotor molecules such as RbCs,
$\Lambda$-doublet molecules such as ThO that have an anomalously small
zero-field splitting, and doublet-$\Sigma$ molecules such as SrF where two
low-lying opposite-parity states can be tuned to zero splitting by an external
magnetic field.",1509.09268v1
2000-12-16,Inhomogeneous Pairing in Highly Disordered s-wave Superconductors,"We study a simple model of a two-dimensional s-wave superconductor in the
presence of a random potential in the regime of large disorder. We first use
the Bogoliubov-de Gennes (BdG) approach to show that, with increasing disorder
the pairing amplitude becomes spatially inhomogeneous, and the system cannot be
described within conventional approaches for studying disordered
superconductors which assume a uniform order parameter. In the high disorder
regime, we find that the system breaks up into superconducting islands (with
large pairing amplitude) separated by an insulating sea. We show that this
inhomogeneity has important implications for the physical properties of this
system, such as superfluid density and the density of states. We find that a
finite spectral gap persists in the density of states for all values of
disorder and we provide a detailed understanding of this remarkable result. We
next generalize Anderson's idea of the pairing of exact eigenstates to include
an inhomogeneous pairing amplitude, and show that it is able to qualitatively
capture many of the nontrivial features of the full BdG analysis. Finally, we
study the transition to a gapped insulating state driven by the quantum phase
fluctuations about the inhomogeneous superconducting state.",0012304v1
2008-12-19,Two-dimensional weakly interacting Bose gas: equation of state,"The equation of state of a weakly interacting two-dimensional Bose gas is
studied at zero temperature by means of quantum Monte Carlo methods. Going down
to as low densities as na^2 ~ 10^{-100} permits us for the first time to obtain
agreement on beyond mean-field level between predictions of perturbative
methods and direct many-body numerical simulation, thus providing an answer to
the fundamental question of the equation of state of a two-dimensional dilute
Bose gas in the universal regime (i.e. entirely described by the gas parameter
na^2). We also show that the measure of the frequency of a breathing collective
oscillation in a trap at very low densities can be used to test the universal
equation of state of a two-dimensional Bose gas.",0812.3844v2
2013-09-23,Exciton fission via ultrafast long-range resonant tunnelling in organic photovoltaic diodes,"We present an exciton/lattice model of the electronic dynamics of primary
photoexcitations in a polymeric semiconductor heterojunction which includes
both polymer pi-stacking, energetic disorder, and phonon relaxation. Results
from our model are consistent with a wide range of recent experimental evidence
that excitons decay directly to well-defined polarons on a sub-100 fs
timescale, which is substantially faster than exciton relaxation processes.
Averaging over multiple samples, we find that as the interfacial offset is
increased, a substantial fraction of the density of electronic states in the
energy region about the initial exciton carries significant charge-transfer
character with two charges separated in the outer regions of the model lattice.
The results indicate a slight increase in the density of such current-producing
states if the region close to the interface is more disordered. However, since
their density of states overlaps the excitation line-shape of the primary
exciton, we show that it is possible that the exciton can decay directly into
current-producing states via tunneling on an ultrafast time-scale. We find this
process to be independent of the location of energetic disorder in the system,
and hence we expect exciton fission via resonant tunnelling to be a ubiquitous
feature of these systems.",1309.6308v1
2002-08-29,Semiclassical spin coherent state method in the weak spin-orbit coupling limit,"We apply the semiclassical spin coherent state method for the density of
states by Pletyukhov et al. (2002) in the weak spin-orbit coupling limit and
recover the modulation factor in the semiclassical trace formula found by Bolte
and Keppeler (1998, 1999).",0208047v1
2001-10-15,A note on Borromean correlations in multipartite quantum systems,"If a pure state of a multipartite quantum system is Borromean, that is, its
density matrix becomes product after tracing out any its component then the
initial state is product itself. This shows the essentially classical nature of
Borromean correlations which can not be achieved by entangled pure states.",0110091v1
2008-08-07,Phenomenological model for two gap states in underdoped high-temperature superconductors and short-range antiferromagnetic correlation effect,"Assuming antiferromagnetic orbital correlations to model the pseudogap state
in the underdoped high-temperature superconductors, we study how this
correlation is distinguished from the d-wave superconductivity correlation with
including the finite-range antiferromagnetic correlation effect. In spite of
the fact that both correlations have the same d-wave symmetry, the
contributions from each correlation is clearly distinguished in the spectral
weight and the density of states.",0808.0952v1
2011-10-23,A genuine maximally seven-qubit entangled state,"Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit
entangled state is presented. We find a seven-qubit state whose marginal
density matrices for subsystems of 1,2- qubits are all completely mixed and for
subsystems of 3-qubits is almost completely mixed.",1110.5011v1
1999-06-23,Geometric Quantum Mechanics,"The manifold of pure quantum states is a complex projective space endowed
with the unitary-invariant geometry of Fubini and Study. According to the
principles of geometric quantum mechanics, the detailed physical
characteristics of a given quantum system can be represented by specific
geometrical features that are selected and preferentially identified in this
complex manifold. Here we construct a number of examples of such geometrical
features as they arise in the state spaces for spin-1/2, spin-1, and spin-3/2
systems, and for pairs of spin-1/2 systems. A study is undertaken on the
geometry of entangled states, and a natural measure is assigned to the degree
of entanglement of a given state for a general multi-particle system. The
properties of this measure are analysed for the entangled states of a pair of
spin-1/2 particles. With the specification of a quantum Hamiltonian, the
resulting Schrodinger trajectory induces a Killing field, which is quasiergodic
on a toroidal subspace of the energy surface. When the dynamical trajectory is
lifted orthogonally to Hilbert space, it induces a geometric phase shift on the
wave function. The uncertainty of an observable in a given state is the length
of the gradient vector of the level surface of the expectation of the
observable in that state, a fact that allows us to calculate higher order
corrections to the Heisenberg relations. A general mixed state is determined by
a probability density function on the state space, for which the associated
first moment is the density matrix. The advantage of a general state is in its
applicability in various attempts to go beyond the standard quantum theory.",9906086v2
2018-09-16,A model Exact Study of the properties of low-lying electronic states of Perylene and Substituted Perylenes,"There is a resurgence of interest in the electronic structure of perylene for
its applications in molecular devices such as organic photovoltaics and organic
light emitting diodes. In this study, we have obtained the low-lying singlet
states of perylene by exactly solving the Parisar-Parr-Pople model Hamiltonian
of this system with 20 sites and 20 electrons, in the VB basis where
dimensionality is $\sim$ 5.92 billion. The triplet states of perylene are
obtained using a DMRG scheme with symmetry adaptation. The one and two photon
states are very close in energy $\sim$ 3.2 eV while the lowest triplet state is
slightly below 1.6 eV indicating that perylene is a good candidate for singlet
fission. To explore the tunability of the electronic states, we have studied
donor-acceptor substituted perylenes. The two donors and two acceptors are
substituted symmetrically either at the four bay sites or four peri sites. In
all the bay substitution and one peri substitution at moderate D/A strength,
the optical gap is lowered to about 2.8 eV. These molecules can be used as blue
emitters. We have also reported bond orders in all the cases and perylene as
well as substituted perylenes can be viewed as two weakly coupled naphthalene
in the singlet states but in triplets these bonds tend to be comparable to
other bonds in strength. The charge densities in substituted perylenes are
mostly localized around the substitution sites in the ground state. The
positive spin densities in triplets are concentrated around the peri and bay
sites with the remaining sites having small spin densities of either sign.",1809.05909v1
2010-07-06,On variations of the brightness of type Ia supernovae with the age of the host stellar population,"Recent observational studies of type Ia supernovae (SNeIa) suggest
correlations between the peak brightness of an event and the age of the
progenitor stellar population. This trend likely follows from properties of the
progenitor white dwarf (WD), such as central density, that follow from
properties of the host stellar population. We present a statistically
well-controlled, systematic study utilizing a suite of multi-dimensional SNeIa
simulations investigating the influence of central density of the progenitor WD
on the production of Fe-group material, particularly radioactive Ni-56, which
powers the light curve. We find that on average, as the progenitor's central
density increases, production of Fe-group material does not change but
production of Ni-56 decreases. We attribute this result to a higher rate of
neutronization at higher density. The central density of the progenitor is
determined by the mass of the WD and the cooling time prior to the onset of
mass transfer from the companion, as well as the subsequent accretion heating
and neutrino losses. The dependence of this density on cooling time, combined
with the result of our central density study, offers an explanation for the
observed age-luminosity correlation: a longer cooling time raises the central
density at ignition thereby producing less Ni-56 and thus a dimmer event. While
our ensemble of results demonstrates a significant trend, we find considerable
variation between realizations, indicating the necessity for averaging over an
ensemble of simulations to demonstrate a statistically significant result.",1007.0910v1
2014-11-12,Neutron stars and supernova explosions in the framework of Landau's theory,"A general formula of the symmetry energy for many-body interaction is
proposed and the commonly used two-body interaction symmetry energy is
recovered. Within Landau's theory (Lt), we generalize two equations of state
(EoS) CCS$\delta$3 and CCS$\delta$5 to asymmetric nuclear matter. We assume
that the density and density difference between protons and neutrons divided by
their sum are order parameters. We use different EoS to study neutron stars by
solving the TOV equations. We demonstrate that different EoS give different
mass and radius relation for neutron stars even when they have exactly the same
ground state (gs) properties ($E/A$, $\rho_0$, $K$, $S$, $L$ and $K_{sym}$).
Furthermore, for one EoS we change $K_{sym}$ and fix all the other gs
parameters. We find that for some $K_{sym}$ the EoS becomes unstable at high
density even for neutron matter. This suggests that a neutron star (NS) can
exist below and above the instability region but in different states: a quark
gluon plasma (QGP) at high density and baryonic matter at low density. If the
star's central density is in the instability region, then we associate these
conditions to the occurrence of Supernovae (SN).",1411.3030v1
2019-04-18,Constraining the equation of state of high-density cold matter using nuclear and astronomical measurements,"The increasing richness of data related to cold dense matter, from laboratory
experiments to neutron-star observations, requires a framework for constraining
the properties of such matter that makes use of all relevant information. Here,
we present a rigorous but practical Bayesian approach that can include diverse
evidence, such as nuclear data and the inferred masses, radii, tidal
deformabilities, moments of inertia, and gravitational binding energies of
neutron stars. We emphasize that the full posterior probability distributions
of measurements should be used rather than, as is common, imposing a cut on the
maximum mass or other quantities. Our method can be used with any
parameterization of the equation of state (EOS). We use both a spectral
parameterization and a piecewise polytropic parameterization with variable
transition densities to illustrate the implications of current measurements and
show how future measurements in many domains could improve our understanding of
cold catalyzed matter. We find that different types of measurements will play
distinct roles in constraining the EOS in different density ranges. For
example, better symmetry energy measurements will have a major influence on our
understanding of matter somewhat below nuclear saturation density but little
influence above that density. In contrast, precise radius measurements or
multiple tidal deformability measurements of the quality of those from GW170817
or better will improve our knowledge of the EOS over a broader density range.",1904.08907v2
2004-02-17,Gaussian relative entropy of entanglement,"For two gaussian states with given correlation matrices, in order that
relative entropy between them is practically calculable, I in this paper
describe the ways of transforming the correlation matrix to matrix in the
exponential density operator. Gaussian relative entropy of entanglement is
proposed as the minimal relative entropy of the gaussian state with respect to
separable gaussian state set. I prove that gaussian relative entropy of
entanglement achieves when the separable gaussian state is at the border of
separable gaussian state set and inseparable gaussian state set. For two mode
gaussian states, the calculation of gaussian relative entropy of entanglement
is greatly simplified from searching for a matrix with 10 undetermined
parameters to 3 variables. The two mode gaussian states are classified as four
types, numerical evidence strongly suggests that gaussian relative entropy of
entanglement for each type is realized by the separable state within the same
type.For symmetric gaussian state it is strictly proved that it is achieved by
symmetric gaussian state.",0402109v3
2022-01-07,Formation of probability density waves and probability current density waves by excitation and decay of a doublet of quasistationary states of a three-barrier heterostructure upon scattering of gaussian wave packets,"A numerical-analytical simulation of scattering by a three-barrier
heterostructure of an electronic Gaussian wave packet, the spectral width of
which is on the order of the distance between the levels of the doublet of
quasi-stationary states, is carried out. It is shown that as a result of
scattering, damped waves of electron charge and current densities are formed
outside the double well, their characteristics are determined by the structure
of the initial wave packet and the poles of the scattering amplitudes. The
frequency of these waves is equal to the difference frequency of the doublet,
the wavenumber is the difference between the wave numbers of free motion of
electrons with resonant energies, and the speed of their propagation is the
ratio of these quantities. The system can go into the regime of repetition or
amplification of the emission of electron waves if a periodic resonant pumping
of the doublet population is provided by scattering of a series of coherent
wave packets.",2201.02288v1
2023-05-01,Origin and stability of the charge density wave in ScV$_6$Sn$_6$,"Kagome metals are widely recognized as versatile platforms for exploring
novel topological properties, unconventional electronic correlations, magnetic
frustration, and superconductivity. In the $R$V$_6$Sn$_6$ family of materials
($R$ = Sc, Y, Lu), ScV$_6$Sn$_6$ hosts an unusual charge density wave ground
state as well as structural similarities with the $A$V$_3$Sb$_5$ system ($A$ =
K, Cs, Rb). In this work, we combine Raman scattering spectroscopy with
first-principles lattice dynamics calculations to reveal the charge density
wave state in ScV$_6$Sn$_6$. In the low temperature phase, we find a five-fold
splitting of the V-containing totally symmetric mode near 240 cm$^{-1}$
suggesting that the density wave acts to mix modes of $P$6/$mmm$ and
$R$$\bar{3}$$m$ symmetry - an effect that we quantify by projecting phonons of
the high symmetry state onto those of the lower symmetry structure. We also
test the stability of the density wave state under compression and find that
both physical and chemical pressure act to quench the effect. We discuss these
findings in terms of symmetry and the structure-property trends that can be
unraveled in this system.",2305.01086v1
2014-01-17,Exact quantum dynamics of yrast states in the finite 1D Bose gas,"We demonstrate that the quantum dynamics of yrast states in the
one-dimensional (1D) Bose gas gives an illustrative example to equilibration of
an isolated quantum many-body system. We first formulate the energy spectrum of
yrast states in terms of the dressed energy by applying the method of
finite-size corrections. We then review the exact time evolution of quantum
states constructed from yrast states shown by the Bethe ansatz. In time
evolution the density profile of an initially localized quantum state
constructed from yrast states collapses into a flat profile in the case of a
large particle number such as N=1000, while recurrence of the localized state
occurs in the case of a small particle number such as N=20. We suggest that the
dynamical relaxation behavior for the large N case is consistent with the
viewpoint of typicality for generic quantum states: the expectation values of
local operators valuated in most of quantum states are very close to those of
the micro-canonical ensemble.",1401.4262v1
2015-07-21,Causes of high-temperature superconductivity in the hydrogen sulfide electron-phonon system,"The electron and phonon spectra, as well as the density of electron and
phonon states of the stable orthorhombic structure of hydrogen sulfide (SH2) at
pressures 100-180 GPa have been calculated. It is found that the set of
parallel planes of hydrogen atoms is formed at pressure ~175 GPa as a result of
structural changes in the unit cell of the crystal under pressure. There should
be complete concentration of hydrogen atoms in these planes. As a result the
electron properties of the system acquire a quasi-two-dimensional character.
The features of in phase and antiphase oscillations of hydrogen atoms in these
planes leading to two narrow high-energy peaks in the phonon density of states
are investigated.",1507.05749v1
2016-06-17,Density of States under non-local interactions II. Simplified polynomially screened interactions,"Following [5], we analyze regularity properties of single-site probability
distributions of the random potential and of the Integrated Density of States
(IDS) in the Anderson models with infinite-range interactions. In the present
work, we study in detail a class of polynomially decaying interaction
potentials of rather artificial (piecewise-constant) form, and give a complete
proof of infinite smoothness of the IDS in an arbitrarily large finite domain
subject to the fluctuations of the entire, infinite random environment. A
variant of this result, based as in [5] on the harmonic analysis of probability
measures, results in a proof of spectral and dynamical Anderson localization in
the considered models.",1606.05618v1
2021-05-12,Local charge conservation law as a source of gauge condition in quantum electrodynamics,"A formulation of quantum electrodynamics is proposed, in which the local law
of conservation of electric charge serves as the source of the gauge condition.
The equations of motion of the gauge variable and the density of the charge
distribution in space following from this law are introduced into the quantum
theory as additional conditions. Along with fixing the gauge, the interaction
of charges in the modified quantum theory is described by the dynamics of the
charge distribution density. The asymptotic states of free particles at spatial
infinity are replaced by the initial and final states of the electromagnetic
system in the form of charged wave packets.",2105.05533v1
2022-09-29,Density of states in locally ordered amorphous organic semiconductors: emergence of the exponential tails,"We present a simple model of the local order in amorphous organic
semiconductors which naturally produces a spatially correlated exponential
density of states (DOS). The dominant contribution to the random energy
landscape is provided by electrostatic contributions from dipoles or
quadrupoles. An assumption of the preferable parallel orientation of neighbor
quadrupoles or antiparallel orientation of dipoles directly leads to the
formation of the exponential tails of the DOS even for a moderate size of the
ordered domains. The insensitivity of the exponential tail formation to the
details of the microstructure of the material suggests that this mechanism is
rather common in amorphous organic semiconductors.",2209.14640v1
2014-10-23,Temperature Dependent Symmetry to Asymmetry Transition in Wide Quantum Wells,"Quasi-two dimensional electron systems exhibit peculiar transport effects
depending on their density profiles and temperature. A usual two dimensional
electron system is assumed to have a $\delta$ like density distribution along
the crystal growth direction. However, once the confining quantum well is
sufficiently large, this situation is changed and the density can no longer be
assumed as a $\delta$ function. In addition, it is known that the density
profile is not a single peaked function, instead can present more than one
maxima, depending on the well width. In this work, the electron density
distributions in the growth direction considering a variety of wide quantum
wells are investigated as function of temperature. We show that, the double
peak in the density profile varies from symmetric (similar peak height) to
asymmetric while changing the temperature for particular growth parameters. The
alternation from symmetric to asymmetric density profiles is known to exhibit
intriguing phase transitions and is decisive in defining the properties of the
ground state wavefunction in the presence of an external magnetic field, i.e
from insulating phases to even denominator fractional quantum Hall states.
Here, by solving the temperature and material dependent Schr\""odinger and
Poisson equations self-consistently, we found that such a phase transition may
elaborated by taking into account direct Coulomb interactions together with
temperature.",1410.6426v1
2006-03-06,Edge states generated by spin-orbit coupling at domain walls in magnetic semiconductors,"Electronic states localized at domain walls between ferromagnetically ordered
phases in two-dimensional electron systems are generated by moderate spin-orbit
coupling. The spin carried by these states depends on the slope of the magnetic
background at the domain wall. The number of localized states is determined by
a real space topological number, and spin perpendicular to the ferromagnetic
order accumulates in these localized states at domain walls. These trapped
states may be observed in experiments that probe either spin density or
conduction paths in quantum wells.",0603145v3
2007-02-23,Current induced transition of anisotropic quantum Hall states,"We compare the energies of the striped Hall state and the anisotropic charge
density wave (ACDW) state at half-filled third and higher Landau levels in the
system with injected currents. With no injected current, the ACDW state has a
lower energy. We find that the striped Hall state becomes the lower energy
state when the injected current exceeds a critical value. The critical value is
estimated as about 0.04-0.05 nA.",0702543v1
2007-07-03,Excited state quantum phase transitions in many-body systems,"Phenomena analogous to ground state quantum phase transitions have recently
been noted to occur among states throughout the excitation spectra of certain
many-body models. These excited state phase transitions are manifested as
simultaneous singularities in the eigenvalue spectrum (including the gap or
level density), order parameters, and wave function properties. In this
article, the characteristics of excited state quantum phase transitions are
investigated. The finite-size scaling behavior is determined at the mean field
level. It is found that excited state quantum phase transitions are universal
to two-level bosonic and fermionic models with pairing interactions.",0707.0325v1
2013-04-29,High temperature Bose-Einstein condensation into an excited state at equilibrium,"We describe Bose-Einstein condensation of strongly interacting particles into
a quantum state which is an excited single-particle state, but becomes the
ground state as density increases because it minimizes the interaction energy
compared to other states. Mean field calculations for a graphene potential just
wide enough for two closely interacting layers of molecular hydrogen show
condensation at temperatures up to 60 K. In the condensed state, molecules hop
between layers, increasing the first peak in the pair-correlation function just
past the hard core repulsion diameter.",1304.7731v2
2020-07-22,Magnetic field induced global paramagnetic response in Fulde-Ferrell superconducting strip,"We theoretically study magnetic response of a
superconductor/ferromagnet/normal-metal (SFN) strip in an in-plane
Fulde--Ferrell (FF) state. We show that unlike to ordinary superconducting
strip the FF strip can be switched from diamagnetic to paramagnetic and then
back to diamagnetic state by {\it increasing} the perpendicular magnetic field.
Being in paramagnetic state FF strip exhibits magnetic field driven second
order phase transition from FF state to the ordinary state without spatial
modulation along the strip. We argue that the global paramagnetic response is
connected with peculiar dependence of sheet superconducting current density on
supervelocity in FF state and it exists in nonlinear regime.",2007.11351v1
2006-12-27,Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics,"We discuss and motivate the form of the generator of a nonlinear quantum
dynamical group 'designed' so as to accomplish a unification of quantum
mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum
Thermodynamics (QT). Its conceptual foundations differ from those of (von
Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information
theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the
same mathematics, and for zero entropy states it reduces to standard unitary
QM. The nonlinear dynamical group of QT is construed so that the second law
emerges as a theorem of existence and uniqueness of a stable equilibrium state
for each set of mean values of the energy and the number of constituents. It
implements two fundamental ansatzs. The first is that in addition to the
standard QM states described by idempotent density operators (zero entropy), a
strictly isolated system admits also states that must be described by
non-idempotent density operators (nonzero entropy). The second is that for such
additional states the law of causal evolution is determined by the simultaneous
action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear
dissipative generator which conserves the mean values of the energy and the
number of constituents, and (in forward time) drives any density operator, no
matter how far from TE, in the 'direction' of steepest entropy ascent (maximal
entropy increase). The equation of motion can be solved not only in forward
time, to describe relaxation towards TE, but also backwards in time, to
reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle
from which the system originates.",0612215v1
2021-07-02,Convergence of reconstructed density matrix to a pure state using maximal entropy approach,"Impressive progress has been made in the past decade in the study of
technological applications of varied types of quantum systems. With industry
giants like IBM laying down their roadmap for scalable quantum devices with
more than 1000-qubits by the end of 2023, efficient validation techniques are
also being developed for testing quantum processing on these devices. The
characterization of a quantum state is done by experimental measurements
through the process called quantum state tomography (QST) which scales
exponentially with the size of the system. However, QST performed using
incomplete measurements is aptly suited for characterizing these quantum
technologies especially with the current nature of noisy intermediate-scale
quantum (NISQ) devices where not all mean measurements are available with high
fidelity. We, hereby, propose an alternative approach to QST for the complete
reconstruction of the density matrix of a quantum system in a pure state for
any number of qubits by applying the maximal entropy formalism on the pairwise
combinations of the known mean measurements. This approach provides the best
estimate of the target state when we know the complete set of observables which
is the case of convergence of the reconstructed density matrix to a pure state.
Our goal is to provide a practical inference of a quantum system in a pure
state that can find its applications in the field of quantum error mitigation
on a real quantum computer that we intend to investigate further.",2107.01191v1
2015-05-19,From holography towards real-world nuclear matter,"Quantum chromodynamics is notoriously difficult to solve at nonzero baryon
density, and most models or effective theories of dense quark or nuclear matter
are restricted to a particular density regime and/or a particular form of
matter. Here we study dense (and mostly cold) matter within the holographic
Sakai-Sugimoto model, aiming at a strong-coupling framework in the wide density
range between nuclear saturation density and ultra-high quark matter densities.
The model contains only three parameters, and we ask whether it fulfills two
basic requirements of real-world cold and dense matter, a first-order onset of
nuclear matter and a chiral phase transition at high density to quark matter.
Such a model would be extremely useful for astrophysical applications because
it would provide a single equation of state for all densities relevant in a
compact star. Our calculations are based on two approximations for baryonic
matter, firstly an instanton gas and secondly a homogeneous ansatz for the
non-abelian gauge fields on the flavor branes of the model. While the instanton
gas shows chiral restoration at high densities but an unrealistic second-order
baryon onset, the homogeneous ansatz behaves exactly the other way around. Our
study thus provides all ingredients that are necessary for a more realistic
model and allows for systematic improvements of the applied approximations.",1505.04886v2
2018-08-24,Detailed Balance and Exact Results for Density Fluctuations in Supersonic Turbulence,"The probabilistic approach to turbulence is applied to investigate density
fluctuations in supersonic turbulence. We derive kinetic equations for the
probability distribution function (PDF) of the logarithm of the density field,
$s$, in compressible turbulence in two forms: a first-order partial
differential equation involving the average divergence conditioned on the flow
density, $\langle \nabla \cdot {\bs u} | s\rangle$, and a Fokker-Planck
equation with the drift and diffusion coefficients equal to $-\langle {\bs u}
\cdot \nabla s | s\rangle$ and $\langle {\bs u} \cdot \nabla s | s\rangle$,
respectively. Assuming statistical homogeneity only, the detailed balance at
steady state leads to two exact results, $\langle \nabla \cdot {\bs u} | s
\rangle =0$, and $\langle {\bs u} \cdot \nabla s | s\rangle=0$. The former
indicates a balance of the flow divergence over all expanding and contracting
regions at each given density. The exact results provide an objective criterion
to judge the accuracy of numerical codes with respect to the density statistics
in supersonic turbulence. We also present a method to estimate the effective
numerical diffusion as a function of the flow density and discuss its effects
on the shape of the density PDF.",1808.08302v2
2016-08-10,Competing interactions in population-imbalanced two-component Bose-Einstein condensates,"We consider a two-component Bose-Einstein condensate with and without
synthetic ""spin-orbit"" interactions in two dimensions. Density- and
phase-fluctuations of the condensate are included, allowing us to study the
impact of thermal fluctuations and density-density interactions on the physics
originating with spin-orbit interactions. In the absence of spin-orbit
interactions, we find that inter-component density interactions deplete the
minority condensate. The thermally driven phase transition is driven by coupled
density and phase-fluctuations, but is nevertheless shown to be a
phase-transition in the Kosterlitz-Thouless universality class with close to
universal amplitude ratios irrespective of whether both the minority- and
majority condensates exist in the ground state, or only one condensate exists.
In the presence of spin-orbit interactions we observe three separate phases,
depending on the strength of the spin-orbit coupling and inter-component
density-density interactions: a phase-modulated phase with uniform amplitudes
for small intercomponent interactions, a completely imbalanced, effectively
single-component, condensate for intermediate spin-orbit coupling strength and
suficciently large inter-component interactions, and a phase-modulated
\textit{and} amplitude-modulated phase for sufficiently large values of both
the spin-orbit coupling and the inter-component density-density interactions.
The phase which is modulated by a single $\bv q$-vector only is observed to
transition into an isoptropic liquid through a strong de-pinning transition
with periodic boundary conditions, which weakens with open boundaries.",1608.03300v1
2023-06-21,Decoupled Boundary Handling in SPH,"Particle-based boundary representations are frequently used in Smoothed
Particle Hydrodynamics (SPH) due to their simple integration into fluid
solvers. Commonly, incompressible fluid solvers estimate the current density
and corresponding forces in case the current density exceeds the rest density
to push fluid particles apart. Close to the boundary, the calculation of the
fluid particles' density involves both, neighboring fluid and neighboring
boundary particles, yielding an overestimation of density, and, subsequently,
wrong pressure forces and wrong velocities leading to the disturbed fluid
particles' behavior in the vicinity of the boundary. In this paper, we present
a detailed explanation of this disturbed fluid particle behavior, which is
mainly due to the combined or coupled handling of the fluid-fluid particle and
the fluid-boundary particle interaction. We propose the decoupled handling of
both interaction types, leading to two densities for a given fluid particle,
i.e., fluid-induced density and boundary-induced density. In our approach, we
alternately apply the corresponding fluid-induced and boundary-induced forces
during pressure estimation. This separation avoids force overestimation and
reduces unintended fluid dynamics near the boundary, as well as a consistent
fluid-boundary distance across different fluid amounts and different
particle-based boundary handling methods. We compare our method with two
regular state-of-the-art methods in different experiments and show how our
method handles detailed boundary shapes.",2306.12277v1
2010-06-23,Separability criteria for several classes of $n$-partite quantum states,"In this paper, we mainly discuss the separability of $n$-partite quantum
states from elements of density matrices. Practical separability criteria for
different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some
of them are also sufficient conditions for genuine entanglement of $n$-partite
quantum states. Moreover, one of the resulting criteria is also necessary and
sufficient for a class of $n$-partite states.",1006.4516v2
2010-09-14,Bound states in the continuum in graphene quantum dot structures,"The existence of bound states in the continuum was predicted at the dawn of
quantum mechanics by von Neumann and Wigner. In this work we discuss the
mechanism of formation of these exotic states and the feasibility to observe
them experimentally in symmetrical heterostructures composed by segments of
graphene ribbons with different widths forming a graphene quantum dot. We
identify the existence of bound states in the continuum in these graphene
quantum dot systems by means of local density of states and electronic
conductance calculations.",1009.2711v1
2013-07-04,Relative volume of separable bipartite states,"Every choice of an orthonormal frame in the d-dimensional Hilbert space of a
system corresponds to one set of all mutually commuting density matrices or,
equivalently, a classical statistical state space of the system; the quantum
state space itself can thus be profitably viewed as an SU(d) orbit of classical
state spaces, one for each orthonormal frame. We exploit this connection to
study the relative volume of separable states of a bipartite quantum system.
While the two-qubit case is studied in considerable analytic detail, for higher
dimensional systems we fall back on Monte Carlo. Several new insights seem to
emerge from our study.",1307.1454v2
2022-08-09,Explicit expressions for stationary states of the Lindblad equation for a finite state space,"The Lindblad equation describes the time evolution of a density matrix of a
quantum mechanical system. Stationary solutions are obtained by time-averaging
the solution, which will in general depend on the initial state. We provide an
analytical expression for the steady states of the Lindblad equation using the
quantum jump unraveling, a version of an ergodic theorem, and the stationary
probabilities of the corresponding discret-time Markov chains. Our result is
valid when the number of states appearing the in quantum trajectory is finite.
The classical case of a Markov jump-process is recovered as a special case, and
differences between the two are discussed.",2208.04954v1
2022-08-23,Optimization of the number of intrinsic states included in the discrete Generator Coordinate Method,"We present a mechanism to efficiently pre-select the number of intrinsic
many-body states that are used to define the many-body wave functions within
the discrete Generator Coordinate Method (GCM). This procedure, based on the
proper definition of a natural basis of orthonormal states, does not require
the evaluation of the non-diagonal Hamiltonian kernels to do the selection and
helps to reduce the numerical instabilities. The performance of the method is
analyzed in detail in the ground state and $0^{+}$ excited states of some
selected nuclei computed with the Gogny energy density functional.",2208.10870v1
1995-04-26,"The Single-Particle density of States, Bound States, Phase-Shift Flip, and a Resonance in the Presence of an Aharonov-Bohm Potential","Both the nonrelativistic scattering and the spectrum in the presence of the
Aharonov-Bohm potential are analyzed. The single-particle density of states
(DOS) for different self-adjoint extensions is calculated. The DOS provides a
link between different physical quantities and is a natural starting point for
their calculation. The consequences of an asymmetry of the S matrix for the
generic self-adjoint extension are examined.
  I. Introduction
  II. Impenetrable flux tube and the density of states
  III. Penetrable flux tube and self-adjoint extensions
  IV. The S matrix and scattering cross sections
  V. The Krein-Friedel formula and the resonance
  VI. Regularization
  VII. The R --> 0 limit and the interpretation of self-adjoint extensions
  VIII. Energy calculations
  IX. The Hall effect in the dilute vortex limit
  X. Persistent current of free electrons in the plane pierced by a flux tube
  XI. The 2nd virial coefficient of nonrelativistic interacting anyons
  XII. Discussion of the results and open questions",9504107v2
1996-08-29,Repulsive particles on a two-dimensional lattice,"The problem of finding the minimum-energy configuration of particles on a
lattice, subject to a generic short-ranged repulsive interaction, is studied
analytically. The study is relevant to charge ordered states of interacting
fermions, as described by the spinless Falicov-Kimball model. For a range of
particle density including the half-filled case, it is shown that the
minimum-energy states coincide with the large-U neutral ground state ionic
configurations of the Falicov-Kimball model, thus providing a characterization
of the latter as ``most homogeneous'' ionic arrangements. These obey
hierarchical rules, leading to a sequence of phases described by the Farey
tree. For lower densities, a new family of minimum-energy configurations is
found, having the novel property that they are aperiodic even when the particle
density is a rational number. In some cases there occurs local phase
separation, resulting in an inherent sensitivity of the ground state to the
detailed form of the interaction potential.",9608155v2
2005-11-14,Ferromagnetism of Ga$_{1-x}$Mn$_x$As and Weiss theory of Curie temperature in the coherent potential approximation,"The zinc-blende GaAs-based III-V diluted magnetic semiconductors (DMS)are
studied in the coherent potential approximation(CPA). In this work, we use the
exact Hilbert transformation of the face-centered cubic(fcc) density of states
(DOS), which is different from the usual semi-circle density of states employed
in our previous work. Our calculated relation of ground-state energy and
impurity magnetization shows that ferromagnetism is always favorable at low
temperatures. For very weak Kondo coupling, the density of states (DOS) of the
host semiconductor is modified slightly. Impurity band can be generated at the
host band bottom only when Kondo coupling is strong enough. Using Weiss
molecular theory, we predict a nonlinear relation of Curie temperature with
respect to Kondo coupling, as is different from the conclusion of our previous
calculations based on semicircle DOS. The agreement of our calculated $T_{\rm
C}$ with measured values is convincing.",0511320v3
1998-11-27,Ionization equilibrium and equation of state of hydrogen plasmas in strong magnetic fields,"We study hydrogen plasmas at magnetic fields B ~ 10^{12}-10^{13} Gauss,
densities ~ 10^{-3}-10^3 g/cc and temperatures T ~ 10^{5.5}-10^{6.5} K, typical
of photospheres of middle-aged cooling neutron stars. We construct an
analytical free energy model of the partially ionized plasma, including into
consideration the decentred atomic states, which arise due to the thermal
motion across the strong field. We show that these states, neglected in
previous studies, may contribute appreciably into thermodynamics of the outer
atmospheric layers at density below 1 g/cc and typical B and T. We take into
account Coulomb non-ideality of the ionized component of the plasma affected by
intense magnetic field. Ionization degree, occupancies and equation of state
are calculated, and their dependences on the temperature, density and magnetic
field are studied.",9811051v1
2007-05-27,In-medium nuclear interactions of low-energy hadrons,"Experimental and theoretical developments of the last decade in the study of
exotic atoms and some related low-energy reactions are reviewed, in order to
provide information on the in-medium hadron-nucleon t matrix over a wide range
of densities up to central nuclear densities. In particular, we review pionic
deeply bound atomic states and related evidence for partial restoration of
chiral symmetry in dense nuclear matter. The case for relatively narrow deeply
bound atomic states for antikaons and antiprotons is made, based on the physics
of strong nuclear absorption. Recent experimental suggestions for signals of
antikaon-nuclear deeply bound states are reviewed, and dynamical models for
calculating binding energies, widths and densities of antikaon nuclear states
are discussed. Specific features of low-energy in-medium interactions of kaons,
antiprotons and of Sigma hyperons are discussed, and suggestions to study
experimentally Cascade atoms are reviewed.",0705.3965v2
2007-11-03,A new equation of state for dark energy,"In the contemporary Cosmology, dark energy is modeled as a perfect fluid,
having a very simple equation of state: pressure is proportional to dark energy
density. As an alternative, I propose a more complex equation of state, with
pressure being function of three variables: dark energy density, matter density
and the size of the Universe. One consequence of the new equation is that, in
the late-time Universe, cosmological scale factor is linear function of time;
while the standard cosmology predicts an exponential function.The new equation
of state allows attributing a temperature to the physical vacuum, a temperature
proportional to the acceleration of the expansion of the Universe. The vacuum
temperature decreases with the expansion of the Universe, approaching (but
never reaching) the absolute zero.",0711.0439v4
2008-11-26,Matrix product simulations of non-equilibrium steady states of quantum spin chains,"Time-dependent density matrix renormalization group method with a matrix
product ansatz is employed for explicit computation of non-equilibrium steady
state density operators of several integrable and non-integrable quantum spin
chains, which are driven far from equilibrium by means of Markovian couplings
to external baths at the two ends. It is argued that even though the
time-evolution can not be simulated efficiently due to fast entanglement
growth, the steady states in and out of equilibrium can be typically accurately
approximated, so that chains of length of the order n ~ 100 are accessible. Our
results are demonstrated by performing explicit simulations of steady states
and calculations of energy/spin densities/currents in several problems of heat
and spin transport in quantum spin chains. Previously conjectured relation
between quantum chaos and normal transport is re-confirmed with high acurracy
on much larger systems.",0811.4188v2
2011-08-02,Composition and stability of hybrid stars with hyperons and quark color-superconductivity,"The recent measurement of a $1.97\pm 0.04$ solar-mass pulsar places a
stringent lower bound on the maximum mass of compact stars and therefore
challenges the existence of any agents that soften the equation of state of
ultra-dense matter. We investigate whether hyperons and/or quark matter can be
accommodated in massive compact stars by constructing an equation of state
based on a combination of phenomenological relativistic hyper-nuclear density
functional and an effective model of quantum chromodynamics (the
Nambu-Jona-Lasinio model). Stable configurations are obtained with $M \ge 1.97
M_{\sun}$ featuring hyper-nuclear and quark matter in color superconducting
state if the equation of state of nuclear matter is stiff above the saturation
density, the transition to quark matter takes place at a few times the nuclear
saturation density, and the repulsive vector interactions in quark matter are
substantial.",1108.0559v2
2014-02-13,Disorder driven inhomogeneous phase in the 2D-superconducting film of titanium nitride,"Typically the superconducting phase weakens at several points with the
increase in disorder before it is distroyed in the 2d-thin films. This may lead
to an inhomogeneous superconducting state without a continuous phase. Here we
present scanning tunneling spectroscopy measurements at 0.1 K in the disordered
polycrystalline film of TiN describing the nanoscale size features of the
superconducting state. The imaging shows imcommensurate charge density
modulations, originating at the crystalline bounadries, and intercepted on
large scale by the beat patterns in the regions of overlap. Electronic
coherence is maintained over length scale minimum of crystalline sizes, and
suffers scattering across low angle crystalline boundaries. The superconducting
state fluctuates at the positions of the charge density modulations and zones
of the weak phase appear in the vicinity of the beats. Our data shows that the
BCS-like behavior evolves into the V-shaped density of states in such
inhomogeneous regions as a result of the competition between the
superconducting correlations with that of the strong electron-electron
repulsive interactions assisted by the inelastic scattering at the crystalline
boundaries.",1402.3178v3
2015-03-02,Generalized Pauli constraints in reduced density matrix functional theory,"Functionals of the one-body reduced density matrix (1-RDM) are routinely
minimized under Coleman's ensemble $N$-representability conditions. Recently,
the topic of pure-state $N$-representability conditions, also known as
generalized Pauli constraints, received increased attention following the
discovery of a systematic way to derive them for any number of electrons and
any finite dimensionality of the Hilbert space. The target of this work is to
assess the potential impact of the enforcement of the pure-state conditions on
the results of reduced density-matrix functional theory calculations. In
particular, we examine whether the standard minimization of typical 1-RDM
functionals under the ensemble $N$-representability conditions violates the
pure-state conditions for prototype 3-electron systems. We also enforce the
pure-state conditions, in addition to the ensemble ones, for the same systems
and functionals and compare the correlation energies and optimal occupation
numbers with those obtained by the enforcement of the ensemble conditions
alone.",1503.00746v2
2017-02-21,Impurity scattering on the surface of topological insulator thin films,"We address the electronic structure of the surface states of topological
insulator thin films with embedded local non-magnetic and magnetic impurities.
Using the $T$-matrix expansion of the real space Green's function, we derive
the local density of electrons states and corresponding spin resolved
densities. We show that the effects of the impurities can be tuned by applying
an electric field between the surface layers. The emerging magnetic states are
expected to play an important role both in ferromagnetic mechanism of magnetic
topological insulators as well as in its transport properties. In the case of
magnetic impurities, we have categorized the possible cases for different
spin-directions of the impurities as well as the spin-direction in which the
spin resolved density of electron states is calculated and related this to the
spin susceptibility of the system.",1702.06424v1
2018-12-19,Two-dimensional Mixture of Dipolar Fermions: Equation of State and Magnetic Phases,"We study a two-component mixture of fermionic dipoles in two dimensions at
zero temperature, interacting via a purely repulsive $1/r^3$ potential. This
model can be realized with ultracold atoms or molecules, when their dipole
moments are aligned in the confinement direction orthogonal to the plane. We
characterize the unpolarized mixture by means of the Diffusion Monte Carlo
technique. Computing the equation of state, we identify the regime of validity
for a mean-field theory based on a low-density expansion and compare our
results with the hard-disk model of repulsive fermions. At high density, we
address the possibility of itinerant ferromagnetism, namely whether the ground
state can be fully polarized in the fluid phase. Within the fixed-node
approximation, we show that the accuracy of Jastrow-Slater trial wave
functions, even with the typical two-body backflow correction, is not
sufficient to resolve the relevant energy differences. By making use of the
iterative-backflow improved trial wave functions, we observe no signature of a
fully-polarized ground state up to the freezing density.",1812.08064v2
2018-05-26,On the quantitative calculation of the cosmological constant of the quantum vacuum,"It is widely believed that as one of the candidates for dark energy, the
cosmological constant should relate directly with the quantum vacuum. Despite
decades of theoretical effects, however, there is still no quantitative
interpretation of the observed cosmological constant. In this work, we consider
the quantum state of the whole universe including the quantum vacuum. Everett's
relative-state formulation, vacuum quantum fluctuations and the validity of
Einstein's field equation at macroscopic scales imply that our universe wave
function might be a superposition of states with different cosmological
constants. In the density matrix formulation of this quantum universe, the
quasi-thermal equilibrium state is described by a specific cosmological
constant with the maximum probability. Without any fitting parameter, the ratio
between the vacuum energy density due to the cosmological constant (dark
energy) and the critical density of the universe is 68.85% based on simple
equations in our theoretic model, which agrees very well with the best current
astronomical observations of 68.5%.",1805.10440v1
2018-09-10,Discrete and Weyl density of states for photons and phonons,"The current density of states (DOS) calculations do not take into account the
essential discreteness of the state space, since they rely on the unbounded
continuum approximation. Recently, discrete DOS based on the
quantum-mechanically allowable minimum energy interval has been introduced for
quadratic dispersion relation. In this work, we consider systems exhibiting
linear dispersion relation, particularly photons and phonons, and calculate the
related density and number of states (NOS). Also, a Weyl's conjecture-based DOS
function is calculated for photons and phonons by considering the bounded
continuum approach. We show that discrete DOS function reduces to expressions
of bounded and unbounded continua in the appropriate limits. The fluctuations
in discrete DOS completely disappear under accumulation operators. It's
interesting that relative errors of NOS and DOS functions with respect to
discrete ones are exactly the same as the ones for quadratic dispersion
relation. Furthermore, the application of discrete and Weyl DOS for the
calculation of internal energy of a photon gas is presented and importance of
discrete DOS is discussed. It's shown that discrete DOS function given in this
work needs to be used whenever the low energy levels of a physical system are
heavily occupied.",1809.03495v1
2021-09-14,Vibrational density of states capture the role of dynamic allostery in protein evolution,"Previous studies of the flexibilities of ancestral proteins suggests that
proteins evolve their function by altering their native state ensemble. Here we
propose a more direct method of visualizing this by measuring the changes in
the vibrational density of states (VDOS) of proteins as they evolve. Through
analysis of VDOS profiles of ancestral and extant proteins we observe that
$\beta$-lactamase and thioredoxins evolve by altering their density of states
in the terahertz region. Particularly, the shift in VDOS profiles between
ancestral and extant proteins suggests that nature utilize dynamic allostery
for functional evolution. Moreover, we also show that VDOS profile of
individual position can be used to describe the flexibility changes,
particularly those without any amino acid substitution.",2109.07004v1
2021-10-12,Exotic Superfluid Phases in Spin Polarized Systems on Optical Lattices,"Leveraging cutting-edge numerical methodologies, we study the ground state of
the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on
systems at high density and small spin polarization, corresponding to the
parameter regime believed to be most favorable to the formation of the elusive
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study
of large lattice sizes, hosting nearly $500$ atoms, provides strong evidence of
the stability of the FFLO state in this regime, as well as a high-accuracy
characterization of its properties. Our results for the density correlation
function reveal the existence of density order in the system, suggesting the
possibility of an intricate coexistence of long-range orders in the ground
state. The ground-state properties are seen to differ significantly from the
standard mean-field description, providing a compelling avenue for future
theoretical and experimental explorations of the interplay between interaction
and superfluidity in an exotic phase of matter.",2110.06159v1
2022-06-30,Discrete integrable systems and random Lax matrices,"We study properties of Hamiltonian integrable systems with random initial
data by considering their Lax representation. Specifically, we investigate the
spectral behaviour of the corresponding Lax matrices when the number $N$ of
degrees of freedom of the system goes to infinity and the initial data is
sampled according to a properly chosen Gibbs measure. We give an exact
description of the limit density of states for the exponential Toda lattice and
the Volterra lattice in terms of the Laguerre and antisymmetric Gaussian
$\beta$-ensemble in the high temperature regime. For generalizations of the
Volterra lattice to short range interactions, called INB additive and
multiplicative lattices, the focusing Ablowitz--Ladik lattice and the focusing
Schur flow, we derive numerically the density of states. For all these systems,
we obtain explicitly the density of states in the ground states.",2206.15371v4
2024-03-04,Effects of AB-flux and gap on magnetic graphene quantum dots,"We consider magnetic graphene quantum dots (MGQDs) and study the impact of
the Aharonov-Bohm (AB) flux and gap on the scattering process of electrons. Our
emphasis is on the finite lifetimes of quasi-bound states arising from the
interaction between electrons and the magnetic field within the dot. Initially,
we calculate the scattering coefficients, scattering efficiency, and
probability density by ensuring the continuity of eigenspinors at the boundary
of MGQD. The results indicate that as the gap increases, the quasi-bound states
reach higher maxima. We show that an increase in AB-flux leads to a generation
of quasi-bound states requiring less magnetic field, and the scattering
efficiency starts to take non-zero values at smaller MGQD sizes. The analysis
of probability density shows that the quasi-bound states, corresponding to
non-resonantly excited scattering modes, exhibit a significant improvement in
the concentrated density at MGQD. The improvement is a result of reducing the
diffraction phenomenon and suppressing the Klein effect through an increase in
AB-flux and gap. This increases the probability of retaining the electron for a
longer period of time.",2403.02206v1
2005-08-17,The properties of kaonic nuclei in relativistic mean-field theory,"The static properties of some possible light and moderate kaonic nuclei, from
C to Ti, are studied in the relativistic mean-field theory. The 1s and 1p state
binding energies of $K^-$ are in the range of $73\sim 96$ MeV and $22\sim 63$
MeV, respectively. The binding energies of 1p states increase monotonically
with the nucleon number A. The upper limit of the widths are about $42\pm 14$
MeV for the 1s states, and about $71\pm 10$ MeV for the 1p states. The lower
limit of the widths are about $12\pm 4$ MeV for the 1s states, and $21\pm 3$
MeV for the 1p states. If $V_{0}\leq 30$ MeV, the discrete $K^-$ bound states
should be identified in experiment. The shrinkage effect is found in the
possible kaonic nuclei. The interior nuclear density increases obviously, the
densest center density is about $2.1\rho_{0}$.",0508031v2
2019-11-25,Modular zero modes and sewing the states of QFT,"We point out an important difference between continuum relativistic quantum
field theory (QFT) and lattice models with dramatic consequences for the theory
of multi-partite entanglement. On a lattice given a collection of density
matrices $\rho^{(1)},\rho^{(2)}, \cdots, \rho^{(n)}$ there is no guarantee that
there exists an $n$-partite pure state $|\Omega\rangle_{12\cdots n}$ that
reduces to these marginals. The state $|\Omega\rangle_{12\cdots n}$ exists only
if the eigenvalues of the density matrices $\rho^{(i)}$ satisfy certain polygon
inequalities. We show that in QFT, as opposed to lattice systems, splitting the
space into $n$ non-overlapping regions any collection of local states
$\omega^{(1)},\omega^{(2)},\cdots \omega^{(n)}$ come from the restriction of a
global pure state. The reason is that rotating any local state $\omega^{(i)}$
by unitary $U_i$ localized in the $i^{th}$ region we come arbitrarily close to
any other local state $\psi^{(i)}$. We construct explicit examples of such
local unitaries using the cocycle.",1911.11153v4
2013-08-05,Imaging the Kondo Insulating Gap on SmB6,"Topological insulators host spin-polarized surface states which robustly span
the band gap and hold promise for novel applications. Recent theoretical
predictions have suggested that topologically protected surface states may
similarly span the hybridization gap in some strongly correlated heavy fermion
materials, particularly SmB6. However, the process by which the Sm 4f electrons
hybridize with the 5d electrons on the surface of SmB6, and the expected
Fermi-level gap in the density of states out of which the predicted topological
surface states must arise, have not been directly measured. We use scanning
tunneling microscopy to conduct the first atomic resolution spectroscopic study
of the cleaved surface of SmB6, and to reveal a robust hybridization gap which
universally spans the Fermi level on four distinct surface morphologies despite
shifts in the f band energy. Using a cotunneling model, we separate the density
of states of the hybridized bands from which the predicted topological surface
states must be disentangled. On all surfaces we observe residual spectral
weight spanning the hybridization gap down to the lowest T, which is consistent
with a topological surface state.",1308.1085v2
2022-02-10,Discovering Quantum Phase Transitions with Fermionic Neural Networks,"Deep neural networks have been extremely successful as highly accurate wave
function ans\""atze for variational Monte Carlo calculations of molecular ground
states. We present an extension of one such ansatz, FermiNet, to calculations
of the ground states of periodic Hamiltonians, and study the homogeneous
electron gas. FermiNet calculations of the ground-state energies of small
electron gas systems are in excellent agreement with previous initiator full
configuration interaction quantum Monte Carlo and diffusion Monte Carlo
calculations. We investigate the spin-polarized homogeneous electron gas and
demonstrate that the same neural network architecture is capable of accurately
representing both the delocalized Fermi liquid state and the localized Wigner
crystal state. The network is given no \emph{a priori} knowledge that a phase
transition exists, but converges on the translationally invariant ground state
at high density and spontaneously breaks the symmetry to produce the
crystalline ground state at low density.",2202.05183v3
2022-05-12,Efficient Quantum State Tracking in Noisy Environments,"Quantum state tomography, which aims to find the best description of a
quantum state -- the density matrix, is an essential building block in quantum
computation and communication. Standard techniques for state tomography are
incapable of tracking changing states and often perform poorly in the presence
of environmental noise. Although there are different approaches to solve these
problems theoretically, experimental demonstrations have so far been sparse.
Our approach, matrix-exponentiated gradient tomography, is an online tomography
method that allows for state tracking, updates the estimated density matrix
dynamically from the very first measurements, is computationally efficient, and
converges to a good estimate quickly even with noisy data. The algorithm is
controlled via a single parameter, its learning rate, which determines the
performance and can be tailored in simulations to the individual experiment. We
present an experimental implementation of matrix-exponentiated gradient
tomography on a qutrit system encoded in the transverse spatial mode of
photons. We investigate the performance of our method on stationary and
evolving states, as well as significant environmental noise, and find
fidelities of around 95% in all cases.",2205.06389v1
2004-12-19,Thermal melting of density waves on the square lattice,"We present the theory of the effect of thermal fluctuations on commensurate
""p x p"" density wave ordering on the square lattice (p >= 3, integer). For the
case in which this order is lost by a second order transition, we argue that
the adjacent state is generically an incommensurate striped state, with
commensurate p-periodic long range order along one direction, and
incommensurate quasi-long-range order along the orthogonal direction. We also
present the routes by which the fully disordered high temperature state can be
reached. For p=4, and at special commensurate densities, the ""4 x 4""
commensurate state can melt directly into the disordered state via a self-dual
critical point with non-universal exponents.",0412498v1
2009-06-08,Frustrated Bose condensates in optical lattices,"We study the Bose-condensed ground states of bosons in a two-dimensional
optical lattice in the presence of frustration due to an effective vector
potential, for example, due to lattice rotation. We use a mapping to a large-S
frustrated magnet to study quantum fluctuations in the condensed state. Quantum
effects are introduced by considering a 1/S expansion around the classical
ground state. The large-S regime should be relevant to systems with many
particles per site. As the system approaches the Mott insulating state, the
hole density becomes small. Our large-S results show that, even when the system
is very dilute, the holes remain a (partially) condensed system. Moreover, the
superfluid density is comparable to the condensate density. In other words, the
large-S regime does not display an instability to noncondensed phases. However,
for cases with fewer than 1/3 flux quantum per lattice plaquette, we find that
the fractional condensate depletion increases as the system approaches the Mott
phase, giving rise to the possibility of a noncondensed state before the Mott
phase is reached for systems with smaller S.",0906.1600v2
2012-06-28,Correlated Phases of Population Imbalanced Fermi-Fermi Mixtures on an Optical Lattice,"We study a two species fermion mixture with different populations on a square
lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive
interaction. Such a model can be realized in a cold atom system with fermionic
atoms in two different hyperfine states loaded on an optical lattice and with
tunable inter-species interaction strength via external fields. For a
two-dimensional square lattice, when at least one of the fermion species is
close to half-filling, the system is highly affected by lattice effects. With
the majority species near half-filling and varying densities for the minority
species, we find that several correlated phases emerge as the ground state,
including a spin density wave state, a charge density wave state with stripe
structure, and various p-wave BCS pairing states for both species. We study
this system using a functional renormalization group method, determine its
phase diagram at weak coupling, discuss the origin and characteristics of each
phase, and provide estimates for the critical temperatures.",1206.6797v3
2019-03-18,Toroidal states in $^{28}$Si with covariant density functional theory in 3D lattice space,"The toroidal states in $^{28}$Si with spin extending to extremely high are
investigated with the cranking covariant density functional theory on a 3D
lattice. Thirteen toroidal states with spin $I$ ranging from 0 to 56$\hbar$ are
obtained, and their stabilities against particle emissions are studied by
analyzing the density distributions and potentials. The excitation energies of
the toroidal states at $I=28$, 36, 44$\hbar$ reasonably reproduce the observed
three resonances extracted from the 7-$\alpha$ de-excitation of $^{28}$Si. The
$\alpha$ clustering of these toroidal states is supported by the
$\alpha$-localization function.",1903.07234v2
2022-10-19,Competing ferromagnetic superconducting states in europium-based iron pnictides,"In europium-based iron pnictides superconducting Fe-planes can be influenced
by a Zeeman field originated from the neighboring Eu-planes. The field tends to
induce spin-density waves with a ferromagnetic average which coexists with the
superconducting order by forming complementary patterns of the superconducting
and magnetic order parameters in a Fulde-Ferrell-Larkin-Ovchinnikov phase and a
two-dimensional textured-superconducting phase. The hard gap around the Fermi
energy disappears in these fragile inhomogeneous superconducting states, which
features, instead, V-shaped spin-resolved local density of states. The
inhomogeneous states are also competing with either a homogeneous
superconducting or a homogeneous ferromagnetic state, manifesting the
intertwining influences of the magnetic orders in Fe and Eu planes, the
spin-density wave band structure, and the superconducting pairing order.",2210.10312v1
2014-01-07,Dynamics of a first order transition to an absorbing state,"A granular system confined in a quasi two-dimensional box that is vertically
vibrated can transit to an absorbing state in which all particles bounce
vertically in phase with the box, with no horizontal motion. In principle, this
state can be reached for any density lower than the one corresponding to one
complete monolayer, which is then the critical density. Below this critical
value, the transition to the absorbing state is of first order, with long
metastable periods, followed by rapid transitions driven by homogeneous
nucleation. Molecular dynamics simulations and experiments show that there is a
dramatic increase on the metastable times far below the critical density; in
practice, it is impossible to observe spontaneous transitions close to the
critical density. This peculiar feature is a consequence of the non-equilibrium
nature of this first order transition to the absorbing state. A Ginzburg-Landau
model, with multiplicative noise, describes qualitatively the observed
phenomena and explains the macroscopic size of the critical nuclei. The nuclei
become of small size only close to a second critical point where the active
phase becomes unstable via a saddle node bifurcation. It is only close to this
second critical point that experiments and simulations can evidence spontaneous
transitions to the absorbing state while the metastable times grow dramatically
moving away from it.",1401.1839v2
2014-01-06,Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data,"In this paper we focus on a type of inverse problem in which the data is
expressed as an unknown function of the sought and unknown model function (or
its discretised representation as a model parameter vector). In particular, we
deal with situations in which training data is not available. Then we cannot
model the unknown functional relationship between data and the unknown model
function (or parameter vector) with a Gaussian Process of appropriate
dimensionality. A Bayesian method based on state space modelling is advanced
instead. Within this framework, the likelihood is expressed in terms of the
probability density function ($pdf$) of the state space variable and the sought
model parameter vector is embedded within the domain of this $pdf$. As the
measurable vector lives only inside an identified sub-volume of the system
state space, the $pdf$ of the state space variable is projected onto the space
of the measurables, and it is in terms of the projected state space density
that the likelihood is written; the final form of the likelihood is achieved
after convolution with the distribution of measurement errors. Application
motivated vague priors are invoked and the posterior probability density of the
model parameter vectors, given the data is computed. Inference is performed by
taking posterior samples with adaptive MCMC. The method is illustrated on
synthetic as well as real galactic data.",1401.1052v1
2018-05-10,Third family of compact stars within a nonlocal chiral quark model equation of state,"A class of hybrid compact star equations of state is investigated that joins
by a Maxwell construction a low-density phase of hadronic matter, modeled by a
relativistic meanfield approach with excluded nucleon volume, with a
high-density phase of color superconducting two-flavor quark matter, described
within a nonlocal covariant chiral quark model. We find the conditions on the
vector meson coupling in the quark model under which a stable branch of hybrid
compact stars occurs in the cases with and without diquark condensation. We
show that these hybrid stars do not form a third family disconnected from the
second family of ordinary neutron stars unless additional (de)confining effects
are introduced with a density-dependent bag pressure. A suitably chosen density
dependence of the vector meson coupling assures that at the same time the
$2~$M$_\odot$ maximum mass constraint is fulfilled on the hybrid star branch. A
twofold interpolation method is realized which implements both, the density
dependence of a confining bag pressure at the onset of the hadron-to-quark
matter transition as well as the stiffening of quark matter at higher densities
by a density-dependent vector meson coupling. For three parametrizations of
this class of hybrid equation of state the properties of corresponding compact
star sequences are presented, including mass twins of neutron and hybrid stars
at 2.00, 1.39 and 1.20 $M_\odot$, respectively. The sensitivity of the hybrid
equation of state and the corresponding compact star sequences to variations of
the interpolation parameters at the 10% level is investigated and it is found
that the feature of third family solutions for compact stars is robust against
such a variation. This advanced description of hybrid star matter allows to
interpret GW170817 as a merger not only of two neutron stars but also of a
neutron star with a hybrid star or of two hybrid stars.",1805.04105v3
2006-12-07,Density matrix of a quantum field in a particle-creating background,"We consider the time evolution of a quantized field in backgrounds that
violate the vacuum stability (particle-creating backgrounds). Our aim is to
study the exact form of the final quantum state (the density operator at a
final instant of time) that has emerged from a given arbitrary initial state
(from a given arbitrary density operator at the initial time instant) in the
course of the evolution. We find a generating functional that allows us to have
the density operators for any initial state. Averaging over states of a
subsystem of antiparticles (particles), we obtain explicit forms for reduced
density operators for subsystems of particles (antiparticles). Studying
one-particle correlation functions, we establish a one-to-one correspondence
between these functions and the reduced density operators. It is shown that in
the general case a presence of bosons (e.g. gluons) in an initial state
increases the creation rate of the same kind of bosons. We discuss the question
(and its relation to the initial stage of quark-gluon plasma formation) whether
a thermal form of one-particle distribution can appear even if the final state
of the complete system is not a thermal equilibrium. In this respect, we
discuss some cases when a pair creation by an electric-like field can mimic a
one-particle thermal distribution. We apply our technics to some QFT problems
in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric,
and metric. In particular, we study the time and temperature behavior of mean
numbers of created particles provided switching on and off effects of the
external field are negligible. It is shown that at high temperatures and in
slowly varying electric fields the rate of particle creation is essentially
time-dependent.",0612064v3
2012-10-28,"Toward an artificial Mott insulator: Correlations in confined, high-density electron liquids in SrTiO3","We investigate correlation physics in high-density, two-dimensional electron
liquids that reside in narrow SrTiO3 quantum wells. The quantum wells are
remotely doped via an interfacial polar discontinuity and the three-dimensional
(3D) carrier density is modulated by changing the width of the quantum well. It
is shown that even at 3D densities well below one electron per site,
short-range Coulomb interactions become apparent in transport, and an
insulating state emerges at a critical density. We also discuss the role of
disorder in the insulating state.",1210.7497v1
2013-05-30,Density Operator Description of Atomic Ordered Spatial Modes in Cavity QED,"We present a quantum Monte-Carlo simulation for a pumped atom in a strong
coupling cavity with dissipation, where two ordered spatial modes are formed
for the atomic probability density, with the peaks distributed either only in
the odd sites or only in the even ones of the lattice formed by the cavity
field. A mixed state density operator model, which describes the coupling
between different atomic spatial modes and the corresponding cavity field
components, is proposed, which goes beyond the pure state interpretation. We
develop a new decomposition treatment to derive the atomic spatial modes as
well as the cavity field statistics from the simulation results for the steady
state. With this treatment, we also investigate the dynamical process for the
probabilities of the atomic spatial modes in the adiabatic limit. According to
the analysis of the fitting error between the simulation results and the
density operator model, the latter is a good description for the system.",1305.7083v1
2014-12-26,Glass-like slow dynamics in a colloidal solid with multiple ground states,"We study the phase ordering dynamics of a two dimensional model colloidal
solid using molecular dynamics simulations. The colloid particles interact with
each other with a Hamaker potential modified by the presence of equatorial
""patches"" of attractive and negative regions. The total interaction potential
between two such colloids is, therefore, strongly directional and has
three-fold symmetry. Working in the canonical ensemble, we determine the
tentative phase diagram in the density-temperature plane which features three
distinct crystalline ground states viz, a low density honeycomb solid followed
by a rectangular solid at higher density, which eventually transforms to a
close packed triangular structure as the density is increased further. We show
that when cooled rapidly from the liquid phase along isochores, the system
undergoes a transition to a ""strong glass"" while slow cooling gives rise to
crystalline phases. We claim that geometrical frustration arising from the
presence of many crystalline ground states causes glassy ordering and dynamics
in this solid. Our results may be easily confirmed by suitable experiments on
patchy colloids.",1412.7915v1
2015-05-07,"Green's Dyadic, Spectral Function, Local Density of States, and Fluctuation Dissipation Theorem","The spectral functions are studied in conjunction with the dyadic Green's
functions for various media. The dyadic Green's functions are found using the
eigenfunction expansion method for homogeneous, inhomogeneous, periodic,
lossless, lossy, and anisotropic media, guided by the Bloch- Floquet theorem.
For the lossless media cases, the spectral functions can be directly related to
the photon local density of states, and hence, to the electromagnetic energy
density. For the lossy case, the spectral function can be related to the field
correlation function. Because of these properties, one can derive properties
for field correlations and the Langevin-source correlations without resorting
to the fluctuation dissipation theorem. The results are corroborated by the
fluctuation dissipation theorem. An expression for the local density of states
for lossy, inhomogeneous, and dispersive media has also been suggested.",1505.01586v1
2016-03-08,Tight-Binding Approximations to Time-Dependent Density Functional Theory - a fast approach for the calculation of electronically excited states,"We propose a new method of calculating electronically excited states that
combines a density functional theory (DFT) based ground state calculation with
a linear response treatment that employs approximations used in the
time-dependent density functional based tight binding (TD-DFTB) approach. The
new method termed TD-DFT+TB does not rely on the DFTB parametrization and is
therefore applicable to systems involving all combinations of elements. We show
that the new method yields UV/Vis absorption spectra that are in excellent
agreement with computationally much more expensive time-dependent density
functional theory (TD-DFT) calculations. Errors in vertical excitation energies
are reduced by a factor of two compared to TD-DFTB.",1603.02571v3
2017-08-13,Mixing Times for a Constrained Ising Process on the Two-Dimensional Torus at Low Density,"We study a kinetically constrained Ising process (KCIP) associated with a
graph $G$ and density parameter $p$; this process is an interacting particle
system with state space $\{ 0, 1 \}^{G}$, the location of the particles. The
`constraint' in the name of the process refers to the rule that a vertex cannot
change its state unless it has at least one neighbour in state `1'. The KCIP
has been proposed by statistical physicists as a model for the glass
transition. In this note, we study the mixing time of a KCIP on the
2-dimensional torus $G = \mathbb{Z}_{L}^{2}$ in the low-density regime $p =
\frac{c}{L^{2}}$ for arbitrary $0 < c < \infty$, extending our previous results
for the analogous process on the torus $\mathbb{Z}_{L}^{d}$ in dimension $d
\geq 3$. Our general approach is similar, but the extension requires more
delicate bounds on the behaviour of the process at intermediate densities.",1708.03838v1
2014-06-01,"Instanton Bags, High Density Holographic QCD and Chiral Symmetry Restoration","We describe the simplest example of an instanton bag in Euclidean space. It
consists of a monopole wall and a Kaluza-Klein monopole wall, lifted to one
higher dimension, trapping the instanton charge in the middle. This object has
finite instanton density in a three-dimensional volume.
  Baryon physics in holographic QCD models gets translated into a
multi-instanton problem in the bulk, and a state with a high density baryonic
charge consists of a non-diluted multi-instanton solution. The instanton bag is
a good candidate for this high-density state. We compute its parameters via
moduli stabilization. Chiral symmetry restoration is exhibited by this state,
and it is a direct consequence of its non-diluted features.",1406.0205v2
2019-01-16,nEoS: Neutron Star Equation of State from hadron physics alone,"We contribute a publicly available set of tables and code to provide
Equations of State (EoS) for matter at neutron star densities. Our EoSes are
constrained only by input from hadron physics and fundamental principles,
without feedback from neutron star observations, and so without relying on
General Relativity. They can therefore be used to test General Relativity
itself, as well as modified gravity theories, with neutron star observables,
without logical circularity. We have adapted state of the art results from NN
chiral potentials for the low--density limit, pQCD results for the
asymptotically high-density EoS, and use monotonicity and causality as the only
restrictions for intermediate densities, for the EoS sets to remain as
model-independent as is feasible today.",1901.05271v1
2019-06-16,Static Correlation Density Functional Theory,"Over the years, several schemes have been proposed to describe multireference
systems with Kohn-Sham Density Functional Theory. Problematic is the
combination of two aspects: the Kohn-Sham reference wavefunction is usually
taken to be a single Slater determinant, and approximate exchange-correlation
functionals are typically derived form the local density approximation. In this
work, we develop a theoretical framework that foregoes the single Slater
determinant and instead employs thermal states as reference states for
zero-temperature interacting systems. We provide convenient definitions of
static and dynamic correlation functionals via an adiabatic connection
approach. The formalism and computational results indicate that the entropic
term of the thermal reference state is a good approximation to the static
correlation functional. Hence, this work validates several reported results in
the literature and motivates additional developments of static correlation
density functionals.",1906.06661v2
2019-10-19,Ground state properties and shape evolution in Pt isotopes within the covariant density functional theory,"In this work, the ground-state properties of the platinum isotopic chain,
160-238Pt, are studied within the covariant density functional theory. The
calculations are carried out for a large number of even-even Pt isotopes by
using the density-dependent point-coupling and the density dependent
meson-exchange effective interactions. All ground-state properties such as the
binding energy, separation energy, two-neutron shell gap, rms-radii for
neutrons and protons and quadrupole deformation are discussed and compared with
available experimental data, and with the predictions of some nuclear models
such as the Relativistic Mean Field (RMF) model with NL3 functional and the
Hartree Fock Bogoliubov (HFB) method with SLy4 Skyrme force. The shape phase
transition for Pt isotopic chain is also studied. Its corresponding total
energy curves as well as the potential energy surfaces confirm the transition
from prolate to oblate shapes at 188Pt contrary to some studies predictions and
in agreement with others. Overall, a good agreement is found between the
calculated and experimental results wherever available.",1910.08775v2
2023-11-20,Dense $\textrm{QCD}_2$ with matrix product states,"We study one-flavor $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ lattice QCD in
($1+1$) dimensions at zero temperature and finite density using matrix product
states and the density matrix renormalization group. We compute physical
observables such as the equation of state, chiral condensate, and quark
distribution function as functions of the baryon number density. As a physical
implication, we discuss the inhomogeneous phase at nonzero baryon density,
where the chiral condensate is inhomogeneous, and baryons form a crystal. We
also discuss how the dynamical degrees of freedom change from hadrons to quarks
through the formation of quark Fermi seas.",2311.11643v1
2006-06-20,A First-Principles Method for Open Electronic Systems,"We prove that the electron density function of a real physical system can be
uniquely determined by its values on any finite subsystem. This establishes the
existence of a rigorous density-functional theory for any open electronic
system. By introducing a new density functional for dissipative interactions
between the reduced system and its environment, we subsequently develop a
time-dependent density-functional theory which depends in principle only on the
electron density of the reduced system. In the steady-state limit, the
conventional first-principles nonequilibrium Green's function formulation for
the current is recovered. A practical scheme is proposed for the new density
functional: the wide-band limit approximation, which is applied to simulate the
transient current through a model molecular device.",0606169v1
2016-08-25,Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix,"Quantum Monte Carlo (QMC) methods are one of the most important tools for
studying interacting quantum many-body systems. The vast majority of QMC
calculations in interacting fermion systems require a constraint to control the
sign problem. The constraint involves an input trial wave function which
restricts the random walks. We introduce a systematically improvable constraint
which relies on the fundamental role of the density or one-body density matrix.
An independent-particle calculation is coupled to an auxiliary-field QMC
calculation. The independent-particle solution is used as the constraint in
QMC, which then produces the input density or density matrix for the next
iteration. The constraint is optimized by the self-consistency between the
many-body and independent-particle calculations. The approach is demonstrated
in the two-dimensional Hubbard model by accurately determining the ground state
when collective modes separated by tiny energy scales are present in the
magnetic and charge correlations. Our approach also provides an ab initio way
to predict effective interaction parameters for independent-particle
calculations.",1608.07154v2
2023-09-01,Calculation of microscopic nuclear level densities based on covariant density functional theory,"A microscopic method for calculating nuclear level density (NLD) based on the
covariant density functional theory (CDFT) is developed. The particle-hole
state density is calculated by combinatorial method using the single-particle
levels schemes obtained from the CDFT. Then the level densities are obtained by
taking into account collective effects such as vibration and rotation. Our
results are compared with those from other NLD models, including
phenomenological, microstatistical, and non-relativistic HFB combinatorial
models. The comparison suggests that the general trends among these models are
basically the same, except for some deviations from different NLD models. In
addition, the NLDs of the CDFT combinatorial method with normalization are
compared with experimental data, including the observed cumulative number of
levels at low excitation energy and the measured NLDs. Compared with the
existing experimental data, the CDFT combinatorial method can give reasonable
results.",2309.00354v1
1994-03-17,Can Density-matrix renormalization group be Applied to two dimensional systems?,"In order to extend the density-matrix renormalization-group (DMRG) method to
two-dimensional systems, we formulate two alternative methods to prepare the
initial states. We find that the number of states that is needed for accurate
energy calculations grows exponentially with the linear system size. We also
analyze how the states kept in the DMRG method manage to preserve both the
intrablock and interblock Hamiltonians, which is the key to the high accuracy
of the method. We also prove that the energy calculated on a finite cluster is
always a variational upper bound.",9403069v1
1995-05-22,Broken rotation symmetry in the fractional quantum Hall system,"We demonstrate that the two-dimensonal electron system in a strong
perpendicular magnetic field has stable states which break rotational but not
translational symmetry. The Laughlin fluid becomes unstable to these states in
quantum wells whose thickness exceeds a critical value which depends on the
electron density. The order parameter at 1/3 reduced density resembles that of
a nematic liquid crystal, in that a residual two-fold rotation axis is present
in the low symmetry phase. At filling factors 1/5 and 1/7, there are states
with four- and six-fold axes, as well. We discuss the experimental detection of
these phases.",9505099v1
1999-07-12,Quantum Hall Transitions in Field Induced Spin Density Wave Systems,"Field Induced Spin Density Wave (FISDW) systems exhibit coexistence phases
between well defined quantum Hall plateau phases with even integers 2N and 2N'.
We show that a disordered coexistence region accounts for the observed peaks in
the longitudinal resistivity as the field varies between plateaux. It also
results in a random spin mixing which yields two energy split extended states.
The longitudinal resistance is expected to show peaks witha temperature (T)
dependent width proportional to the kappa's power of T. The peak width should
saturate below the non-nesting interlayer coupling of order 40 mK",9907170v1
2009-07-02,Novel Low-Temperature Behavior in Classical Many-Particle Systems,"We show that classical many-particle systems interacting with certain soft
pair interactions in two dimensions exhibit novel low-temperature behaviors.
Ground states span from disordered to crystalline. At some densities, a large
fraction of normal-mode frequencies vanish. Lattice ground-state configurations
have more vanishing frequencies than disordered ground states at the same
density and exhibit vanishing shear moduli. For the melting transition from a
crystal, the thermal expansion coefficient is negative. These unusual results
are attributed to the topography of the energy landscape.",0907.0447v1
2013-12-04,Excitations and quasi-one-dimensionality in field-induced nematic and spin density wave states,"We study the excitation spectrum and dynamical response functions for several
quasi-one-dimensional spin systems in magnetic fields without dipolar spin
order transverse to the field. This includes both nematic phases, which harbor
""hidden"" breaking of spin-rotation symmetry about the field and have been
argued to occur in high fields in certain frustrated chain systems with
competing ferromagnetic and antiferromagnetic interactions, and spin density
wave states, in which spin-rotation symmetry is truly unbroken. Using
bosonization, field theory, and exact results on the integrable sine-Gordon
model, we establish the collective mode structure of these states, and show how
they can be distinguished experimentally.",1312.0992v1
2014-12-29,Probing barrier transmission in ballistic graphene,"We derive the local density of states from itinerant and boundary states
around transport barriers and edges in graphene and show that the itinerant
states lead to mesoscale undulations that could be used to probe their
scattering properties in equilibrium without the need for lateral transport
measurements. This finding will facilitate vetting of extended structural
defects such as grain boundaries or line defects as transport barriers for
switchable graphene resonant tunneling transistors. We also show that barriers
could exhibit double minima and that the charge density away from highly
reflective barriers and edges scales as $x^{-2}$.",1412.8512v1
2017-11-20,Quantum Quench dynamics in Non-local Luttinger Model: Rigorous Results,"We investigate, in the Luttinger model with fixed box potential, the time
evolution of an inhomogeneous state prepared as a localized fermion added to
the noninteracting ground state. We proved that, if the state is evolved with
the interacting Hamiltonian, the averaged density has two peaks moving in
opposite directions, with a constant but renormalized velocity. We also proved
that a dynamical `Landau quasi-particle weight' appears in the oscillating part
of the averaged density, asymptotically vanishing with large time. The results
are proved with the Mattis-Lieb diagonalization method. A simpler proof with
the exact Bosonization formulas is also provided.",1711.07507v1
2023-04-04,Quantum Fisher Information for Different States and Processes in Quantum Chaotic Systems,"The quantum Fisher information (QFI) associated with a particular process
applied to a many-body quantum system has been suggested as a diagnostic for
the nature of the system's quantum state, e.g., a thermal density matrix vs. a
pure state in a system that obeys the eigenstate thermalization hypothesis
(ETH). We compute the QFI for both an energy eigenstate and a thermal density
matrix for a variety of processes in a system obeying ETH, including a change
in the hamiltonian that is either sudden (a quench), slow (adiabatic), or
followed by contact with a heat bath. We compare our results with earlier
results for a local unitary transformation.",2304.01657v1
2001-02-13,Vibrational spectrum of topologically disordered systems,"The topological nature of the disorder of glasses and supercooled liquids
strongly affects their high-frequency dynamics. In order to understand its main
features, we analytically studied a simple topologically disordered model,
where the particles oscillate around randomly distributed centers, interacting
through a generic pair potential. We present results of a resummation of the
perturbative expansion in the inverse particle density for the dynamic
structure factor and density of states. This gives accurate results for the
range of densities found in real systems.",0102230v2
2003-07-17,On the validity of the Boltzmann equation to describe low density granular systems,"The departure of a granular gas in the instable region of parameters from the
initial homogeneous cooling state is studied. Results from Molecular Dynamics
and from Direct Monte Carlo simulation of the Boltzmann equation are compared.
It is shown that the Boltzmann equation accurately predicts the low density
limit of the system. The relevant role played by the parallelization of the
velocities as time proceeds and the dependence of this effect on the density is
analyzed in detail.",0307410v1
2005-05-29,A uniqueness theorem in a density-matrix functional theory,"Uniqueness of effective interaction defined in an extension of the Kohn-Sham
theory is proved, if the model with a non-degenerate ground state exists and to
reproduce a correlation function as well as the single-particle density of an
electron system. The two-body interaction term is regarded as a Hubbard-type
short range interaction term. The interaction strength is a functional of an
element of a two-body reduced density matrix of the electron system. The
uniqueness theorem gives a basic principle for effective description of
electron systems.",0505703v2
2006-03-20,Analytic solution of charge density of single wall carbon nanotube in conditions of field electron emission,"We derived the analytic solution of induced electrostatic potential along
single wall carbon nanotubes. Under the hypothesis of constant density of
states in the charge-neutral level, we are able to obtain the linear density of
excess charge in an external field parallel to the tube axis.",0603509v2
2002-11-05,All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity,"Via a straightforward integration of the Einstein equations with cosmological
constant, all static circularly symmetric perfect fluid 2+1 solutions are
derived. The structural functions of the metric depend on the energy density,
which remains in general arbitrary. Spacetimes for fluids fulfilling linear and
polytropic state equations are explicitly derived; they describe, among others,
stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate
fermions, incoherent and pure radiation. As a by--product, we demonstrate the
uniqueness of the constant energy density perfect fluid within the studied
class of metrics. A full similarity of the perfect fluid solutions with
constant energy density of the 2+1 and 3+1 gravities is established.",0211014v1
2003-10-10,Spontaneous symmetry breaking in strong-coupling lattice QCD at high density,"We determine the patterns of spontaneous symmetry breaking in strong-coupling
lattice QCD in a fixed background baryon density. We employ a
next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f)
chiral symmetry of the continuum theory. We find that the global symmetry of
the ground state varies with N_f and with the background baryon density. In all
cases the condensate breaks the discrete rotational symmetry of the lattice as
well as part of the chiral symmetry group.",0310032v2
1999-11-09,Parity Dependence of Nuclear Level Densities,"A simple formula for the ratio of the number of odd- and even-parity states
as a function of temperature is derived. This formula is used to calculate the
ratio of level densities of opposite parities as a function of excitation
energy. We test the formula with quantum Monte Carlo shell model calculations
in the $(pf+g_{9/2})$-shell. The formula describes well the transition from low
excitation energies where a single parity dominates to high excitations where
the two densities are equal.",9911036v1
2008-12-13,Spin-Transfer Torque in Helical Spin-Density Waves,"The current driven magnetisation dynamics of a helical spin-density wave is
investigated. Expressions for calculating the spin-transfer torque of real
systems from first principles density functional theory are presented. These
expressions are used for calculating the spin-transfer torque for the spin
spirals of Er and fcc Fe at two different lattice volumes. It is shown that the
calculated torque induces a rigid rotation of the order parameter with respect
to the spin spiral axis. The torque is found to depend on the wave vector of
the spin spiral and the spin-polarisation of the Fermi surface states. The
resulting dynamics of the spin spiral is also discussed.",0812.2509v1
2011-06-16,The liquid-vapor interface of the restricted primitive model of ionic fluids from a density functional approach,"We investigate the liquid-vapor interface of the restricted primitive model
for an ionic fluid using a density functional approach. The applied theory
includes the electrostatic contribution to the free energy functional arising
from the bulk energy equation of state and the mean spherical approximation for
a restricted primitive model, as well as the associative contribution, due to
the formation of pairs of ions. We compare the density profiles and the values
of the surface tension with previous theoretical approaches.",1106.3236v1
2018-05-14,Terminal Holographic Complexity,"We introduce a quasilocal version of holographic complexity adapted to
`terminal states' such as spacelike singularities. We use a modification of the
action-complexity ansatz, restricted to the past domain of dependence of the
terminal set, and study a number of examples whose symmetry permits explicit
evaluation, to conclude that this quantity enjoys monotonicity properties after
the addition of appropriate counterterms. A notion of `complexity density' can
be defined for singularities by a coarse-graining procedure. This definition
assigns finite complexity density to black hole singularities but vanishing
complexity density to either generic FRW singularities or chaotic BKL
singularities. We comment on the similarities and differences with Penrose's
Weyl curvature criterion.",1805.05291v1
2017-10-19,Holographic picture of heavy vector mesons in a finite density plasma,"We present the results of a holographic model for heavy vector mesons inside
a plasma at finite temperature and density. The spectral function shows a nice
description of the dissociation of the mesons in the medium, corresponding to
the decrease in the height of the peaks as the temperature and (or) the density
increase. We consider the case of bottomonium states at finite temperature and
also the case of charmonium dissociation at zero temperature but finite
chemical potential.",1710.07111v1
2022-09-09,A Laplace Mixture Representation of the Horseshoe and Some Implications,"The horseshoe prior, defined as a half Cauchy scale mixture of normal,
provides a state of the art approach to Bayesian sparse signal recovery. We
provide a new representation of the horseshoe density as a scale mixture of the
Laplace density, explicitly identifying the mixing measure. Using the
celebrated Bernstein--Widder theorem and a result due to Bochner, our
representation immediately establishes the complete monotonicity of the
horseshoe density and strong concavity of the corresponding penalty.
Consequently, the equivalence between local linear approximation and
expectation--maximization algorithms for finding the posterior mode under the
horseshoe penalized regression is established. Further, the resultant estimate
is shown to be sparse.",2209.04510v2
2017-01-13,Fast Reconstruction of High-qubit Quantum States via Low Rate Measurements,"Due to the exponential complexity of the resources required by quantum state
tomography (QST), people are interested in approaches towards identifying
quantum states which require less effort and time. In this paper, we provide a
tailored and efficient method for reconstructing mixed quantum states up to
$12$ (or even more) qubits from an incomplete set of observables subject to
noises. Our method is applicable to any pure or nearly pure state $\rho$, and
can be extended to many states of interest in quantum information processing,
such as multi-particle entangled $W$ state, GHZ state and cluster states that
are matrix product operators of low dimensions. The method applies the quantum
density matrix constraints to a quantum compressive sensing optimization
problem, and exploits a modified Quantum Alternating Direction Multiplier
Method (Quantum-ADMM) to accelerate the convergence. Our algorithm takes $8,35$
and $226$ seconds respectively to reconstruct superposition state density
matrices of $10,11,12$ qubits with acceptable fidelity, using less than $1 \%$
of measurements of expectation. To our knowledge it is the fastest realization
that people can achieve using a normal desktop. We further discuss applications
of this method using experimental data of mixed states obtained in an ion trap
experiment of up to $8$ qubits.",1701.03695v6
2011-11-14,Time-reversal symmetry breaking state near the surface of $s_{\pm}$-superconductor,"The structure of superconducting order parameter near the surface of a
two-band superconductor with $s_{\pm}$ order parameter in the bulk is
theoretically investigated. The main parameter of the surface, which determines
the appropriate physics is the coefficient of the interband scattering
$R_{12}$. For small $R_{12}$ the superconducting order parameter is only
suppressed to some extent near the surface for the both bands. For intermediate
and strong interband scattering there are two possible non-trivial surface
states of the order parameter: (i) purely real solution, where the symmetry of
the superconducting state near the surface is changed from $s_{\pm}$ to
conventional $s_{++}$ and (ii) time-reversal symmetry breaking (TRB) state. In
this state the order parameters in the two bands acquire phases $\phi_{1,2}(x)
\neq (0,\pi)$ upon approaching the surface. We argue that at low temperatures
the TRB surface state can be more energetically favorable than the $s_{\pm} \to
s_{++}$ time reversal symmetry conserving state (TR). For higher temperatures
up to $T_c$ only the TR state can exist. The transition between the two
temperature regions is rather sharp. Signatures of the transition between the
TRB and the TR surface states can be detected by the measurements of the local
density of states and the angle-resolved density of states.",1111.3130v1
2002-07-28,Sliding Density-Wave in Sr_{14}Cu_{24}O_{41} Ladder Compounds,"We used transport and Raman scattering measurements to identify the
insulating state of self-doped spin 1/2 two-leg ladders of Sr_{14}Cu_{24}O_{41}
as a weakly pinned, sliding density wave with non-linear conductivity and a
giant dielectric response that persists to remarkably high temperatures.",0207666v1
1994-08-18,Anharmonic decay of phonons in semiconductors from first-principles calculations,"The anharmonic contribution to phonon lifetime and its temperature dependence
is calculated from first principle in C, Si and Ge using third-order
density-functional perturbation theory. Good agreement with available
experimental data is obtained. Different competing two-phonon decay channels
are compared and correlated with the density of final states.",9408051v1
2004-10-08,Instability toward biexciton crystallization in one-dimensional electron-hole systems,"One-dimensional (1D) electron-hole (e-h) systems in a high-density regime is
investigated by means of bozonization techniques. It turned out that the
systems are insulating even at the high density limit and that the exciton Mott
transition (insulator-to-metal transition) never occurs at absolute zero
temperature. The insulating ground state exhibits a strong instability towards
the crystallization of biexcitons.",0410193v1
2003-10-15,Loops and Power Counting in the High Density Effective Field Theory,"We introduce the high density effective theory of QCD. We discuss, in
particular, the problem of developing a consistent power counting scheme.",0310176v1
2008-10-20,Recent theoretical progress in perturbative QCD,"We review selected recent theoretical activity in perturbative QCD. We focus
on progress in the description of parton densities, including latest
developments in neural network parton densities, on the description of high
multiplicity final states at the LHC at leading and next-to-leading order, on
progress in next-to-next-to-leading order, and on novel developments in jets
physics.",0810.3524v1
2014-10-22,Smooth densities for SDEs driven by subordinated Brownian motion with Markovian switching,"In this paper we consider a class of stochastic differential equations driven
by subordinate Brownian motion with Markovian switching. We use Malliavin
calculus to study the smoothness of the density for the solution under uniform
H\""ormander's type condition.",1410.5913v2
2018-05-18,The Sub-Geometric Phases in Density Matrix,"In this letter, the generalization of geometric phase in density matrix is
presented, we show that the extended sub-geometric phase have unified
expression whatever in adiabatic or nonadiabatic procedure, the relations
between them and the usual Berry phase or Aharonov-Anandan phase are
established. We also demonstrated the influence of sub-geometric phases on the
physical observables. Finally, our treatment is naturally used to investigate
the geometric phase in mixed state.",1805.07355v1
2023-09-12,Limited regularity of a specific electronic reduced density matrix for molecules,"We consider an electronic bound state of the usual, non-relativistic,
molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons
(N>1). Near appropriate electronic collisions, we prove that the (N-1)-particle
electronic reduced density matrix is not smooth.",2309.06318v2
2024-01-26,Data-dependent density estimation for the Fokker-Planck equation in higher dimensions,"We present a new strategy to approximate the global solution of the
Fokker-Planck equation efficiently in higher dimensions and show its
convergence. The main ingredients are the Euler scheme to solve the associated
stochastic differential equation and a histogram method for tree-structured
density estimation on a data-dependent partitioning of the state space R^d.",2401.14685v1
2019-09-20,A geometric measure of non-classicality,"This paper aims to stress the role of the Cahill-Glauber quasi-probability
densities in defining, detecting, and quantifying the non-classicality of field
states in quantum optics. The distance between a given pure state and the set
of all pure classical states is called here a geometric degree of
non-classicality. As such, we investigate non-classicality of a pure
single-mode state of the radiation field by using the coherent states as a
reference set of pure classical states. It turns out that any such distance is
expressed in terms of the maximal value of the Husimi $Q$ function. As an
insightful application we consider the de-Gaussification process produced when
preparing a quantum state by adding $p$ photons to a pure Gaussian one. For a
coherent-state input, we get an analytic degree of non-classicality which
compares interestingly with the previously evaluated entanglement potential.
Then we show that addition of a single photon to a squeezed vacuum state causes
a considerable enhancement of non-classicality, especially at weak and moderate
squeezing of the original state. By contrast, addition of further photons is
less effective.",1909.09433v2
2015-06-08,Steady State of Pedestrian Flow in Bottleneck Experiments,"Experiments with pedestrians could depend strongly on initial conditions.
Comparisons of the results of such experiments require to distinguish carefully
between transient state and steady state. In this work, a feasible algorithm -
Cumulative Sum Control Chart - is proposed and improved to automatically detect
steady states from density and speed time series of bottleneck experiments. The
threshold of the detection parameter in the algorithm is calibrated using an
autoregressive model. Comparing the detected steady states with previous
manually selected ones, the modified algorithm gives more reproducible results.
For the applications, three groups of bottleneck experiments are analysed and
the steady states are detected. The study about pedestrian flow shows that the
difference between the flows in all states and in steady state mainly depends
on the ratio of pedestrian number to bottleneck width. When the ratio is higher
than a critical value (approximately 115 persons/m), the flow in all states is
almost identical with the flow in steady state. Thus we have more possibilities
to compare the flows from different experiments, especially when the detection
of steady states is difficult.",1506.02433v1
2018-09-10,Negativity volume of the generalized Wigner function as an entanglement witness for hybrid bipartite states,"In a recent paper, Tilma, Everitt {\it et al.} derived a generalized Wigner
function that can characterize both the discrete and continuous variable
states, i.e., hybrid states. As such, one can expect that the negativity of the
generalized Wigner function applied to the hybrid states can reveal their
nonclassicality, in analogy with the well-known Wigner function defined for the
continuous variable states. In this work, we demonstrate that, indeed, the
negativity volume of the generalized Wigner function of the hybrid bipartite
states can be used as an entanglement witness for such states, provided that it
exceeds a certain critical value. In particular, we study hybrid bipartite
qubit-bosonic states and provide a qubit-Schr\""{o}dinger cat state as an
example. Since the detection of the generalized Wigner function of hybrid
bipartite states in phase space can be experimentally simpler than the
tomographic reconstruction of the corresponding density matrix, our results,
therefore, present a convenient tool in the entanglement identification of such
states.",1809.03617v2
2023-02-06,Three-$α$ configurations of the second $J^π=2^+$ state in $^{12}$C,"We investigate geometric configurations of $\alpha$ ($^4$He nucleus) clusters
in the second $J^\pi=2^+$ state of $^{12}$C, which has been discussed as a
rotational band member of the second $0^+$ state, the Hoyle state. The ground
and excited $0^+$ and $2^+$ states are described by a three-$\alpha$ cluster
model. The three-body Schr\""odinger equation with orthogonality conditions is
accurately solved by the stochastic variational method with correlated Gaussian
basis functions. To analyse the structure of these resonant states in a
convenient form, we introduce a confining potential. The two-body density
distributions together with the spectroscopic information clarify the structure
of these states. We find that main configurations of both the second $0^+$ and
$2^+$ states are acute-angled triangle shapes originating from the
$^8$Be($0^+$)$+\alpha$ configuration. However, the $^8$Be$+\alpha$ components
in the second $2^+$ state become approximately 2/3 because the 8Be subsystem is
hard to excite, indicating that the state is not an ideal rigid rotational band
member of the Hoyle state.",2302.02539v1
2020-01-06,The mean-field limit of quantum Bose gases at positive temperature,"We prove that the grand canonical Gibbs state of an interacting quantum Bose
gas converges to the Gibbs measure of a nonlinear Schr\""odinger equation in the
mean-field limit, where the density of the gas becomes large and the
interaction strength is proportional to the inverse density. Our results hold
in dimensions $d \leq 3$. For $d > 1$ the Gibbs measure is supported on
distributions of negative regularity and we have to renormalize the
interaction. More precisely, we prove the convergence of the relative partition
function and of the reduced density matrices in the $L^r$-norm with optimal
exponent $r$. Moreover, we prove the convergence in the $L^\infty$-norm of
Wick-ordered reduced density matrices, which allows us to control correlations
of Wick-ordered particle densities as well as the asymptotic distribution of
the particle number. Our proof is based on a functional integral representation
of the grand canonical Gibbs state, in which convergence to the mean-field
limit follows formally from an infinite-dimensional stationary phase argument
for ill-defined non-Gaussian measures. We make this argument rigorous by
introducing a white-noise-type auxiliary field, through which the functional
integral is expressed in terms of propagators of heat equations driven by
time-dependent periodic random potentials and can, in turn, be expressed as a
gas of interacting Brownian loops and paths. When the gas is confined by an
external trapping potential, we control the decay of the reduced density
matrices using excursion probabilities of Brownian bridges.",2001.01546v2
2000-11-04,Maximally incompressible neutron star matter,"Relativistic kinetic theory, based on the Grad method of moments as developed
by Israel and Stewart, is used to model viscous and thermal dissipation in
neutron star matter and determine an upper limit on the maximum mass of neutron
stars. In the context of kinetic theory, the equation of state must satisfy a
set of constraints in order for the equilibrium states of the fluid to be
thermodynamically stable and for perturbations from equilibrium to propagate
causally via hyperbolic equations. Application of these constraints to neutron
star matter restricts the stiffness of the most incompressible equation of
state compatible with causality to be softer than the maximally incompressible
equation of state that results from requiring the adiabatic sound speed to not
exceed the speed of light. Using three equations of state based on experimental
nucleon-nucleon scattering data and properties of light nuclei up to twice
normal nuclear energy density, and the kinetic theory maximally incompressible
equation of state at higher density, an upper limit on the maximum mass of
neutron stars averaging 2.64 solar masses is derived.",0011107v2
2011-06-07,Correlations in excited states of local Hamiltonians,"Physical properties of the ground and excited states of a $k$-local
Hamiltonian are largely determined by the $k$-particle reduced density matrices
($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least
enough for the calculation of the ground state and excited state energies.
Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even
the state itself is completely determined by its $k$-RDMs, and therefore
contains no genuine ${>}k$-particle correlations, as they can be inferred from
$k$-particle correlation functions. It is natural to ask whether a similar
result holds for non-degenerate excited states. In fact, for fermionic systems,
it has been conjectured that any non-degenerate excited state of a 2-local
Hamiltonian is simultaneously a unique ground state of another 2-local
Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version
of this conjecture states that any non-degenerate excited state of a 2-local
Hamiltonian is uniquely determined by its 2-matrix among all the pure
$n$-particle states. We construct explicit counterexamples to show that both
conjectures are false. It means that correlations in excited states of local
Hamiltonians could be dramatically different from those in ground states. We
further show that any non-degenerate excited state of a $k$-local Hamiltonian
is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely
determined by its $2k$-RDMs (or $2k$-matrix).",1106.1373v2
2008-09-23,Spectral statistics of the quenched normal modes of a network-forming molecular liquid,"We evaluate the density of states of the quenched normal modes of ST2 water,
and their statistical fluctuations, for a range of densities spanning three
regimes of behavior of a hydrogen bonded liquid: a lower-density regime of
random tetrahedral network formation; in the vicinity of a liquid-liquid
critical point; and in a higher-density regime of fragile glass-forming
behavior. For all cases we find that the fluctuations around the mean spectral
densities obey the predictions of the Gaussian orthogonal ensemble of random
matrix theory. We also measure the participation ratio of the normal modes
across the entire frequency range, and find behavior consistent with the
majority of modes being of an extended nature, rather than localized.",0809.3954v2
2022-12-03,Dark Energy Density and IS (Israel-Stewart) Bulk Viscosity Model,"We investigate the thermodynamics of a dark energy bulk viscosity model as a
cosmic fluid. In this regard, the two theories of Eckart and Israel-Stewart
(IS) are the basis of our work. Therefore, we first investigate the
thermodynamics of cosmic fluids in the dark energy bulk viscosity model and the
general relationships. Then, we express the thermodynamic relationships of
Eckart's theory. Due to the basic equations of Eckart's theory and Friedmann's
equations, we consider two states, one is $p=-\rho$ (standard) and the other is
$p\neq-\rho$ (non-standard). In the standard state, we define the pressure
$(p)$, energy density $(\rho)$, and bulk viscosity coefficient $(\xi)$ of the
cosmic fluid in terms of cosmic time and we obtain its relations. We also
mention that in this standard state, because of $p=-\rho$, the value of $a(t)$
is zero, so $a(t)$ is not defined in this state. But in the non-standard case
$(p\neq-\rho)$ the bulk viscosity coefficient $(\xi)$ is zero and only the
scale factor and pressure and energy density of the cosmic fluid is defined. We
also consider two states of constant and variable bulk viscosity coefficients
and obtain three Hubble constant parameters and scale factors in terms of
cosmic time, and energy density in terms of the scale factor. In the state of
variable bulk viscosity coefficient, we consider the viscosity coefficient as
the power-law from energy density $(\xi=\alpha\rho^{s})$, which is $\alpha>0$
and a constant. Following, we discuss the dissipative effects of cosmic fluids
and examine the effects of energy density for dark energy in the
Israel-Stewart(IS) theory. The results are comprehensively presented in two
tables (1) and (2).",2212.03818v2
2020-05-15,Dynamics of the vacuum state in a periodically driven Rydberg chain,"We study the dynamics of the periodically driven Rydberg chain starting from
the state with zero Rydberg excitations (vacuum state denoted by $|0\rangle$)
using a square pulse protocol in the high drive amplitude limit. We show, using
exact diagonalization for finite system sizes ($L\le 26$), that the Floquet
Hamiltonian of the system, within a range of drive frequencies which we chart
out, hosts a set of quantum scars which have large overlap with the $|0\rangle$
state. These scars are distinct from their counterparts having high overlap
with the maximal Rydberg excitation state ($|\mathbb{Z}_2\rangle$); they
coexist with the latter class of scars and lead to persistent coherent
oscillations of the density-density correlator starting from the $|0\rangle$
state. We also identify special drive frequencies at which the system undergoes
perfect dynamic freezing and provide an analytic explanation for this
phenomenon. Finally, we demonstrate that for a wide range of drive frequencies,
the system reaches a steady state with sub-thermal values of the
density-density correlator. The presence of such sub-thermal steady states,
which are absent for dynamics starting from the $|\mathbb{Z}_2\rangle$ state,
imply a weak violation of the eigenstate thermalization hypothesis in finite
sized Rydberg chains distinct from that due to the scar-induced persistent
oscillations reported earlier. We conjecture that in the thermodynamic limit
such states may exist as pre-thermal steady states that show anomalously slow
relaxation. We supplement our numerical results by deriving an analytic
expression for the Floquet Hamiltonian using a Floquet perturbation theory in
the high amplitude limit which provides an analytic, albeit qualitative,
understanding of these phenomena at arbitrary drive frequencies. We discuss
experiments which can test our theory.",2005.07715v1
2011-04-10,Entropic algorithms and the lid method as exploration tools for complex landscapes,"Monte Carlo algorithms such as the Wang-Landau algorithm and similar
`entropic' methods are able to accurately sample the density of states of model
systems and thereby give access to thermal equilibrium properties at any
temperature. Thermal equilibrium is however not achievable at low temperatures
in glassy systems. Such systems are characterized by a multitude of metastable
configurations, pictorially referred to as `valleys' of an energy landscape.
Geometrical properties of the landscape, e.g. the local density of states
describing the distribution in energy of the states belonging to a single
valley, are key to understand the dynamical properties of such systems. In this
paper we combine the lid algorithm, a tool for landscape exploration previously
applied to a range of models, with the Wang-Swendsen algorithm. To test this
improved exploration tool, we consider a paradigmatic complex system, the
Edwards-Andersom model in two and three spatial dimension. We find a striking
difference between the energy dependence of the local density of states in the
two cases: nearly flat in the first case, and nearly exponential in the second.
The lid dependence of the data is analyzed to estimate the form of the global
density of states.",1104.1780v2
2023-08-25,Evidence of the Coulomb gap in the density of states of MoS$_2$,"$\mathrm{MoS_2}$ is an emergent van der Waals material that shows promising
prospects in semiconductor industry and optoelectronic applications. However,
its electronic properties are not yet fully understood. In particular, the
nature of the insulating state at low carrier density deserves further
investigation, as it is important for fundamental research and applications. In
this study, we investigate the insulating state of a dual-gated exfoliated
bilayer $\mathrm{MoS_2}$ field-effect transistor by performing magnetotransport
experiments. We observe positive and non-saturating magnetoresistance, in a
regime where only one band contributes to electron transport. At low electron
density ($\sim 1.4\times 10^{12}~\mathrm{cm^{-2}}$) and a perpendicular
magnetic field of 7 Tesla, the resistance exceeds by more than one order of
magnitude the zero field resistance and exponentially drops with increasing
temperature. We attribute this observation to strong electron localization.
Both temperature and magnetic field dependence can, at least qualitatively, be
described by the Efros-Shklovskii law, predicting the formation of a Coulomb
gap in the density of states due to Coulomb interactions. However, the
localization length obtained from fitting the temperature dependence exceeds by
more than one order of magnitude the one obtained from the magnetic field
dependence. We attribute this discrepancy to the presence of a nearby metallic
gate, which provides electrostatic screening and thus reduces long-range
Coulomb interactions. The result of our study suggests that the insulating
state of $\mathrm{MoS_2}$ originates from a combination of disorder-driven
electron localization and Coulomb interactions.",2308.13337v2
2007-10-05,Axial anomaly and magnetism of nuclear and quark matter,"We consider the response of the QCD ground state at finite baryon density to
a strong magnetic field B. We point out the dominant role played by the
coupling of neutral Goldstone bosons, such as pi^0, to the magnetic field via
the axial triangle anomaly. We show that, in vacuum, above a value of B ~
m_pi^2/e, a metastable object appears - the pi^0 domain wall. Because of the
axial anomaly, the wall carries a baryon number surface density proportional to
B. As a result, for B ~ 10^{19} G a stack of parallel pi^0 domain walls is
energetically more favorable than nuclear matter at the same density.
Similarly, at higher densities, somewhat weaker magnetic fields of order B ~
10^{17}-10^{18} G transform the color-superconducting ground state of QCD into
new phases containing stacks of axial isoscalar (eta or eta') domain walls. We
also show that a quark-matter state known as ``Goldstone current state,'' in
which a gradient of a Goldstone field is spontaneously generated, is
ferromagnetic due to the axial anomaly. We estimate the size of the fields
created by such a state in a typical neutron star to be of order
10^{14}-10^{15} G.",0710.1084v2
2008-11-15,Universality of shear-banding instability and crystallization in sheared granular fluid,"The linear stability analysis of an uniform shear flow of granular materials
is revisited using several cases of a Navier-Stokes'-level constitutive model
in which we incorporate the global equation of states for pressure and thermal
conductivity (which are accurate up-to the maximum packing density $\nu_{m}$)
and the shear viscosity is allowed to diverge at a density $\nu_\mu$ ($<
\nu_{m}$), with all other transport coefficients diverging at $\nu_{m}$. It is
shown that the emergence of shear-banding instabilities (for perturbations
having no variation along the streamwise direction), that lead to shear-band
formation along the gradient direction, depends crucially on the choice of the
constitutive model. In the framework of a dense constitutive model that
incorporates only collisional transport mechanism, it is shown that an accurate
global equation of state for pressure or a viscosity divergence at a lower
density or a stronger viscosity divergence (with other transport coefficients
being given by respective Enskog values that diverge at $\nu_m$) can induce
shear-banding instabilities, even though the original dense Enskog model is
stable to such shear-banding instabilities. For any constitutive model, the
onset of this shear-banding instability is tied to a {\it universal} criterion
in terms of constitutive relations for viscosity and pressure, and the sheared
granular flow evolves toward a state of lower ""dynamic"" friction, leading to
the shear-induced band formation, as it cannot sustain increasing dynamic
friction with increasing density to stay in the homogeneous state. A similar
criterion of a lower viscosity or a lower viscous-dissipation is responsible
for the shear-banding state in many complex fluids.",0811.2459v1
2021-07-21,A Quantum Mechanics Conservation of Energy Equation for Stationary States with Real Valued Wave Functions,"Many-body quantum-mechanical stationary states that have real valued
wavefunctions are shown to satisfy a classical conservation of energy equation
with a kinetic energy function. The terms in the equation depend on the
probability distribution, and, in addition, pressure and velocity functions,
but these functions also depend on the probability distribution. There are two
possible directions of the velocity that satisfy the energy equation. A linear
momentum function is defined that integrates to zero, and this property is
consistent with the expectation value of the linear momentum for stationary
states with real-valued wave functions. The energy equation is integrated to
obtain a version of the well known energy equation involving reduced density
matrices, where the kinetic energy functional of the one-particle density
matrix is replaced by a function of the electron density and a velocity
function. Also, the noninteracting kinetic energy functional from the
Hohenberg--Kohn theorem is given as an explicit functional of the orbital
densities. For the purpose of describing the behavior of particles in a
stationary state, a model based on the energy equation is constructed. The
model is evaluated for the two different velocity directions using the grounds
state of the particle in a one-dimensional box and the hydrogen atom. For one
velocity direction, equations of motions with contradictory properties are
obtained, and, in the other, an unstable system is found. A discussion is given
with suggestions of additional elements that might improve the model.",2107.10311v1
2014-07-07,Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations,"In the paper we consider the problem of the rigorous description of the
kinetic evolution in the presence of initial correlations of quantum large
particle systems. One of the developed approaches consists in the description
of the evolution of quantum many-particle systems within the framework of
marginal observables in mean field scaling limit. Another method based on the
possibility to describe the evolution of states within the framework of a
one-particle marginal density operator governed by the generalized quantum
kinetic equation in case of initial states specified by a one-particle marginal
density operator and correlation operators.",1407.1633v1
2020-03-12,Mg decorated Boron doped Graphene for Hydrogen Storage,"First principles based DFT calculations performed to insight structural and
electronic properties of Boron doped Magnesium atom decorated graphene sheet
for application of hydrogen storage. The four H2 molecules stably binds
magnesium atom with Boron doped graphene sheet. The average binding energy
extracted in the range-0.566 to -0.687 eV/H2.Partial density of states of
complex system shows s and d orbitals of H2 molecule and Mg atom at -0.1eV
overlaps of main peaks indicates strong hybridizing and binding of s and d
orbitals of H2 and Mg atom respectively. The gravimetric capacity of studied
complex system reaching approximately 8.26 wt% hydrogen. HOMO & LUMO study
shows stability of complex system.DOS investigation reveals the electronic
density of states of complex system.",2003.13429v1
2019-07-12,Origin of energy shift in kaonic atom and kaon-nucleus interaction,"The $K^-$-nucleus optical potential is revisited to investigate its global
feature phenomenologically. It is a puzzle that the energy shift is found to be
repulsive in all of the observed kaonic atom, although the $K^-N$ interaction
is known to be so attractive as to form the $\Lambda(1405)$ resonance. To solve
this puzzle, we examine the $K^-$ optical potential in the linear density
approximation and determine the potential parameters of each kaonic atom so as
to reproduce the observed energy shift and absorption width. We find two types
of the potentials. One potential has a so large real part as to provide nuclear
states with the same quantum number to the atomic state in the last orbit. The
level repulsion between the atomic state and the nuclear states takes place due
to their mixing, and it makes the atomic state shifted repulsively. The other
type of the potential has a large imaginary part and the imaginary part works
repulsively for atomic states. We find that only the latter solution reproduce
a wide of the observed data, and thus is realized as a $K^-$-nucleus potential
for kaonic atom. In the linear nuclear density optical potential, the picture
that the repulsive shifts in the atomic states stem from the existence of the
nuclear states does not globally stand up. This implies that the $K^-$-nucleus
optical potential should have a large imaginary part. We examine some nonlinear
density effects and find that the conclusion does not change. We also confirm
that the conventionally known optical potentials are categorized into the
latter type of the potential.",1907.05626v1
1995-09-21,Spectroscopy of Local Density of States Fluctuations in a Disordered Conductor (Experiment),"The local density of states of a degenerate semiconductor is investigated at
low magnetic fields. In order to realize this experiment, we designed a
strongly asymmetric double-barrier heterostructure with heavily doped contacts
and study the resonant tunneling transport through the lowest localized
(zero-dimensional) level in the quantum well. Fine structure in the tunneling
current as a function of bias voltage and magnetic field images mesoscopic
fluctuations of the local density of states in the emitter contact. Our
quantitative analysis demonstrates that the fluctuation pattern originates from
quantum interference of diffusive electron waves in the three-dimensional
disordered system on the length scale of the mean free path. Since the
fluctuations reflect the properties of the electron states below the Fermi
level, the observed mesoscopic effect is temperature insensitive.",9509137v3
1997-08-12,Self-consistent interface properties of d and s-wave superconductors,"We develop a method to solve the Bogoliubov de Gennes equation for
superconductors self-consistently, using the recursion method. The method
allows the pairing interaction to be either local or non-local corresponding to
s and d-wave superconductivity, respectively. Using this method we examine the
properties of various S-N and S-S interfaces. In particular we calculate the
spatially varying density of states and order parameter for the following
geometries (i) s-wave superconductor to normal metal, (ii) d-wave
superconductor to normal metal, (iii) d-wave superconductor to s-wave
superconductor. We show that the density of states at the interface has a
complex structure including the effects of normal surface Friedel oscillations,
the spatially varying gap and Andeev states within the gap, and the subtle
effects associated with the interplay of the gap and the normal van Hove peaks
in the density of states. In the case of bulk d-wave superconductors the
surface leads to mixing of different order parameter symmetries near the
interface and substantial local filling in of the gap.",9708086v1
1998-04-10,Evolution of the Density of States Gap in a Disordered Superconductor,"It has only recently been possible to study the superconducting state in the
attractive Hubbard Hamiltonian via a direct observation of the formation of a
gap in the density of states N(w). Here we determine the effect of random
chemical potentials on N(w) and show that at weak coupling, disorder closes the
gap concurrently with the destruction of superconductivity. At larger, but
still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the
point at which off-diagonal long range order vanishes. This change in the
elementary excitations of the insulating phase corresponds to a crossover
between Fermi- and Bose-Insulators. These calculations represent the first
computation of the density of states in a finite dimensional disordered fermion
model via the Quantum Monte Carlo and maximum entropy methods.",9804122v1
1993-04-06,Semiclassical Gravity Theory and Quantum Fluctuations,"We discuss the limits of validity of the semiclassical theory of gravity in
which a classical metric is coupled to the expectation value of the stress
tensor. It is argued that this theory is a good approximation only when the
fluctuations in the stress tensor are small. We calculate a dimensionless
measure of these fluctuations for a scalar field on a flat background in
particular cases, including squeezed states and the Casimir vacuum state. It is
found that the fluctuations are small for states which are close to a coherent
state, which describes classical behavior, but tend to be large otherwise. We
find in all cases studied that the energy density fluctuations are large
whenever the local energy density is negative. This is taken to mean that the
gravitational field of a system with negative energy density, such as the
Casimir vacuum, is not described by a fixed classical metric but is undergoing
large metric fluctuations. We propose an operational scheme by which one can
describe a fluctuating gravitational field in terms of the statistical behavior
of test particles. For this purpose we obtain an equation of the form of the
Langevin equation used to describe Brownian motion.",9304008v1
2007-07-27,Pairing states of a polarized Fermi gas trapped in a one-dimensional optical lattice,"We study the properties of a one-dimensional (1D) gas of fermions trapped in
a lattice by means of the density matrix renormalization group method, focusing
on the case of unequal spin populations, and strong attractive interaction. In
the low density regime, the system phase-separates into a well defined
superconducting core and a fully polarized metallic cloud surrounding it. We
argue that the superconducting phase corresponds to a 1D analogue of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of
tightly bound bosonic pairs with a finite center-of-mass momentum that scales
linearly with the magnetization. In the large density limit, the system allows
for four phases: in the core, we either find a Fock state of localized pairs or
a metallic shell with free spin-down fermions moving in a fully filled
background of spin-up fermions. As the magnetization increases, the Fock state
disappears to give room for a metallic phase, with a partially polarized
superconducting FFLO shell and a fully polarized metallic cloud surrounding the
core.",0707.4172v4
2007-08-23,From Microscales to Macroscales in 3D: Selfconsistent Equation of State for Supernova and Neutron Star Models,"First results from a fully self-consistent, temperature-dependent equation of
state that spans the whole density range of neutron stars and supernova cores
are presented. The equation of state (EoS) is calculated using a mean-field
Hartree-Fock method in three dimensions (3D). The nuclear interaction is
represented by the phenomenological Skyrme model in this work, but the EoS can
be obtained in our framework for any suitable form of the nucleon-nucleon
effective interaction. The scheme we employ naturally allows effects such as
(i) neutron drip, which results in an external neutron gas, (ii) the variety of
exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii)
the subsequent dissolution of these nuclei into nuclear matter. In this way,
the equation of state is calculated across phase transitions without recourse
to interpolation techniques between density regimes described by different
physical models. EoS tables are calculated in the wide range of densities,
temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000
processors simultaneously.",0708.3197v1
2009-10-08,Local density of states and superconducting gap in the iron chalcogenide superconductor Fe$_{1+δ}$Se$_{1-x}$Te$_{x}$ observed by scanning tunneling spectroscopy,"We report on the first investigation of the quasiparticle local density of
states and superconducting gap in the iron chalcogenide superconductor
Fe$_{1+\delta}$Se$_{1-x}$Te$_{x}$ ($T_{\mathrm{c}} \sim 14$ K). The surface of
a cleaved crystal revealed an atomic square lattice, superimposed on the
inhomogeneous background, with a lattice constant of $\sim 3.8$ \AA without any
reconstruction. Tunneling spectra measured at 4.2 K exhibit the superconducting
gap, which completely disappears at 18 K, with a magnitude of $\sim 2.3$ meV,
corresponding to $2\Delta / k_{\mathrm{B}}T_{\mathrm{c}}=3.8$.In stark contrast
to the cuprate superconductors, the value of the observed superconducting gap
is relatively homogeneous, following a sharp distribution with a small standard
deviation of 0.23 meV. Conversely, the normal-state local density of states
observed above $T_{\mathrm{c}}$ shows spatial variation over a wide energy
range of more than 1 eV, probably due to the excess iron present in the
crystal.",0910.1485v3
2014-02-05,On the nonlocality of the state and wave equation of Treeby and Cox,"In this paper it is shown that the state equation of Treeby and Cox [B. E.
Treeby and B. T. Cox, J. Acoust. Soc. Am. \textbf{127} 5, (2010)] is
\emph{nonlocal}, more precisely, a \emph{local} density variation causes an
\emph{instant global} pressure variation and a \emph{local} pressure variation
can only be caused by an \emph{instant global} density variation. This is in
contrast to all frequency dependent dissipative state equations known to the
author. Moreover, it is shown that the Green function $G$ of the wave equation
of Treeby and Cox cannot have a \emph{finite} wave front speed, i.e. there
exists no finite $c_F>0$ such that $$
  G(\mathbf{x},t) = 0 \qquad\mbox{for}\qquad |\mathbf{x}|/c_F > t $$ holds,
where $|\mathbf{x}|/c_F$ corresponds to the \emph{travel time} of a wave
propagating with speed $c_F$ from point $\mathbf{0}$ to point $\mathbf{x}$. As
a consequence, the density and pressure waves satisfying (i) the state equation
of Treeby and Cox, (ii) the equation of motion and (iii) the equation of
continuity do not have a \emph{finite} wave front speed.",1402.1081v1
2015-09-10,Exploring structural inhomogeneities in glasses during cavitation,"Using large-scale molecular dynamics simulations for a system of $10^6$
particles, the response of a dense amorphous solid to the continuous expansion
of its volume is investigated. We find that the spatially uniform glassy state
becomes unstable via the formation of cavities, which eventually leads to
failure. By scanning through a wide range of densities and temperatures, we
determine the state points at which the instability occurs and thereby provide
estimates of the co-existence density of the resultant glass phase. Evidence
for long-lived, inhomogeneous configurations with a negative pressure is found,
where the frozen-in glass structure contains spherical cavities or a network of
void space. Furthermore, we demonstrate the occurrence of hysteretic effects
when the cavitated solid is compressed to regain the dense glassy state. As a
result, a new glass state is obtained, the pressure of which is different from
the initial one due to small density inhomogeneities that are generated by the
dilation-compression cycle.",1509.03158v1
2016-10-24,Anisotropic superconducting gaps in YNi$_2$B$_2$C: A first-principles investigation,"We calculate superconducting gaps and quasiparticle density of states of
YNi$_2$B$_2$C in the framework of the density functional theory for
superconductors to investigate the origin of a highly anisotropic
superconducting gaps in this material. Calculated phonon frequencies, the
quasiparticle density of states, and the transition temperature show good
agreement with experimental results. From our calculation of superconducting
gaps and orbital character analysis, we establish that the orbital character
variation of the Fermi surface is the key factor of the anisotropic gap. Since
the electronic states that consist of mainly Ni $3 d$ orbitals couple weakly
with phonons, the superconducting gap function is suppressed for the
corresponding states, which results in the anisotropy observed in the
experiments. These results are hints to increase the transition temperature of
materials in the borocarbide family.",1610.07329v2
2017-05-18,"Many-body dynamics of holes in a driven, dissipative spin chain of Rydberg superatoms","Strong dipole-dipole interactions between atoms in high-lying Rydberg states
can suppress multiple Rydberg excitations within a micron-sized trapping volume
and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms
in optical microtraps then form Rydberg superatoms with collectively enhanced
transition rates to the singly excited state. These superatoms can represent
mesoscopic, strongly-interacting spins. We study a regular array of such
effective spins driven by a laser field tuned to compensate the
interaction-induced level shifts between neighboring superatoms. During the
initial transient, a few excited superatoms seed a cascade of resonantly
facilitated excitation of large clusters of superatoms. Due to spontaneous
decay, the system then relaxes to the steady state having nearly universal
Rydberg excitation density $\rho_{\mathrm{R}} = 2/3$. This state is
characterized by highly-nontrivial equilibrium dynamics of quasi-particles --
excitation holes in the lattice of Rydberg excited superatoms. We derive an
effective many-body model that accounts for hole mobility as well as continuous
creation and annihilation of holes upon collisions with each other. We find
that holes exhibit a nearly incompressible liquid phase with highly
sub-Poissonian number statistics and finite-range density-density correlations.",1705.06532v2
2018-11-07,An Extension of ETH to Non-Equilibrium Steady States,"We extend the notion of the Eigenstate Thermalization Hypothesis (ETH) to
Open Quantum Systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan
(GKLS) Master Equation. We present evidence that the eigenstates of
non-equilibrium steady state (NESS) density matrices obey a generalization of
ETH in boundary-driven systems when the bulk Hamiltonian is non-integrable,
just as eigenstates of Gibbs density matrices are conjectured to do in
equilibrium. This generalized ETH, which we call NESS-ETH, can be used to
obtain representative pure states that reproduce the expectation values of
few-body operators in the NESS. The density matrices of these representative
pure states can be further interpreted as weak solutions of the GKLS Master
Equation. Additionally, we explore the validity and breakdown of NESS-ETH in
the presence of symmetries, integrability and many-body localization in the
bulk Hamiltonian.",1811.03114v2
2019-05-03,QCD equation of state at finite baryon density with fugacity expansion,"We explore the QCD equation of state at finite baryon density through an
expansion in baryon number fugacity, making use of the recent lattice data on
the four leading Fourier coefficients of the expansion. A state-of-the-art
description of the lattice data at both imaginary $\mu_B$ and $\mu_B = 0$ is
provided by the cluster expansion model (CEM). The CEM pressure function has
three temperature dependent input parameters, which we fix by parameterizing
the available lattice QCD data. This results in a crossover model of the QCD
equation of state at finite baryon density, which can be used in fluid
dynamical simulations of heavy-ion collisions.",1905.01031v1
2020-07-13,Topological states in qubit arrays induced by density-dependent coupling,"Topological states of light open exciting possibilities in quantum photonics
promising the topological protection of quantum entanglement. Here, we put
forward an approach to realize the topological states of photon pairs mediated
by the effective density-dependent coupling which is manifested as the
dependence of the tunneling amplitude on the number of photons. As a specific
platform, we investigate the arrays of nearest-neighbor coupled transmon
qubits, where the effective density-dependent coupling is engineered by
inserting auxiliary frequency-detuned resonators. We prove the topological
origin of the designed model by the direct evaluation of the Zak phase
highlighting the feasibility of our proposal for state-of-the-art fabrication
technologies.",2007.06395v1
2017-07-06,Efficiency of fermionic quantum distillation,"We present a time-dependent density-matrix renormalization group
investigation of the quantum distillation process within the Fermi--Hubbard
model on a quasi-1D ladder geometry. The term distillation refers to the
dynamical, spatial separation of singlons and doublons in the sudden expansion
of interacting particles in an optical lattice, i.e., the release of a cloud of
atoms from a trapping potential. Remarkably, quantum distillation can lead to a
contraction of the doublon cloud, resulting in an increased density of the
doublons in the core region compared to the initial state. As a main result, we
show that this phenomenon is not limited to chains that were previously
studied. Interestingly, there are additional dynamical processes on the two-leg
ladder such as density oscillations and selftrapping of defects that lead to a
less efficient distillation process. An investigation of the time evolution
starting from product states provides an explanation for this behaviour.
Initial product states are also considered, since in optical lattice
experiments such states are often used as the initial setup. We propose
configurations that lead to a fast and efficient quantum distillation.",1707.01792v3
2021-03-17,Micromagnetic description of twisted spin spirals in the B20 chiral magnet FeGe from first principles,"Using the model of classical Heisenberg exchange and Dzyaloshinskii-Moriya
(DM) interaction we show that the ground state of B20 FeGe chiral magnet is a
superposition of twisted helical spin-density waves formed by different
sublattices of the crystal. Such twisted spin-density waves propagate in the
same direction but with different phases and different directions of the
rotation axes. We derive an advanced micromagnetic expression describing the
exchange and DM interaction for such magnetic structures. By employing
first-principles calculations based on density functional theory and using our
micromagnetic model we show that the magnitude of the spin-spiral twist in B20
FeGe is of the same order as global spiraling. While the energy difference
between the ground state of twisted spirals and the FM state is in good
agreement with the experimental results, for the spin spirals without a twist
it is smaller by factor three. In addition, we verify our results by employing
spin dynamics simulations. This calls for new experiments exploring the ground
state properties of B20 chiral magnets.",2103.09800v2
2021-05-06,Exact analytical solution for density matrix of a non-equilibrium polariton Bose-Einstein condensate,"In this letter, we give an analytical quantum description of a
non-equilibrium polariton Bose-Einstein condensate (BEC) based on the solution
of the master equation for the full polariton density matrix in the limit of
fast thermalization. We find the density matrix of a non-equilibrium BEC, that
takes into account quantum correlations between all polariton states. We show
that the formation of BEC is accompanied by the build-up of cross-correlations
between the ground state and the excited states reaching their highest values
at the condensation threshold. Despite the non-equilibrium nature of polariton
systems, we show the average population of polariton states exhibits the
Bose-Einstein distribution with an almost zero effective chemical potential
above the condensation threshold similar to an equilibrium BEC. We demonstrate
that above threshold the effective temperature of polariton condensate drops
below the reservoir temperature.",2105.02940v2
2022-09-01,Theoretical description of the first-order phase transition of aluminum from a superconducting to normal state by the current-density functional theory for superconductors,"We show that the current-density functional theory for superconductors
(sc-CDFT) can describe the magnetic-field-induced first-order phase transition
of aluminum from a superconducting state to a normal state. This is
accomplished by introducing a model for the magnetic field dependence of the
attractive interaction between superconducting electrons. This model states
that the surface potential well produced by the penetrating magnetic field
leads to the magnetic field dependence of the attractive interaction.
Specifically, the electron density near the surface increases with the magnetic
field due to the surface potential well, which causes the reduction in the
attractive interaction due to the screening effect. We also develop the
calculation scheme to solve the gap equation of the sc-CDFT with taking into
account the magnetic field dependence of the attractive interaction. It is
shown that calculation results of the magnetic field dependence of the
superconducting gap are in good agreement with experimental results of the
first-order phase transition.",2209.00298v1
1997-12-02,The Cosmic Baryon Budget,"We present an estimate of the global budget of baryons in all states, with
conservative estimates of the uncertainties, based on all relevant information
we have been able to marshal. Most of the baryons today are still in the form
of ionized gas, which contributes a mean density uncertain by a factor of about
four. Stars and their remnants are a relatively minor component, comprising for
our best-guess plasma density only about 17% of the baryons, while populations
contributing most of the blue starlight comprise less than 5%. The formation of
galaxies and of stars within them appears to be a globally inefficient process.
The sum over our budget, expressed as a fraction of the critical Einstein-de
Sitter density, is in the range $0.007\lsim\Omega_B\lsim 0.041$, with a best
guess $\Omega_B\sim 0.021$ (at Hubble constant 70 km/s/Mpc). The central value
agrees with the prediction from the theory of light element production and with
measures of the density of intergalactic plasma at redshift $z\sim 3$. This
apparent concordance suggests we may be close to a complete survey of the major
states of the baryons.",9712020v2
2000-12-06,Modified relative entropy of entanglement for multi-party systems,"We present the modified relative entropy of entanglement for multi-party
systems by a given relative density matrix which is spanned by a linear
combination of the direct products of so-called basis of relative density
matrices and reduced density matrices for every party. For three qubit system
in a pure state we derive out the explicit and closed expression of our
relative density matrix which is a function of the components of the state
vector of three qubits. Through computing the modified relative entropy of
entanglement of some important and interesting examples, we display the main
behaviors and elementary properties of the modified relative entropy of
entanglement and compare it with the generalized entanglement of formation.
Moreover, we also propose an assistant, as the upper bound, of the modified
relative entropy of entanglement.",0012029v3
2018-10-04,"Comments on Failures of van der Waals Equation at the Gas Liquid Critical Point, L. V. Woodcock, International Journal of Thermophysics 2018 39 120","These comments are a response to the discussion presented in the above paper
concerning the New comment on Gibbs Density Surface of Fluid Argon, Revised
Critical Parameters by Umirzakov. Here we show that Woodcocks results obtained
for the dependencies for the isochoric heat capacity, excess Gibbs energy and
coexisting difference functional of argon, and coexisting densities of liquid
and vapor of the van der Waals fluid and presented in all Figures are
incorrect, his Table includes incorrect values of coexisting difference
functional, his paper includes many incorrect equations, mathematical and
logical errors and physically incorrect assertions concerning the temperature
dependences of the isochoric heat capacity and entropy of real fluids, most of
the his conclusions are based on the above errors, incorrect data, incorrect
comparisons and incorrect dependencies; and most of his conclusions are
invalid. We also show that the van der Waals equation of state quantitatively
describes the dependencies of saturation pressure on vapor density and
temperature near critical point, and the equation of state can describe
qualitatively the reduced excess Gibbs energy, rigidity and densities of
coexisting liquid and vapor of argon, including the region near critical point.",1810.02699v1
2012-03-17,Accurate ab initio spin densities,"We present an approach for the calculation of spin density distributions for
molecules that require very large active spaces for a qualitatively correct
description of their electronic structure. Our approach is based on the
density-matrix renormalization group (DMRG) algorithm to calculate the spin
density matrix elements as basic quantity for the spatially resolved spin
density distribution. The spin density matrix elements are directly determined
from the second-quantized elementary operators optimized by the DMRG algorithm.
As an analytic convergence criterion for the spin density distribution, we
employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.
2011, 134, 224101] to build an accurate complete-active-space
configuration-interaction (CASCI) wave function from the optimized matrix
product states. The spin density matrix elements can then also be determined as
an expectation value employing the reconstructed wave function expansion.
Furthermore, the explicit reconstruction of a CASCI-type wave function provides
insights into chemically interesting features of the molecule under study such
as the distribution of $\alpha$- and $\beta$-electrons in terms of Slater
determinants, CI coefficients, and natural orbitals. The methodology is applied
to an iron nitrosyl complex which we have identified as a challenging system
for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].",1203.3888v2
2018-11-13,Stress in a polymer brush,"We study the stress distribution in a polymer brush material over a range of
graft densities using molecular dynamics (MD) simulations and theory. Flexible
polymer chains are treated as beads connected by nonlinear springs governed by
a modified finitely extensible nonlinear elastic (FENE) potential in MD
simulations. Simulations confirmed the quartic variation of the normal stress
parallel to the substrate, within the bulk of the brush, as predicted in our
previous work, for low graft densities. However, in the high graft density
regime, the Gaussian chain elasticity assumption is violated by finite
extensibility effects (force-extension divergence) and the restriction to
binary interaction among monomers is insufficient. This motivated us to extend
a semi-analytical strong stretching mean field theory (SST) for polymer
brushes, based on Langevin chains and a modified Carnahan-Starling equation of
state to model monomer interactions. Our extended theory elucidates the stress
and monomer density profiles obtained from MD simulations, as well as
reproduces Gaussian chain results for small graft densities. A good agreement
is observed between predictions of MD and Langevin chain SST for monomer
density profile, end density profile and stress profile in high graft density
regime, without fitting parameters (virial coefficients). Quantitative
comparisons of MD results with various available theories suggest that excluded
volume correlations may be important.",1811.05089v1
2023-12-22,Fermions at finite density in the path integral approach,"We study relativistic fermionic systems in $3+1$ spacetime dimensions at
finite chemical potential and zero temperature, from a path-integral point of
view. We show how to properly account for the $i\varepsilon$ term that projects
on the finite density ground state, and compute the path integral analytically
for free fermions in homogeneous external backgrounds, using complex analysis
techniques. As an application, we show that the ${\rm U}(1)$ symmetry is always
linearly realized for free fermions at finite charge density, differently from
scalars. We study various aspects of finite density QED in a homogeneous
magnetic background. We compute the free energy density, non-perturbatively in
the electromagnetic coupling and the external magnetic field, obtaining the
finite density generalization of classic results of Euler--Heisenberg and
Schwinger. We also obtain analytically the magnetic susceptibility of a
relativistic Fermi gas at finite density, reproducing the de Haas--van Alphen
effect. Finally, we consider a (generalized) Gross--Neveu model for $N$
interacting fermions at finite density. We compute its non-perturbative
effective potential in the large-$N$ limit, and discuss the fate of the ${\rm
U}(1)$ vector and $\mathbb{Z}_2^A$ axial symmetries.",2312.14753v2
2020-03-10,The Discrete-Time Facilitated Totally Asymmetric Simple Exclusion Process,"We describe the translation invariant stationary states of the one
dimensional discrete-time facilitated totally asymmetric simple exclusion
process (F-TASEP). In this system a particle at site $j$ in $Z$ jumps, at
integer times, to site $j+1$, provided site $j-1$ is occupied and site $j+1$ is
empty. This defines a deterministic noninvertible dynamical evolution from any
specified initial configuration on $\{0,1\}^{Z}$. When started with a Bernoulli
product measure at density $\rho$ the system approaches a stationary state,
with phase transitions at $\rho=1/2$ and $\rho=2/3$. We discuss various
properties of these states in the different density regimes $0<\rho<1/2$,
$1/2<\rho<2/3$, and $2/3<\rho<1$; for example, we show that the pair
correlation $g(j)=\langle\eta(i)\eta(i+j)\rangle$ satisfies, for all $n\in Z$,
$\sum_{j=kn+1}^{k(n+1)}g(j)=k\rho^2$, with $k=2$ when $0 \le \rho \le 1/2$ and
$k=3$ when $2/3 \le \rho \le 1$, and conjecture (on the basis of simulations)
that the same identity holds with $k=6$ when $1/2 \le \rho \le 2/3$. The
$\rho<1/2$ stationary state referred to above is also the stationary state for
the deterministic discrete-time TASEP at density $\rho$ (with Bernoulli initial
state) or, after exchange of particles and holes, at density $1-\rho$.",2003.04995v3
2010-03-29,Thermodynamic Properties of Holographic Multiquark and the Multiquark Star,"We study thermodynamic properties of the multiquark nuclear matter. The
dependence of the equation of state on the colour charges is explored both
analytically and numerically in the limits where the baryon density is small
and large at fixed temperature between the gluon deconfinement and chiral
symmetry restoration. The gravitational stability of the hypothetical
multiquark stars are discussed using the Tolman-Oppenheimer-Volkoff equation.
Since the equations of state of the multiquarks can be well approximated by
different power laws for small and large density, the content of the multiquark
stars has the core and crust structure. We found that most of the mass of the
star comes from the crust region where the density is relatively small. The
mass limit of the multiquark star is determined as well as its relation to the
star radius. For typical energy density scale of $10\text{GeV}/\text{fm}^{3}$,
the converging mass and radius of the hypothetical multiquark star in the limit
of large central density are approximately $2.6-3.9$ solar mass and 15-27 km.
The adiabatic index and sound speed distributions of the multiquark matter in
the star are also calculated and discussed. The sound speed never exceeds the
speed of light and the multiquark matters are thus compressible even at high
density and pressure.",1003.5470v2
2017-05-12,Exactly solvable flat-foldable quadrilateral origami tilings,"We consider several quadrilateral origami tilings, including the Miura-ori
crease pattern, allowing for crease-reversal defects above the ground state
which maintain local flat-foldability. Using exactly solvable models, we show
that these origami tilings can have phase transitions as a function of crease
state variables, as a function of the arrangement of creases around vertices,
and as a function of local layer orderings of neighboring faces. We use the
exactly solved cases of the staggered odd 8-vertex model as well as Baxter's
exactly solved 3-coloring problem on the square lattice to study these origami
tilings. By treating the crease-reversal defects as a lattice gas, we find
exact analytic expressions for their density, which is directly related to the
origami material's elastic modulus. The density and phase transition analysis
has implications for the use of these origami tilings as tunable metamaterials;
our analysis shows that Miura-ori's density is more tunable than Barreto's
Mars, for example. We also find that there is a broader range of tunability as
a function of the density of layering defects compared to as a function of the
density of crease order defects before the phase transition point is reached;
material and mechanical properties that depend on local layer ordering
properties will have a greater amount of tunability. The defect density of
Barreto's Mars, on the other hand, can be increased until saturation without
passing through a phase transition point. We further consider relaxing the
requirement of local flat-foldability by mapping to a solvable case of the
16-vertex model, demonstrating a different phase transition point for this
case.",1705.04710v1
2019-10-24,Free energy of the self-interacting relativistic lattice Bose gas at finite density,"The density of state approach has recently been proposed as a potential route
to circumvent the sign problem in systems at finite density. In this study,
using the Linear Logarithmic Relaxation (LLR) algorithm, we extract the
generalised density of states, which is defined in terms of the imaginary part
of the action, for the self-interacting relativistic lattice Bose gas at finite
density. After discussing the implementation and testing the reliability of our
approach, we focus on the determination of the free energy difference between
the full system and its phase-quenched counterpart. Using a set of lattices
ranging from $4^4$ to $16^4$ , we show that in the low density phase, this
overlap free energy can be reliably extrapolated to the thermodynamic limit.
The numerical precision we obtain with the LLR method allows us to determine
with sufficient accuracy the expectation value of the phase factor, which is
used in the calculation of the overlap free energy, down to values of ${\cal
O}(10^{-480})$. When phase factor measurements are extended to the dense phase,
a change of behaviour of the overlap free energy is clearly visible as the
chemical potential crosses a critical value. Using fits inspired by the
approximate validity of mean-field theory, which is confirmed by our
simulations, we extract the critical chemical potential as the non-analyticity
point in the overlap free energy, obtaining a value that is in agreement with
other determinations. Implications of our findings and potential improvements
of our methodology are also discussed.",1910.11026v1
2011-03-25,Necessary and sufficient conditions for local manipulation of multipartite pure quantum states,"Suppose several parties jointly possess a pure multipartite state, |\psi>.
Using local operations on their respective systems and classical communication
(i.e. LOCC) it may be possible for the parties to transform deterministically
|\psi> into another joint state |\phi>. In the bipartite case, Nielsen
majorization theorem gives the necessary and sufficient conditions for this
process of entanglement transformation to be possible. In the multipartite
case, such a deterministic local transformation is possible only if both the
states in the same stochastic LOCC (SLOCC) class. Here we generalize Nielsen
majorization theorem to the multipartite case, and find necessary and
sufficient conditions for the existence of a local separable transformation
between two multipartite states in the same SLOCC class. When such a
deterministic conversion is not possible, we find an expression for the maximum
probability to convert one state to another by local separable operations. In
addition, we find necessary and sufficient conditions for the existence of a
separable transformation that converts a multipartite pure state into one of a
set of possible final states all in the same SLOCC class. Our results are
expressed in terms of (1) the stabilizer group of the state representing the
SLOCC orbit, and (2) the associate density matrices (ADMs) of the two
multipartite states. The ADMs play a similar role to that of the reduced
density matrices, when considering local transformations that involves pure
bipartite states. We show in particular that the requirement that one ADM
majorize another is a necessary condition but in general far from being also
sufficient as it happens in the bipartite case.",1103.5096v2
2016-08-01,Analysis of Neutron Stars Observations Using a Correlated Fermi Gas Model,"Background: The nuclear symmetry energy is a fundamental ingredient in
determining the equation of state (EOS) of neutron stars (NS). Recent
terrestrial experiments constrain both its value and slope at nuclear
saturation density, however, its value at higher densities is unknown. Assuming
a Free Fermi-gas (FFG) model for the kinetic symmetry energy, the high-density
extrapolation depends on a single parameter, the density dependence of the
potential symmetry energy. The Correlated Fermi-gas (CFG) model improves on the
FFG model by including the effects of short-range, correlated, high-momentum,
nucleons in nuclear matter. Using the CFG model for the kinetic symmetry energy
along with constraints from terrestrial measurements leads to a much softer
density dependence for the potential symmetry energy. Purpose: Examine the
ability of the FFG and CFG models to describe NS observables that are directly
sensitive to the symmetry energy at high-density. Specifically, examine the
ability of the CFG model, with its softer density dependence of the potential
symmetry energy, to describe a two solar-mass NS. Methods: Using a Bayesian
analysis of NS observables we compare the CFG and FFG models and examine the
resulting parameters in the NS EOS and the density dependence of the potential
symmetry energy. Results: Despite the large difference in the density
dependence of the potential part of the symmetry energy, both models can
describe the NS data and support a two solar-mass NS. The different density
dependences has only a small effect on the NS EOS. Conclusions: While sensitive
to the high-density values of the symmetry energy, NS observables alone are not
enough to distinguish between the CFG and FFG models. This indicates that the
NS EOS, obtain from Bayesian analysis of NS observables, is robust and is not
sensitive to the exact nuclear model used for the kinetic symmetry energy.",1608.00487v1
2010-07-01,Density functional study of the magnetic properties of $Bi_{4}Mn$ clusters: Discrepancy between theory and experiment,"We have performed collinear and non collinear calculations on neutral Bi4Mn,
and collinear ones on ionized Bi4Mn with charges +1 and -1 to find out why
theoretical calculations will not predict the magnetic state found in the
experiment. We have used the density functional theory to find a fit between
the theoretical prediction of the magnetic moment with the experimental value.
Our calculations have consisted in a structure search of local energy minima,
and then a search of the magnetic lowest energy state for each resulting
isomer. The geometry optimization found 3 local minima whose fundamental state
is the doublet spin state, which could not be found in previous theoretical
works, but they are higher in energy than the lowest-lying isomer by
approximately 1.75 eV. This magnetic state could help understand the
experiment. Calculations of non-collinear magnetic states for the Bi4Mn do not
lower the total magnetic moment. We conclude arguing how the 3 isomers with
doublet state could actually be the ones measured in the experiment.",1007.0196v1
2012-08-03,Detecting Entanglement with Partial State Information,"We introduce a sequence of numerical tests that can determine the
entanglement or separability of a state even when there is not enough
information to completely determine its density matrix. Given partial
information about the state in the form of linear constraints on the density
matrix, the sequence of tests can prove that either all states satisfying the
constraints are entangled, or there is at least one separable state that
satisfies them. The algorithm works even if the values of the constraints are
only known to fall in a certain range. If the states are entangled, an
entanglement witness is constructed and lower bounds on entanglement measures
and related quantities are provided; if a separable state satisfies the
constraints, a separable decomposition is provided to certify this fact.",1208.0860v2
2014-08-26,Exotic magnetic phases in an Ising-spin Kondo lattice model on a kagome lattice,"Magnetic and electronic states of an Ising-spin Kondo lattice model on a
kagome lattice are investigated by a Monte Carlo simulation. In addition to the
conventional ferromagnetic and ferrimagnetic orders, we show that this model
exhibits several thermally-induced phases, such as partially disordered,
Kosteritz-Thouless-like, and loop-liquid states. In the partially disordered
state, we show that the magnetic transition is associated with the charge-gap
formation. We find that the density of state shows characteristic peaks
reflecting the underlying spin texture. In the loop-liquid state, we also find
a peak in a different manner in the density of states as well as in the optical
conductivity. This is a consequence of the formation of closed loops of the
same spin sites in the loop-liquid state. Our results elucidates the peculiar
cooperation between thermal fluctuations and the spin-charge interplay in this
frustrated itinerant electron system.",1408.5998v2
2014-06-02,Composite Fermions in Medium: Extending the Lipkin Model,"The role of phase space occupation effects for the formation of two- and
three-particle bound states in a dense medium is investigated within an
algebraic approach suitable for systems with short-range interactions. It is
shown that for two-fermion bound states due to the account of the exchange
symmetry (phase space occupation) effect (Pauli blocking) in a dense medium the
binding energy is reduced and vanishes at a critical density (Mott effect). For
three-fermion bound states, within a Faddeev equation approach, the
intermediate formation of pair correlations leads to the representation as a
suitably symmetrized fermion-boson bound state. It is shown that the Bose
enhancement of fermion pairs can partially compensate the Pauli blocking
between the fermions. This leads to the general result obtained by algebraic
methods: three-fermion bound states in a medium with high phase space
occupation appear necessarily as Borromean states beyond the Mott density of
the two-fermion bound state.",1406.0396v3
2020-04-24,Study of single-particle resonant states with Green's function method,"The relativistic mean field theory with the Green's function method is taken
to study the single-particle resonant states. Different from our previous work
[Phys.Rev.C 90,054321(2014)], the resonant states are identified by searching
for the poles of Green's function or the extremes of the density of states.
This new approach is very effective for all kinds of resonant states, no matter
it is broad or narrow. The dependence on the space size for the resonant
energies, widths, and the density distributions in the coordinate space has
been checked and it is found very stable. Taking $^{120}$Sn as an example, four
new broad resonant states $2g_{7/2}$, $2g_{9/2}$, $2h_{11/2}$ and $1j_{13/2}$
are observed, and also the accuracy for the width of the very narrow resonant
state $1h_{9/2}$ is highly improved to be $1\times 10^{-8}$ MeV. Besides, our
results are very close to those by the complex momentum representation method
and the complex scaling method.",2004.11632v1
2021-09-03,Excited-state quantum phase transitions in spin-orbit coupled Bose gases,"Excited-state quantum phase transitions depend on and reveal the structure of
the whole spectrum of many-body systems. While they are theoretically well
understood, finding suitable signatures and detect them in actual experiments
remains challenging. For instance, in spinor gases, excited-state phases have
been identified and characterized through a topological order parameter that is
challenging to measure in experiments. Here, we propose the Raman-dressed
spin-orbit coupled gas as a novel platform to explore excited-state quantum
phase transitions. In a weakly-coupled regime, the dressed system is equivalent
to a spinor gas with tunable spin-spin interactions. Through this equivalence
we are able to define a new excited-state phase of the dressed gas. The phase
is characterize by the the behavior of the spatial density modulations, or
stripes, induced by spin-orbit coupling, and can in principle be measured in
current state-of-the-art experiments with ultracold atoms. Conversely, we show
that the properties of the excited phase can be exploited to prepare stripe
states with large and stable density modulations.",2109.01495v1
2013-04-22,Entanglement entropy in particle decay,"The decay of a parent particle into two or more daughter particles results in
an entangled quantum state as a consequence of conservation laws in the decay
process. Recent experiments at Belle and BaBar take advantage of quantum
entanglement and the correlations in the time evolution of the product
particles to study CP and T violations. If one (or more) of the product
particles are not observed, their degrees of freedom are traced out of the pure
state density matrix resulting from the decay, leading to a mixed state density
matrix and an entanglement entropy. This entropy is a measure of the loss of
information present in the original quantum correlations of the entangled
state. We use the Wigner-Weisskopf method to construct an approximation to this
state that evolves in time in a {\em manifestly unitary} way. We then obtain
the entanglement entropy from the reduced density matrix of one of the daughter
particles obtained by tracing out the unobserved states, and follow its time
evolution. We find that it grows over a time scale determined by the lifetime
of the parent particle to a maximum, which when the width of the parent
particle is narrow, describes the phase space distribution of maximally
entangled Bell-like states. The method is generalized to the case in which the
parent particle is described by a wave packet localized in space. Possible
experimental avenues to measure the entanglement entropy in the decay of mesons
at rest are discussed.",1304.6110v3
2019-02-25,Duality between density function and value function with applications in constrained optimal control and Markov Decision Process,"Density function describes the density of states in the state space of a
dynamic system or a Markov Decision Process (MDP). Its evolution follows the
Liouville equation. We show that the density function is the dual of the value
function in the optimal control problems. By utilizing the duality, constraints
that are hard to enforce in the primal value function optimization such as
safety constraints in robot navigation, traffic capacity constraints in traffic
flow control can be posed on the density function, and the constrained optimal
control problem can be solved with a primal-dual algorithm that alternates
between the primal and dual optimization. The primal optimization follows the
standard optimal control algorithm with a perturbation term generated by the
density constraint, and the dual problem solves the Liouville equation to get
the density function under a fixed control strategy and updates the
perturbation term. Moreover, the proposed method can be extended to the case
with exogenous disturbance, and guarantee robust safety under the worst-case
disturbance. We apply the proposed method to three examples, a robot navigation
problem and a traffic control problem in sim, and a segway control problem with
experiment.",1902.09583v3
2014-06-02,Spacetime Average Density (SAD) Cosmological Measures,"The measure problem of cosmology is how to obtain normalized probabilities of
observations from the quantum state of the universe. This is particularly a
problem when eternal inflation leads to a universe of unbounded size so that
there are apparently infinitely many realizations or occurrences of
observations of each of many different kinds or types, making the ratios
ambiguous. There is also the danger of domination by Boltzmann Brains. Here two
new Spacetime Average Density (SAD) measures are proposed, Maximal Average
Density (MAD) and Biased Average Density (BAD), for getting a finite number of
observation occurrences by using properties of the Spacetime Average Density
(SAD) of observation occurrences to restrict to finite regions of spacetimes
that have a preferred beginning or bounce hypersurface. These measures avoid
Boltzmann brain domination and appear to give results consistent with other
observations that are problematic for other widely used measures, such as the
observation of a positive cosmological constant.",1406.0504v2
2002-04-29,Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach,"We have applied the momentum space version of the Density Matrix
Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study
the accuracy of the algorithm in the new context. We have shown numerically
that it is possible to determine the desired accuracy of the method in advance
of the calculations by dynamically controlling the truncation error and the
number of block states using a novel protocol which we dubbed Dynamical Block
State Selection (DBSS). The relationship between the real error and truncation
error has been studied as a function of the number of orbitals and the fraction
of filled orbitals. We have calculated the ground state of the molecules
CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our
largest calculations were carried out with 57 orbitals, the largest number of
block states was 1500--2000, and the largest dimensions of the Hilbert space of
the superblock configuration was 800.000--1.200.000.",0204602v1
2010-02-02,Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions,"The study of the entanglement properties of systems of N fermions has
attracted considerable interest during the last few years. Various separability
criteria for pure states of N identical fermions have been recently discussed
but, excepting the case of two-fermions systems, these criteria are difficult
to implement and of limited value from the practical point of view. Here we
advance simple necessary and sufficient separability criteria for pure states
of N identical fermions. We found that to be identified as separable a state
has to comply with one single identity involving either the purity or the von
Neumann entropy of the single-particle reduced density matrix. These criteria,
based on the verification of only one identity, are drastically simpler than
the criteria discussed in the recent literature. We also derive two
inequalities verified respectively by the purity and the entropy of the single
particle, reduced density matrix, that lead to natural entanglement measures
for N-fermion pure states. Our present considerations are related to some
classical results from the Hartree-Fock theory, which are here discussed from a
different point of view in order to clarify some important points concerning
the separability of fermionic pure states.",1002.0465v1
2014-05-09,Ground State Energies of Interacting Electrons from Projected Densities of Transitions,"For interacting electrons in solids, Heisenberg's equation is used to
calculate the distribution in energy of transitions induced by adding an
electron to an atomic-like spin orbital. This is the projected density of
transitions which includes transitions between grounds states, as well as
between other states differing by one electron. The energy of a ground state is
then calculated as the sum of the least energies of transitions starting with
the ground state of no electrons and adding one electron with each transition.
This method is applied to the construction of ground states for a simple model
of the hydrogen molecule, and to interaction effects on the relative cohesion
of HCP and FCC structures of transition metals.",1405.2288v2
2017-12-22,Evolution of the entanglement of the $N00N$-type of states in a coupled two cavity system via an adiabatic approximation,"We study a system of two cavities each encapsulating a qubit and an
oscillator degrees of freedom. An ultrastrong interaction strength between the
qubit and the oscillator is assumed, and the photons are allowed to hop between
the cavities. A partition of the time scale between the fast moving oscillator
and the slow moving qubit allows us to set up an adiabatic approximation
procedure where we employ the delocalized degrees of freedom to diagonalize the
Hamiltonian. The time evolution of the $N00N$-type initial states now
furnishes, for instance, the reduced density matrix of a bipartite system of
two qubits. For a macroscopic size of the $N00N$ component of the initial state
the sudden death of the entanglement between the qubits and its continued null
value are prominently manifest as the information percolates to the qubits
after long intervals. For the low photon numbers of the initial states the
dynamics produces almost maximally entangled two-qubit states, which by
utilizing the Hilbert-Schmidt distance between the density matrices, are
observed to be nearly pure generalized Bell states.",1712.08398v1
2023-06-16,Nonlocality of the energy density for all single-photon states,"The nonlocality of single-photon states has been analyzed from several
different but interrelared perspectives. In this article, we propose a
demonstration based on the electromagnetic energy density observable and on the
anti-local property of the frequency operator $\Omega=c(-\Delta)^{1/2}$. The
present proof is based on the standard quantization of the electromagnetic
field, which can be formulated equivalently in the momentum representations or
in the position representations of Landau and Peierls [Z. Phys. {\bf 62}, 188
(1930)] and of Bia{\l}ynicki-Birula [\textit{Progress in Optics}, edited by E.
Wolf (Elsevier, Amsterdam, 1996)]. Our proof extends to all single-photon
states the results of Bia{\l}ynicki-Birula, which were formulated for two
particular classes of states, those involving a uniform localization [Phys.
Rev. Lett. {\bf80}, 5247 (1998)] or alternatively states that are electrically
or magnetically localized [Phys.Rev. A {\bf79}, 032112 (2009)]. Our approach is
formulated in terms of Knight's definition of strict localization [J. Math.
Phys. {\bf 2}, 459 (1961)], based on the comparison of expectation values of
single-photon states of local observables with those of the vacuum.",2306.09793v3
1995-12-18,Two-electron state in a disordered 2D island: pairing caused by the Coulomb repulsion,"We show the existence of bound two-electron states in an almost depleted
two-dimensional island. These two-electron states are carried by special
compact configurations of four single-electron levels. The existence of these
states does not require phonon mediation, and is facilitated by the
disorder-induced potential relief and by the electron-electron repulsion only.
The density of two-electron states is estimated and their evolution with the
magnetic field is discussed.",9512125v1
2002-01-10,Stability of rotating states in a weakly-interacting Bose-Einstein condensate,"We investigate the lowest state of a rotating, weakly-interacting
Bose-Einstein condensate trapped in a harmonic confining potential that is
driven by an infinitesimally asymmetric perturbation. Although in an
axially-symmetric confining potential the gas has an axially-symmetric
single-particle density distribution, we show that in the presence of the small
asymmetric perturbation its lowest state is the one given by the mean-field
approximation, which is a broken-symmetric state. We also estimate the rate of
relaxation of angular momentum when the gas is no longer driven by the
asymmetric perturbation and identify two regimes of ""slow"" and ""fast""
relaxation. States of certain symmetry are found to be more robust.",0201150v1
2006-12-18,Dimer states in atomic mixtures,"A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms
is studied in an optical lattice. Inelastic scattering processes between both
atomic species excite the heavy atoms and renormalize the tunneling rate as
well as the interaction of the light atoms. An effective Hamiltonian for the
latter is derived that describes tunneling of single fermions, tunneling of
fermionic pairs and an exchange of fermionic spins. Low energy states of this
Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for
moderate interaction, and a density wave of paired fermions for strong
effective attraction.",0612417v2
2001-09-13,"Quantum Operations, State Transformations and Probabilities","In quantum operations, probabilities characterise both the degree of the
success of a state transformation and, as density operator eigenvalues, the
degree of mixedness of the final state. We give a unified treatment of
pure-to-pure state transformations, covering both probabilistic and
deterministic cases. We then discuss the role of majorization in describing the
dynamics of mixing in quantum operations. The conditions for mixing enhancement
for all initial states are derived. We show that mixing is monotonically
decreasing for deterministic pure-to-pure transformations, and discuss the
relationship between these transformations and deterministic LOCC entanglement
transformations.",0109060v2
2007-03-26,A Decomposition of Separable Werner States,"We derive an integral convex combination of product states for a range of
separable Werner states. Our method consists of expanding the sought-after
local density operators in terms of Wigner operators. For dimension d=2, our
decomposition holds for the whole separable range of Werner states, while for
d>2 it is valid for a subset of separable Werner states. We illustrate the
general method with the explicit examples d=2 and d=3.",0703240v1
2016-03-30,Angle Resolved Photo-Emission Spectroscopy signature of the Resonant Excitonic State,"We calculate the Angle Resolved PhotoEmission Spectroscopy (ARPES) signature
of the Resonant Excitonic State (RES) that was proposed as the Pseudo-Gap state
of cuprate superconductors [ArXiv 1510.03038]. This new state can be described
as a set of excitonic (particle-hole) patches with an internal checkerboard
modulation. Here, we modelize the RES as a charge order with $\bf{2p_{F}}$ wave
vectors, where $\bf{2p_{F}}$ is the ordering vector connecting two opposite
sides of the Fermi surface. We calculate the spectral weight and the density of
states in the RES and we find that our model correctly reproduces the opening
of the PG in Bi-2201.",1603.09178v1
2010-05-19,Robustness of topologically protected surface states in layering of Bi2Te3 thin films,"Bulk Bi2Te3 is known to be a topological insulator. We investigate surface
states of Bi2Te3(111) thin films using density-functional theory including
spin-orbit coupling. We construct a method to unambiguously identify surface
states of thin film topological insulators. Applying this method for one to six
quintuple layers of Bi2Te3, we find that the topological nature of the surface
states remains robust with the film thickness and that the films of three or
more quintuple layers have topologically non-trivial or protected surface
states, in agreement with recent experiments.",1005.3476v1
2017-01-17,Pseudogaps in strongly interacting Fermi gases,"A central challenge in modern condensed matter physics is developing the
tools for understanding nontrivial yet unordered states of matter. One
important idea to emerge in this context is that of a ""pseudogap"": the fact
that under appropriate circumstances the normal state displays a suppression of
the single particle spectral density near the Fermi level, reminiscent of the
gaps seen in ordered states of matter. While these concepts arose in a solid
state context, it is now being explored in cold gases. This article reviews the
current experimental and theoretical understanding of the normal state of
strongly interacting Fermi gases, with particular focus on the phenomonology
which is traditionally associated with the pseudogap.",1701.04838v1
2017-12-06,Effects of ground-state correlations on dipole and quadrupole excitations of $^{40}$Ca and $^{48}$Ca,"The effects of ground-state correlations on the dipole and quadrupole
excitations are studied for $^{40}$Ca and $^{48}$Ca using the extended random
phase approximation (ERPA) derived from the time-dependent density-matrix
theory. Large effects of the ground-state correlations are found in the
fragmentation of the giant quadrupole resonance in $^{40}$Ca and in the
low-lying dipole strength in $^{48}$Ca. It is discussed that the former is due
to a mixing of different configurations in the ground state and the latter is
from the partial occupation of the neutron single-particle states. The dipole
and quadrupole strength distributions below 10 MeV calculated in ERPA are in
qualitatively agreement with experiment.",1712.02006v1
2019-10-08,Invariant Vector and Majorana Star Representations of Qutrit States,"The Qutrit state density matrix is of order 3 and depends on 8 parameters in
general case. Visualization of this 8-dimensional state space is practically
impossible using 8-dimensional vectors commonly used. Recently a 3-dimensional
vector representation of the Qutrit state space (also called Invariant Vector
Representation) has been proposed [1]. In this work we present the
time-evolution of the IVR vectors for the Qutrit Cascade or {\Xi}-model to
emphasize the advantages of the IVR and also relate IVR vectors to well-known
stars of the Majorana State Representation (MSR).",1910.03664v1
2001-07-28,Particle-hole symmetric localization in two dimensions,"We revisit two-dimensional particle-hole symmetric sublattice localization
problem, focusing on the origin of the observed singularities in the density of
states $\rho(E)$ at the band center E=0. The most general such system [R. Gade,
Nucl. Phys. B {\bf 398}, 499 (1993)] exhibits critical behavior and has
$\rho(E)$ that diverges stronger than any integrable power-law, while the
special {\it random vector potential model} of Ludwiget al [Phys. Rev. B {\bf
50}, 7526 (1994)] has instead a power-law density of states with a continuously
varying dynamical exponent. We show that the latter model undergoes a dynamical
transition with increasing disorder--this transition is a counterpart of the
static transition known to occur in this system; in the strong-disorder regime,
we identify the low-energy states of this model with the local extrema of the
defining two-dimensional Gaussian random surface. Furthermore, combining this
``surface fluctuation'' mechanism with a renormalization group treatment of a
related vortex glass problem leads us to argue that the asymptotic low $E$
behavior of the density of states in the {\it general} case is $\rho(E) \sim
E^{-1} e^{-|\ln E|^{2/3}}$, different from earlier prediction of Gade. We also
study the localized phases of such particle-hole symmetric systems and identify
a Griffiths ``string'' mechanism that generates singular power-law
contributions to the low-energy density of states in this case.",0107582v1
2007-01-05,Origin and roles of a strong electron-phonon interaction in cuprate oxide superconductors,"A strong electron-phonon interaction arises from the modulation of the
superexchange interaction by lattice vibrations. It is responsible for the
softening of the half-breathing modes around (pm pi/a,0) and (0, pm pi/a) in
the two-dimensional Brillouin zone, with a being the lattice constant of CuO_2
planes, as is studied in Phys. Rev. B70, 184514 (2004). Provided that
antiferromagnetic spin fluctuations are developed around Q=(pm 3 pi/4a, pm
pi/a) and (pm pi/a, pm 3 pi/4a), the electron-phonon interaction can also cause
the softening of Cu-O bond stretching modes around 2Q, or around (pm pi/2a,0)
and (0, pm pi/2a). The softening around 2Q is accompanied by the development of
charge fluctuations corresponding to the so called 4a-period stripe or
4a*4a-period checker-board state. However, an observation that the 4a-period
modulating part or the 2Q part of the density of states is almost symmetric
with respect to the chemical potential contradicts a scenario that the
stabilization of a single-2Q or double-2Q charge density wave following the
complete softening of the 2Q bond stretching modes is responsible for the
ordered stripe or checker-board state. It is proposed that the stripe or
checker-board state is simply a single-Q or double-Q spin density wave, whose
second-harmonic effects can explain the observed almost symmetric 2Q part of
the density of states. The strong electron-phonon interaction can play no or
only a minor role in the occurrence of d gamma-wave superconductivity in
cuprate oxides.",0701088v1
2010-09-06,Nonequilibrium ionization states and cooling rates of the photoionized enriched gas,"Nonequilibrium (time-dependent) cooling rates and ionization state
calculations are presented for low-density gas enriched with heavy elements
(metals) and photoionized by external ultraviolet/X-ray radiation. We consider
a wide range of gas densities and metallicities and also two types of external
radiation field: a power-law and the extragalactic background spectra. We have
found that both cooling efficiencies and ionic composition of enriched
photoionized gas depend significantly on the gas metallicity and density, the
flux amplitude, and the shape of ionizing radiation spectrum. The cooling rates
and ionic composition of gas in nonequilibrium photoionization models differ
strongly (by a factor of several) from those in photoequilibrium due to
overionization of the ionic states in the nonequilibrium case. The difference
is maximal at low values of the ionization parameter and similar in magnitude
to that between the equlibrium and nonequilibrium cooling rates in the
collisionally controlled gas. In general, the nonequilibrium effects are
notable at $T\simlt 10^6$ K. In this temperature range, the mismatch of the
ionic states and their ratios between the photoequilibrium and the
photo-nonequilibrium models reach a factor of several. The net result is that
the time-dependent energy losses due to each chemical element (i.e. the
contributions to the total cooling rate) differ singificantly from the
photoequilibrium ones. We advocate the use of nonequilibrium cooling rates and
ionic states for gas with near-solar (and above) metallicity exposed to an
arbitrary ionizing radiation flux. We provide a parameter space (in terms of
temperature, density, metallicity and ionizing radiation flux), where the
nonequilibrium cooling rates are to be used. (abridged)",1009.1026v2
2014-08-28,Coffman-Kundu-Wootters inequality for fermions,"We derive an inequality for three fermions with six single particle states
which reduces to the sum of the famous Coffman-Kundu-Wootters inequalities when
an embedded three qubit system is considered. We identify the quantities which
are playing the role of the concurrence, the three-tangle and the invariant
$\det \rho_A+\det \rho_B+\det \rho_C$ for this tripartite system. We show that
this latter one is almost interchangeable with the von Neumann entropy and
conjecture that it measures the entanglement of one fermion with the rest of
the system. We prove that the vanishing of the fermionic ""concurrence"" implies
that the two particle reduced density matrix is a mixture of separable states.
Also the vanishing of this quantitiy is only possible in the GHZ class, where
some genuie tripartite entanglement is present and in the separable class.
Based on this we conjecture that this ""concurrence"" measures the amount of
entanglement between pairs of fermions. We identify the well-known
""spin-flipped"" density matrix in the fermionic context as the reduced density
matrix of a special particle-hole dual state. We show that in general this dual
state is always canonically defined by the Hermitian inner product of the
fermionic Fock space and that it can be used to calculate SLOCC covariants. We
show that Fierz identities known from the theory of spinors relate SLOCC
covariants with reduced density matrix elements of the state and its
""spin-flipped"" dual.",1408.6735v1
2016-03-18,Interplay of charge density wave and multiband superconductivity in 2$H$-Pd$_x$TaSe$_2$,"2$H$-TaSe$_2$ has been one of unique transition metal dichalcogenides
exhibiting several phase transitions due to a delicate balance among competing
electronic ground states. An unusual metallic state at high-$T$ is sequentially
followed by an incommensurate charge density wave (ICDW) state at $\approx$ 122
K and a commensurate charge density wave (CCDW) state at $\approx$ 90 K, and
superconductivity at $T_{\rm{C}}\sim$0.14 K. Upon systematic intercalation of
Pd ions into TaSe$_2$, we find that CCDW order is destabilized more rapidly
than ICDW to indicate a hidden quantum phase transition point at
$x$$\sim$0.09-0.10. Moreover, $T_{\rm{C}}$ shows a dramatic enhancement up to
3.3 K at $x$ = 0.08, $\sim$24 times of $T_{\rm{C}}$ in 2$H$-TaSe$_2$, in
proportional to the density of states $N(E_F)$. Investigations of upper
critical fields $H_{c2}$ in single crystals reveal evidences of multiband
superconductivity as temperature-dependent anisotropy factor $\gamma_H$ =
$H_{c2}^{ab}$/$H_{c2}^{c}$, quasi-linear increase of $H_{c2}^{c}(T)$, and an
upward, positive-curvature in $H_{c2}^{ab}(T)$ near $T_{\rm{C}}$. Furthermore,
analysis of temperature-dependent electronic specific heat corroborates the
presence of multiple superconducting gaps. Based on above findings and
electronic phase diagram vs $x$, we propose that the increase of $N(E_F)$ and
effective electron-phonon coupling in the vicinity of CDW quantum phase
transition should be a key to the large enhancement of $T_{\rm{C}}$ in
Pd$_x$TaSe$_2$.",1603.05769v1
2019-07-01,Manifolds of classical probability distributions and quantum density operators in infinite dimensions,"The manifold structure of subsets of classical probability distributions and
quantum density operators in infinite dimensions is investigated in the context
of $C^{*}$-algebras and actions of Banach-Lie groups. Specificaly, classical
probability distributions and quantum density operators may be both described
as states (in the functional analytic sense) on a given $C^{*}$-algebra
$\mathscr{A}$ which is Abelian for Classical states, and non-Abelian for
Quantum states. In this contribution, the space of states $\mathscr{S}$ of a
possibly infinite-dimensional, unital $C^{*}$-algebra $\mathscr{A}$ is
partitioned into the disjoint union of the orbits of an action of the group
$\mathscr{G}$ of invertible elements of $\mathscr{A}$. Then, we prove that the
orbits through density operators on an infinite-dimensional, separable Hilbert
space $\mathcal{H}$ are smooth, homogeneous Banach manifolds of
$\mathscr{G}=\mathcal{GL}(\mathcal{H})$, and, when $\mathscr{A}$ admits a
faithful tracial state $\tau$ like it happens in the Classical case when we
consider probability distributions with full support, we prove that the orbit
through $\tau$ is a smooth, homogeneous Banach manifold for $\mathscr{G}$.",1907.00732v2
2014-07-16,Density-matrix based numerical methods for discovering order and correlations in interacting systems,"We review recently introduced numerical methods for the unbiased detection of
the order parameter and/or dominant correlations, in many-body interacting
systems, by using reduced density matrices. Most of the paper is devoted to the
""quasi-degenerate density matrix"" (QDDM) which is rooted in Anderson's
observation that the degenerate symmetry-broken states valid in the
thermodynamic limit, are manifested in finite systems as a set of low-energy
""quasi-degenerate"" states (in addition to the ground state). This method, its
original form due to Furukawa et al.[Phys. Rev. Lett. 96, 047211 (2006)], is
given a number of improvements here, above all the extension from two-fold
symmetry breaking to arbitrary cases. This is applied to two test cases (1)
interacting spinless hardcore bosons on the triangular lattice and (2) a
spin-1/2 antiferromagnetic system at the percolation threshold. In addition, we
survey a different method called the ""correlation density matrix"", which
detects (possibly long-range) correlations only from the ground state, but
using the reduced density matrix from a cluster consisting of two spatially
separated regions.",1407.4189v1
2007-07-20,Targeted Excited State Algorithms,"To overcome the limitations of the traditional state-averaging approaches in
excited state calculations, where one solves for and represents all states
between the ground state and excited state of interest, we have investigated a
number of new excited state algorithms. Building on the work of van der Vorst
and Sleijpen (SIAM J. Matrix Anal. Appl., 17, 401 (1996)), we have implemented
Harmonic Davidson and State-Averaged Harmonic Davidson algorithms within the
context of the Density Matrix Renormalization Group (DMRG). We have assessed
their accuracy and stability of convergence in complete active space DMRG
calculations on the low-lying excited states in the acenes ranging from
naphthalene to pentacene. We find that both algorithms offer increased accuracy
over the traditional State-Averaged Davidson approach, and in particular, the
State-Averaged Harmonic Davidson algorithm offers an optimal combination of
accuracy and stability in convergence.",0707.3121v1
2009-01-10,Anisotropic ground states of the quantum Hall system with currents,"Anisotropic states at half-filled third and higher Landau levels are
investigated in the system with a finite electric current. We study the
response of the striped Hall state and the anisotropic charge density wave
(ACDW) state against the injected current using the effective action. Current
distributions and a current dependence of the total energy are determined for
both states. With no injected current, the energy of the ACDW state is lower
than that of the striped Hall state. We find that the energy of the ACDW state
increases faster than that of the striped Hall state as the injected current
increases. Hence, the striped Hall state becomes the lower energy state when
the current exceeds the critical value. The critical value is estimated at
about 0.04 - 0.05 nA which is much smaller than the current used in the
experiments. Our calculations are performed using a block diagonalization
technique on a von Neumann lattice. We review this technique in this thesis.",0901.1358v1
2007-02-14,Anisotropic ground states of the quantum Hall system with currents,"Anisotropic states at half-filled higher Landau levels are investigated in
the system with a finite electric current. We study the response of the striped
Hall state and the anisotropic charge density wave (ACDW) state against the
injected current using the effective action. Current distributions and a
current dependence of the total energy are determined for both states. With no
injected current, the energy of the ACDW state is lower than that of the
striped Hall state. We find that the energy of the ACDW state increases faster
than that of the striped Hall state as the injected current increases. Hence,
the striped Hall state becomes the lower energy state when the current exceeds
the critical value. The critical value is estimated at about 0.04-0.07 nA,
which is much smaller than the current used in the experiments.",0702326v2
2021-05-07,Gaussian Continuous-Variable Isotropic State,"Inspired by the definition of the non-Gaussian two-parametric continuous
variable analogue of an isotropic state introduced by Mi\v{s}ta et al. [Phys.
Rev. A, 65, 062315 (2002); arXiv:quant-ph/0112062], we propose to take the
Gaussian part of this state as an independent state by itself, which yields a
simple, but with respect to the correlation structure interesting example of a
two-mode Gaussian analogue of an isotropic state. Unlike conventional isotropic
states which are defined as a convex combination of a thermal and an entangled
density operator, the Gaussian version studied here is defined by a convex
combination of the corresponding covariance matrices and can be understood as
entangled pure state with additional Gaussian noise controlled by a mixing
probability. Using various entanglement criteria and measures, we study the
non-classical correlations contained in this state. Unlike the previously
studied non-Gaussian two-parametric isotropic state, the Gaussian state
considered here features a finite threshold in the parameter space where
entanglement sets in. In particular, it turns out that it exhibits an analogous
phenomenology as the finite-dimensional two-qubit isotropic state.",2105.03141v3
2011-10-03,Effects of equation of state on nuclear suppression and the initial entropy density of quark gluon plasma,"We study the effects of the equation of state on the nuclear suppression of
heavy flavours in quark gluon plasma and estimate the initial entropy density
of the system produced at the highest RHIC energy. For this purpose we have
used the experimental data on the charged particle multiplicity and the nuclear
suppression of single electron spectra originating from the semi-leptonic
decays of open charm and beauty mesons. We have used inputs from lattice QCD to
minimize the model dependence of the results. We obtain the value of the
initial entropy density which varies from 20 to 59 /fm$^3$ depending on the
value of the velocity of sound that one uses for the analysis. Our
investigation leads to a conservative value of the initial entropy density
$\sim 20/$fm$^3$ with corresponding initial temperature $\sim 210$ MeV well
above the value of the transition temperature predicted by lattice QCD.",1110.0294v1
2020-04-21,Dimension dependence of numerical simulations on gravitational waves from protoneutron stars,"We examine the eigenfrequencies of gravitational waves from the protoneutron
stars (PNSs) provided via the core-collapse supernovae, focusing on how the
frequencies depend on the dimension of numerical simulations especially for the
early phase after core bounce. As expected, we find that the time evolution of
gravitational wave frequencies depends strongly on the dimension of numerical
simulation as well as the equation of state for high density matter. Even so,
we find that the fundamental frequency as a function of PNS average density and
the ratio of the specific eigenfrequencies to the fundamental frequency as a
function of PNS properties are independent of the dimension of the numerical
simulations, where the dependence of the equation of state is also very weak in
this early postbounce phase. Thus, one can safely discuss the gravitational
wave frequencies of the PNSs as a function of the PNS average density or
compactness even with the frequencies obtained from the one dimensional
simulations. We also provide phenomenological relation between the compactness
and average density as well as the relation among the $f$-, $p$-, and $g$- mode
frequencies.",2004.09871v1
2023-08-14,Implications of supermassive neutron stars for the form of the equation of state of hybrid stars,"The observations of PSR J0952-0607 and the second object in GW190814 event
indicate the possible existence of supermassive neutron stars. In this work, by
using the Constant-Sound-Speed (CSS) parametrization to describe the equation
of state (EOS) of quark matter, the constraints on the EOS parameters from
supermassive hybrid stars are investigated through the Maxwell and Gibbs
constructions. It is shown that to support a supermassive hybrid star, a lower
transition energy density, a smaller energy density discontinuity and a higher
sound speed of quark matter are favored. For the constructed hybrid star EOS
model, the maximum mass of the corresponding hybrid stars will not meet the
lower mass limit of the second object in GW190814 if the energy density
discontinuity takes a value higher than $180~{\rm MeV~fm^{-3}}$. Moreover, it
is confirmed that the supermassive neutron star observation can also rule out
the existence of twin stars as a supermassive hybrid star requires a relatively
small energy density discontinuity. Finally, we give a rough estimate of the
lower limit of the dimensionless tidal deformability of neutron stars which
ranges from 2 to 3.",2308.06993v1
2015-04-14,Vestigial chiral and charge orders from bidirectional spin-density waves: Application to the iron-based superconductors,"Recent experiments in optimally hole-doped iron arsenides have revealed a
novel magnetically ordered ground state that preserves tetragonal symmetry,
consistent with either a charge-spin density wave (CSDW), which displays a
non-uniform magnetization, or a spin-vortex crystal (SVC), which displays a
non-collinear magnetization. Here we show that, similarly to the partial
melting of the usual stripe antiferromagnet into a nematic phase, either of
these phases can also melt in two stages. As a result, intermediate
paramagnetic phases with vestigial order appears: a checkerboard charge
density-wave for the CSDW ground state, characterized by an Ising-like order
parameter, and a remarkable spin-vorticity density-wave for the SVC ground
state -- a triplet d-density wave characterized by a vector chiral order
parameter. We propose experimentally detectable signatures of these phases,
show that their fluctuations can enhance the superconducting transition
temperature, and discuss their relevance to other correlated materials.",1504.03656v3
2014-05-30,"Density functional study of electronic structure, elastic and optical properties of MNH$_2$ (M=Li, Na, K, Rb)","We report systematic first principles density functional study on the
electronic structure, elastic and optical properties of nitrogen based solid
hydrogen storage materials LiNH$_2$, NaNH$_2$, KNH$_2$, and RbNH$_2$. The
ground state structural properties are calculated by using standard density
functional theory and also dispersion corrected density functional theory. We
find that van der Waals interactions are dominant in LiNH$_2$ whereas they are
relatively weak in other alkali metal amides. The calculated elastic constants
show that all the compounds are mechanically stable and LiNH$_2$ is found to be
stiffer material among the alkali metal amides. The melting temperatures are
calculated and which follows the order RbNH$_2$ $<$ KNH$_2$ $<$ NaNH$_2$ $<$
LiNH$_2$. The electronic band structure is calculated by using the Tran-Blaha
modified Becke-Johnson potential and found that all the compounds are
insulators with a considerable band gap. The [NH$_2$]$^-$ derived states are
completely dominating in the entire valence band region while the metal atom
states occupy the conduction band. The calculated band structure is used to
analyze the different interband optical transitions occur between valence and
conduction bands. Our calculations show that these materials have considerable
optical anisotropy.",1405.7783v1
2018-09-14,Non-Gibbs states on a Bose-Hubbard lattice,"We study the equilibrium properties of the repulsive quantum Bose-Hubbard
model at high temperatures in arbitrary dimensions, with and without disorder.
In its microcanonical setting the model conserves energy and particle number.
The microcanonical dynamics is characterized by a pair of two densities: energy
density $\varepsilon$ and particle number density $n$. The macrocanonical Gibbs
distribution also depends on two parameters: the inverse nonnegative
temperature $\beta$ and the chemical potential $\mu$. We prove the existence of
non-Gibbs states, that is, pairs $(\varepsilon,n)$ which cannot be mapped onto
$(\beta,\mu)$. The separation line in the density control parameter space
between Gibbs and non-Gibbs states $\varepsilon \sim n^2$ corresponds to
infinite temperature $\beta=0$. The non-Gibbs phase cannot be cured into a
Gibbs one within the standard Gibbs formalism using negative temperatures.",1809.05371v5
2019-04-01,The abundance and physical properties of O VII and O VIII X-ray absorption systems in the EAGLE simulations,"We use the EAGLE cosmological, hydrodynamical simulations to predict the
column density and equivalent width distributions of intergalactic O VII
($E=574$ eV) and O VIII ($E=654$ eV) absorbers at low redshift. These two ions
are predicted to account for 40% of the gas-phase oxygen, which implies that
they are key tracers of cosmic metals. We find that their column density
distributions evolve little at observable column densities from redshift 1 to
0, and that they are sensitive to AGN feedback, which strongly reduces the
number of strong (column density $N \gtrsim 10^{16} \, \mathrm{cm}^{-2})$
absorbers. The distributions have a break at $N \sim 10^{16} \,
\mathrm{cm}^{-2}$, corresponding to overdensities of $\sim 10^{2}$, likely
caused by the transition from sheet/filament to halo gas. Absorption systems
with $N \gtrsim 10^{16} \mathrm{cm}^{-2}$ are dominated by collisionally
ionized O VII and O VIII, while the ionization state of oxygen at lower column
densities is also influenced by photoionization. At these high column
densities, O VII and O VIII arising in the same structures probe systematically
different gas temperatures, meaning their line ratio does not translate into a
simple estimate of temperature. While O VII and O VIII column densities and
covering fractions correlate poorly with the H I column density at
$N_{\mathrm{H \, I}} \gtrsim 10^{15} \, \mathrm{cm}^{-2}$, O VII and O VIII
column densities are higher in this regime than at the more common, lower H I
column densities. The column densities of O VI and especially Ne VIII, which
have strong absorption lines in the UV, are good predictors of the strengths of
O VII and O VIII absorption and can hence aid in the detection of the X-ray
lines.",1904.01057v2
1995-01-09,Thermally Induced Density Perturbations in the Inflation Era,"The possibility of thermally induced initial density perturbations in
inflationary cosmology is examined. The fluctuation dynamics of a scalar field
plus thermal bath system during slow roll is described by a Langevin-like
equation. Fluctuation-dissipation arguments show that for a wide parameter
range within the standard inflation model, the thermal fluctuations of the
scalar field can dominate its quantum fluctuations. The initial amplitude of
density perturbations is found to lie in a range which is consistent with the
recent observations of cosmic temperature fluctuations.",9501024v1
1998-10-06,Density PDFs of Super-Sonic Turbulence,"The question of the shape of the density PDF for supersonic turbulence is
addressed, using both analytical and numerical methods. For isothermal
supersonic turbulence, the PDF is Log-Normal, with a width that scales
approximately linearly with the Mach number. For a polytropic equation of
state, with an effective gamma smaller than one, the PDF becomes skewed and
reminiscent of (but not equal to) a power law on the high density side.",9810074v1
2006-12-06,A Phantom does not Result from a Backreaction,"The backreaction of nonlinear inhomogeneities to the cosmic expansion is
analyzed in the framework of general relativity with a cosmological constant.
By defining the spatially averaged matter energy density, we find that the
cosmological constant induces a new type of backreaction whose equation of
state is $p=-4/3 \rho$, where $\rho$ and $p$ are the effective energy density
and effective pressure of the backreaction in the averaged Friedmann universe.
However, the effective density is negative, and thus it decreases the
acceleration caused by the cosmological constant.",0612151v2
1996-01-09,A possible phase diagram of a t-J ladder model,"We investigate a t-J ladder model by numerical diagonalization method. By
calculating correlation functions and assuming the Luttinger liquid relation,
we obtained a possible phase diagram of the ground state as a function of J/t
and electron density $n$. We also found that behavior of correlation functions
seems to consist with the prediction of Luttinger liquid relation. The result
suggests that the superconducting phase appear in the region of $J/t
\displaystyle{ \mathop{>}_{\sim}} 0.5$ for high electron density and $J/t
\displaystyle{ \mathop{>}_{\sim}} 2.0$ for low electron density.",9601027v1
1997-10-29,Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains,"We present a rotationally invariant matrix product method (MPM) of isotropic
spin chains. This allows us to deal with a larger number of variational MPM
parameters than those considered earlier by other authors. We also show the
relation between the MPM and the DMRG method of White. In our approach the
eigenstates of the density matrix associated with the MPM are used as
variational parameters together with the standard MPM parameters. We compute
the ground state energy density and the spin correlation length of the spin 1
Heisenberg chain.",9710310v1
1999-08-26,Magnons in real materials from density-functional theory,"We present an implementation of the adiabatic spin-wave dynamics of Niu and
Kleinman. This technique allows to decouple the spin and charge excitations of
a many-electron system using a generalization of the adiabatic approximation.
The only input for the spin-wave equations of motion are the energies and Berry
curvatures of many-electron states describing frozen spin spirals. The latter
are computed using a newly developed technique based on constrained
density-functional theory, within the local spin density approximation and the
pseudo-potential plane-wave method. Calculations for iron show an excellent
agreement with experiments.",9908386v1
1999-10-08,Glass Transition in a 2D Lattice Model,"The dynamics of compaction of hard cross-shaped pentamers on the 2D square
lattice is investigated. The addition of new particles is controlled by
diffusive relaxation. It is shown that the filling process terminates at a
glassy phase with a limiting coverage density \rho_{rcp}=0.171626(3), lower
than the density of closest packing \rho_{cp}=0.2, and the long time filling
rate vanishes like (\rho_{rcp}-\rho(t))^2. For the entire density regime the
particles form an amorphous phase, devoid of any crystalline order. Therefore,
the model supports a stable random packing state, as opposed to the hard disks
system. Our results may be relevant to recent experiments studying the
clustering of proteins on bilayer lipid membranes.",9910128v1
2002-07-12,Organization and instabilities of entangled active polar filaments,"We study the dynamics of an entangled, isotropic solution of polar filaments
coupled by molecular motors which generate relative motion of the filaments in
two and three dimensions. We investigate the stability of the homogeneous state
for constant motor concentration taking into account excluded volume and
entanglement. At low filament density the system develops a density
instability, while at high filament density entanglement effects drive the
instability of orientational fluctuations.",0207320v1
2005-10-20,Basic Properties of a Vortex in a Noncentrosymmetric Superconductor,"We numerically study the vortex core structure in a noncentrosymmetric
superconductor such as CePt3Si without mirror symmetry about the xy plane.
  A single vortex along the z axis and a mixed singlet-triplet Cooper pairing
model are considered.
  The spatial profiles of the pair potential, local density of states,
supercurrent density, and radially-textured magnetic moment density around the
vortex are obtained in the clean limit on the basis of the quasiclassical
theory of superconductivity.",0510548v1
2003-12-02,The Strangeness Signal in Hadron Production at Relativistic Energy,"Strangeness enhancement is discussed as a feature specific to relativistic
nuclear collisions which create a fireball of strongly interacting matter at
high energy density. At very high energy this is suggested to be partonic
matter, but at lower energy it should consist of yet unknown hadronic degrees
of freedom. The freeze-out of this high density state to a hadron gas can tell
us about properties of fireball matter. The hadron gas at the instant of its
formation captures conditions directly at the QCD phase boundary at top SPS and
RHIC energy, chiefly the critical temperature and energy density.",0312039v1
1996-09-05,Renormalization Effects in a Dilute Bose Gas,"The low-density expansion for a homogeneous interacting Bose gas at zero
temperature can be formulated as an expansion in powers of $\sqrt{\rho a^3}$,
where $\rho$ is the number density and $a$ is the S-wave scattering length.
Logarithms of $\rho a^3$ appear in the coefficients of the expansion. We show
that these logarithms are determined by the renormalization properties of the
effective field theory that describes the scattering of atoms at zero density.
The leading logarithm is determined by the renormalization of the pointlike $3
\to 3$ scattering amplitude.",9609047v1
1997-08-05,Estimating the nuclear level density with the Monte Carlo shell model,"A method for making realistic estimates of the density of levels in even-even
nuclei is presented making use of the Monte Carlo shell model (MCSM). The
procedure follows three basic steps: (1) computation of the thermal energy with
the MCSM, (2) evaluation of the partition function by integrating the thermal
energy, and (3) evaluating the level density by performing the inverse Laplace
transform of the partition function using Maximum Entropy reconstruction
techniques. It is found that results obtained with schematic interactions,
which do not have a sign problem in the MCSM, compare well with realistic
shell-model interactions provided an important isospin dependence is accounted
for.",9708007v1
2005-04-01,Density inhomogeneities in heavy ion collisions around the critical point,"We study the hydrodynamical expansion of a hot and baryon-dense quark fluid
coupled to classical real-time evolution of the long wavelength modes of the
chiral field. Significant density inhomogeneities develop dynamically when the
transition to the symmetry-broken state occurs. We find that the amplitude of
the density inhomogeneities is larger for expansion trajectories crossing the
line of first-order transitions than for crossovers, which could provide some
information on the location of a critical point. A few possible experimental
signatures for inhomogeneous decoupling surfaces are mentioned briefly.",0504003v2
2005-06-28,Isospin Transport at Fermi Energies,"In this paper we investigate isospin transport mechanisms in semi-peripheral
collisions at Fermi energies. The effects of the formation of a low density
region (neck) between the two reaction partners and of pre-equilibrium emission
on the dynamics of isospin equilibration are carefully analyzed. We clearly
identify two main contributions to the isospin transport: isospin diffusion due
to the $N/Z$ ratio and isospin drift due to the density gradients. Both effects
are sensitive to the symmetry part of the nuclear Equation of State (EOS), in
particular to the value and slope around saturation density.",0506078v1
1998-10-28,Density Matrices and Geometric Phases for n-state Systems,"An explicit parameterization is given for the density matrices for $n$-state
systems. The geometry of the space of pure and mixed states and the entropy of
the $n$-state system is discussed. Geometric phases can arise in only specific
subspaces of the space of all density matrices. The possibility of obtaining
nontrivial abelian and nonabelian geometric phases in these subspaces is
discussed.",9810084v1
2007-05-30,Ground-State Properties of a One-Dimensional System of Hard Rods,"A quantum Monte Carlo simulation of a system of hard rods in one dimension is
presented and discussed. The calculation is exact since the analytical form of
the wavefunction is known, and is in excellent agreement with predictions
obtained from asymptotic expansions valid at large distances. The analysis of
the static structure factor and the pair distribution function indicates that a
solid-like and a gas-like phases exist at high and low densities, respectively.
The one-body density matrix decays following a power-law at large distances and
produces a divergence in the low density momentum distribution at k=0 which can
be identified as a quasi-condensate.",0705.4377v1
2008-01-04,$N$-representability of the Jastrow wave function pair density of the lowest-order,"We have recently proposed a density functional scheme for calculating the
ground-state pair density (PD) within the Jastrow wave function PDs of the
lowest-order (LO-Jastrow PDs) [M. Higuchi and K. Higuchi, Phys. Rev. A
\textbf{75}, 042510 (2007)]. However, there remained an arguable problem on the
$N$-representability of the LO-Jastrow PD. In this paper, the sufficient
conditions for the $N$-representability of the LO-Jastrow PD are derived. These
conditions are used as the constraints on the correlation function of the
Jastrow wave function. A concrete procedure to search the suitable correlation
function is also presented.",0801.0615v1
2008-06-06,Two-phase coexistence in the hard-disk model,"A two-dimensional system of 10000 hard disks with square periodic boundary
conditions, at a density in the middle of the 2-phase region predicted from
equation-of-state data, when subjected to a weak external uniform force, is
seen to phase separate. Thermodynamic profiles of the inhomogeneous two-phase
system agree with the local density approximation (LDA) of density functional
theory. There is no indication of any mesophase.",0806.1109v2
2009-04-24,"Itinerant magnetic multipole moments of rank five, triakontadipoles, as the hidden order in URu$_{2}$Si$_{2}$","A broken symmetry ground state without any magnetic moments has been
calculated by means of local-density-approximation to density functional theory
plus a local exchange term, the so-called LDA+$U$ approach, for
URu$_{2}$Si$_{2}$. The solution is analysed in terms of a multipole tensor
expansion of the itinerant density matrix and is found to be a non-trivial
magnetic multipole. Analysis and further calculations show that this type of
multipole enters naturally in time reversal breaking in presence of large
effective spin-orbit coupling and co-exists with magnetic moments for most
magnetic actinides",0904.3883v1
2010-01-14,Classical density-functional theory for water,"We introduce a new computationally efficient and accurate classical
density-functional theory for water and apply it to hydration of hard spheres
and inert gas atoms. We find good agreement with molecular dynamics simulations
for the hydration of hard spheres and promising agreement for the solvation of
inert gas atoms in water. Finally, we explore the importance of the
orientational ambiguity in state-of-the-art continuum theories of water, which
are based on the molecular density only.",1001.2350v2
2010-07-07,Theory of correlated electron transport and inelastic tunneling spectroscopy,"For a non-superconducting system, the electronic tunneling current through an
insulating barrier is calculated, including interaction effects. The exact
Hamiltonian of the full system is projected onto the subspaces of the ""left""
and ""right"" leads. In the weak tunneling limit the well-known tunneling
Hamiltonian is recovered, along with an additional term. This additional term
originates from the projection of the electron-electron interaction onto each
subsystem and corresponds to correlated tunneling. It is shown that the
tunneling current is determined by---in addition to the single-particle density
of states---the spin-spin and density-density susceptibilities. The signatures
of which have recently been observed in several experiments.",1007.1238v1
2013-04-16,Thermodynamics of Strongly Correlated One-Dimensional Bose Gases,"We investigate the thermodynamics of one-dimensional Bose gases in the
strongly correlated regime. To this end, we prepare ensembles of independent 1D
Bose gases in a two-dimensional optical lattice and perform high-resolution in
situ imaging of the column-integrated density distribution. Using an inverse
Abel transformation we derive effective one-dimensional line-density profiles
and compare them to exact theoretical models. The high resolution allows for a
direct thermometry of the trapped ensembles. The knowledge about the
temperature enables us to extract thermodynamic equations of state such as the
phase-space density, the entropy per particle and the local pair correlation
function.",1304.4625v1
2014-01-06,$J/ψ$ in a hot baryonic plasma,"We calculate the bound state properties of $J/\psi$ in a hot and dense QCD
plasma using phenomenological potentials augmented by inputs from perturbative
QCD. The temperature and density region of study will be relevant in future
heavy ion collision experiments at FAIR. We find that the effect of baryon
density on the dissociation of $J/\psi$ is small in this regime. However we
indicate that if there is a critical end point in the QCD phase diagram then
strong density fluctuation will dissociate charmonia near hadronization. The
measurement of $J/\psi$ suppression can therefore signify the existence of the
critical point unambiguously.",1401.1110v1
2014-01-08,"Many faces of the Landau gauge gluon propagator at zero and finite temperature: positivity violation, spectral density and mass scales","We address several aspects of gluon propagation at zero and finite
temperature. In particular, we study the violation of spectral positivity, we
discuss a method to extract the K\""all\'{e}n-Lehmann spectral density of a
particle (be it elementary or bound state) propagator and apply it to compute
gluon spectral densities from lattice data. Furthermore, we also consider the
interpretation of the Landau gauge gluon propagator at finite temperature as a
massive type bosonic propagator.",1401.1554v1
2014-11-17,Optimal Reduction of Multivariate Dirac Mixture Densities,"This paper is concerned with the optimal approximation of a given
multivariate Dirac mixture, i.e., a density comprising weighted Dirac
distributions on a continuous domain, by an equally weighted Dirac mixture with
a reduced number of components. The parameters of the approximating density are
calculated by minimizing a smooth global distance measure, a generalization of
the well-known Cram\'{e}r-von Mises Distance to the multivariate case. This
generalization is achieved by defining an alternative to the classical
cumulative distribution, the Localized Cumulative Distribution (LCD), as a
characterization of discrete random quantities (on continuous domains), which
is unique and symmetric also in the multivariate case. The resulting
approximation method provides the basis for various efficient nonlinear state
and parameter estimation methods.",1411.4586v1
2015-04-16,Squeezing and entanglement of density oscillations in a Bose-Einstein condensate,"The dispersive interaction of atoms and a far-detuned light field allows
nondestructive imaging of the density oscillations in Bose-Einstein
condensates. Starting from a ground state condensate, we investigate how the
measurement back action leads to squeezing and entanglement of the quantized
density oscillations. In particular, we show that properly timed, stroboscopic
imaging and feedback can be used to selectively address specific eigenmodes and
avoid excitation of non-targeted modes of the system.",1504.04241v1
2016-09-24,On the Almost Everywhere Stability of Discrete-Time Dynamical Systems,"For a dynamical system, it is known that the existence of a Lyapunov-type
density function, called Lyapunov density or Rantzer's density function,
implies convergence of Lebesgue almost all solutions to an equilibrium. Using
the duality between Frobenius-Perron and Koopmann operators, we generalize this
result from equilibrium to invariant sets, both for continuous- and
discrete-time. Furthermore, some redundant assumptions that exist in the
literature of almost everywhere stability for discrete-time, such as the local
stability of the attractor and the compactness of the state space, has been
removed.",1609.07539v3
2017-02-20,Comprehensive classification for Bose-Fermi mixtures,"We present analytical studies of a boson-fermion mixture at zero temperature
with spin-polarized fermions. Using the Thomas-Fermi approximation for bosons
and the local-density approximation for fermions, we find a large variety of
different density shapes. In the case of continuous density, we obtain analytic
conditions for each configuration for attractive as well as repulsive
boson-fermion interaction. Furthermore, we analytically show that all the
scenarios we describe are minima of the grand-canonical energy functional.
Finally, we provide a full classification of all possible ground states in the
interpenetrative regime. Our results also apply to binary mixtures of bosons.",1702.06050v1
2017-08-28,Singularities of the density of states of random Gram matrices,"For large random matrices $X$ with independent, centered entries but not
necessarily identical variances, the eigenvalue density of $XX^*$ is
well-approximated by a deterministic measure on $\mathbb{R}$. We show that the
density of this measure has only square and cubic-root singularities away from
zero. We also extend the bulk local law in [arXiv:1606.07353] to the vicinity
of these singularities.",1708.08442v2
2016-05-12,Theory of charge density wave non-contact friction,"A mechanism is proposed to describe the occurrence of distance-dependent
dissipation peaks in the dynamics of an atomic force microscope tip oscillating
over a surface characterized by a charge density wave state. The dissipation
has its origin in the hysteretic behavior of the tip oscillations occurring at
positions compatible with a localized phase slip of the charge density wave.
This model is supported through static and dynamic numerical simulations of the
tip surface interaction and is in good qualitative agreement with recently
performed experiments on a NbSe$_2$ sample.",1605.03711v1
2019-01-17,Charge Density Wave in a Doped Kondo Chain,"We report the existence of the charge density wave (CDW) in the ground state
of 1D Kondo lattice model at the filling of n=0.75 in the weak coupling region.
The CDW is driven by the effective Coulomb repulsion mediated by the localized
spins. Based on our numerical results using the density matrix renormalization
group method, we show that the CDW phase appears in the paramagnetic region
previously known as the Tomonaga-Luttinger liquid. The emergence of this phase
serves as an example of CDW phase induced without bare repulsive interactions,
and enriches the phase diagram of the 1D Kondo lattice model.",1901.05643v1
2021-08-19,Singularity degree of structured random matrices,"We consider the density of states of structured Hermitian random matrices
with a variance profile. As the dimension tends to infinity the associated
eigenvalue density can develop a singularity at the origin. The severity of
this singularity depends on the relative positions of the zero submatrices. We
provide a classification of all possible singularities and determine the
exponent in the density blow-up, which we label the singularity degree.",2108.08811v2
2023-02-08,Disentangling Learning Representations with Density Estimation,"Disentangled learning representations have promising utility in many
applications, but they currently suffer from serious reliability issues. We
present Gaussian Channel Autoencoder (GCAE), a method which achieves reliable
disentanglement via flexible density estimation of the latent space. GCAE
avoids the curse of dimensionality of density estimation by disentangling
subsets of its latent space with the Dual Total Correlation (DTC) metric,
thereby representing its high-dimensional latent joint distribution as a
collection of many low-dimensional conditional distributions. In our
experiments, GCAE achieves highly competitive and reliable disentanglement
scores compared with state-of-the-art baselines.",2302.04362v1
2023-07-16,"Electrostatic shielding effect and Binding energy shift of MoS2, MoSe2 and MoTe2 materials","In this paper, the electronic structure and bond properties of MoS2, MoSe2
and MoTe2 are studied. Density functional theory (DFT) calculates combined with
the binding energy and bond-charge (BBC) model to obtain electronic structure,
binding energy shift and bond properties. It is found that electrostatic
shielding by electron exchange is the main cause of density fluctuation. A
method for calculating the density of Green's function with energy level shift
is established. It provides new methods and ideas for the further study of the
binding energy, bond states and electronic properties of nanomaterials.",2307.08035v4
2023-11-19,Global Strong Solutions to the incompressible Magnetohydrodynamic Equations with Density-Dependent Viscosity and Vacuum in 3D Exterior Domains,"The nonhomogeneous incompressible Magnetohydrodynamic Equations with
density-dependent viscosity is studied in three-dimensional (3D) exterior
domains with slip boundary conditions. The key is the constraint of an
additional initial value condition $B_0\in L^p (1\leqslant p<12/7)$, which
increase decay-in-time rates of the solutions, thus we obtain the global
existence of strong solutions provided the gradient of the initial velocity and
initial magnetic field is suitably small. In particular, the initial density is
allowed to contain vacuum states and large oscillations. Moreover, the
large-time behavior of the solution is also shown.",2311.12873v1
2011-03-29,New effective recombination coefficients for nebular N II lines,"Here we report new ${\it ab initio}$ calculations of the effective
recombination coefficients for the \ion{N}{ii} recombination spectrum. We have
taken into account the density dependence of the coefficients arising from the
relative populations of the fine-structure levels of the ground state of the
recombining ion, an elaboration that has not been attempted before for this
ion, and it opens up the possibility of electron density determination via
recombination line analysis. Photoionization cross-sections, bound state
energies, and the oscillator strengths of \ion{N}{ii} with $n \leq 11$ and $l
\leq 4$ have been obtained using the close-coupling R-matrix method in the
intermediate coupling scheme. Photoionization data were computed that
accurately map out the near-threshold resonances and were used to derive
recombination coefficients, including radiative and dielectronic recombination.
Also new is including the effects of dielectronic recombination via high-$n$
resonances lying between the $^2$P$^{\rm o}$\,$_{1/2}$ and $^2$P$^{\rm
o}$\,$_{3/2}$ levels. The new calculations are valid for temperatures down to
an unprecedentedly low level (approximately 100 K). The newly calculated
effective recombination coefficients allow us to construct plasma diagnostics
based on the measured strengths of the \ion{N}{ii} optical recombination lines
(ORLs).
  The derived effective recombination coefficients are fitted with analytic
formulae as a function of electron temperature for different electron
densities. The dependence of the emissivities of the strongest transitions of
\ion{N}{ii} on electron density and temperature is illustrated. Potential
applications of the current data to electron density and temperature
diagnostics for photoionized gaseous nebulae are discussed. We also present a
method of determining electron temperature and density simultaneously.",1103.5558v1
2020-06-29,Variational density functional calculations of excited states via direct optimization,"The development of variational density functional theory approaches to
excited electronic states is impeded by limitations of the commonly used
self-consistent field (SCF) procedure. A method based on a direct optimization
approach as well as the maximum overlap method is presented and the performance
compared with previously proposed SCF strategies. Excited-state solutions
correspond to saddle points of the energy as a function of the electronic
degrees of freedom. The approach presented here makes use of a preconditioner
determined with the help of the maximum overlap method to guide the convergence
on a target nth-order saddle point. The method is found to be more robust and
to converge faster than previously proposed SCF approaches for a set of 89
excited states of molecules. A limited-memory formulation of the symmetric
rank-one method for updating the inverse Hessian is found to give the best
performance. A conical intersection for the carbon monoxide molecule is
calculated without resorting to fractional occupation numbers. Calculations on
excited states of the hydrogen atom and a doubly excited state of the
dihydrogen molecule using a self-interaction corrected functional are
presented. For these systems, the self-interaction correction is found to
improve the accuracy of density functional calculations of excited states.",2006.15922v2
2004-10-15,Stability of the mixed phase in hybrid stars,"The transition from hadronic matter to quark matter in the core of neutron
stars is likely to be associated with the appearance of a mixed phase, leading
to a smooth variation of the star density profile. We discuss the results of a
systematic study of the properties of the mixed pase upon Coulomb and surface
effects. A state of the art nonrelativistic equation of state of nuclear matter
has been used for the low density phase, while quark matter has been described
within the MIT bag model, including the effect of perturbative one-gluon
exchange interactions. The implications for neutron star structure are
discussed.",0410376v1
1996-05-10,Enhancement of the Kondo temperature of magnetic impurities in metallic point contacts due to the fluctuations of the local density of states,"The effect of local density of states (LDOS) fluctuations on the dynamics of
a Kondo impurities in a small metallic point contact (PC) is studied. To
estimate the spatial and energy dependent LDOS fluctuations we investigate a
model PC by means of a transfer matrix formalism. For small PC's in the
nanometer scale we find that near to the orifice strong LDOS fluctuations
develop. These fluctuations may shift the Kondo temperature by several orders
of magnitude, and result in a strong broadening of the PC Kondo peak in
agreement with the results of recent measurements.",9605063v1
1999-11-12,Energy and entropy of metastable states in glassy systems,"We investigate the multi-valley energy landscape of a 3-D on-lattice network
model for covalent glasses, numerically determining the shape of the valleys,
the local density of states, the density of minima and the local connectivity.
We present some of these quantities in a graphical birds-eye view of the
landscape, and discuss their implications for the relaxation dynamics and
cooling behavior of glasses. The strong similarities between the landscape of
this model and those of other complex systems point to the possibility of a
common low-temperature dynamical description.",9911197v1
2000-06-02,Nanometer Scale Mapping of the Density of States in an Inhomogeneous Superconductor,"Using high speed scanning tunneling spectroscopy, we perform a full mapping
of the quasiparticle density of states (DOS) in single crystals of
BiPbSrCaCuO(2212). The measurements carried out at 5 K showed a complex spatial
pattern of important variations of the local DOS on the nanometer scale.
Superconducting areas are co-existing with regions of a smooth and larger
gap-like DOS structure. The superconducting regions are found to have a minimum
size of about 3 nm. The role of Pb-introduced substitutional disorder in the
observed spatial variations of the local DOS is discussed.",0006039v1
2006-12-19,Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards,"We consider the effect of spin-orbit coupling on the low energy excitation
spectrum of an Andreev billiard (a quantum dot weakly coupled to a
superconductor), using a dynamical numerical model (the spin Andreev map).
Three effects of spin-orbit coupling are obtained in our simulations: In zero
magnetic field: (1) the narrowing of the distribution of the excitation gap;
(2) the appearance of oscillations in the average density of states. In strong
magnetic field: (3) the appearance of a peak in the average density of states
at zero energy. All three effects have been predicted by random-matrix theory.",0612501v1
2005-09-03,"Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality","In \cite{Elek} we proved that the limit of a weakly convergent sequence of
finite graphs can be viewed as a graphing or a continuous field of infinite
graphs. Thus one can associate a type $II_1$-von Neumann algebra to such graph
sequences. We show that in this case the integrated density of states exists
that is the weak limit of the spectra of the graph Laplacians of the finite
graphs is the KNS-spectral measure of the graph Laplacian of the limit
graphing. Using this limit technique we prove a Cheeger type inequality for
finite graphs.",0509062v2
2013-05-14,Asymptotics of $L_p$-norms of Hermite polynomials and Rényi entropy of Rydberg oscillator states,"The asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which
describes the R\'enyi entropy of order $p$ of the associated quantum oscillator
probability density, is determined for $n\to\infty$ and $p>0$. Then, it is
applied to the calculation of the R\'enyi entropy of the quantum-mechanical
probability density of the highly-excited (Rydberg) states of the isotropic
oscillator.",1305.3071v1
2018-11-18,Fluctuations in small systems,"We review the main features of event-by-event fluctuations of the content of
the Fock states of onia (as models for dilute hadrons, or as bare hadronic
components of virtual photons), as well as some of their observable
consequences. We briefly address the total scattering cross section of a small
onium off a nucleus, then of two small onia. Finally, we explain that the
multiplicity in the final state of collisions of large onia with nuclei may
directly be related to the gluon density in the former. We provide first
predictions for the event-by-event fluctuations of the gluon density.",1811.07394v1
2013-08-13,Correlation of the critical parameters of the gas-liquid phase transition and the density of the crystal at zero absolute temperature,"The empirical formula of Timmermanns connecting the density of the crystal at
zero absolute temperature with the parameters of the critical point of the
gas-liquid phase transition is derived theoretically from the Van der Waals
equation of state using the conditions of phase equilibrium. Two equations of
state with three parameters describing the critical point of any pure substance
are considered. The formula is derived approximately from the first equation
and exactly from the second one.",1308.2842v1
2020-09-17,Hölder regularity of the integrated density of states for quasi-periodic long-range operators on $\ell^2(\Z^d)$,"We prove the H\""older continuity of the integrated density of states for a
class of quasi-periodic long-range operators on $\ell^2(\Z^d)$ with large
trigonometric polynomial potentials and Diophantine frequencies. Moreover, we
give the H\""older exponent in terms of the cardinality of the level sets of the
potentials, which improves, in the perturbative regime, the result obtained by
Goldstein and Schlag \cite{gs2}. Our approach is a combination of Aubry
duality, generalized Thouless formula and the regularity of the Lyapunov
exponents of analytic quasi-periodic $GL(m,\C)$ cocycles which is proved by
quantitative almost reducibility method.",2009.08004v1
2015-12-09,Half-width of local spectral density of states given by width of nonperturbative parts of eigenfunctions: The Wigner-band-matrix model,"It is shown that, for a Hamiltonian with a band structure, the half width of
local spectral density of states, or strength function, is closely related to
the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the
Wigner-band random-matrix model, making use of a generalized Brillouin-Wigner
perturbation theory, we derive analytical expressions for the width of the NPT
parts under weak and strong perturbation. An iterative algorithm is given, by
which the NPT widths can be computed efficiently, and is used in numerical test
of the analytical predictions.",1512.02701v1
1998-08-24,ORFEUS II echelle spectra: Absorption by H_2 in the LMC,"We present the first detection of molecular hydrogen (H_2) UV absorption
profiles on the line of sight to the LMC. The star LH 10:3120 in the LMC was
measured with the ORFEUS telescope and the Tuebingen echelle spectrograph
during the space shuttle mission of Nov./Dec. 1996. 16 absorption lines from
the Lyman band are used to derive the column densities of H_2 for the lowest 5
rotational states in the LMC gas. For these states we find a total column
density of N(H_2)=6.6 x 10^18$ cm^-2 on this individual line of sight. We
obtain equivalent excitation temperatures of T < 50 K for the rotational ground
state and T = 470 K for 0 < J < 6 by fitting the population densities of the
rotational states to theoretical Boltzmann distributions. We conclude that UV
pumping dominates the population of the higher rotational levels, as known from
the H_2 gas in the Milky Way. (Research supported in part by the DARA)",9808256v1
1997-06-23,Resonant scattering in a strong magnetic field: exact density of states,"We study the structure of 2D electronic states in a strong magnetic field in
the presence of a large number of resonant scatterers. For an electron in the
lowest Landau level, we derive the exact density of states by mapping the
problem onto a zero-dimensional field-theoretical model. We demonstrate that
the interplay between resonant and non-resonant scattering leads to a
non-analytic energy dependence of the electron Green function. In particular,
for strong resonant scattering the density of states develops a gap in a finite
energy interval. The shape of the Landau level is shown to be very sensitive to
the distribution of resonant scatterers.",9706233v3
2001-03-21,Andreev levels in a single-channel conductor,"We calculate the subgap density of states of a disordered single-channel
normal metal connected to a superconductor at one end (NS junction) or at both
ends (SNS junction). The probability distribution of the energy of a bound
state (Andreev level) is broadened by disorder. In the SNS case the two-fold
degeneracy of the Andreev levels is removed by disorder leading to a splitting
in addition to the broadening. The distribution of the splitting is given
precisely by Wigner's surmise from random-matrix theory. For strong disorder
the mean density of states is largely unaffected by the proximity to the
superconductor, because of localization, except in a narrow energy region near
the Fermi level, where the density of states is suppressed with a log-normal
tail.",0103445v3
2005-04-22,Density minimum and liquid-liquid phase transition,"We present a high-resolution computer simulation study of the equation of
state of ST2 water, evaluating the liquid-state properties at 2718 state
points, and precisely locating the liquid-liquid critical point (LLCP)
occurring in this model. We are thereby able to reveal the interconnected set
of density anomalies, spinodal instabilities and response function extrema that
occur in the vicinity of a LLCP for the case of a realistic, off-lattice model
of a liquid with local tetrahedral order. In particular, we unambiguously
identify a density minimum in the liquid state, define its relationship to
other anomalies, and show that it arises due to the approach of the liquid
structure to a defect-free random tetrahedral network of hydrogen bonds.",0504574v1
2007-02-27,"Superconductivity, Charge Orderings and Phase Separations in Systems with Local Electron Pairing","We study two effective models developed for description of superconductors
with short-coherence length: (i) the extended Hubbard model with on-site
attraction and intersite repulsion, (ii) the model of hard-core charged bosons
on a lattice. The analysis is concentrated on the problem of phase separations
and competition between superconductivity (SS) and charge-density-wave (CDW)
orderings. The phase diagrams of the systems are shown to consist of at least
seven different states, including 3 types of phase separated (PS) states:
CDW-SS (PS1), CDW-normal (PS2) and the state of electron droplets (PS3). By
taking into account the PS states and the effects of longer-range
density-density interactions (beyond nearest neighbours) our work substantially
generalizes and modifies the conclusions of previous works concerning the
models considered.",0702638v1
2010-11-14,Nonequilibrium Phase Diagram of a Driven-Dissipative Many-Body System,"We study the nonequilibrium dynamics of a many-body bosonic system on a
lattice, subject to driving and dissipation. The time-evolution is described by
a master equation, which we treat within a generalized Gutzwiller mean field
approximation for density matrices. The dissipative processes are engineered
such that the system, in the absence of interaction between the bosons, is
driven into a homogeneous steady state with off-diagonal long range order. We
investigate how the coherent interaction affects qualitatively the properties
of the steady state of the system and derive a nonequilibrium phase diagram
featuring a phase transition into a steady state without long range order. The
phase diagram exhibits also an extended domain where an instability of the
homogeneous steady state gives rise to a persistent density pattern with
spontaneously broken translational symmetry. In the limit of small particle
density, we provide a precise analytical description of the time-evolution
during the instability. Moreover, we investigate the transient following a
quantum quench of the dissipative processes and we elucidate the prominent role
played by collective topological variables in this regime.",1011.3207v1
2013-02-19,Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation,"Using density functional molecular dynamics simulations, we determine the
equation of state for hydrogen-helium mixtures spanning density-temperature
conditions typical of giant planet interiors, ~0.2-9 g/cc and 1000-80000 K for
a typical helium mass fraction of 0.245. In addition to computing internal
energy and pressure, we determine the entropy using an ab initio thermodynamic
integration technique. A comprehensive equation of state (EOS) table with 391
density-temperature points is constructed and the results are presented in form
of two-dimensional free energy fit for interpolation. Deviations between our ab
initio EOS and the semi-analytical EOS model by Saumon and Chabrier are
analyzed in detail, and we use the results for initial revision of the inferred
thermal state of giant planets with known values for mass and radius. Changes
are most pronounced for planets in the Jupiter mass range and below. We present
a revision to the mass-radius relationship which makes the hottest exoplanets
increase in radius by ~0.2 Jupiter radii at fixed entropy and for masses
greater than ~0.5 Jupiter mass. This change is large enough to have possible
implications for some discrepant ""inflated giant exoplanets"".",1302.4691v1
2016-06-03,The effect of anisotropy on the absorption spectrum and the density of states of two-dimensional Frenkel exciton systems with Gaussian diagonal disorder,"On the optical absorption and the density of states of Frenkel exciton
systems on square, rectangular, and triangular lattices with nearest-neighbor
interactions and a Gaussian distribution of transition frequencies. The
analysis is based on an elliptic integral approach that gives results over the
entire spectrum. It is found that the absorption is weakly affected by the
anisotropy in contrast to the density of states where the effects can be much
stronger. The results for the square lattice are in good agreement with the
finite array calculations of Schreiber and Toyozawa. Our findings suggest that
the coherent potential approximation can be useful in interpreting the optical
properties of two-dimensional systems with dominant nearest-neighbor
interactions and Gaussian diagonal disorder where the optically excited states
are Frenkel excitons.",1606.01130v1
2020-07-02,A new and efficient implementation of CC3,"We present a new and efficient implementation of the closed shell coupled
cluster singles and doubles with perturbative triples method (CC3) in the
electronic structure program $e^T$. Asymptotically, a ground state calculation
has an iterative cost of $4n_{\text{V}}^{4}n_{\text{O}}^{3}$ floating point
operations (FLOP), where $n_{\text{V}}$ and $n_{\text{O}}$ are the number of
virtual and occupied orbitals respectively. The Jacobian and transpose Jacobian
transformations, required to iteratively solve for excitation energies and
transition moments, both require $8n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP. We
have also implemented equation of motion (EOM) transition moments for CC3. The
EOM transition densities require recalculation of triples amplitudes, as
$n_{\text{V}}^{3}n_{\text{O}}^{3}$ tensors are not stored in memory. This
results in a noniterative computational cost of
$10n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP for the ground state density and
$26n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP per state for the transition
densities. The code is compared to the CC3 implementations in CFOUR, Dalton and
Psi4. We demonstrate the capabilities of our implementation by calculating
valence and core excited states of L-proline.",2007.01088v2
2016-08-23,Equation of state for neutron star matter with NJL model and Dirac-Brueckner-Hartree-Fock approximation,"As the interior density of a neutron star can become very high, it has been
expected and discussed that quark matter may exist inside it. To describe the
transition from hadron to quark phases (and vice versa), there are mainly two
methods; one is the first-order phase transition, and the other is the
crossover phenomenon. In the present study, using the flavor-SU (3) NJL model
with the vector coupling interaction, we have calculated the equation of state
for the quark phase at high density. Furthermore, for the hadron phase at low
density, we have used two kinds of the equations of state; one is a relatively
soft one by the QHD model, and the other is a stiff one calculated with
relativistic Brueckner-Hartree-Fock approximation. Using those equations of
state for the two phases, we have investigated the influence of various choices
of parameters concerning the crossover region on the mass and radius of a
neutron star.",1608.06449v1
2021-01-01,Locality of the windowed local density of states,"We introduce a generalization of local density of states which is ""windowed""
with respect to position and energy, called the windowed local density of
states (wLDOS). This definition generalizes the usual LDOS in the sense that
the usual LDOS is recovered in the limit where the position window captures
individual sites and the energy window is a delta distribution. We prove that
the wLDOS is local in the sense that it can be computed up to arbitrarily small
error using spatial truncations of the system Hamiltonian. Using this result we
prove that the wLDOS is well-defined and computable for infinite systems
satisfying some natural assumptions. We finally present numerical computations
of the wLDOS at the edge and in the bulk of a ""Fibonacci SSH model"", a
one-dimensional non-periodic model with topological edge states.",2101.00272v2
2021-12-31,Entanglement and seniority,"We study mode-entanglement in the seniority model, derive analytic formulas
for the one-body reduced density matrix of states with seniority $\nu =
0,\;1,\;2$, and $\nu=3$, and also determine the particle number dependence of
the one-body reduced density matrix for arbitrary seniority. We carry out
numerical calculations for the lightest calcium isotopes and for $^{94}{\rm
Ru}$ nucleus, and investigate the structure of their ground and low energy
yrast states. We investigate the fulfillment of several predictions of the
seniority model regarding the behavior of one-mode entropies, which we compare
with the results of configuration interaction (CI) and density matrix
renormalization group (DMRG) computations. For $^{94}{\rm Ru}$, the seniority
model accounts for the $0g_{9/2}$ mode entropies, but seniority mixing is
important for certain yrast states. Interaction induced quantum fluctuations
decrease the occupation of the $0f_{5/2}$, $1p_{3/2}$ and $1p_{1/2}$ shells,
and amount in finite mode entropies on these shells, too, clearly outside the
scope of the simple $(0g_{9/2})^4$ seniority model. The $0f_{7/2}$ shell based
seniority model is more accurate for the light ${\rm Ca}$ isotopes, but
seniority mixing is substantial for some $^{44}{\rm Ca}$ yrast states, too.",2112.15513v1
2023-05-22,Conformal Field Theories generated by Chern Insulators under Quantum Decoherence,"We demonstrate that the fidelity between a pure state trivial insulator and
the mixed state density matrix of a Chern insulator under decoherence can be
mapped to a variety of two-dimensional conformal field theories (CFT); more
specifically, the quantity $\mathcal{Z} = \text{tr}\{ \hat{\rho}^D_c
\hat{\rho}_\Omega \}$ is mapped to the partition function of the desired CFT,
where $\hat{\rho}^D_c$ and $\hat{\rho}_\Omega$ are respectively the density
matrices of the decohered Chern insulator and a pure state trivial insulator.
For a pure state Chern insulator with Chern number $2N$, the fidelity
$\mathcal{Z}$ is mapped to the partition function of the $\text{U}(2N)_1$ CFT;
under weak decoherence, the Chern insulator density matrix can experience
certain instability, and the ""partition function"" $\mathcal{Z}$ can flow to
other interacting CFTs with smaller central charges. The R\'{e}nyi relative
entropy $\mathcal{F} = - \log \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}$
is mapped to the free energy of the CFT, and we demonstrate that the central
charge of the CFT can be extracted from the finite size scaling of
$\mathcal{F}$, analogous to the well-known finite size scaling of $2d$ CFT.",2305.13410v1
2015-07-27,Experimental consequences of $p_z$-wave spin triplet superconductivity in A$_2$Cr$_3$As$_3$,"The experimental observable properties of the triplet $p_z$-wave pairing
state, proposed by Wu {\em et al.} [arXiv:1503.06707] in quasi-one dimensional
A$_2$Cr$_3$As$_3$ materials, are theoretically investigated. This pairing state
is characterized by the line nodes on the $k_z=0$ plane on the Fermi surfaces.
Based on the three-band tight binding model, we obtain the specific heat,
superfluid density, Knight shift and spin relaxation rate and find that all
these properties at low temperature ($T\ll T_c$) show powerlaw behaviors and
are consistent available experiments. Particularly, the superfluid density
determined by the $p_z$-wave pairing state in this quasi-one dimensional system
is anisotropic: the in-plane superfluid density varies as
$\Delta\rho_{\parallel}\sim T$ but the out-plane one varies as
$\Delta\rho_{\perp}\sim T^3$ at low temperature. The anisotropic upper critical
field reported in experiment is consistent with the $S_z=0$ (i.e.,
$(\uparrow\downarrow+\downarrow\uparrow)$) $p_z$-wave pairing state. We also
suggest the phase-sensitive dc-SQUID measurements to pin down the triplet
$p_z$-wave pairing state.",1507.07451v2
2001-01-29,Vacuum energy and cosmological constant: View from condensed matter,"The condensed matter examples, in which the effective gravity appears in the
low-energy corner as one of the collective modes of quantum vacuum, provide a
possible answer to the question, why the vacuum energy is so small. This answer
comes from the fundamental ``trans-Planckian'' physics of quantum liquids. In
the effective theory of the low energy degrees of freedom the vacuum energy
density is proportional to the fourth power of the corresponding ``Planck''
energy appropriate for this effective theory. However, from the exact ``Theory
of Everything'' of the quantum liquid it follows that its vacuum energy density
is exactly zero without fine tuning, if: there are no external forces acting on
the liquid; there are no quasiparticles which serve as matter; no space-time
curvature; and no boundaries which give rise to the Casimir effect. Each of
these four factors perturbs the vacuum state and induces the nonzero value of
the vacuum energy density of order of energy density of the perturbation. This
is the reason, why one must expect that in each epoch the vacuum energy density
is of order of matter density of the Universe, or/and of its curvature, or/and
of the energy density of smooth component -- the quintessence.",0101111v4
2007-07-26,Geometric measures of entanglement and the Schmidt decomposition,"In the standard geometric approach to a measure of entanglement of a pure
state, $\sin^2\theta$ is used, where $\theta$ is the angle between the state to
the closest separable state of products of normalized qubit states. We consider
here a generalization of this notion to separable states consisting of products
of unnormalized states of different dimension. In so doing, the entanglement
measure $\sin^2\theta$ is found to have an interpretation as the distance
between the state to the closest separable state. We also find the components
of the closest separable state and its norm have an interpretation in terms of,
respectively, the eigenvectors and eigenvalues of the reduced density matrices
arising in the Schmidt decomposition of the state vector.",0707.4020v2
2003-01-23,Statistics of delta peaks in the spectral density of large random trees,"We present an analysis of the spectral density of the adjacency matrix of
large random trees. We show that there is an infinity of delta peaks at all
real numbers which are eigenvalues of finite trees. By exact enumerations and
Monte-Carlo simulations, we have numerical estimations of the heights of peaks.
In the large tree limit, the sum of their heights is 0.19173 +- 0.00005.
Moreover all associated eigenvectors are strictly localized on a finite number
of nodes. The rest of the spectral density is a function which vanishes at all
positions of peaks, which are a dense subset of real numbers: so this function
is almost everywhere discontinuous.
  Keywords: random tree, spectral density, density of states, adjacency matrix,
localization, delta peak.",0301437v1
2006-09-12,Low Densities Instability of Relativistic Mean Field Models,"The effects of the symmetry energy softening of the relativistic mean field
(RMF) models on the properties of matter with neutrino trapping are
investigated. It is found that the effects are less significant than those in
the case without neutrino trapping. The weak dependence of the equation of
state on the symmetry energy is shown as the main reason of this finding. Using
different RMF models the dynamical instabilities of uniform matters, with and
without neutrino trapping, have been also studied. The interplay between the
dominant contribution of the variation of matter composition and the role of
effective masses of mesons and nucleons leads to higher critical densities for
matter with neutrino trapping. Furthermore, the predicted critical density is
insensitive to the number of trapped neutrinos as well as to the RMF model used
in the investigation. It is also found that additional nonlinear terms in the
Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of
instability, which occurs at relatively high densities. The reason is that the
effective sigma meson mass in their models increases as a function of the
matter density.",0609026v1
1998-01-28,Weighted Density Functionals for Ferroelectric Materials,"The weighted density approximation, its implementation and its application to
ferroelectric materials is discussed. Calculations are presented for several
perovskite oxides and related materials. In general the weighted density
approximation is found to be superior to either the local density or
generalized gradient approximation for the ground state. Electronic structures
are little changed. The linear response of the weighted density approximation
is calculated for the homogeneous electron gas, and found to be improved
relative to the local density result, but not in full agreement with existing
Monte Carlo data. It is shown that the agreement can be further improved by a
simple modification. Calculations of the ferroelectric soft mode in KNbO$_3$
suggest that the low temperature distortion is approximately 20% smaller than
indicated by existing experiments.",9801301v1
2018-04-26,Hierarchical Density Order Embeddings,"By representing words with probability densities rather than point vectors,
probabilistic word embeddings can capture rich and interpretable semantic
information and uncertainty. The uncertainty information can be particularly
meaningful in capturing entailment relationships -- whereby general words such
as ""entity"" correspond to broad distributions that encompass more specific
words such as ""animal"" or ""instrument"". We introduce density order embeddings,
which learn hierarchical representations through encapsulation of probability
densities. In particular, we propose simple yet effective loss functions and
distance metrics, as well as graph-based schemes to select negative samples to
better learn hierarchical density representations. Our approach provides
state-of-the-art performance on the WordNet hypernym relationship prediction
task and the challenging HyperLex lexical entailment dataset -- while retaining
a rich and interpretable density representation.",1804.09843v1
2021-01-22,Chiral Bloch states in single layer graphene with Rashba spin-orbit coupling: Spectrum and spin current density,"We study the Bloch spectrum and spin physics of 2D massless Dirac electrons
in single layer graphene subject to a one dimensional periodic Kronig-Penney
potential and Rashba spin-orbit coupling. The Klein paradox exposes novel
features in the band dispersion and in graphene spintronics. In particular it
is shown that: (1) The Bloch energy dispersion $\veps(p)$ has unusual
structure: There are {\it two Dirac points} at Bloch momenta $\pm p \ne 0$ and
a narrow band emerges between the wide valence and conduction bands. (2) The
charge current and the spin density vector vanish. (3) Yet, all the
non-diagonal elements of the spin current density tensor are finite and their
magnitude increases linearly with the spin-orbit strength. In particular, there
is a spin density current whose polarization is perpendicular to the graphene
plane. (4) The spin density currents are space-dependent, hence their
continuity equation includes a finite spin torque density.",2101.09224v1
2019-01-12,On non-parametric density estimation on linear and non-linear manifolds using generalized Radon transforms,"Here we present a new non-parametric approach to density estimation and
classification derived from theory in Radon transforms and image
reconstruction. We start by constructing a ""forward problem"" in which the
unknown density is mapped to a set of one dimensional empirical distribution
functions computed from the raw input data. Interpreting this mapping in terms
of Radon-type projections provides an analytical connection between the data
and the density with many very useful properties including stable
invertibility, fast computation, and significant theoretical grounding. Using
results from the literature in geometric inverse problems we give uniqueness
results and stability estimates for our methods. We subsequently extend the
ideas to address problems in manifold learning and density estimation on
manifolds. We introduce two new algorithms which can be readily applied to
implement density estimation using Radon transforms in low dimensions or on low
dimensional manifolds embedded in $\mathbb{R}^d$. We test our algorithms
performance on a range of synthetic 2-D density estimation problems, designed
with a mixture of sharp edges and smooth features. We show that our algorithm
can offer a consistently competitive performance when compared to the
state-of-the-art density estimation methods from the literature.",1901.03780v3
2016-02-17,Ground state of the U2Mo compound: Physical properties of the Omega-phase,"Using ab initio calculations, unexpected structural instability was recently
found in the ground state of the U$_2$Mo compound. Instead of the unstable
$I4/mmm$ structure, in this work the $P6/mmm$ ($\# 191$) space group, usually
called $\Omega$-phase, is proposed as the fundamental state. Electronic and
elastic properties are studied in this work in order to characterize the
physical properties of the new ground state. The stability of the
$\Omega$-phase is studied by means of its elastic constants calculation and
phonon dispersion spectrum. Analysis of isotropic indices shows that the new
phase is a ductile material with a minimal degree of anisotropy, suggesting
that U$_2$Mo in the $P6/mmm$ structure is an elastic isotropic material.
Analysis of charge density, density of electronic states (DOS) and the
character of the bands revealed a high level of hybridization between
$d$-molybdenum electronic states and $d$- and $f$-uranium ones.",1602.05552v1
2018-03-01,Analytic Representation of Canonical Average From Fine Structure of Density of States,"Expectation value of dynamical variables in thermodynamically equilibrium
state can be typically provided through well-known canonical average. The
average includes tremendous number of possible states considered far beyond
practically handled, which makes it difficult to obtain analytic representation
of the average to clarify how the expectation value connects with given
interaction: i.e., the relationship is generally understood in phonomenological
manner except for modest, simple models. Here we show that the relationship is
explicitly clarified for discrete large systems, where the configurational
density of states for any single pair correlation is represented in terms of
linear combination of Dirac delta function and its derivatives. The significant
advantage of the present representation is that it can decompose contributions
to macroscopic dynamical variables into harmonicity and anharmonicity in terms
of their underlying structural degree of freedom, which will lead to find a set
of special microscopic state to characterize macroscopic properties in
equilibrium state for classical many-body systems.",1804.03498v1
2018-08-10,Equation of state for QCD with a critical point from the 3D Ising Model,"Current knowledge of the finite-density QCD equation of state from first
principles is limited to a Taylor expansion in the baryonic chemical potential
around $\mu_B=0$. By means of a scaling form for the equation of state of the
3D Ising model and a non-universal, parametrized map to QCD coordinates, we
construct a family of equations of state matching state of the art first
principle Lattice QCD calculations and including the correct critical behavior,
which can be readily employed in hydrodynamical simulations of heavy ion
collisions at finite density, covering most of the BES range at RHIC. This
contribution reports on work done within the Fluctuations/Equation of State
working group of the BEST Collaboration.",1808.03695v1
2024-04-08,Quench dynamics of interacting bosons: generalized coherent states versus multi-mode Glauber states,"Multi-mode Glauber coherent states (MMGS) as well as Bloch states with zero
quasi-momentum, which are a special case of generalized coherent states (GCS),
are frequently used to describe condensed phases of bosonic many-body systems.
The difference of two-point correlators of MMGS and GCS vanishes in the
thermodynamic limit. Using the established expansion of GCS in terms of MMGS,
we derive a Fourier-type relation between the (auto-)correlation functions of
the two different time-evolved states. This relation reveals that the
(auto-)correlation and thus the dynamical free energy density for the two cases
are still different, even in the thermodynamic limit, due to the lack of the
U(1) symmetry of the MMGS. Analytic results for the deep lattice model of
interacting bosons for increasing filling factors show multiple sharp
structures in the dynamical free energy-density of increasing complexity. These
are explained using the evolution of Husimi functions in phase space.",2404.05471v1
2018-08-15,Configuration-Controlled Many-Body Localization and the Mobility Emulsion,"We uncover a new non-ergodic phase, distinct from the many-body localized
(MBL) phase, in a disordered two-leg ladder of interacting hardcore bosons. The
dynamics of this emergent phase, which has no single-particle analog and exists
only for strong disorder and finite interaction, is determined by the many-body
configuration of the initial state. Remarkably, this phase features the
$\textit{coexistence}$ of localized and extended many-body states at fixed
energy density and thus does not exhibit a many-body mobility edge, nor does it
reduce to a model with a single-particle mobility edge in the noninteracting
limit. We show that eigenstates in this phase can be described in terms of
interacting emergent Ising spin degrees of freedom (""singlons"") suspended in a
mixture with inert charge degrees of freedom (""doublons"" and ""holons""), and
thus dub it a $\textit{mobility emulsion}$ (ME). We argue that grouping
eigenstates by their doublon/holon density reveals a transition between
localized and extended states that is invisible as a function of energy
density. We further demonstrate that the dynamics of the system following a
quench may exhibit either thermalizing or localized behavior depending on the
doublon/holon density of the initial product state. Intriguingly, the
ergodicity of the ME is thus tuned by the initial state of the many-body
system. These results establish a new paradigm for using many-body
configurations as a tool to study and control the MBL transition. The ME phase
may be observable in suitably prepared cold atom optical lattices.",1808.05220v2
2010-03-04,A vacuum component of the Universe must evolve,"The evolution of a vacuum component of the Universe is investigated in the
quantum as well as the classical regimes. Probably our Universe has arisen as a
vacuum fluctuation and very probably that it has had a high symmetry for
Planckian parameters. Besides, vacuum energy density has to be a positive one.
In the early epochs during its cooling the Universe had been losing the high
symmetry by phase transitions since condensates of quantum fields carried
negative contributions (78 orders) to its positive energy density. It was the
period of the Universe evolution during the first parts of the first second of
its life. After the last phase transition (quark-hadron) the vacuum energy `has
hardened'. In this moment its energy density can be calculated using the
Zeldovich's formula inserting an average value of the pseudo-Goldstone boson
masses (pi-mesons) that characterizes this chromodynamical vacuum. The chiral
symmetry was then lost. Dynamics of the equilibrium vacuum after its `hardness'
is considered by applying the holographic conception. In this case the Universe
has been losing vacuum energy (45 orders) on organization of new quantum states
during 13.76 x 10^9 years. Using this conception we can get solution of the
cosmological constant problem. 123 crisis orders problem may be resolved. The
density of vacuum energy cannot have a constant value in principle because of
the new quantum states are organized during expansion of the Universe but the
equation of state vacuum w= - 1 should be naturally constant. The density of
vacuum energy from z=0 up to z=10^11 is also calculated in the classical regime
of the Universe evolution.",1003.1025v4
2015-09-08,Relativistic Mean-Field Models with Scaled Hadron Masses and Couplings: Hyperons and Maximum Neutron Star Mass,"An equation of state of cold nuclear matter with an arbitrary isotopic
composition is studied within a relativistic mean-field approach with hadron
masses and coupling constants depending self-consistently on the scalar
mean-field. All hadron masses decrease universally with the scalar field
growth, whereas meson-nucleon coupling constants can vary differently. More
specifically we focus on two modifications of the KVOR model studied
previously. One extension of the model (KVORcut) demonstrates that the equation
of state stiffens if the increase of the scalar-field magnitude with the
density is bounded from above at some value for baryon densities above the
saturation nuclear density. This can be realized if the nucleon vector-meson
coupling constant changes rapidly as a function of the scalar field slightly
above the desired value. The other version of the model (MKVOR) utilizes a
smaller value of the nucleon effective mass at the nuclear saturation density
and a saturation of the scalar field in the isospin asymmetric matter induced
by a strong variation of the nucleon isovector-meson coupling constant as
function of the scalar field. A possibility of hyperonization of the matter in
neutron star interiors is incorporated. Our equations of state fulfill majority
of known empirical constraints including the pressure-density constraint from
heavy-ion collisions, direct Urca constraint, gravitational-baryon mass
constraint for the pulsar J0737-3039B, and the constraint on the maximum mass
of the neutron stars.",1509.02538v2
2012-09-24,New parameterization of Skyrme's interaction for regularized multi-reference energy density functional calculations,"[Background] Symmetry restoration and configuration mixing in the spirit of
the generator coordinate method based on energy density functionals have become
widely used techniques in low-energy nuclear structure physics. Recently, it
has been pointed out that these techniques are ill-defined for standard Skyrme
functionals, and a regularization procedure has been proposed to remove the
resulting spuriosities from such calculations. This procedure imposes an
integer power of the density for the density dependent terms of the functional.
At present, only dated parameterizations of the Skyrme interaction fulfill this
condition. [Purpose] To construct a set of parameterizations of the Skyrme
energy density functional for multi-reference energy density functional
calculations with regularization using the state-of-the-art fitting protocols.
[Method] The parameterizations were adjusted to reproduce ground state
properties of a selected set of doubly magic nuclei and properties of nuclear
matter. Subsequently, these parameter sets were validated against properties of
spherical and deformed nuclei. [Results] Our parameter sets successfully
reproduce the experimental binding energies and charge radii for a wide range
of singly-magic nuclei. Compared to the widely used SLy5 and to the SIII
parameterization that has integer powers of the density, a significant
improvement of the reproduction of the data is observed. Similarly, a good
description of the deformation properties at $A\sim 80$ was obtained.
[Conclusions] We have constructed new Skyrme parameterizations with integer
powers of the density and validated them against a broad set of experimental
data for spherical and deformed nuclei. These parameterizations are tailor-made
for regularized multi-reference energy density functional calculations and can
be used to study correlations beyond the mean-field in atomic nuclei.",1209.5258v1
2011-05-19,Testing Skyrme energy-density functionals with the QRPA in low-lying vibrational states of rare-earth nuclei,"Although nuclear energy density functionals are determined primarily by
fitting to ground state properties, they are often applied in nuclear
astrophysics to excited states, usually through the quasiparticle random phase
approximation (QRPA). Here we test the Skyrme functionals SkM* and SLy4 along
with the self-consistent QRPA by calculating properties of low-lying
vibrational states in a large number of well-deformed even-even rare-earth
nuclei. We reproduce trends in energies and transition probabilities associated
with gamma-vibrational states, but our results are not perfect and indicate the
presences of multi-particle-hole correlations that are not included in the
QRPA. The Skyrme functional SkM* performs noticeably better than SLy4. In a few
nuclei, changes in the treatment of the pairing energy functional have a
significant effect. The QRPA is less successful with ""beta-vibrational"" states
than with the gamma-vibrational states.",1105.3817v1
2016-01-05,Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory,"In [J. Chem. Phys. 143, 054102 (2015)] I have derived conditions to
characterize the kernel of the retarded response function, under the assumption
that the initial state is a ground state. In this article I demonstrate its
generalization to mixed states (ensembles). To make the proof work, the weights
in the ensemble need to be decreasing for increasing energies of the pure
states from which the mixed state is constructed. The resulting conditions are
not easy to verify, but under the additional assumptions that the ensemble
weights are directly related to the energies and that the full spectrum of the
Hamiltonian participates in the ensemble, it is shown that potentials only
belong to the kernel of the retarded response function if they commute with the
initial Hamiltonian. These additional assumptions are valid for thermodynamic
ensembles, which makes this result also physically relevant. The conditions on
the potentials for the thermodynamic ensembles are much stronger than in the
pure state (zero temperature) case, leading to a much less involved kernel when
the conditions are applied to the retarded one-body reduced density matrix
response function.",1601.00747v1
2019-10-31,First-principles Study of Spiral Spin Density Waves in Monolayer MnCl$_2$ Using Generalized Bloch Theorem,"We investigated the spiral spin density waves in the monolayer 1T-MnCl$_2$
for a set of spiral vectors based on first-principles calculations. The
magnetic ground states were evaluated by means of the generalized Bloch theorem
within the linear combination of pseudo-atomic orbitals. To reach our purpose,
a flat spiral configuration was constructed for the Mn magnetic atom by fixing
the direction of its magnetic moment. We confirmed that the ground state was a
spiral ground state. We also clarified that a phase transition from a spiral
ground state to the other ground states, such as the ferromagnetic state or the
antiferromagnetic state, appears when introducing the hole-electron doping.
Therefore, we justify that introducing the hole-electron doping tunes the phase
transition in the monolayer 1T-MnCl$_2$.",1910.14278v1
1999-03-15,Interplay of spin density wave and superconductivity with different pairing symmetry,"A model study for the coexistence of the spin density wave and
superconductivity is presented. With reference to the recent angle resolved
photo emmission experimental data in high T_c cuprates, presence of the nested
pieces of bands is assumed. The single band Hubbard model, therefore, when
treated within the Hatree-Fock mean field theory leads to a spin density wave
(SDW) ground state. The superconductivity (SC) is assumed to be due to a
generalised attractive potential with a separable form without specifying to
any particular origin. It therefore allows a comparative study of the
coexistence of superconductivity of different order parameter symmetry with the
spin density wave state. We find that the phase diagram, comprising of the
amplitudes of the respective gaps (SC and SDW) Vs. band filling resembles to
that of the high T_c cuprates only when the order parameter of the
superconducting phase has d-wave symmetry. Thermal variation of different order
parameters (e.g, SC and SDW) also show interesting coexistence and reentrance
behaviors that are consistent with experimental observations, specially for the
borocarbides.",9903234v1
2004-11-12,Static properties of positive ions in atomic Bose-Einstein condensates,"The excess number of atoms around an ion immersed in a Bose-Einstein
condensate is determined as a function of the condensate density far from the
ion. We use thermodynamic arguments to demonstrate that in the limit of low
densities the excess number of atoms is proportional to the ratio of the
atom-ion and atom-atom scattering lengths. For denser systems we calculate the
excess number from solutions of the Gross-Pitaevskii equation using a model
potential that has a $1/r^{4}$ attraction coming from the polarization of the
neutral atoms and a hard core repulsion at short distances. We show that there
exist in general many solutions to the Gross-Pitaevskii equation for a given
condensate density, the maximum number of solutions being related to the number
of bound states of the Schr\""odinger equation for the same potential. With
increasing density, pairs of these solutions merge and disappear, implying a
discontinuous change of the state of the system.",0411339v1
2005-02-22,Self-organized density patterns of molecular motors in arrays of cytoskeletal filaments,"The stationary states of systems with many molecular motors are studied
theoretically for uniaxial and centered (aster-like) arrangements of
cytoskeletal filaments using Monte Carlo simulations and a two-state model.
Mutual exclusion of motors from binding sites of the filaments is taken into
account. For small overall motor concentration, the density profiles are
exponential and algebraic in uniaxial and centered filament systems,
respectively. For uniaxial systems, exclusion leads to the coexistence of
regions of high and low densities of bound motors corresponding to motor
traffic jams, which grow upon increasing the overall motor concentration. These
jams are insensitive to the motor behavior at the end of the filament. In
centered systems, traffic jams remain small and an increase in the motor
concentration leads to a flattening of the profile, if the motors move inwards,
and to the build-up of a concentration maximum in the center of the aster if
motors move outwards. In addition to motors density patterns, we also determine
the corresponding patterns of the motor current.",0502024v1
2017-12-04,Local available energetics of multicomponent compressible stratified fluids,"We extend the local theory of available potential energy (APE) to a general
multicomponent compressible stratified fluid, accounting for the effects of
diabatic sinks and sources. As for simple compressible fluids, the total
potential energy density of a fluid parcel is the sum of its available elastic
energy (AEE) and APE density. These respectively represent the adiabatic
compression/expansion work needed to bring it from its reference pressure to
its actual pressure and the work against buoyancy forces required to move it
from its reference state position to its actual position. Our expression for
the APE density is new and derived using only elementary manipulations of the
equations of motion; it is significantly simpler than existing published
expressions, while also being more transparently linked to the relevant form of
APE density for the Boussinesq and hydrostatic primitive equations. Our new
framework is used to clarify the links between some aspects of the energetics
of Boussinesq and real fluids, as well as to shed light on the physical basis
underlying the choice of reference state(s) in local APE theory.",1712.01051v3
2022-05-18,Fate of density waves in the presence of a higher order van Hove singularity,"Topological transitions in electronic band structures, resulting in van Hove
singularities in the density of states, can considerably affect various types
of orderings in quantum materials. Regular topological transitions (of neck
formation or collapse) lead to a logarithmic divergence of the electronic
density of states (DOS) as a function of energy in two-dimensions. In addition
to the regular van Hove singularities, there are higher order van Hove
singularities (HOVHS) with a power-law divergences in DOS. By employing
renormalization group (RG) techniques, we study the fate of a spin-density wave
phase formed by nested parts of the Fermi surface, when a HOVHS appears in
parallel. We find that the phase formation can be boosted by the presence of
the singularity, with the critical temperature increasing by orders of
magnitude. We discuss possible applications of our findings to a range of
quantum materials such as Sr$_3$Ru$_2$O$_7$, Sr$_2$RuO$_4$ and transition metal
dichalcogenides.",2205.08828v2
2015-07-02,Bose condensation and the Casimir effects of an imperfect Bose gas in a d-dimensional configuration space,"Some properties of an ideal gas of massive bosons in a mean field potential
and, confined between two infinite parallel slabs in a d-dimensional
configuration space are investigated systematically. Here, one particle density
of states approach is employed to study the critical temperature, shift of
density, Casimir effects and critical exponents, starting from the evaluation
of the grand canonical free energy in d-dimension. We have found that, the
shift of density, Casimir force and the critical temperature depend on the
space dimensionality. But the Casimir force decays as an inverse power law of
the distance between two slabs in the condensate and, decays exponentially in
the non-condensed state situated very close to the point of phase transition.
Most importently, this study enabled us to predict the shift of the density of
excited bosons due to mean field potential, and also the dimensional dependence
of the critical exponent. The form of the critical exponent is found to be
$\frac{1}{d-2}$ for the imperfect Bose gas. This leads to a value of critical
exponent $1$ for $d=3$.",1507.00673v1
2019-04-25,Time-dependent potential impurity in topological insulator,"We consider periodically driven potential impurities coupled to the surface
states of a two-dimensional topological insulator. The problem is addressed by
means of two models, out which the first model is an effective continuum
Hamiltonian for the surface states, whereas the Kane-Mele lattice model is our
second approach. While both models result in drastic changes in the local
density of electron states with increasing amplitude and frequency of the
driving field, the linearly low energy local density of electron states remains
in the continuum model, however, with an increased Fermi velocity. The spectrum
of the continuum model remains gapless under the emergence of new impurity
resonances near the Fermi energy. The Kane-Mele lattice model represents a
finite size system, with edge states appearing at the boundary of the system.
We, thus, consider the impurity at two different positions, one at the boundary
and one at the center of the lattice. In the former case, a reduction and
broadening of the low energy local density of electron states result with
increasing amplitude of the driving field. On the other hand, there are no new
resonances emerging in the spectrum. In the latter case, the spectrum is gapped
both in the absence of the impurity as well as for weak amplitudes of the
driving field, while the gap tends to fill up with impurity states with
increasing amplitude.",1904.11275v1
2022-02-10,Initial State Dependent Dynamics Across Many-body Localization Transition,"We investigate quench dynamics across many-body localization (MBL) transition
in an interacting one dimensional system of spinless fermions with aperiodic
potential. We consider a large number of initial states characterized by the
number of kinks, $N_{kinks}$, in the density profile. On the delocalized side
of the MBL transition the dynamics becomes faster with increase in $N_{kinks}$
such that the decay exponent, $\gamma$, in the density imbalance increases with
increase in $N_{kinks}$. The growth exponent of the mean square displacement
which shows a power-law behaviour $\langle x^2(t) \rangle \sim t^\beta$ in the
long time limit is much larger than the exponent $\gamma$ for 1-kink and other
low kink states though $\beta \sim 2\gamma$ for a charge density wave state. As
the disorder strength increases $\gamma_{N_{kink}} \rightarrow 0$ at some
critical disorder, $h_{N_{kinks}}$ which is a monotonically increasing function
of $N_{kinks}$. A 1-kink state always underestimates the value of disorder at
which the MBL transition takes place but $h_{1-kink}$ coincides with the onset
of the sub-diffusive phase preceding the MBL phase. This is consistent with the
dynamics of interface broadening for the 1-kink state. We show that the
bipartite entanglement entropy has a logarithmic growth $a \ln(Vt)$ not only in
the MBL phase but also in the delocalised phase and in both the phases the
coefficient $a$ increases with $N_{kinks}$ as well as with the interaction
strength $V$. We explain this dependence of dynamics on the number of kinks in
terms of the normalized participation ratio of initial states in the eigenbasis
of the interacting Hamiltonian.",2202.05217v3
2022-10-18,Local thermodynamical equilibrium and relativistic dissipation,"We introduce a class of relativistic fluid states satisfying the relativistic
local thermodynamical equilibrium postulate (abbreviated as relativistic (LTE)
postulate). States satisfying this postulate, are states ""near equilibrium"" (a
term defined precisely in the course of the paper) and permit us to attach a
fictitious ""local thermodynamical equilibrium"" state that fits event by event
the actual fluid state. They single out an admissible class of rest frames
relative to which thermodynamical variables like the energy density,
thermodynamical pressure, stresses, particle number density (or densities)
measured by observers at rest relative to these frames are becoming frame
independent provided second (or higher) order deviations from the fictitious
state of ""local thermodynamical equilibrium"" are ignored. We have verified this
property for a large class of theories of relativistic dissipation that include
the Hiscock-Lindblom class of first order theories, the Eckart and
Landau-Lifshitz theories, the Israel-Stewart transient thermodynamics, the
Liu-M\""uller-Ruggeri theory, fluids of divergence type and the latest developed
(BDNK) theory. Moreover, the phenomenological equations describing first order
deviations from the fictitious ""local thermodynamical equilibrium"" state
satisfy equations that remain form invariant under change of frame within the
class of admissible frames. We proved this property for the Hiscock-Lindblom
class of first order theories the Eckart and Landau-Lifshitz theories, the
Israel-Stewart transient thermodynamics and the Liu-M\""uller-Ruggeri theory of
relativistic dissipation the (BDNK) theory and we expect that the same property
to hold for the class of relativistic fluids of divergence type.",2210.10213v1
2008-01-21,Phase Diagram of Cold Polarized Fermi Gas in Two Dimensions,"The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas
in the BCS-BEC crossover are systematically and analytically investigated. In
the BCS-Leggett mean field theory, the transition from unpolarized superfluid
phase to normal phase is always of first order. For a homogeneous system, the
two critical Zeeman fields and the critical population imbalance are
analytically determined in the whole coupling parameter region, and the
superfluid-normal mixed phase is shown to be the ground state between the two
critical fields. The density profile in the presence of a harmonic trap
calculated in the local density approximation exhibits a shell structure, a
superfluid core at the center and a normal shell outside. For weak interaction,
the normal shell contains a partially polarized cloud with constant density
difference surrounded by a fully polarized state. For strong interaction, the
normal shell is totally in fully polarized state with a density profile
depending only on the global population imbalance. The di-fermion bound states
can survive in the whole highly imbalanced normal phase.",0801.3127v4
2014-02-17,Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension,"We investigate the vacuum polarization and the Casimir energy of a Dirac
field coupled to a scalar potential in one spatial dimension. Both of these
effects have a common cause which is the distortion of the spectrum due to the
coupling with the background field. Choosing the potential to be a symmetrical
square-well, the problem becomes exactly solvable and we can find the whole
spectrum of the system, analytically. We show that the total number of states
and the total density remain unchanged as compared with the free case, as one
expects. Furthermore, since the positive- and negative-energy eigenstates of
the fermion are fermion-number conjugates of each other and there is no
zero-energy bound state, the total density and the total number of negative and
positive states remain unchanged, separately. Therefore, the vacuum
polarization in this model is zero for any choice of the parameters of the
potential. It is important to note that although the vacuum polarization is
zero due to the symmetries of the model, the Casimir energy of the system is
not zero in general. In the graph of the Casimir energy as a function of the
depth of the well there is a maximum approximately when the bound energy levels
change direction and move back towards their continuum of origin. The Casimir
energy for a fixed value of the depth is a linear function of the width and is
always positive. Moreover, the Casimir energy density (the energy density of
all the negative-energy states) and the energy density of all the
positive-energy states are exactly the mirror images of each other. Finally,
computing the total energy of a valence fermion present in the lowest fermionic
bound state, taking into account the Casimir energy, we find that the lowest
bound state is almost always unstable for the scalar potential.",1402.3922v1
1998-01-12,Quasiclassical theory of twin boundaries in High-T_c superconductors,"We investigate the electronic structure of twin boundaries in
orthorhombically distorted high-T$_c$ materials using the quasiclassical theory
of superconductivity. At low temperatures we find a local instability to a
time-reversal symmetry breaking state at the twin boundary. This state yields
spontaneous currents along the twin boundary that are microscopically explained
by the structure of the quasiparticle bound states. We calculate the local
density of states and find a splitting in the zero-bias peak once the
spontaneous currents set in. This splitting is measurable by STM techniques and
is a unique signature of time-reversal breaking states at a twin boundary.",9801107v1
1998-07-24,Nucleation of superconducting pairing states at mesoscopic scales at zero temperature,"We find the spin polarized disordered Fermi liquids are unstable to the
nucleation of superconducting pairing states at mesoscopic scales even when
magnetic fields which polarize the spins are substantially higher than the
critical one. We study the probability of finding superconducting pairing
states at mesoscopic scales in this limit. We find that the distribution
function depends only on the film conductance. The typical length scale at
which pairing takes place is universal, and decreases when the magnetic field
is increased. The number density of these states determines the strength of the
random exchange interactions between mesoscopic pairing states.",9807334v1
2003-12-17,Kondo Effect and Surface-State Electrons,"We have used low temperature scanning tunneling spectroscopy and atomic
manipulation to study the role of surface-state electrons in the Kondo effect
of an isolated cobalt atom adsorbed on Ag(111). We show that the observed Kondo
signature remains unchanged in close proximity of a monoatomic step, where the
local density of states of the surface-state electrons is strongly perturbed.
This result indicates a minor role for surface-state electrons in the Kondo
effect of cobalt, compared to bulk electrons. A possible explanation for our
findings is presented.",0312434v1
2005-02-10,Adsorption-induced constraint on delocalization of electron states in an Au chain on NiAl(110),"We have carried out a density functional study of the localized constraint on
the delocalized, unoccupied resonance states in a mono atomic Au chain on a
NiAl(110) surface by adsorption of a CO molecule on one of the adatoms in the
chain. This constraint was observed recently by scanning tunnelling microscopy
and spectroscopy. The repulsive interaction of the occupied 5${\sigma}$
molecular state with the unoccupied, resonance state in a Au adatom in the
chain is found to break the degeneracy of the Au adatom-induced resonance
states and to disrupt their delocalization in the chain.",0502258v1
2006-10-09,Magnetic interface states in graphene-based quantum wires,"The electronic states of a finite-width graphene sheet in the presence of an
electrostatic confining potential and a perpendicular magnetic field are
investigated. The confining potential shifts the Landau levels inside the well
and creates current-carrying states at or close to the interface with the
barriers in addition to the edge states caused by the finite width of the
sheet. Detailed energy spectra are given as a function of the quantum wire
parameters. The dependence of the density of states on the confinement
potential is evaluated for finite and zero magnetic field.",0610237v1
2001-11-26,Exact positivity of the Wigner and P-functions of a Markovian open system,"We discuss the case of a Markovian master equation for an open system, as it
is frequently found from environmental decoherence. We prove two theorems for
the evolution of the quantum state. The first one states that for a generic
initial state the corresponding Wigner function becomes strictly positive after
a finite time has elapsed. The second one states that also the P-function
becomes exactly positive after a decoherence time of the same order. Therefore
the density matrix becomes exactly decomposable into a mixture of Gaussian
pointer states.",0111139v2
2004-05-28,Qutrit state engineering with biphotons,"The novel experimental realization of three-level optical quantum systems is
presented. We use the polarization state of biphotons to generate a specific
sequence of states that are used in the extended version of BB84 protocol. We
experimentally verify the orthogonality of the basis states and demonstrate the
ability to easily switch between them. The tomography procedure is employed to
reconstruct the density matrices of generated states.",0405169v5
2008-10-10,Quantum Ratchets on Maximally Uniform States in Phase Space: Semiclassical Full-Chaos Regime,"A generic kind of quantum chaotic ratchet is introduced, based on initial
states that are \emph{uniform} in phase space with the \emph{maximal possible}
resolution of one Planck cell. Unlike a classical phase-space uniform density,
such a state usually carries a \emph{nonzero} ratchet current, even in
\emph{symmetric} systems. This quantum ratchet effect basically emerges from
the generic asymmetry of the state quasicoordinates in the Planck cell. It is
shown, on the basis of exact results, general arguments, and extensive
numerical evidence, that in a semiclassical full-chaos regime the variance of
the current over all the states is nearly proportional to the chaotic-diffusion
rate and to the square of the scaled Planck constant. Experimental realizations
are suggested.",0810.1831v1
2012-08-09,Contextual Entropy and Reconstruction of Quantum States,"We introduce a new notion of entropy for quantum states, called contextual
entropy, and show how it unifies Shannon and von Neumann entropy. The main
result is that from the knowledge of the contextual entropy of a quantum state
of a finite-dimensional system, one can reconstruct the quantum state, i.e.,
the density matrix, if the Hilbert space is of dimension 3 or greater. We
present an explicit algorithm for this state reconstruction and relate our
result to Gleason's theorem.",1208.2046v1
2013-07-06,Bipartite concurrence and localized coherence,"Based on a proposed coherence measure, we show that the local coherence of a
bipartite quantum pure state (coherence of its reduced density matrix) is
exactly the same as the minimal average co- herence with all potential
pure-state realizations under consideration. In particular, it is shown that
bipartite concurrence of pure states just captures the maximal difference
between local coherence and the average coherence of one subsystem induced by
local operations on the other subsystem with the assistance of classical
communications, which provides an alternative operational meaning for bipartite
concurrence of pure states. The relation between concurrence and the proposed
coherence measure can also be extended to bipartite mixed states.",1307.1760v1
2008-07-02,Semigroup of positive maps for qudit states and entanglement in tomographic probability representation,"Stochastic and bistochastic matrices providing positive maps for spin states
(for qudits) are shown to form semigroups with dense intersection with the Lie
groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density
matrix of a qudit state is shown to be described by a spin tomogram determined
by an orbit of the bistochastic semigroup acting on a simplex. A class of
positive maps acting transitively on quantum states is introduced by relating
stochastic and quantum stochastic maps in the tomographic setting. Finally, the
entangled states of two qubits and Bell inequalities are given in the framework
of the tomographic probability representation using the stochastic semigroup
properties.",0807.0329v1
2018-09-13,Holography of negative energy states,"Quantum states with negative energy densities have been long known to exist
in quantum field theories. We explore the structure of such states for
holographic theories using quantum information theory tools and show how
certain negative energy states are naturally captured by the thermodynamics of
black holes with hyperbolic horizon at zero temperature, suggesting that they
provide a dual description of those states. Our results give a satisfying field
theory understanding of the distinct thermodynamics of such black holes.",1809.04793v2
2021-09-30,Excited-state DMRG made simple with FEAST,"We introduce DMRG[FEAST], a new method for optimizing excited-state many-body
wave functions with the density matrix renormalization group (DMRG) algorithm.
Our approach applies the FEAST algorithm, originally designed for large-scale
diagonalization problems, to matrix product state wave functions. We show that
DMRG[FEAST] enables the stable optimization of both low- and high-energy
eigenstates, therefore overcoming the limitations of state-of-the-art
excited-state DMRG algorithms. We demonstrate the reliability of DMRG[FEAST] by
calculating anharmonic vibrational excitation energies of molecules with up to
30 fully coupled degrees of freedom.",2110.00092v1
2020-12-28,From finite nuclei to neutron stars : the essential role of high-order density dependence in effective forces,"A unified description of finite nuclei and equation of state of neutron stars
present a major challenge as well as opportunities for understandings of
nuclear interactions.Inspired by the Lee-Huang-Yang formula of hard-sphere
gases, we developed effective nuclear interactions with an additional
high-order density dependent term.The original Skyrme force SLy4 is widely used
in studies of neutron stars but is not satisfied for global descriptions of
finite nuclei. The refitted SLy4${'}$ force can improve descriptions of finite
nuclei but slightly reduces the radius of neutron star of 1.4 solar mass.We
found that the extended SLy4 force with a higher-order density dependence can
properly describe properties of both finite nuclei and GW170817 binary neutron
stars, including the mass-radius relation and the tidal deformability. This
demonstrated the essential role of high-order density dependence at ultrahigh
densities. Our work provides a unified and predictive model for neutron stars,
as well as new insights for the future development of effective interactions.",2012.14083v2
2021-07-19,Reconstruction of the Density Power Spectrum from Quasar Spectra using Machine Learning,"We describe a novel end-to-end approach using Machine Learning to reconstruct
the power spectrum of cosmological density perturbations at high redshift from
observed quasar spectra. State-of-the-art cosmological simulations of structure
formation are used to generate a large synthetic dataset of line-of-sight
absorption spectra paired with 1-dimensional fluid quantities along the same
line-of-sight, such as the total density of matter and the density of neutral
atomic hydrogen. With this dataset, we build a series of data-driven models to
predict the power spectrum of total matter density. We are able to produce
models which yield reconstruction to accuracy of about 1% for wavelengths $k
\leq 2 h Mpc^{-1}$, while the error increases at larger $k$. We show the size
of data sample required to reach a particular error rate, giving a sense of how
much data is necessary to reach a desired accuracy. This work provides a
foundation for developing methods to analyse very large upcoming datasets with
the next-generation observational facilities.",2107.09082v1
2006-10-11,Generalized Bell inequality for mixed states with variable constraints,"In this paper, we present a generalized Bell inequality for mixed states. The
distinct characteristic is that the inequality has variable bound depending on
the decomposition of the density matrix. The inequality has been shown to be
more refined than the previous Bell inequality. It is possible that a separable
mixed state can violate the Bell inequality.",0610086v1
2003-05-29,Spurious modes in extended RPA theories,"Necessary conditions that the spurious state associated with the
translational motion and its double-phonon state have zero excitation energy in
extended RPA (ERPA) theories which include both one-body and two-body
amplitudes are investigated using the small amplitude limit of the
time-dependent density-matrix theory (STDDM). STDDM provides us with a quite
general form of ERPA as compared with other similar theories in the sense that
all components of one-body and two-body amplitudes are taken into account. Two
conditions are found necessary to guarantee the above property of the single
and double spurious states: The first is that no truncation in the
single-particle space should be made. This condition is necessary for the
closure relation to be used and is common for the single and double spurious
states. The second depends on the mode. For the single spurious state all
components of the one-body amplitudes must be included, and for the double
spurious state all components of one-body and two-body amplitudes have to be
included. It is also shown that the Kohn theorem and the continuity equations
for transition densities and currents hold under the same conditions as the
spurious states. ERPA theories formulated using the Hartree-Fock ground state
have a non-hermiticity problem. A method for formulating ERPA with hermiticity
is also proposed using the time-dependent density-matrix formalism.",0305087v1
2020-09-24,Exciton-Trion-Polaritons in Two-Dimensional Materials,"We present a many-body theory for exciton-trion-polaritons in doped
two-dimensional materials. Exciton-trion-polaritons are robust coherent hybrid
excitations involving excitons, trions, and photons. Signatures of these
polaritons have been recently seen in experiments. In these polaritons, the
2-body exciton states are coupled to the material ground state via
exciton-photon interaction and the 4-body trion states are coupled to the
exciton states via Coulomb interaction. The trion states are not directly
optically coupled to the material ground state. The energy-momentum dispersion
of these polaritons exhibit three bands. We calculate the energy band
dispersions and the compositions of polaritons at different doping densities
using Green's functions. The energy splittings between the polariton bands, as
well as the spectral weights of the polariton bands, depend on the strength of
the Coulomb coupling between the excitons and the trions and which in turn
depends on the doping density. The excitons are Coulomb coupled to both bound
and unbound trion states. The latter are exciton-electron scattering states and
their inclusion is necessary to capture the spectral weight transfer among the
polariton bands as a function of the doping density.",2009.13069v2
2001-02-02,Vertical magneto-tunneling through a quantum dot and the density of states of small electronic systems,"One-electron tunneling through a quantum dot with a strong magnetic field in
the direction of the current is studied. The linear magneto-conductance is
computed for a model parabolic dot with seven electrons in the intermediate
states and for different values of the magnetic field. It is shown that the dot
density of states at low excitation energies can be extracted from a precise
measurement of the conductance at the upper edge of the Coulomb blockade
diamond. We parametrized the density of states with a single ``temperature''
parameter (in the so called ``constant temperature approximation''), and found
that this parameter depends very weakly on the magnetic field.",0102030v1
2002-07-26,Dynamic correlations in symmetric electron-electron and electron-hole bilayers,"The ground-state behavior of the symmetric electron-electron and
electron-hole bilayers is studied by including dynamic correlation effects
within the quantum version of Singwi, Tosi, Land, and Sjolander (qSTLS) theory.
The static pair-correlation functions, the local-field correction factors, and
the ground-state energy are calculated over a wide range of carrier density and
layer spacing. The possibility of a phase transition into a density-modulated
ground state is also investigated. Results for both the electron-electron and
electron-hole bilayers are compared with those of recent diffusion Monte Carlo
(DMC) simulation studies. We find that the qSTLS results differ markedly from
those of the conventional STLS approach and compare in the overall more
favorably with the DMC predictions. An important result is that the qSTLS
theory signals a phase transition from the liquid to the coupled Wigner crystal
ground state, in both the electron-electron and electron-hole bilayers, below a
critical density and in the close proximity of layers (d <~ r_sa_0^*), in
qualitative agreement with the findings of the DMC simulations.",0207644v1
2000-02-28,Operational criterion and constructive checks for the separability of low rank density matrices,"We consider low rank density operators $\varrho$ supported on a $M\times N$
Hilbert space for arbitrary $M$ and $N$ ($M\leq N$) and with a positive partial
transpose (PPT) $\varrho^{T_A}\ge 0$. For rank $r(\varrho) \leq N$ we prove
that having a PPT is necessary and sufficient for $\varrho$ to be separable; in
this case we also provide its minimal decomposition in terms of pure product
states. It follows from this result that there is no rank 3 bound entangled
states having a PPT. We also present a necessary and sufficient condition for
the separability of generic density matrices for which the sum of the ranks of
$\varrho$ and $\varrho^{T_A}$ satisfies $r(\varrho)+r(\varrho^{T_A}) \le
2MN-M-N+2$. This separability condition has the form of a constructive check,
providing thus also a pure product state decomposition for separable states,
and it works in those cases where a system of couple polynomial equations has a
finite number of solutions, as expected in most cases.",0002089v1
2009-05-11,Investigation of chiral density wave mean field Hamiltonian,"We start with the chiral density wave(CDW)mean field Hamiltonian in the
momentum space for the pseudo-gapped state of YBCO in the absence of magnetic
field, including the momentum conserving inter-layer tunneling matrix elements
in the Hamiltonian for the tetragonal case, with the principal component of the
order parameter corresponding to idx2-y2 and the secondary one to the dxy. With
the eigenvalues and the eigenvectors of the Hamiltonian matrix we write down
expression for Berry curvature(BC). Only two BC peaks of same magnitude and
opposite signs are obtained at the nodal points of the reconstructed Fermi
surface (RFS) for the pure idx2-y2-density wave case. We establish a relation
between thermodynamic potential of the system and certain spectral functions
for the CDW state. This yields an expression for entropy in closed form. We
show that the transition to the CDW state is a first order one and the entropy
per unit cell increases in this state. We also investigate anomalous Nernst
effect theoretically.",0905.1533v1
2010-03-10,Entanglement in valence-bond-solid states on symmetric graphs,"We study quantum entanglement in the ground state of the
Affleck-Kennedy-Lieb-Tasaki (AKLT) model defined on two-dimensional graphs with
reflection and/or inversion symmetry. The ground state of this spin model is
known as the valence-bond-solid state. We investigate the properties of reduced
density matrix of a subsystem which is a mirror image of the other one. Thanks
to the reflection symmetry, the eigenvalues of the reduced density matrix can
be obtained by numerically diagonalizing a real symmetric matrix whose elements
are calculated by Monte Carlo integration. We calculate the von Neumann entropy
of the reduced density matrix. The obtained results indicate that there is some
deviation from the naive expectation that the von Neumann entropy per valence
bond on the boundary between the subsystems is $\ln 2$. This deviation is
interpreted in terms of the hidden spin chain along the boundary between the
subsystems. In some cases where graphs are on ladders, the numerical results
are analytically or algebraically confirmed.",1003.2007v2
2010-07-19,"Reply to Comment ""Density of states and critical behavior of the three-dimensional Coulomb Glass""","We reply to the Comment by Mobius and Richter [arXiv:0908.3092, Phys. Rev.
Lett. 105, 039701 (2010)] on ""Density of States and Critical Behavior of the
Coulomb Glass"" [arXiv:0805.4640, Phys. Rev. Lett. 102, 067205 (2009)] and
address the issues raised with our results on the density of states. In
addition, we correct our statements about the random displacement version of
the Coulomb glass model where the Wigner crystal is not as robust to disorder
as stated. Still, our main result of a lack of a finite-temperature transition
in the Coulomb glass remains unchallenged.",1007.3073v1
2012-08-25,Spin dynamics of possible density wave states in the pseudogap phase of the high temperature superconductors,"In a recent inelastic neutron scattering experiment in the pseudogap state of
the high temperature superconductor $\mathrm{YBa_{2}Cu_{3}O_{6.6}}$ an unusual
`vertical' dispersion of the spin excitations with a large in-plane anisotropy
was observed. In this paper we discuss in detail the spin susceptibility of the
singlet $d$-density wave, the triplet $d$-density wave, as well as the more
common spin density wave orders with hopping anisotropies. From numerical
calculations within the framework of random phase approximation, we find nearly
vertical dispersion relations for spin excitations with anisotropic
incommensurability at low energy $\omega \le 90 meV$, which are reminiscent of
the experiments. At very high energy $\omega \ge 165 meV$, we also find
energy-dependent incommensurability. Although there are some important
difference between the three cases, unpolarized neutron measurements cannot
discriminate between these alternate possibilities; the vertical dispersion,
however, is a distinct feature of all three density wave states in contrast to
the superconducting state, which shows an hour-glass shape dispersion.",1208.5108v1
2012-10-03,"Simultaneous Estimation of Dimension, States and Measurements: Computation of representative density matrices and POVMs","This investigation continues a program aiming at obtaining effective quantum
models to describe measurement statistics. In [Stark, arXiv:1209.5737 (2012)],
we have described how the Gram matrix associated to the prepared states and the
performed POVM elements can be estimated via convex relaxation of a rank
minimization problem. This Gram matrix determines the density matrices and the
POVM elements uniquely up to simultaneous rotations (with respect to the
Hilbert-Schmidt inner product) in the vector space of Hermitian matrices.
However, when the description of the experiment needs to be connected to
textbook quantum mechanics, explicit expressions for the states and the POVM
elements in terms of positive semidefinite matrices are required. In this
paper, we describe a heuristic algorithm that takes the state-meaurement Gram
matrix as input and searches explicit realizations of this Gram matrix in terms
of quantum mechanically valid density matrices and POVM elements.",1210.1105v1
2013-06-24,Density profiles and collective modes of a Bose-Einstein condensate with light-induced spin-orbit coupling,"The phases of a Bose-Einstein condensate (BEC) with light-induced spin-orbit
coupling (SOC) are studied within the mean-field approximation. The mixed BEC
phase, in which the system condenses in a superposition of two plane wave
states, is found to be stable for sufficiently small light-atom coupling,
becoming unstable in a continuous fashion with increasing light-atom coupling.
The structure of the phase diagram at fixed chemical potential for bosons with
SOC is shown to imply an unusual density dependence for a trapped mixed BEC
phase, with the density of one dressed spin state increasing with increasing
radius, providing a unique experimental signature of this state. The collective
Bogoliubov sound mode is shown to also provide a signature of the mixed BEC
state, vanishing as the boundary to the regime of phase separation is
approached.",1306.5717v2
2013-12-02,Nodeless superconducting gap induced by odd parity pair density wave in underdoped cuprates,"We present a theoretical model to show that the transition from an
antiferromagnetic (AFM) phase to the $d_{x^2-y^2}$-wave superconductivity
occurs through a robust companion of a finite momentum pairing between $({\bf
k},\uparrow)$ and $(-{\bf k}-{\bf Q},\downarrow)$ electrons, namely
pair-density wave (PDW) state, where ${\bf Q}=(\pi,\pi)$ is the AFM wavevector.
Interestingly, the spatial structure of the PDW is constrained to be a
$p+ip$-wave symmetry, which follows $p_{\bf k}=p_{-{\bf k}-{\bf Q}}$ under
fermions exchange in cuprates, dictating a spin-singlet pairing. Furthermore,
the PDW state produces a fully gapped quasiparticle spectrum which explains
recent observations of the fully gapped quasiparticle structure of lightly
doped cuprates in the hole doping side. We study the stability of all three
phases within the self-consistent mean-field theory. Finally, we calculate the
superfluid density to propose its exponential temperature dependence as a test
to the SC origin of this fully gapped state, while the phase modulation of the
PDW state can be visualized by scanning probes.",1312.0544v4
2014-04-14,Extending the range of real time density matrix renormalization group simulations,"We discuss a few simple modifications to time-dependent density matrix
renormalization group (DMRG) algorithms which allow to access larger time
scales. We specifically aim at beginners and present practical aspects of how
to implement these modifications almost effortlessly within any standard matrix
product state (MPS) based formulation of the method. Most importantly, we show
how to 'combine' the Schroedinger and Heisenberg time evolutions of arbitrary
pure states |psi> and operators A in the evaluation of
<A>_psi(t)=<psi|A(t)|psi>. This includes quantum quenches. The generalization
(non-)thermal mixed state dynamics <A>_rho(t)=Tr[rho A(t)] induced by an
initial density matrix rho is straightforward. In the context of equilibrium
(ground state or finite temperature T>0) correlation functions, one can extend
the simulation time by a factor of two by 'exploiting time translation
invariance', which is efficiently implementable within MPS DMRG. We present a
simple analytic argument for why a recently-introduced disentangler succeeds in
reducing the effort of time-dependent simulations at T>0. Finally, we advocate
the python programming language as an elegant option for beginners to set up a
DMRG code.",1404.3704v1
2014-07-29,Failure of steady state thermodynamics in lattice gases under nonuniform drive,"To be useful, steady state thermodynamics (SST) must be self-consistent and
have predictive value. Although consistency of SST was recently verified for
driven lattice gases under global weak exchange, I show here that it does not
predict the coexisting densities in athermal stochastic lattice gases under a
nonuniform drive. I consider the lattice gas with nearest-neighbor exclusion on
the square lattice, with nearest-neighbor hopping (NNE dynamics), and with
hopping to both nearest and next-nearest neighbors (NNE2 dynamics). Part of the
system is subject to a drive $D$ that favors hopping along one direction, while
the other part is free of the drive. Thus the steady state represents
coexistence between two subsystems, one far from equilibrium and the other in
equilibrium, which exchange particles along the interfaces. The dimensionless
chemical potential $\mu^*(\rho,D) = \mu/k_B T$ for the lattice gas with density
$\rho$ is readily determined in studies of a uniform system. Under the
nonuniform drive, however, equating the chemical potentials of the coexisting
subsystems does not yield the coexisting densities. The steady state chemical
potential is, moreover, different in the coexisting bulk regions, contrary to
the basic principles of thermodynamics. These results cast serious doubt on the
predictive value of SST.",1407.7899v1
2016-02-18,Confinement transition to density wave order in metallic doped spin liquids,"Insulating quantum spin liquids can undergo a confinement transition to a
valence bond solid state via the condensation of topological excitations of the
associated gauge theory. We extend the theory of such transitions to
fractionalized Fermi liquids (FL*): these are metallic doped spin liquids in
which the Fermi surfaces only have gauge neutral quasiparticles. Using insights
from a duality transform on a doped quantum dimer model for the U(1)-FL* state,
we show that projective symmetry group of the theory of the topological
excitations remains unmodified, but the Fermi surfaces can lead to additional
frustrating interactions. We propose a theory for the confinement transition of
$\mathbb{Z}_2$-FL* states via the condensation of visons. A variety of
confining, incommensurate density wave states are possible, including some that
are similar to the incommensurate $d$-form factor density wave order observed
in several recent experiments on the cuprate superconductors.",1602.05954v2
2018-04-19,Absence of ferromagnetism in VSe2 caused by its charge density wave phase,"In this study we present a detailed ab initio analysis of the magnetic
properties of VSe2 . Ab initio calculations in the so-called 1T structure yield
a ferromagnetic phase as most stable, with a magnetic moment of about 0.6 {\mu}
B /V. According to our calculations this ferromagnetic state is on the verge of
instability. We have modeled ab initio the charge density wave state reported
in the literature. This introduces a periodic lattice distortion leading to a
supercell with periodicity 4a x 4a x 3c (4a x 4a for the monolayer) in which we
have fully relaxed the atomic positions. We demonstrate that this structural
rearrangement causes a strong reduction in the density of states at the Fermi
level and the ground state of the system becomes non-magnetic for the bulk. In
the monolayer limit the rearrangement induces a Peierls distortion causing an
energy gap opening at the Fermi level and the quenching of ferromagnetism.",1804.07102v2
2018-11-08,Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator,"We study the spectral properties of Markovian driven-dissipative quantum
systems, focusing on the nonlinear quantum van der Pol oscillator as a
paradigmatic example. We discuss a generalized Lehmann representation, in which
single-particle Green's functions are expressed in terms of the eigenstates and
eigenvalues of the Liouvillian. Applying it to the quantum van der Pol
oscillator, we find a wealth of phenomena that are not apparent in the
steady-state density matrix alone. Unlike the steady state, the photonic
spectral function has a strong dependence on interaction strength. Further, we
find that the interplay of interaction and non-equilibrium effects can result
in a surprising ""negative density of states"", associated with a negative
temperature, and we identify two different mechanisms responsible for this
phenomenon.",1811.03518v2
2018-03-22,Imaging the Wigner Crystal of Electrons in One Dimension,"The quantum crystal of electrons, predicted more than eighty years ago by
Eugene Wigner, is still one of the most elusive states of matter. Here, we
present experiments that observe the one-dimensional Wigner crystal directly,
by imaging its charge density in real-space. To measure this fragile state
without perturbing it, we developed a new scanning probe platform that utilizes
a pristine carbon nanotube as a scanning charge perturbation to image, with
minimal invasiveness, the many-body electronic density within another nanotube.
The obtained images, of few electrons confined in one-dimension, match those of
strongly interacting crystals, with electrons ordered like pearls on a
necklace. Comparison to theoretical modeling demonstrates the dominance of
Coulomb interactions over kinetic energy and the weakness of exchange
interactions. Our experiments provide direct evidence for this long-sought
electronic state, and open the way for studying other fragile interacting
states by imaging their many-body density in real-space.",1803.08523v1
2017-12-07,Elliptic Flow and the Nuclear Equation of State,"New constraints for the nuclear equation of state at suprasaturation
densities have been obtained by measuring collective particle flows in
heavy-ion reactions at relativistic energies. Ratios and differences of neutron
and hydrogen flows in 197Au + 197Au collisions at 400 MeV/nucleon were used in
studies of the asymmetric-matter equation of state. The comparison with
predictions of transport models favors a moderately soft to linear density
dependence, consistent with ab-initio nuclear matter theories. Model
predictions suggest that comprehensive data sets collected at higher bombarding
energies will provide information on the asymmetric-matter equation of state in
the density range up to two or three times the saturation value.",1712.03093v1
2019-07-17,Quantum channel correction with twisted light using compressive sensing,"Compressive sensing is used to perform high-dimensional quantum channel
estimation with classical light. As an example, we perform a numerical
simulation for the case of a three-dimensional classically non-separable state
that is propagated through atmospheric turbulence. Using singular value
thresholding algorithm based compressive sensing, we determine the channel
matrix, which we subsequently use to correct for the atmospheric turbulence
induced distortions. As a measure of the success of the procedure, we calculate
the fidelity and the trace distance of the corrected density matrix with
respect to the input state, and compare the results with those of the density
matrix for the uncorrected state. Furthermore, we quantify the amount of
classical non-separability in the density matrix of the corrected state by
calculating its negativity. The results show that compressive sensing could
contribute in the development and implementation of free-space quantum and
optical communication systems.",1907.07379v2
2022-02-11,Fragmented Cooper pair condensation in striped superconductors,"Condensation of bosons in Bose-Einstein condensates or Cooper pairs in
superconductors refers to a macroscopic occupation of a few single- or
two-particle states. A condensate is called ""fragmented"" if not a single, but
multiple states are macroscopically occupied. While fragmentation is known to
occur in particular Bose-Einstein condensates, we propose that fragmentation
naturally takes place in striped superconductors. To this end, we investigate
the nature of the superconducting ground state realized in the two-dimensional
$t$-$t^\prime$-$J$ model. In the presence of charge density modulations, the
condensate is shown to be fragmented and composed of partial condensates
located on the stripes. The fragments of the condensates hybridize to form an
extended macroscopic wave function across the system. The results are obtained
from evaluating the singlet-pairing two-particle density matrix of the ground
state on finite cylinders computed via the density matrix renormalization group
(DMRG) method. Our results shed light on the intricate relation between stripe
order and superconductivity in systems of strongly correlated electrons.",2202.05850v2
2022-03-28,Optimisation-free Classification and Density Estimation with Quantum Circuits,"We demonstrate the implementation of a novel machine learning framework for
probability density estimation and classification using quantum circuits. The
framework maps a training data set or a single data sample to the quantum state
of a physical system through quantum feature maps. The quantum state of the
arbitrarily large training data set summarises its probability distribution in
a finite-dimensional quantum wave function. By projecting the quantum state of
a new data sample onto the quantum state of the training data set, one can
derive statistics to classify or estimate the density of the new data sample.
Remarkably, the implementation of our framework on a real quantum device does
not require any optimisation of quantum circuit parameters. Nonetheless, we
discuss a variational quantum circuit approach that could leverage quantum
advantage for our framework.",2203.14452v3
2023-02-01,Density peak clustering using tensor network,"Tensor networks, which have been traditionally used to simulate many-body
physics, have recently gained significant attention in the field of machine
learning due to their powerful representation capabilities. In this work, we
propose a density-based clustering algorithm inspired by tensor networks. We
encode classical data into tensor network states on an extended Hilbert space
and train the tensor network states to capture the features of the clusters.
Here, we define density and related concepts in terms of fidelity, rather than
using a classical distance measure. We evaluate the performance of our
algorithm on six synthetic data sets, four real world data sets, and three
commonly used computer vision data sets. The results demonstrate that our
method provides state-of-the-art performance on several synthetic data sets and
real world data sets, even when the number of clusters is unknown.
Additionally, our algorithm performs competitively with state-of-the-art
algorithms on the MNIST, USPS, and Fashion-MNIST image data sets. These
findings reveal the great potential of tensor networks for machine learning
applications.",2302.00192v1
2018-05-25,A Multi-Scan Labeled Random Finite Set Model for Multi-object State Estimation,"State space models in which the system state is a finite set--called the
multi-object state--have generated considerable interest in recent years.
Smoothing for state space models provides better estimation performance than
filtering by using the full posterior rather than the filtering density. In
multi-object state estimation, the Bayes multi-object filtering recursion
admits an analytic solution known as the Generalized Labeled Multi-Bernoulli
(GLMB) filter. In this work, we extend the analytic GLMB recursion to propagate
the multi-object posterior. We also propose an implementation of this so-called
multi-scan GLMB posterior recursion using a similar approach to the GLMB filter
implementation.",1805.10038v1
2008-07-02,How edge states are destroyed in disordered mesoscopic samples?,"We report theoretical investigations on how edge states are destroyed in
disordered mesoscopic samples by calculating a ""phase diagram"" in terms of
energy versus disorder strength $(E,W)$, and magnetic field versus disorder
strength $(B,W)$, in the integer quantum Hall regime. It is found that as the
disorder strength $W$ increases, edge states are destroyed one by one if
transmission eigen-channels are used to characterize the edge states. Near the
insulating regime, transmission eigen-channels are closed one by one in the
same order as edges states are destroyed. To identify those edge states which
have survived disorder, we introduce a generalized current density that can be
calculated and visualized.",0807.0340v1
1995-07-19,Paired States in the Even Integer Quantum Hall Effect,"We argue that a new type of quantum Hall state requiring non-perturbative
Landau level mixing arises at low electron density. In these states, up and
down spin electrons pair to form spinless bosons that condense into a bosonic
quantum Hall state. We describe a wavefunction for a paired quantum Hall state
at $\nu=2$ and argue that it is stabilized by a BCS instability arising in flux
attachment calculations. Based on this state, we derive a new global phase
diagram for the integral quantum Hall effect with spin. Additional experimental
implications are discussed.",9507077v1
1999-08-19,"Energy spectrum, density of states and optical transitions in strongly biased narrow-gap quantum wells","We study theoretically the effect of an electric field on the electron states
and far-infrared optical properties in narrow-gap lead salt quantum wells. The
electron states are described by a two-band Hamiltonian. An application of a
strong electric field across the well allows the control of the energy gap
between the two-dimensional (2D) states in a wide range. A sufficiently strong
electric field transforms the narrow-gap quantum well to a nearly gapless 2D
system, whose electron energy spectrum is described by linear dispersion
relations \epsilon_{\sigma} (k) ~\pm (k-k_{\sigma}), where k_{\sigma} are the
field-dependent 2D momenta corresponding to the minimum energy gaps for the
states with spin numbers \sigma. Due to the field-induced shift of the 2D
subband extrema away from k=0 the density of states has inverse-square-root
divergencies at the edges. This property may result in a considerable increase
of the magnitude of the optical absorption and in the efficiency of the
electrooptical effect.",9908284v1
2000-01-04,Roton Instability of the Spin Wave Excitation in the Fully Polarized Quatum Hall State and the Phase Diagram at $ν= 2$,"We consider the effect of interactions on electrons confined to two
dimensions at Landau level filling $\nu=2$, with the specific aim to determine
the range of parameters where the fully polarized state is stable. We calculate
the charge and the spin density collective modes in random phase approximation
(RPA) including vertex corrections (also known as time dependent Hartree Fock),
and treating the Landau level mixing accurately within the subspace of a single
particle hole pair. It is found that the spin wave excitation mode of the fully
polarized state has a roton minimum which deepens as a result of the
interaction induced Landau level mixing, and the energy of the roton vanishes
at a critical Zeeman energy signaling an instability of the fully polarized
state at still lower Zeeman energies. The feasibility of the experimental
observation of the roton minimum in the spin wave mode and its softening will
be discussed. The spin and charge density collective modes of the unpolarized
state are also considered, and a phase diagram for the $\nu =2$ state as a
function of $r_{S}$ and the Zeeman energy is obtained.",0001036v1
2009-12-01,Evolution of Quantum Systems by Diagrams of States,"We explore the main processes involved in the evolution of general quantum
systems by means of Diagrams of States, a novel method to graphically represent
and analyze how quantum information is elaborated during computations performed
by quantum circuits. We present quantum diagrams of states for representations
of quantum states by density matrices, partial trace operations, density matrix
purification and time-evolution by Kraus operators. Following these
representations, we describe by diagrams of states the most general
transformations related to singlequbit decoherence and errors. Diagrams of
states prove to be a useful approach to analyze quantum computations, by
offering an intuitive graphic representation of the processing of quantum
information. They also help in conceiving novel quantum computations, from
describing the desired information processing to deriving the final
implementation by quantum gate arrays.",0912.0026v1
2021-03-09,On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution,"It is standard to assume that the Wigner distribution of a mixed quantum
state consisting of square-integrable functions is a quasi-probability
distribution, that is that its integral is one and that the marginal properties
are satisfied. However this is in general not true. We introduce a class of
quantum states for which this property is satisfied, these states are dubbed
""Feichtinger states"" because they are defined in terms of a class of functional
spaces (modulation spaces) introduced in the 1980's by H. Feichtinger. The
properties of these states are studied, which gives us the opportunity to prove
an extension to the general case of a result of Jaynes on the non-uniqueness of
the statistical ensemble generating a density operator. As a bonus we obtain a
result for convex sums of Wigner transforms.",2103.05605v4
2022-02-16,Universal Behavior of Multipartite Entanglement in Crossing the Quantum Critical Point,"We investigate multipartite entanglement of the quantum Ising model with
transverse fields for a slow quantum quench crossing a critical point. The
multipartite entanglement is quantified by quantum Fisher information with the
generator defined as the operator of the ferromagnetic order parameter due to
the system symmetry. The quench dynamics begin with the ground state of the
large transverse field in the paramagnetic phase, and then the transverse field
is driven slowly to cross a quantum critical point and ends with a zero
transverse field. Based on methods of matrix product state, we calculate the
quantum Fisher information density of the final state. Numerical results of
both linear and nonlinear quench show that the quantum Fisher information
density of the final state scales as a power law of the quench rate, which has
an opposite exponent of the Kibble-Zurek scaling. Our results reveal that the
multipartite entanglement provides a new viewpoint to understand the dynamics
of quantum phase transition. Based on the observation of entanglement in the
quenched state, we also expect that our result would inspire approaches for
preparing multipartite entangled states in quantum information processing.",2202.07892v1
2022-10-28,Cosmological states in loop quantum gravity on homogeneous graphs,"We introduce a class of states characterized by proposed conditions of
homogeneity and isotropy in loop quantum gravity and construct concrete
examples given by Bell-network states on a special class of homogeneous graphs.
Such states provide new representations of cosmological spaces that can be
explored for the formulation of cosmological models in the context of loop
quantum gravity. We show that their local geometry is described in an
automorphism-invariant manner by one-node observables analogous to the one-body
observables used in many-body quantum mechanics, and compute the density matrix
representing the restriction of global states to the algebra of one-node
observables. The von Neumann entropy of this density matrix provides a notion
of entanglement entropy of a local region which respects
automorphism-invariance and can be applied to states involving superpositions
of distinct graphs.",2210.16439v2
2000-03-24,On dispersive energy transport and relaxation in the hopping regime,"A new method for investigating relaxation phenomena for charge carriers
hopping between localized tail states has been developed. It allows us to
consider both charge and energy {\it dispersive} transport. The method is based
on the idea of quasi-elasticity: the typical energy loss during a hop is much
less than all other characteristic energies. We have investigated two models
with different density of states energy dependencies with our method. In
general, we have found that the motion of a packet in energy space is affected
by two competing tendencies. First, there is a packet broadening, i.e. the
dispersive energy transport. Second, there is a narrowing of the packet, if the
density of states is depleting with decreasing energy. It is the interplay of
these two tendencies that determines the overall evolution. If the density of
states is constant, only broadening exists. In this case a packet in energy
space evolves into Gaussian one, moving with constant drift velocity and mean
square deviation increasing linearly in time. If the density of states depletes
exponentially with decreasing energy, the motion of the packet tremendously
slows down with time. For large times the mean square deviation of the packet
becomes constant, so that the motion of the packet is ``soliton-like''.",0003408v1
2009-02-26,Phonon spectra in CaFe2As2 and Ca0.6Na0.4Fe2As2: Measurement of the pressure and temperature dependence and comparison with ab-initio and shell model calculations,"We report the pressure and temperature dependence of the phonon
density-of-states in superconducting Ca0.6Na0.4Fe2As2 (Tc=21 K) and the parent
compound CaFe2As2, using inelastic neutron scattering. We observe no
significant change in the phonon spectrum for Ca0.6Na0.4Fe2As2 at 295 K up to
pressures of 5 kbar. The phonon spectrum for CaFe2As2 shows softening of the
low-energy modes by about 1 meV when decreasing the temperature from 300 K to
180 K. There is no appreciable change in the phonon density of states across
the structural and anti-ferromagnetic phase transition at 172 K. These results,
combined with our earlier temperature dependent phonon density of states
measurements for Ca0.6Na0.4Fe2As2, indicate that the softening of low-energy
phonon modes in these compounds may be due to the interaction of phonons with
electron or short-range spin fluctuations in the normal state of the
superconducting compound as well as in the parent compound. The phonon spectra
are analyzed with ab-initio and empirical model calculations giving partial
densities of states and dispersion relations.",0902.4590v1
2012-09-23,More about the stringy limit of black hole equilibria,"We discuss further our proposed modification of the
Susskind-Horowitz-Polchinski scenario in which black hole entropy goes over to
string entropy as one scales the string length scale up and the string coupling
constant down, keeping Newton's constant unchanged. In our approach, based on
our 'matter-gravity entanglement hypothesis', 'string entropy' here should be
interpreted as the likely entanglement entropy between (approximately) the
single long string and the stringy atmosphere which, as we argue, arise in a
pure multistring state of given energy in a (rescaled) box. In a previous
simple analysis, we computed this entropy (with promising results) by assuming
simple exponentially increasing densities of states for both long string and
stringy atmosphere. Here, our starting point is a (more correct) density of
states for each single string with the appropriate inverse-power prefactor and
a low-energy cutoff. We outline how the relevant entanglement entropy should be
calculated for this system and propose a plausible model, which draws on the
work of Mitchell and Turok on the multi-string microcanonical ensemble, in
which we adopt a similar density of states for long string and stringy
atmosphere but now with cutoffs which scale with the total energy, E. With this
scaling, we still find our entanglement entropy grows, in leading order,
linearly with E and this translates to a black-hole entropy which goes as the
square of the black-hole mass, thus retaining most of the promising features of
our previous exponential-density-of-states model and providing further evidence
for our matter-gravity entanglement hypothesis.",1209.5110v1
2014-08-27,Controlled pairing symmetry of the superfluid state in systems of three-component repulsive fermionic atoms in optical lattices,"We investigate the pairing symmetry of the superfluid state in repulsively
interacting three-component (colors) fermionic atoms in optical lattices. When
two of the three color-dependent repulsions are much larger than the other,
pairing symmetry is an extended s wave, although the superfluid state appears
adjacent to the paired Mott insulator in the phase diagram. As the difference
between the three repulsions is decreased in square optical lattices, the
extended s-wave pairing changes into a nodal s-wave pairing and then into a
d-wave pairing. This change in pairing symmetry is attributed to the
competition among the density fluctuations of unpaired atoms, the quantum
fluctuations of the color-density wave, and those of the color-selective
antiferromagnet. This phenomenon can be studied using existing experimental
techniques.We investigate the pairing symmetry of the superfluid state in
repulsively interacting three-component (color) fermionic atoms in optical
lattices. When two of the three color-dependent repulsions are much stronger
than the other, pairing symmetry is an extended $s$ wave although the
superfluid state appears adjacent to the paired Mott insulator in the phase
diagram. On the other hand, when two of the three color-dependent repulsions
are weaker than the other, pairing symmetry is a d_{x^2-y^2}-wave. This change
in pairing symmetry is attributed to the change in the dominant quantum
fluctuations from the density fluctuations of unpaired atoms and the
color-density wave fluctuations to the color-selective antiferromagnet
fluctuations. This phenomenon can be studied using existing experimental
techniques.",1408.6582v3
2015-08-13,Closing the proximity gap in a metallic Josephson junction between three superconductors,"We describe the proximity effect in a short disordered metallic junction
between three superconducting leads. Andreev bound states in the multi-terminal
junction may cross the Fermi level. We reveal that for a quasi-continuous
metallic density of states, crossings at the Fermi level manifest as closing of
the proximity-induced gap. We calculate the local density of states for a wide
range of transport parameters using quantum circuit theory. The gap closes
inside an area of the space spanned by the superconducting phase differences.
We derive an approximate analytic expression for the boundary of the area and
compare it to the full numerical solution. The size of the area increases with
the transparency of the junction and is sensitive to asymmetry. The finite
density of states at zero energy is unaffected by electron-hole decoherence
present in the junction, although decoherence is important at higher energies.
Our predictions can be tested using tunneling transport spectroscopy. To
encourage experiments, we calculate the current-voltage characteristic in a
typical measurement setup. We show how the structure of the local density of
states can be mapped out from the measurement.",1508.03289v2
2018-02-06,Single crystal study of the charge density wave metal LuNiC2,"We report on single crystal growth, single crystal x-ray diffraction,
physical properties and density functional theory (DFT) electronic structure as
well as Fermi surface calculations for two ternary carbides, LuCoC2 and LuNiC2.
Electrical resistivity measurements reveal for LuNiC2 a charge density wave
(CDW) transition at T_{CDW}~ 450 K and, for T > T_{CDW}, a significant
anisotropy of the electrical resistivity, which is lowest along the
orthorhombic a-axis. The analysis of x-ray superstructure reflections suggest a
commensurate CDW state with a Peierls-type distortion of the Ni atom
periodicity along the orthorhombic a-axis. DFT calculations based on the CDW
modulated monoclinic structure model of LuNiC2 as compared to results of the
orthorhombic parent-type reveal the formation of a partial CDW gap at the Fermi
level which reduces the electronic density of states from N(E_{F})= 1.03
states/eV f.u. without CDW to N(E_{F})= 0.46 states/eV f.u. in the CDW state.
The corresponding bare DFT Sommerfeld value of the latter, gamma_{DFT}^{CDW}=
0.90 mJ/molK^2, reaches reasonable agreement with the experimental value gamma=
0.83(5) mJ/mol\,K^2 of LuNiC2. LuCoC2 displays a simple metallic behavior with
neither CDW ordering nor superconductivity above 0.4 K. Its experimental
Sommerfeld coefficient, gamma= 5.9 (1) mJ/molK^2, is in realistic
correspondence with the calculated, bare Sommerfeld coefficient, gamma_{DFT}=
3.82 mJ/molK^2, of orthorhombic LuCoC2.",1802.02061v3
2019-03-21,New Neutron Star Equation of State with Quark-Hadron Crossover,"We present a much improved equation of state for neutron star matter, QHC19,
with a smooth crossover from the hadronic regime at lower densities to the
quark regime at higher densities. We now use the Togashi et al.~equation of
state (Togashi:2017), a generalization of the Akmal-Pandharipande-Ravenhall
equation of state of uniform nuclear matter, in the entire hadronic regime; the
Togashi equation of state consistently describes non-uniform as well as uniform
matter, and matter at beta equilibrium without the need for an interpolation
between pure neutron and symmetric nuclear matter. We describe the quark matter
regime at higher densities with the Nambu--Jona--Lasinio model, now identifying
tight constraints on the phenomenological universal vector repulsion between
quarks and the pairing interaction between quarks arising from the requirements
of thermodynamic stability and causal propagation of sound. The resultant
neutron star properties agree very well with the inferences of the LIGO/Virgo
collaboration, from GW170817, of the pressure vs. baryon density, neutron star
radii, and tidal deformabilities. The maximum neutron star mass allowed by
QHC19 is 2.35 $M_\odot$, consistent with all neutron star mass determinations.",1903.08963v3
2019-09-03,Arrested States in Persistent Active Matter: Gelation without Attraction,"We explore phase separation and kinetic arrest in a model active colloidal
system consisting of self-propelled, hard-core particles with nonconvex shapes.
The passive limit of the model, namely cross-shaped particles on a square
lattice, exhibits a first-order transition from a fluid phase to a solid phase
with increasing density. Quenches into the two-phase coexistence region exhibit
an aging regime. The nonconvex shape of the particles eases jamming in the
passive system and leads to strong inhibition of rotations of the active
particles. Using numerical simulations and analytical modeling, we quantify the
nonequilibrium phase behavior as a function of density and activity. If we view
activity as the analog of attraction strength, the phase diagram exhibits
strong similarities to that of attractive colloids, exhibiting both aging,
glassy states and gel-like arrested states. The two types of dynamically
arrested states, glasses and gels, are distinguished by the appearance of
density heterogenities in the latter. In the infinitely persistent limit, we
show that a coarse-grained model based on the asymmetric exclusion process
quantitatively predicts the density profiles of the gel states. The predictions
remain qualitatively valid for finite rotation rates. Using these results, we
classify the activity-driven phases and identify the boundaries separating
them.",1909.01375v3
2022-08-17,Role of spin-orbit coupling effects in rare-earth metallic tetra-borides : a first principle study,"We have investigated the electronic structure of rare-earth tetraborides,
$\textrm{RB}_{4}$, using first-principle electronic structure methods (DFT)
implemented in Quantum Espresso (QE). In this article we have studied
heather-to neglected strong spin-orbit coupling (SOC) effects present in these
systems on the electronic structure of these system in the non-magnetic ground
state. The calculations were done under GGA and GGA+SO approximations using
ultrasoft pseudopotentials and fully relativistic ultrasoft pseudopotentials
(for SOC case). Perdew-Burke-Ernzerhof generalized gradient approximation
(PBE-GGA) exchange-correlation functionals within the linearized plane-wave
(LAPW) method as implemented in QE were used. The projected density of states
consists of 3 distinct spectral peaks well below the Fermi energy and separated
from the continuum density of states around the Fermi energy. The discrete
peaks arises due to rare-earth $s$-orbital, rare-earth $p$ + B $p$ and B
$p$-orbitals while the continuum arises due to hybridized B $p$, rare-earth $d$
orbitals. Upon inclusion of SOC the peak arising due to rare-earth $p$-orbitals
gets split into two peaks corresponding to $j=0.5$ and $j=1.5$ configurations.
In case of $\textrm{LaB}_{4}$, in the presence of SOC, spin-split $4f$ orbitals
contributes to density of states at the Fermi level while the density of states
at the Fermi level largely remains unaffected for all other materials under
consideration.",2208.08381v1
2022-12-26,Chiral spin liquid state of strongly interacting bosons with a moat dispersion: a Monte Carlo simulation,"We consider a system of strongly interacting bosons in two dimensions with
moat band dispersion which supports an infinitely degenerate energy minimum
along a closed contour in the Brillouin zone. The system has been theoretically
predicted to stabilize a chiral spin liquid (CSL) ground state. In the
thermodynamic limit and vanishing densities, $n\rightarrow 0$, chemical
potential, $\mu$, of the uniform CSL state was shown to scale with $n$ as
$\mu\sim n^2\log ^2n$. Here we perform a Monte Carlo simulation to find the
parametric window for particle density, $n \lesssim \frac{k^2_0}{82 \pi}$,
where $k_0$ is the linear size of the moat (the radius for a circular moat),
for which the scaling $\sim n^2\log ^2n$ in the equation of state of the
homogeneous CSL is preserved. We variationally show that the uniform CSL state
is favorable in an interval beyond the obtained scale and present a schematic
phase diagram for the system. Our results offer some density estimates for
observing the low-density behavior of CSL in time-of-flight experiments with a
recently Floquet-engineered moat band system of ultracold atoms in Phys. Rev.
Lett. 128, 213401 (2022), and for the recent experiments on emergent excitonic
topological order in imbalanced electron-hole bilayers.",2212.12988v2
2023-12-21,Pattern formation in charge density wave states after a quantum quench,"We study post-quench dynamics of charge-density-wave (CDW) order in the
square-lattice $t$-$V$ model. The ground state of this system at half-filling
is characterized by a checkerboard modulation of particle density. A
generalized self-consistent mean-field method, based on the time-dependent
variational principle, is employed to describe the dynamical evolution of the
CDW states. Assuming a homogeneous CDW order throughout the quench process, the
time-dependent mean-field approach is reduced to the Anderson pseudospin
method. Quench simulations based on the Bloch equation for pseudospins produce
three canonical behaviors of order-parameter dynamics: phase-locked persistent
oscillation, Landau-damped oscillation, and dynamical vanishing of the CDW
order. We further develop an efficient real-space von Neumann equation method
to incorporate dynamical inhomogeneity into simulations of quantum quenches.
Our large-scale simulations uncover complex pattern formations in the
post-quench CDW states, especially in the strong quench regime. The emergent
spatial textures are characterized by super density modulations on top of the
short-period checkerboard CDW order. Our demonstration of pattern formation in
quenched CDW states, described by a simple broken $Z_2$ symmetry, underscores
the importance of dynamical inhomogeneity in quantum quenches of many-body
systems with more complex orders.",2312.13727v1
2000-02-10,Neutron Star Structure and the Equation of State,"The structure of neutron stars is considered from theoretical and
observational perspectives. We demonstrate an important aspect of neutron star
structure: the neutron star radius is primarily determined by the behavior of
the pressure of matter in the vicinity of nuclear matter equilibrium density.
In the event that extreme softening does not occur at these densities, the
radius is virtually independent of the mass and is determined by the magnitude
of the pressure. For equations of state with extreme softening, or those that
are self-bound, the radius is more sensitive to the mass. Our results show that
in the absence of extreme softening, a measurement of the radius of a neutron
star more accurate than about 1 km will usefully constrain the equation of
state. We also show that the pressure near nuclear matter density is primarily
a function of the density dependence of the nuclear symmetry energy, while the
nuclear incompressibility and skewness parameters play secondary roles.
  In addition, we show that the moment of inertia and the binding energy of
neutron stars, for a large class of equations of state, are nearly universal
functions of the star's compactness. These features can be understood by
considering two analytic, yet realistic, solutions of Einstein's equations,
due, respectively, to Buchdahl and Tolman. We deduce useful approximations for
the fraction of the moment of inertia residing in the crust, which is a
function of the stellar compactness and, in addition, the presssure at the
core-crust interface.",0002232v1
2012-02-20,Matrix representation of knots and folds: I,"This report presents a unified treatment of the density of states for the
knots and folds of polymer chains. The physical realization of such systems
ranges from DNA molecules to the microscopic configurations of space-time.",1202.4400v2
2020-09-10,How Political is the Spread of COVID-19 in the United States? An Analysis using Transportation and Weather Data,"We investigate the difference in the spread of COVID-19 between the states
won by Donald Trump (Red) and the states won by Hillary Clinton (Blue) in the
2016 presidential election, by mining transportation patterns of US residents
from March 2020 to July 2020. To ensure a fair comparison, we first use a
K-means clustering method to group the 50 states into five clusters according
to their population, area and population density. We then characterize daily
transportation patterns of the residents of different states using the mean
percentage of residents traveling and the number of trips per person. For each
state, we study the correlations between travel patterns and infection rate for
a 2-month period before and after the official states reopening dates. We
observe that during the lock-down, Red and Blue states both displayed strong
positive correlations between their travel patterns and infection rates.
However, after states reopened we find that Red states had higher
travel-infection correlations than Blue states in all five state clusters. We
find that the residents of both Red and Blue states displayed similar travel
patterns during the period post the reopening of states, leading us to conclude
that, on average, the residents in Red states might be mobilizing less safely
than the residents in Blue states. Furthermore, we use temperature data to
attempt to explain the difference in the way residents travel and practice
safety measures.",2009.04612v1
1996-02-22,Entropy Perturbations due to Cosmic Strings,"We examine variations in the equation of state of the cosmic string portion
of the cosmological fluid which lead to perturbations of the background matter
density. These fluctuations in the equation of state are due to variations in
the local density of cosmic string loops and gravitational radiation.
Constructing a crude model of the distribution of entropy perturbations, we
obtain the resulting fluctuation spectrum using a gauge-invariant formalism. We
compute the resulting cosmic microwave background anisotropy, and estimate the
effect of these perturbations on the cosmic string structure formation
scenario.",9602116v1
2000-02-05,Modeling of Tunneling Spectroscopy in HTSC,"The tunneling density of states of HTSC is calculated taking into account
tight binding band structure, group velocity, and tunneling directionality for
s-wave and d-wave gap symmetry. The characteristic density of states has
quasiparticle peaks' asymmetry, flat s-wave and cusplike d-wave case subgap
behavior, and asymmetric background. We consider that the underlying asymmetry
of the conductance peaks is primarily due to the features of quasiparticle
energy spectrum, and the d-wave symmetry enhances the degree of the peaks'
asymmetry. Increasing of the lifetime broadening factor changes the degree of
tunneling conductance peaks' asymmetry, and leads to the confluence of the
quasiparticle and van Hove singularity peaks.",0002077v1
2000-07-26,Quasi-Particle density of states of disordered d-wave superconductors,"We present a numerical study of the quasi-particle density of states
  (DoS) of two-dimensional d-wave superconductors in the presence of
  smooth disorder. We find power law scaling of the DoS with an
  exponent depending on the strength of the disorder and the
  superconducting order parameter in quantitative agreement with the
  theory of Nersesyan et al. (Phys.Rev.Lett. 72,
  2628 (1994)). For strong disorder a transition to a constant DoS
  occurs. Our results are in contrast to the case of short-ranged
  disorder.",0007413v1
2003-10-07,"Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry","Employing the chiral Unitary Ensemble of random matrices we calculate the
probability distribution of the local density of states for zero-dimensional
(""quantum chaotic"") two-sublattice systems at the point of chiral symmetry E=0
and in the presence of uniform absorption. The obtained result can be used to
find the distributions of the reflection coefficent and of the Wigner time
delay for such systems.",0310149v1
2005-10-25,Resonant peak in the density of states in the normal metal / diffusive ferromagnet / superconductor junctions,"The conditions for the formation of zero-energy peak in the density of states
(DOS) in the normal metal / insulator / diffusive ferromagnet / insulator /
s-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel
equations. The DOS of the DF is calculated in various regimes for different
magnitudes of the resistance, Thouless energy and the exchange field of the DF,
as well as for various resistances of the insulating barriers. The conditions
for the DOS peak are formulated for the cases of weak proximity effect (large
resistance of the DF/S interface) and strong proximity effect (small resistance
of the DF/S interface).",0510657v1
2006-12-06,Determination of density of states of thin high-$T_c$ films by FET type microstructures,"A simple electronic experiment with a field effect transistor type
microstructure is suggested. The thin superconductor layer is the source-drain
channel of the layered structure where an AC current is applied. It is
necessary to measure the second harmonic of the source-gate voltage and third
harmonic of the source-drain voltage. The electronic measurement can give the
logarithmic derivative of the density of states which is an important parameter
for fitting of parameters of the band structures.",0612169v1
2005-10-14,Control of mixed-state quantum systems by a train of short pulses,"A density matrix approach is developped for the control of a mixed-state
quantum system using a time-dependent external field such as a train of pulses.
This leads to the definition of a target density matrix constructed in a
reduced Hilbert space as a specific combination of the eigenvectors of a given
observable through weighting factors related with the initial statistics of the
system. A train of pulses is considered as a possible strategy to reach this
target. An illustration is given by considering the laser control of molecular
alignment / orientation in thermal equilibrium.",0510114v1
2008-10-13,Approximate forms of the density of states,"We compare MC calculations of the density of states in SU(2) pure gauge
theory with the weak and strong coupling expansions. Surprisingly, the range of
validity of the two approximations overlap significantly, however the large
order behavior of both expansions appear to be similar to the corresponding
expansions of the plaquette. We discuss the implications for the calculation of
the Fisher's zeros of the partition function.",0810.2252v1
2009-04-08,Tailoring the local density of states of non-radiative field at the surface of nanolayered materials,"The ability to artificially grow in a controllable manner at nanoscale, from
modern deposition techniques, complex structural configurations made with
metallic, polar and semiconductors materials raises today the issue of the
""best"" achievable inner structure to tailor the near-field properties of a
nanostructured medium. In the present work we make a step towards the rational
design of these materials by reporting numerical experimentations demonstrating
the possibility of identifying structural configurations of layered
metallodielectric media specifically designed to control the electromagnetic
density of states in the close vicinity of their surface. These results could
find broad applications in near-field technologies.",0904.1285v1
2009-11-19,Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory,"The role of the discontinuity of the exchange-correlation potential of
density functional theory is studied in the context of electron transport and
shown to be intimately related to Coulomb blockade. By following the time
evolution of an interacting nanojunction attached to biased leads, we find
that, instead of evolving to a steady state, the system reaches a dynamical
state characterized by correlation-induced current oscillations. Our results
establish a dynamical picture of Coulomb blockade manifesting itself as a
periodic sequence of charging and discharging of the nanostructure.",0911.3870v2
2010-02-16,Astrophysical Measurement of the Equation of State of Neutron Star Matter,"We present the first astrophysical measurement of the pressure of cold matter
above nuclear saturation density, based on recently determined masses and radii
of three neutron stars. The pressure at higher densities are below the
predictions of equations of state that account only for nucleonic degrees of
freedom, and thus present a challenge to the microscopic theory of neutron star
matter.",1002.3153v2
2010-04-09,Spin and Charge Currents in SNS Josephson Junction with f-wave Pairing Symmetry,"We study transport properties and also local density of states in a clean
superconductor-normal metal-superconductor Josephson junction with triplet
f-wave superconductors based on the Eilenberger equation. Effects of thickness
of normal metal and misorientation between gap vector of superconductors on the
spin and charge currents are investigated. Spin current, which stems from the
misalignment of d-vectors, in the absence of charge current for some values of
phase difference between superconductors is found. We also find unconventional
behavior of the spin current associated with 0-pitransition. The misalignment
of d-vectors also gives rise to a zero energy peak in the density of states in
the normal metal.",1004.1530v1
2012-08-20,Disordered two-dimensional electron systems with chiral symmetry,"We review the results of our recent numerical investigations on the
electronic properties of disordered two dimensional systems with chiral
unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular
interest is the behavior of the density of states and the logarithmic scaling
of the smallest Lyapunov exponents in the vicinity of the chiral quantum
critical point in the band center at E=0. The observed peaks or depressions in
the density of states, the distribution of the critical conductances, and the
possible non-universality of the critical exponents for certain chiral unitary
models are discussed.",1208.3934v2
2013-02-14,Spectra of Random Operators with absolutely continuous Integrated Density of States,"The structure of the spectrum of random operators is studied. It is shown
that if the density of states measure of some subsets of the spectrum is zero,
then these subsets are empty. In particular follows that absolute continuity of
the IDS implies singular spectra of ergodic operators is either empty or of
positive measure. Our results apply to Anderson and alloy type models,
perturbed Landau Hamiltonians, almost periodic potentials and models which are
not ergodic.",1302.3296v1
2018-05-21,Exact Determination of Moments for Density of States in Multidimensional Configuration Space,"For classical discrete systems on periodic lattice under constant composition
x, we derive explicit expression of any-order moments for configurational
density of states (CDOS). The derived expression clarifies that any-order
moments can always be given by linear combination of the first-order moments,
whose coefficient depends on geometric information of lattice. The expression
enables us to exactly determine system-size (N) dependence of moments, where
analytic representation in terms of N and x is explicitly given up to
lower-order generalized moment. Validity of the derived expression is confirmed
by exact estimation of moments for binary system bcc with finite system size,
considering all possible atomic configuration.",1805.07971v1
2024-03-10,Ergodic properties of one-dimensional incommensurate bilayer materials,"We review ergodic properties of one-dimensional incommensurate bilayer
materials, especially the convergence of the density of states in the
large-volume limit, from the perspective of the theory of ergodic Schr\""odinger
operators. More precisely, we first provide a short introduction to ergodic
Schr\""odinger operators as a unifying concept in spectral theory at a level
accessible for nonspecialists. We then present two natural tight-binding models
of incommensurate bilayer materials in one dimension and prove convergence of
their density of states measures in the large volume limit using ideas from the
theory of ergodic Schr\""odinger operators.",2403.06083v1
2020-04-16,Direct Astrophysical Tests of Chiral Effective Field Theory at Supranuclear Densities,"Recent observations of neutron stars with gravitational waves and X-ray
timing provide unprecedented access to the equation of state (EoS) of cold
dense matter at densities difficult to realize in terrestrial experiments. At
the same time, predictions for the EoS with reliable uncertainty estimates from
chiral effective field theory ($\chi$EFT) bound our theoretical ignorance. In
this work, we analyze astrophysical data using a nonparametric representation
of the neutron-star EoS conditioned on $\chi$EFT to directly constrain the
underlying physical properties of the compact objects. We discuss how the data
alone constrain the EoS at high densities when we condition on $\chi$EFT at low
densities. We also demonstrate how to exploit astrophysical data to directly
test the predictions of $\chi$EFT for the EoS up to twice nuclear saturation
density, and estimate the density at which these predictions might break down.
We find that the existence of massive pulsars, gravitational waves from
GW170817, and NICER observations of PSR J0030+0451 favor $\chi$EFT predictions
for the EoS up to nuclear saturation density over a more agnostic analysis by
as much as a factor of 7 for the quantum Monte Carlo (QMC) calculations used in
this work. While $\chi$EFT predictions using QMC are fully consistent with
gravitational-wave data up to twice nuclear saturation density, NICER
observations suggest that the EoS stiffens relative to these predictions at
nuclear saturation density. Additionally, we marginalize over the uncertainty
in the density at which $\chi$EFT begins to break down, constraining the radius
of a $1.4\,M_\odot$ neutron star to $R_{1.4}=11.40^{+1.38}_{-1.04}$
($12.54^{+0.71}_{-0.63}$) km and the pressure at twice nuclear saturation
density to $p(2n_\mathrm{sat})=14.2^{+18.1}_{-8.4}$ ($28.7^{+15.3}_{-15.0}$)
MeV/fm$^3$ with massive pulsar and gravitational-wave (and NICER) data.",2004.07744v3
2008-01-22,Galaxy-cluster gas-density distributions of the Representative XMM-Newton Cluster Structure Survey (REXCESS),"We present a study of the structural and scaling properties of the gas
distributions in the intracluster medium (ICM) of 31 nearby (z < 0.2) clusters
observed with XMM-Newton, which together comprise the Representative XMM-Newton
Cluster Structure Survey (REXCESS). In contrast to previous studies, this
sample is unbiased with respect to cluster dynamical state, and it fully
samples the cluster X-ray luminosity function. The clusters cover a temperature
range of 2.0 -- 8.5 keV and possess a variety of morphologies. The sampling
strategy allows us to compare clusters with a wide range of central cooling
times on an equal footing. We present non-parametric gas-density profiles out
to distances ranging between 0.8 R_500 and 1.5 R_500. The central gas densities
differ greatly from system to system, with no clear correlation with system
temperature. At intermediate radii the scaled density profiles show much less
scatter, with a clear dependence on system temperature, consistent with the
presence of an entropy excess as suggested in previous literature. However, at
large scaled radii this dependence becomes weaker: clusters with kT > 3 keV
scale self-similarly, with no temperature dependence of gas-density
normalisation. We find some evidence of a correlation between dynamical state
and outer gas density slope, and between dynamical state and both central gas
normalisation and cooling time. We find no evidence of a significant bimodality
in the distributions of central density, density gradient, or cooling time.
Finally, we present the gas mass-temperature relation for the REXCESS sample,
which is consistent with the expectation of self-similar scaling modified by
the presence of an entropy excess in the inner regions of the cluster, and has
a logarithmic intrinsic scatter of ~10%.",0801.3430v3
2006-07-13,Neutron and Proton Transverse Emission Ratio Measurements and the Density Dependence of the Asymmetry Term of the Nuclear Equation of State,"Recent measurements of pre-equilibrium neutron and proton transverse emission
from (112,124)Sn+(112,124)Sn reactions at 50 MeV/A have been completed at the
National Superconducting Cyclotron Laboratory. Free nucleon transverse emission
ratios are compared to those of A=3 mirror nuclei. Comparisons are made to BUU
transport calculations and conclusions concerning the density dependence of the
asymmetry term of the nuclear equation-of-state at sub-nuclear densities are
made. The double-ratio of neutron-proton ratios between two reactions is
employed as a means of reducing first-order Coulomb effects and detector
efficiency effects. Comparison to BUU model predictions indicate a density
dependence of the asymmetry energy that is closer to a form in which the
asymmety energy increases as the square root of the density for the density
region studied. A coalescent-invariant analysis is introduced as a means of
reducing suggested difficulties with cluster emission in total nucleon
emission. Future experimentation is presented.",0607016v2
2021-05-11,A comprehensive DFT based insights into the physical properties of tetragonal Mo5PB2,"Tetragonal Mo5PB2 compound, a recently discovered superconductor, belongs to
technologically important class of materials. It is quite surprising to note
that a large number of physical properties of Mo5PB2, including elastic
properties and their anisotropy, acoustic behavior, electronic (charge density
distribution, electron density difference), thermo-physical, bonding
characteristics, and optical properties have not been carried out at all. In
the present work we have explored all these properties in details for the first
time with density functional theory based first-principles method. Mo5PB2 is
found to be a mechanically stable, elastically anisotropic compound with
ductile character. Moreover, the chemical bonding is interpreted by calculating
the electronic energy density of states, electron density distribution, elastic
properties and Mulliken bond population analysis. Mo5PB2 has a combination of
mainly ionic, metallic, and some covalent bonding characteristics. The compound
possesses high level of machinability. The band structure along with a large
electronic density of states at the Fermi level reveals metallic character.
Calculated values of different thermal parameters of Mo5PB2 are closely related
to the elastic properties. The energy dependent optical parameters show close
assent to the underlying electronic band structure. The optical absorption and
reflectivity spectra and the low energy index of refraction of Mo5PB2 show that
the compound holds promise to be used in optoelectronic device sector. Unlike
the notable anisotropy found in elastic, mechanical properties and minimum
thermal conductivity, the optical parameters are found to be almost isotropic
with respect to the polarization direction of the incident electric field.",2105.04786v1
2018-05-28,On The Peierls Interpretation of Quantum Mechanics,"The brief works of Peierls on the role of the observer in quantum mechanics
are examined, interpreted and expanded to widen accessibility and understanding
of these works. The approach followed here is very much in the spirit adopted
by Peierls who eschewed a `rigorous axiomatic' and aimed at using `logic at the
level of the working physicist'. The fundamental tenet of his work is that the
wavefunction or density matrix represents the knowledge of an observer and that
two observers of the same system may well have different knowledge and will use
different density matrices to describe it. Essential to the understanding of
Peierls's approach is the demonstration given here that the density matrix
generally can be expressed entirely in terms of probabilities of observable
outcomes and that such probabilities are subjective in the first instance.The
process by which the knowledge of two observers may be combined is discussed in
detail for some simple cases and, by using Bayes's theorem, the progress to a
common understanding of the correct density matrix for a given situation
demonstrated. Peierls gave a criterion to ensure that the amalgamation of data
from two observers can never lead to violation of the uncertainty principle :
that the density matrices of two observers must commute. It is pointed out that
it is essential that the density matrices of two observers commute under all
circumstances no matter how inaccurate or even fanciful the data or beliefs
used to construct them. Once this is appreciated it can be shown that Peierls's
density matrix commutation criterion is fully equivalent to the standard result
in quantum mechanics that two observables must commute if they are to be known
precisely and simultaneously,but now extended to imperfectly known mixed states
rather than a single eigenstate.",1805.11162v1
2018-02-21,Collective Dynamics of Self-propelled Semiflexible Filaments,"The collective behavior of active semiflexible filaments is studied with a
model of tangentially driven self-propelled worm-like chains. The combination
of excluded-volume interactions and self-propulsion leads to several distinct
dynamic phases as a function of bending rigidity, activity, and aspect ratio of
individual filaments. We consider first the case of intermediate filament
density. For high-aspect-ratio filaments, we identify a transition with
increasing propulsion from a state of free-swimming filaments to a state of
spiraled filaments with nearly frozen translational motion. For lower aspect
ratios, this gas-of-spirals phase is suppressed with growing density due to
filament collisions; instead, filaments form clusters similar to self-propelled
rods, as activity increases. Finite bending rigidity strongly effects the
dynamics and phase behavior. Flexible filaments form small and transient
clusters, while stiffer filaments organize into giant clusters, similarly as
self-propelled rods, but with a reentrant phase behavior from giant to smaller
clusters as activity becomes large enough to bend the filaments. For high
filament densities, we identify a nearly frozen jamming state at low
activities, a nematic laning state at intermediate activities, and an
active-turbulence state at high activities. The latter state is characterized
by a power-law decay of the energy spectrum as a function of wave number. The
resulting phase diagrams encapsulate tunable non-equilibrium steady states that
can be used in the organization of living matter.",1802.07480v1
1995-04-05,"Pseudospin SU(2) Symmetry Breaking, Charge Density Wave and Superconductivity in the Hubbard Model","In this paper, we discuss physical consequences of pseudospin SU(2) symmetry
breaking in the negative-U Hubbard model at half-filling. If pseudospin
symmetry is spontaneously broken while its unique subgroup U(1) remains
invariant, it will lead to the charge density wave (CDW) ground state.
Furthermore, if the U(1) symmetry is also broken, the ground state will have
the off-diagonal long range order (ODLRO), signaling a superconductor. In this
case, CDW and superconductivity coexist to form a supersolid. Finally, we show
that CDW suppresses, but does not destroy superconductivity.",9504019v1
2001-07-06,Pressure-induced phase transitions of halogen-bridged binuclear metal complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O,"Recent contrasting observations for halogen (X)-bridged binuclear platinum
complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O, that is, pressure-induced Peierls and
reverse Peierls instabilities, are explained by finite-temperature Hartree-Fock
calculations. It is demonstrated that increasing pressure transforms the
initial charge-polarization state into a charge-density-wave state at high
temperatures, whereas the charge-density-wave state oppositely declines with
increasing pressure at low temperatures. We further predict that
higher-pressure experiments should reveal successive phase transitions around
room temperature.",0107128v1
2015-07-13,Continuous matrix product states solution for the mixing/demixing transition in one-dimensional quantum fields,"We solve the mixing-demixing transition in repulsive one-dimensional
bose-bose mixtures. This is done numerically by means of the continuous matrix
product states variational ansatz. We show that the effective low-energy
bosonization theory is able to detect the transition whenever the Luttinger
parameters are exactly computed. We further characterize the transition by
calculating the ground-state energy density, the field-field fluctuations and
the density correlations.",1507.03613v1
2014-05-10,A density-matrix renormalization group Study of one-dimensional incommensurate quantum Frenkel-Kontorova model,"In this paper, the one-dimensional incommensurate quantum Frenkel-Kontorova
model is investigate by a density-matrix renormalization group algorithm.
Special attention is given to the entanglement and the ground state energy. The
energy gap between the ground state and the first excited is also calculated.
From all the numerical results, we have observed an obvious property changes
from the pinned state to the sliding one as the quantum fluctuation is
increased. But no expected quantum critical point can be justified by the
present data.",1405.2902v1
2009-03-31,The role of tap duration for the steady state density of vibrated granular media,"We revisit the problem of compaction of a column of granular matter exposed
to discrete taps. We accurately control the vertical motion of the column,
which allows us to vary the duration T and the amplitude A of single-cycle
sinusoidal taps independently. We find that the density of the material at the
reversible branch depends both on A and T. By comparing the densities on the
reversible branches obtained for a range of values of T, we find that we can
collapse all data when plotted as function of A/T, which scales similar to both
the liftoff velocity and the time of flight of the packing. We further show
that switching between states obtained for different A and T, but chosen such
that their densities on the reversible branches match, does not lead to
appreciable hysteresis. We conclude that the appropriate control parameter for
sinusoidal tapping is not the peak acceleration \Gamma \sim A/T^2, as is
usually assumed, but rather \Gamma T \sim A/T.",0903.5499v3
2013-01-15,Products of Independent Quaternion Ginibre Matrices and their Correlation Functions,"We discuss the product of independent induced quaternion ($\beta=4$) Ginibre
matrices, and the eigenvalue correlations of this product matrix. The joint
probability density function for the eigenvalues of the product matrix is shown
to be identical to that of a single Ginibre matrix, but with a more complicated
weight function. We find the skew-orthogonal polynomials corresponding to the
weight function of the product matrix, and use the method of skew-orthogonal
polynomials to compute the eigenvalue correlation functions for product
matrices of finite size. The radial behavior of the density of states is
studied in the limit of large matrices, and the macroscopic density is
discussed. The microscopic limit at the origin, at the edge(s) and in the bulk
is also discussed for the radial behavior of the density of states.",1301.3343v2
2016-02-02,The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction,"We investigate the ground state density distributions of anti-ferromagnetic
spin-1 Bose gases in one dimensional harmonic potential in the full interacting
regimes. The ground state is obtained by diagonalizing the Hamiltonian in the
Hilbert space composed of the lowest eigenstates of noninteracting Bose gas and
spin components. The study reveals that in the situation of weak spin-dependent
interaction the total density profiles evolve from Gaussian-like distribution
to a Fermi-like shell structure of $N$ peaks with the increasing of
spin-independent interaction. While the increasing spin-exchange interaction
always weaken the fermionization of density distribution such that the total
density profiles show shell structure of less peaks and even show single peak
structure in the limit of strong spin-exchange interaction. The weakening of
fermionization results from the formation of composite atoms induced by
spin-exchange interaction. It is also shown that phase separation occurs for
the spinor Bose gas with weak spin-exchange interaction, meanwhile strong
spin-independent interaction.",1602.00790v1
2020-09-18,Remarks on relativistic scalar models with chemical potential,"We discuss selected aspects of classical relativistic scalar field theories
with nonzero chemical potential. First, we offer a review of classical field
theory at nonzero density within the Lagrangian formalism. The aspects covered
include the question of equivalence of descriptions of finite-density states
using a chemical potential or time-dependent field configurations, the choice
of Hamiltonian whose minimization yields the finite-density equilibrium state,
and the issue of breaking of Lorentz invariance. Second, we demonstrate how the
low-energy effective field theory for Nambu-Goldstone (NG) modes arising from
the spontaneous breakdown of global internal symmetries can be worked out
explicitly by integrating out the heavy (Higgs) fields. This makes it possible
to analyze the spectrum of NG modes and their interactions without having to
deal with mixing of NG and Higgs fields, ubiquitous in the linear-sigma-model
description of spontaneous symmetry breaking.",2009.08895v1
2021-01-08,Implications of PREX-II on the equation of state of neutron-rich matter,"Laboratory experiments sensitive to the equation of state of neutron rich
matter in the vicinity of nuclear saturation density provide the first rung in
a ""density ladder"" that connects terrestrial experiments to astronomical
observations. In this context, the neutron skin thickness of 208Pb (Rskin)
provides a stringent laboratory constraint on the density dependence of the
symmetry energy. In turn, an improved value of Rskin has been reported recently
by the PREX collaboration. Exploiting the strong correlation between Rskin and
the slope of the symmetry energy L within a specific class of relativistic
energy density functionals, we report a value of L=(106 +/- 37)MeV -- that
systematically overestimates current limits based on both theoretical
approaches and experimental measurements. The impact of such a stiff symmetry
energy on some critical neutron-star observables is also examined.",2101.03193v3
2023-02-02,Studies of the equation-of-state of nuclear matter by heavy-ion collisions at intermediate energy in the multi-messenger era,"The study of the equation-of-state (EoS) describing the properties of nuclear
matter away from the normal conditions is a relevant and intriguing topic of
modern nuclear physics. The last decades have witnessed a substantial
experimental progress in derivation of the symmetric matter term of the EoS and
of the so-called symmetry energy for the asymmetric matter, especially at
densities below the saturation point. But it is only in recent years that the
opening of the multi-messenger astronomy era, triggered by detection of
gravitational waves due to the neutron star mergers, has renewed and enlarged
the interest in high-density EoS, being the main ingredient for determining the
structure and properties of neutron stars. In this paper we review our
knowledge obtained from heavy-ion collisions up to the 1 GeV/nucleon regime, on
the EoS above nuclear saturation density. Special emphasis is given on the
still few results on symmetry energy at high densities and their
interconnections with multi-messenger astronomy findings.",2302.01453v1
2023-10-30,Density Estimation for Entry Guidance Problems using Deep Learning,"This work presents a deep-learning approach to estimate atmospheric density
profiles for use in planetary entry guidance problems. A long short-term memory
(LSTM) neural network is trained to learn the mapping between measurements
available onboard an entry vehicle and the density profile through which it is
flying. Measurements include the spherical state representation, Cartesian
sensed acceleration components, and a surface-pressure measurement. Training
data for the network is initially generated by performing a Monte Carlo
analysis of an entry mission at Mars using the fully numerical
predictor-corrector guidance (FNPEG) algorithm that utilizes an exponential
density model, while the truth density profiles are sampled from MarsGRAM. A
curriculum learning procedure is developed to refine the LSTM network's
predictions for integration within the FNPEG algorithm. The trained LSTM is
capable of both predicting the density profile through which the vehicle will
fly and reconstructing the density profile through which it has already flown.
The performance of the FNPEG algorithm is assessed for three different density
estimation techniques: an exponential model, an exponential model augmented
with a first-order fading-memory filter, and the LSTM network. Results
demonstrate that using the LSTM model results in superior terminal accuracy
compared to the other two techniques when considering both noisy and noiseless
measurements.",2310.19684v1
2003-07-08,Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix,"In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that
the many-particle eigenvalues and eigenstates of the many-body density matrix
$\rho_B$ of a block of $B$ sites cut out from an infinite chain of
noninteracting spinless fermions can all be constructed out of the one-particle
eigenvalues and one-particle eigenstates respectively. In this paper we
developed a statistical-mechanical analogy between the density matrix
eigenstates and the many-body states of a system of noninteracting fermions.
Each density matrix eigenstate corresponds to a particular set of occupation of
single-particle pseudo-energy levels, and the density matrix eigenstate with
the largest weight, having the structure of a Fermi sea ground state,
unambiguously defines a pseudo-Fermi level. We then outlined the main ideas
behind an operator-based truncation of the density matrix eigenstates, where
single-particle pseudo-energy levels far away from the pseudo-Fermi level are
removed as degrees of freedom. We report numerical evidence for scaling
behaviours in the single-particle pseudo-energy spectrum for different block
sizes $B$ and different filling fractions $\nbar$. With the aid of these
scaling relations, which tells us that the block size $B$ plays the role of an
inverse temperature in the statistical-mechanical description of the density
matrix eigenstates and eigenvalues, we looked into the performance of our
operator-based truncation scheme in minimizing the discarded density matrix
weight and the error in calculating the dispersion relation for elementary
excitations. This performance was compared against that of the traditional
density matrix-based truncation scheme, as well as against a operator-based
plane wave truncation scheme, and found to be very satisfactory.",0307172v2
2014-02-13,Inhomogeneous quasi-stationary state of dense fluid of inelastic hard spheres,"We study closed dense collections of hard spheres that collide inelastically
with constant coefficient of normal restitution. We find inhomogeneous states
(IS) where the density profile is spatially non-uniform but constant in time.
The states are exact solutions of non-linear partial differential equations
that describe the coupled distributions of density and temperature when
inelastic losses of energy per collision are small. The derivation is performed
without modelling the equations' coefficients that are unknown in the dense
limit (such as the equation of state), using only their scaling form specific
for hard spheres. The IS is exact non-linear state of this many-body system. It
captures a fundamental property of inelastic collections of particles: the
possibility of preserving non-uniform temperature via the interplay of
inelastic cooling and heat conduction, generalizing previous results in the
dilute case. We perform numerical simulations to demonstrate that arbitrary
initial state evolves to the IS in the limit of long times where the container
has the geometry of the channel. The evolution is like gas-liquid transition.
The liquid condenses in a vanishing part of the total volume but takes most of
the mass of the system. However, the gaseous phase, which mass grows only
logarithmically with the system size, is relevant because its fast particles
carry most of the energy of the system. Remarkably, the system self-organizes
to dissipate no energy: the inelastic decay of energy is a power-law
$[1+t/t_c]^{-2}$ where $t_c$ diverges in the thermodynamic limit. This behavior
is caused by unusual spatial distribution of particles: on approach to one of
the container's walls the density grows inversely with the distance. We discuss
the relation of our results to the recently proposed finite-time singularity in
other container's geometries.",1402.4149v1
1995-09-27,An exchange-correlation energy for a two-dimensional electron gas in a magnetic field,"We present the results of a variational Monte Carlo calculation of the
exchange-correlation energy for a spin-polarized two-dimensional electron gas
in a perpendicular magnetic field. These energies are a necessary input to the
recently developed current-density functional theory. Landau-level mixing is
included in a variational manner, which gives the energy at finite density at
finite field, in contrast to previous approaches. Results are presented for the
exchange-correlation energy and excited-state gap at $\nu =$ 1/7, 1/5, 1/3, 1,
and 2. We parameterize the results as a function of $r_s$ and $\nu$ in a form
convenient for current-density functional calculations.",9509170v1
1998-05-27,Unified Treatment of Asymptotic van der Waals Forces,"In a framework for long-range density-functional theory we present a unified
full-field treatment of the asymptotic van der Waals interaction for atoms,
molecules, surfaces, and other objects. The only input needed consists of the
electron densities of the interacting fragments and the static polarizability
or the static image plane, which can be easily evaluated in a ground-state
density-functional calculation for each fragment. Results for separated atoms,
molecules, and for atoms/molecules outside surfaces are in agreement with those
of other, more elaborate, calculations.",9805352v1
1999-09-21,Pauli and orbital effects of magnetic field on charge density waves,"Taking into account both Pauli and orbital effects of external magnetic field
we compute the mean field phase diagram for charge density waves in
quasi-one-dimensional electronic systems. The magnetic field can cause
transitions to CDW states with two types of the shifts of wave vector from its
zero-field value. It can also stabilize the field-induced charge density wave.
Furthermore, the critical temperature shows peaks at a new kind of magic
angles.",9909303v1
2000-09-28,Density of a gas of spin polarized fermions in a magnetic field,"For a fermion gas with equally spaced energy levels that is subjected to a
magnetic field, the particle density is calculated. The derivation is based on
the path integral approach for identical particles, in combination with the
inversion techniques for the generating function of the static response
functions. Explicit results are presented for the ground state density as a
function of the magnetic field with a number of particles ranging from 1 to 45.",0009442v1
2001-03-01,Global Equation of State of two-dimensional hard sphere systems,"Hard sphere systems in two dimensions are examined for arbitrary density.
Simulation results are compared to the theoretical predictions for both the low
and the high density limit, where the system is either disordered or ordered,
respectively. The pressure in the system increases with the density, except for
an intermediate range of volume fractions $0.65 \le \nu \le 0.75$, where a
disorder-order phase transition occurs. The proposed {\em global equation of
state} (which describes the pressure {\em for all densities}) is applied to the
situation of an extremely dense hard sphere gas in a gravitational field and
shows reasonable agreement with both experimental and numerical data.",0103014v1
2001-04-30,Superconductivity in MgB2 and TaB2: A Full-Potential Electronic Structure Comparison,"We present a comparison of electronic structure of MgB2 and TaB2, the two new
superconductors, as well as VB2, calculated using full-potential, density-
functional-based methods in P6/mmm crystal structure. Our results, described in
terms of (i) density of states (DOS), (ii) band-structure, and (iii) the DOS
and the electronic charge density in a small energy window around the Fermi
energy EF. In particular, the charge density around EF in MgB2 and TaB2 show
striking similarity as far as the B plane is concerned. A comparison of their
band-structures, coupled with l-character analysis, indicates that TaB2 has
substantially more p-character than VB2 along A-L and H-A directions near EF.",0104580v1
2001-09-14,Coulomb Effects in Spectral Density and Transverse Conductivity of Layered Metals,"Renormalization of the Coulomb interaction in layered metals results in a
strongly anisotropic plasma mode with low frequencies for small components of
wave vector in the in-plane direction. Interaction of electrons with this mode
was found to lead to an incoherent contribution to the electron spectral
density which spreads up to large energies. In the superconducting state this
reproduces the peak-dip-hump feature similar to that observed in layered
high-T$_c$ superconductors. The incoherent part of the spectral density and
plasmon-assisted electron transitions provide mechanisms for nearly linear
conductivity in the stack direction at large voltages or frequencies.",0109264v1
2003-11-12,Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian,"In this article, we present a set of hierarchy Bloch equations for the
reduced density operators in either canonical or grand canonical ensembles in
the occupation number representation. They provide a convenient tool for
studying the equilibrium quantum statistical mechanics for some model systems.
As an example of their applications, we solve the equations for the model
system with a pairing Hamiltonian. With the aid of its symplectic group
symmetry, we obtain the statistical reduced density matrices with different
orders. As a special instance for the solutions, we also get the reduced
density matrices of the ground state for a superconductor.",0311288v1
2005-02-15,Effects of nanoscale spatial inhomogeneity in strongly correlated systems,"We calculate ground-state energies and density distributions of Hubbard
superlattices characterized by periodic modulations of the on-site interaction
and the on-site potential. Both density-matrix renormalization group and
density-functional methods are employed and compared. We find that small
variations in the on-site potential $v_i$ can simulate, cancel, or even
overcompensate effects due to much larger variations in the on-site interaction
$U_i$. Our findings highlight the importance of nanoscale spatial inhomogeneity
in strongly correlated systems, and call for reexamination of model
calculations assuming spatial homogeneity.",0502355v1
2000-08-15,The strong coupling and the gluon density from jets in DIS,"The extraction of the parameters of perturbative QCD is one of the main tasks
for the HERA experiments. Studies on the structure of the hadronic final states
with jet algorithms give a direct handle on the parton density functions and
the strong coupling strength over a wide kinematic range. In this article, new
results of the H1 and ZEUS collaborations for the strong coupling and the gluon
density in the proton are presented.",0008027v1
1997-07-30,High-density nuclear matter with nonlocal confining solitons,"An infinite system of nonlocal, individually confining solitons is considered
as a model of high-density nuclear matter. The soliton-lattice problem is
discussed in the Wigner-Seitz approximation. The cell size is varied to study
the density dependence of physical quantities of interest. A transition to a
system where quarks can migrate between solitons is found. We argue that this
signals quark deconfinement. The model is applied to the calculation of
selected in-medium properties.",9707054v1
2005-12-27,Isovector Channel Role of Relativistic Mean Field Models in the Neutrino Mean Free Path,"An improvement in the treatment of the isovector channel of relativistic mean
field (RMF) models based on effective field theory (E-RMF) is suggested, by
adding an isovector scalar (delta) meson and using a similar procedure to the
one used by Horowitz and Piekarewicz to adjust the isovector-vector channel in
order to achieve a softer density dependent symmetry energy of the nuclear
matter at high density. Their effects on the equation of state (EOS) at high
density and on the neutrino mean free path (NMFP) in neutron stars are
discussed.",0512093v1
2006-03-11,Shapes of the Nucleon,"Previously defined spin-dependent quark densities that are matrix elements of
specific density operators in proton states of definite spin-polarization
generally have an infinite variety of non-spherical shapes. The present
application is concerned with both charge and matter densities. We show that
the Gross & Agbakpe model nucleon harbors an interesting variety of
non-spherical shapes.",0603035v2
2000-01-14,Positive Maps Which Are Not Completely Positive,"The concept of the {\em half density matrix} is proposed. It unifies the
quantum states which are described by density matrices and physical processes
which are described by completely positive maps. With the help of the
half-density-matrix representation of Hermitian linear map, we show that every
positive map which is not completely positive is a {\em difference} of two
completely positive maps. A necessary and sufficient condition for a positive
map which is not completely positive is also presented, which is illustrated by
some examples.",0001053v1
2009-06-04,Polarization Suppression and Nonmonotonic Local Two-Body Correlations in the Two-Component Bose Gas in One Dimension,"We study the interplay of quantum statistics, strong interactions and finite
temperatures in the two-component (spinor) Bose gas with repulsive
delta-function interactions in one dimension. Using the Thermodynamic Bethe
Ansatz, we obtain the equation of state, population densities and local density
correlation numerically as a function of all physical parameters (interaction,
temperature and chemical potentials), quantifying the full crossover between
low-temperature ferromagnetic and high-temperature unpolarized regimes. In
contrast to the single-component, Lieb-Liniger gas, nonmonotonic behaviour of
the local density correlation as a function of temperature is observed.",0906.0955v1
2010-03-10,Density wave instability in a 2D dipolar Fermi gas,"We consider a uniform dipolar Fermi gas in two-dimensions (2D) where the
dipole moments of fermions are aligned by an orientable external field. We
obtain the ground state of the gas in Hartree-Fock approximation and
investigate RPA stability against density fluctuations of finite momentum. It
is shown that the density wave instability takes place in a broad region where
the system is stable against collapse. We also find that the critical
temperature can be a significant fraction of Fermi temperature for a realistic
system of polar molecules.",1003.2029v1
2010-03-24,Exponential increase of energy level density in atoms: Th and Th II,"We present analytical estimates and numerical calculations showing that the
energy level density in open-shell atoms increases exponentially with increase
of excitation energy. As an example, we use the relativistic Hartree-Fock and
configuration interaction methods to calculate the density of states of Th and
Th II. The result is used to estimate the effect of electrons on the nuclear
transition which is considered for the use in a nuclear clock.",1003.4576v1
2011-06-09,Chirality and Orbital Order in Charge Density Waves,"We show that the recently observed chirality in the charge ordered phase of
TiSe2 can be understood as a form of orbital ordering. The microscopic
mechanism driving the transition between the novel chiral state and the
non-chiral charge density wave is discussed, and shown to be of a general form,
thus allowing for a broad class of materials to display this type of orbitally
ordered chiral charge density wave.",1106.1930v1
2011-06-14,Combination of many-body and density-functional theories,"A framework for developing new approximate electronic structure methods is
presented, in which the correlation energy of a many-electron system in the
ground state is computed as in the single-reference second-order many-body
perturbation theory but with the reference one-body Hamiltonian modified by
additional (generally non-local) potentials which are universal functionals of
the Hartree-Fock density. The existence of such functionals that reproduce the
exact correlation energy justifies the search for approximate models which may
overcome some important deficiencies of the traditional density-functional
methods and also perform better than the usual low-order wavefunction methods.",1106.2744v1
2011-09-28,On Variable Density Compressive Sampling,"We advocate an optimization procedure for variable density sampling in the
context of compressed sensing. In this perspective, we introduce a minimization
problem for the coherence between the sparsity and sensing bases, whose
solution provides an optimized sampling profile. This minimization problem is
solved with the use of convex optimization algorithms. We also propose a
refinement of our technique when prior information is available on the signal
support in the sparsity basis. The effectiveness of the method is confirmed by
numerical experiments. Our results also provide a theoretical underpinning to
state-of-the-art variable density Fourier sampling procedures used in magnetic
resonance imaging.",1109.6202v1
2012-05-18,Elasticity of Diamond at High Pressures and Temperatures,"We combine density functional theory within the local density approximation,
the quasiharmonic approximation, and vibrational density of states to calculate
single crystal elastic constants, and bulk and shear moduli of diamond at
simultaneous high pressures and temperatures in the ranges of 0-500 GPa and
0-4800 K. Comparison with experimental values at ambient pressure and high
temperature shows an excellent agreement for the first time with our
first-principles results validating our method. We show that the anisotropy
factor of diamond increases to 40% at high pressures and becomes temperature
independent.",1205.4227v1
2012-09-19,Holographic vector mesons in a hot and dense medium,"We investigate vector meson spectral functions at finite temperature and
density through the soft wall model, a bottom-up holographic approach to QCD.
We find narrow resonances at small values of the parameters, becoming broader
as temperature and density increase. We study dissociation of such states,
occurring when no peak can be distinguished in the spectral function. We also
find a decreasing of the mass of vector mesons at increasing temperature and
density. Finally, a discussion of these results is presented.",1209.4198v1
2013-05-02,Density Functional Theory for Superconductors with Particle-hole Asymmetric Electronic Structure,"To extend the applicability of density functional theory for superconductors
(SCDFT) to systems with significant particle-hole asymmetry, we construct a new
exchange-correlation kernel entering the gap equation. We show that the kernel
is numerically stable and does not diverge even in the low temperature limit.
Solving the gap equation for model systems with the present kernel analytically
and numerically, we find that the asymmetric component of electronic density of
states, which has not been considered with the previous kernel, systematically
decreases transition temperature (Tc). We present a case where the decrease of
Tc amounts to several tens of percent.",1305.0390v1
2015-03-10,Carrier statistics and quantum capacitance effects on mobility extraction in two-dimensional crystal semiconductor field-effect transistors,"In this work, the consequence of the high band-edge density of states on the
carrier statistics and quantum capacitance in transition metal dichalcogenide
two-dimensional semiconductor devices is explored. The study questions the
validity of commonly used expressions for extracting carrier densities and
field-effect mobilities from the transfer characteristics of transistors with
such channel materials. By comparison to experimental data, a new method for
the accurate extraction of carrier densities and mobilities is outlined. The
work thus highlights a fundamental difference between these materials and
traditional semiconductors that must be considered in future experimental
measurements.",1503.03015v1
2015-11-23,Critical current density and trapped field in HTS with asymmetric magnetization loops,"Applications of the extended critical state model are considered. The trapped
magnetic field, the penetration field and the field dependence of the critical
current density are analysed. The critical current density and the trapped
field in superconducting grains depend on the grain size. Asymmetry of the
hysteresis curves relative to the M = 0 axis is related to the scale of the
current circulation.",1511.07225v1
2017-08-21,Density profiles of two-component Bose-Einstein condensates interacting with a Laguerre-Gaussian Beam,"The density profiles of trapped two-component Bose-Einstein condensates (BEC)
and its microscopic interaction with Laguerre Gaussian (LG) beam are studied.
We consider the $^{87}$Rb BEC in two hyperfine spin components. The wavelength
of the LG beam is assumed to be comparable to the atomic de-Broglie wavelength.
Competitions between intra- and inter-component interactions produce
interesting density structures of the ground state of BEC. We demonstrate
vortex-antivortex interference and its dependence on the inter-component
interactions and Raman transitions.",1708.06170v3
2021-02-25,Transition Density of an Infinite-dimensional diffusion with the Jack Parameter,"From the Poisson-Dirichlet diffusions to the $Z$-measure diffusions, they all
have explicit transition densities. In this paper, we will show that the
transition densities of the $Z$-measure diffusions can also be expressed as a
mixture of a sequence of probability measures on the Thoma simplex. The
coefficients are still the transition probabilities of the Kingman coalescent
stopped at state $1$. This fact will be uncovered by a dual process method in a
special case where the $Z$-measure diffusions is established through up-down
chain in the Young graph.",2102.12681v3
2022-05-09,Empirically Equivalent Distributions in Ontological Models of Quantum Mechanics,"We consider ontological models of a quantum system, assuming that not all
probability distributions over the space $\Lambda$ of ontic states are
preparable, only those belonging to a certain set C. We assume further that
every POVM with a finite value space can be measured and that for every density
matrix there exists a distribution in C whose outcome statistics is given by
the density matrix. We show that this mapping from C to the set of density
matrices must be many-to-one, that is, that there must be empirically
indistinguishable distributions in C. This shows that there must be limitations
to knowledge in the sense of facts in nature that cannot be discovered
empirically.",2205.04331v1
1996-01-25,A Low-Density Closed Universe,"Matter with an equation of state $p=-\rho/3$ may arise in certain scalar
field theories, and the energy density of this matter decreases as $a^{-2}$
with the scale factor $a$ of the Universe. In this case, the Universe could be
closed but still have a nonrelativistic-matter density $\Omega_0<1$.
Furthermore, the cosmic microwave background could come from a
causally-connected region at the other side of the Universe. This model is
currently viable and might be tested by a host of forthcoming observations.",9601147v1
1998-03-02,Evolution of Hole and Spin Dynamics in High Temperature Superconductors within the Small Hole Density Limit of the t-J Model,"The evolution of hole and spin dynamics in high temperature superconductors
is studied within the self-consistent noncrossing approximation of the t-J
model in the small hole density limit. As the doping concentration is
increased, long-range electron correlations disappear rapidly and the
quasiparticle energy band becomes considerably narrow. At a small hole density
long-range antiferromagnetic order is destroyed leading to the inadequacy of
spin wave basis approximation near small wave vectors. Spin excitations near
the antiferromagnetic zone boundary are strongly renormalized and damped but
they are still well described within spin wave basis approximation.",9803016v1
2002-07-17,Density-Matrix functional theory of strongly-correlated lattice fermions,"A density functional theory (DFT) of lattice fermion models is presented,
which uses the single-particle density matrix gamma_{ij} as basic variable. A
simple, explicit approximation to the interaction-energy functional W[gamma] of
the Hubbard model is derived from exact dimer results, scaling properties of
W[gamma] and known limits. Systematic tests on the one-dimensional chain show a
remarkable agreement with theBethe-Ansatz exact solution for all interaction
regimes and band fillings. New results are obtained for the ground-state
energyand charge-excitation gap in two dimensions. A successful description of
strong electron correlations within DFT is achieved.",0207429v1
2004-09-01,Electronic structure of amorphous germanium disulfide via density functional molecular dynamics simulations,"Using density functional molecular dynamics simulations we study the
electronic properties of glassy g-GeS$_2$. We compute the electronic density of
states, which compares very well with XPS measurements, as well as the partial
EDOS and the inverse participation ratio. We show the electronic contour plots
corresponding to different structural environments, in order to determine the
nature of the covalent bonds between the atoms. We finally study the local
atomic charges, and analyze the impact of the local environment on the charge
transfers between the atoms. The broken chemical order inherent to amorphous
systems leads to locally charged zones when integrating the atomic charges up
to nearest-neighbor distances.",0409029v1
1994-10-24,An Exact Calculation of the Energy Density of Cosmological Gravitational Waves,"In this paper we calculate the Bogoliubov coefficients and the energy density
of the stochastic gravitational wave background for a universe that undergoes
inflation followed by radiation domination and matter domination, using a
formalism that gives the Bogoliubov coefficients as continous functions of
time. By making a reasonable assumption for the equation of state during
reheating, we obtain in a natural way the expected high frequency cutoff in the
spectral energy density.",9410033v1
2001-03-22,Density perturbations in an Universe dominated by the Chaplygin gas,"We study the fate of density perturbations in an Universe dominate by the
Chaplygin gas, which exhibit negative pressure. We show that it is possible to
obtain the value for the density contrast observed in large scale structure of
the Universe by fixing a free parameter in the equation of state of this gas.
The negative character of pressure must be significant only very recently.",0103083v1
1997-01-28,A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model,"A scaling hypothesis for the n-particle spectral densities of the O(3)
nonlinear sigma-model is described. It states that for large particle numbers
the n-particle spectral densities are ``self-similar'' in being basically
rescaled copies of a universal shape function. This can be viewed as a
2-dimensional, but non-perturbative analogue of the KNO scaling in QCD.
Promoted to a working hypothesis, it allows one to compute the two point
functions at ``all'' energy or length scales. In addition, the values of two
non-perturbative constants (needed for a parameter-free matching of the
perturbative and the non-perturbative regime) are determined exactly.",9701156v1
2004-05-26,Bounding quantities related to the packing density of 1(L+1)L...2,"We bound several quantities related to the packing density of the patterns
1(L+1)L...2. These bounds sharpen results of B\'ona, Sagan, and Vatter and give
a new proof of the packing density of these patterns, originally computed by
Stromquist in the case L=2 and by Price for larger L. We end with comments and
conjectures.",0405512v1
2006-02-13,Level density of a Fermi gas: average growth and fluctuations,"We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.",0602044v1
2007-04-20,Competing superfluid and density-wave ground-states of fermionic mixtures with mass imbalance in optical lattices,"We study the effect of mass imbalance on the phase diagram of a two-component
fermionic mixture with attractive interactions in optical lattices. Using
static and dynamical mean-field theories, we show that the pure superfluid
phase is stable for all couplings when the mass imbalance is smaller than a
limiting value. For larger imbalance, phase separation between a superfluid and
a charge-density wave takes place when the coupling exceeds a critical
strength. The harmonic trap induces a spatial segregation of the two phases,
with a rapid variation of the density at the boundary.",0704.2660v1
2008-04-15,Density dependence of symmetry free energy of hot nuclei,"The density and excitation energy dependence of symmetry energy and symmetry
free energy for finite nuclei are calculated microscopically in a
microcanonical framework taking into account thermal and expansion effects. A
finite-range momentum and density dependent two-body effective interaction is
employed for this purpose. The role of mass, isospin and equation of state
(EoS) on these quantities is also investigated; our calculated results are in
consonance with the available experimental data.",0804.2459v2
2009-07-27,Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas,"We derive a $1/c$-expansion for the single-particle density matrix of a
strongly interacting time-dependent one-dimensional Bose gas, described by the
Lieb-Liniger model ($c$ denotes the strength of the interaction). The formalism
is derived by expanding Gaudin's Fermi-Bose mapping operator up to $1/c$-terms.
We derive an efficient numerical algorithm for calculating the density matrix
for time-dependent states in the strong coupling limit, which evolve from a
family of initial conditions in the absence of an external potential. We have
applied the formalism to study contraction dynamics of a localized wave packet
upon which a parabolic phase is imprinted initially.",0907.4608v1
2011-09-18,Influence of density dependent symmetry energy on Elliptical flow,"The effect of density dependent symmetry energy on elliptical flow is studied
using isospin-dependent quantum molecular dynamics model(IQMD). We have used
the reduced isospin- dependent cross-section with hard(H) equation of state to
study the sensitivity of elliptical flow towards symmetry energy in the energy
range of 50 - 1000 MeV/nucleon. The elliptical flow becomes zero at a
particular energy termed as transition energy. A systematic effort has been
made to pin down the transition energy for the density dependent symmetry
energy.",1109.3852v1
2014-04-03,Functional renormalization group approach to neutron matter,"The chiral nucleon-meson model, previously applied to systems with equal
number of neutrons and protons, is extended to asymmetric nuclear matter.
Fluctuations are included in the framework of the functional renormalization
group. The equation of state for pure neutron matter is studied and compared to
recent advanced many-body calculations. The chiral condensate in neutron matter
is computed as a function of baryon density. It is found that, once
fluctuations are incorporated, the chiral restoration transition for pure
neutron matter is shifted to high densities, much beyond three times the
density of normal nuclear matter.",1404.0882v2
2015-07-24,Upper bounds of spin-density wave energies in the homogeneous electron gas,"Studying the jellium model in the Hartree-Fock approximation, Overhauser has
shown that spin density waves (SDW) can lower the energy of the Fermi gas, but
it is still unknown if these SDW are actually relevant for the phase diagram.
In this paper, we give a more complete description of SDW states. We show that
a modification of the Overhauser ansatz explains the behavior of the jellium at
high density compatible with previous Hartree-Fock simulations.",1507.06884v1
2017-05-08,Single Charge-Exchange Reactions and the Neutron Density at the Surface of the Nucleus,"In this work we study the charge-exchange reaction to Isobaric Analog State
using two types of transition densities. We show that for projectiles that do
not probe the interior of the nucleus but mostly the surface of this nucleus,
distinct differences in the cross-section arise when the two types of
transition densities are employed. We demonstrate this by considering the
(3He,t) reaction.",1705.02847v1
2018-11-15,Pauli rearrangement potential for a scattering state with the interaction in chiral effective field theory,"The Pauli rearrangement potential given by the second-order diagram is
evaluated for a nucleon optical model potential (OMP) with $G$ matrices of the
nucleon-nucleon interaction in chiral effective field theory. The results
obtained in nuclear matter are applied for $^{40}$Ca in a local-density
approximation. The repulsive effect is of the order of 5MeV at the normal
density. The density dependence indicates that the real part of the microscopic
OMP becomes shallower in a central region, but is barely affected in a surface
area. This improves the overall resemblance of the microscopic OMP to the
empirical one.",1811.06164v1
2019-12-15,Non-equilibrium $d-$ wave pair density wave order parameter in superconducting cuprates,"We investigate the nonequilibrium pair density wave order parameter in a
simple microscopic model with the ground state $d-$ wave spatially uniform
superconductivity. After pushing the system out of equilibrium by a short-time
induced order parameter, the system can exhibit robust free nondecaying
oscillations of nonuniform superconducting order. In the weak nonequilibrium
regime, the frequency of these oscillations is about $2\Delta/\hbar$ and the
amplitude can be explained qualitatively by features of equilibrium free
energy. In case when the system was taken far from equilibrium, it transits to
a non-linear regime where even metastable coexistence of $d-$ wave
superconducting and pair density wave gaps are possible.",1912.07080v1
2022-09-21,Multi band Fermi surface in 1T-VSe2 and its implication for charge density wave phase,"Here, our angle resolved photoemission spectroscopy experiment reveled that
the surface band structure of the 1T-VSe2 host electronic states that was not
predicted or probed before. Earlier claims to support charge density wave phase
can be all explained in terms of these new findings. Its Fermi surface found to
be not gaped at any point of the Brillouin zone and warping effect on the
electronic structure, attributed to the lattice distortion previously, is due
to the different dispersion of the multiple bands. Based on these new findings
and interpretations, charge density wave induced modification on the electronic
structure of 1T-VSe2 needs to be reconstructed in the future studies.",2209.10054v1
2023-09-21,A mixture of ellipsoidal densities for 3D data modelling,"In this paper, we propose a new ellipsoidal mixture model. This model is
based a new probability density function belonging to the family of elliptical
distributions and designed to model points spread around an ellipsoidal
surface. Then, we consider a mixture model based on this density, whose
parameters are estimated with the help of an EM algorithm. The properties of
the estimates are studied theoretically and empirically. The algorithm is
compared to a state of the art ellipse fitting method and experimented on 3D
data.",2309.11916v1
2024-01-15,Stability constraint for spin equation of state,"A generalized Frenkel condition is proposed for use in spin hydrodynamics to
relate the spin density and spin polarization (or spin chemical potential)
tensors. It allows for independent treatment of electric- and magnetic-like
components of the spin density tensor, which helps to fulfill the stability
conditions recently derived in the literature. The generalized Frenkel
condition extrapolates between the original Frenkel condition, where only the
magnetic-like part of the spin tensor is present, and the case where the spin
density tensor is directly proportional to the spin polarization tensor. We
also demonstrate that our approach is supported by the result of a microscopic
calculation.",2401.07608v1
2014-03-30,The Fibonacci Hamiltonian,"We consider the Fibonacci Hamiltonian, the central model in the study of
electronic properties of one-dimensional quasicrystals, and provide a detailed
description of its spectrum and spectral characteristics (namely, the optimal
H\""older exponent of the integrated density of states, the dimension of the
density of states measure, the dimension of the spectrum, and the upper
transport exponent) for all values of the coupling constant (in contrast to all
previous quantitative results, which could be established only in the regime of
small or large coupling).
  In particular, we show that the spectrum of this operator is a dynamically
defined Cantor set and that the density of states measure is exact-dimensional;
this implies that all standard fractal dimensions coincide in each case. We
show that all the gaps of the spectrum allowed by the gap labeling theorem are
open for all values of the coupling constant. Also, we establish strict
inequalities between the four spectral characteristics in question, and provide
the exact large coupling asymptotics of the dimension of the density of states
measure (for the other three quantities, the large coupling asymptotics were
known before).
  A crucial ingredient of the paper is the relation between spectral properties
of the Fibonacci Hamiltonian and dynamical properties of the Fibonacci trace
map (such as dimensional characteristics of the non-wandering hyperbolic set
and its measure of maximal entropy as well as other equilibrium measures,
topological entropy, multipliers of periodic orbits). We establish exact
identities relating the spectral and dynamical quantities, and show the
connection between the spectral quantities and the thermodynamic pressure
function.",1403.7823v1
2012-12-14,Asymptotic silence in loop quantum cosmology,"The state of asymptotic silence, characterized by causal disconnection of the
space points, emerges from various approaches aiming to describe gravitational
phenomena in the limit of large curvatures. In particular, such behavior was
anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous
conjecture put forward in the early seventies of the last century. While the
BKL conjecture is based on purely classical considerations, one can expect that
asymptotic silence should have its quantum counterpart at the level of a more
fundamental theory of quantum gravity, which is the relevant description of
gravitational phenomena in the limit of large energy densities. Here, we
summarize some recent results which give support to such a possibility. More
precisely, we discuss occurrence of the asymptotic silence due to
polymerization of space at the Planck scale, in the framework of loop quantum
cosmology. In the discussed model, the state of asymptotic silence is realized
at the energy density $\rho = \rho_c/2$, where $\rho_c$ is the maximal allowed
energy density, being of the order of the Planck energy density. At energy
densities $\rho > \rho_c/2$, the universe becomes 4D Euclidean space without
causal structure. Therefore, the asymptotic silence appears to be an
intermediate state of space between the Lorentzian and Euclidean phases.",1212.3527v1
2023-03-13,Resource-efficient Direct Characterization of General Density Matrix,"Sequential weak measurements allow the direct extraction of individual
density-matrix elements instead of globally reconstructing the whole density
matrix, opening a new avenue for the characterization of quantum systems.
Nevertheless, the requirement of multiple coupling for each qudit of quantum
systems and the lack of appropriate precision evaluation constraint its
applicability extension, especially for multi-qudit quantum systems. Here, we
propose a resource-efficient scheme (RES) to directly characterize the density
matrix of general multi-qudit systems, which not only optimizes the
measurements but also establishes a feasible estimation analysis. In this
scheme, an efficient observable of quantum system is constructed such that a
single meter state coupled to each qudit is sufficient to extract the
corresponding density-matrix element. An appropriate model based on the
statistical distribution of errors are used to evaluate the precision and
feasibility of the scheme. We experimentally apply the RES to the direct
characterization of general single-photon qutrit states and two-photon
entangled states. The results show that the RES outperforms the sequential
schemes in terms of efficiency and precision in both weak- and strong- coupling
scenarios. This work sheds new light on the practical characterization of
large-scale quantum systems and investigation of their non-classical
properties.",2303.06903v1
2013-12-31,Higher-order symmetry energy of nuclear matter and the inner edge of neutron star crusts,"The parabolic approximation to the equation of state of the isospin
asymmetric nuclear matter (ANM) is widely used in the literature to make
predictions for the nuclear structure and the neutron star properties. Based on
the realistic M3Y-Paris and M3Y-Reid nucleon-nucleon interactions, we
investigate the effects of the higher-order symmetry energy on the proton
fraction in neutron stars and the location of the inner edge of their crusts
and their core-crust transition density and pressure, thermodynamically.
Analytical expressions for different-order symmetry energy coefficients of ANM
are derived using the realistic interactions mentioned above. It is found that
the higher-order terms of the symmetry energy coefficients up to its
eighth-order (E$_{sym8}$) contributes substantially to the proton fraction in
$\beta$ stable neutron star matter at different nuclear matter densities, the
core-crust transition density and pressure. Even by considering the symmetry
energy coefficients up to E$_{sym8}$, we obtain a significant change of about
40$\%$ in the transition pressure value from the one based on the exact
equation of state. Using equations of state based on both Paris and Reid
effective interactions which provide saturation incompressibility of symmetric
nuclear matter in the range of 220 MeV$\leq$K$_0$$\leq$270 MeV, we estimate the
ranges 0.090 fm$^{-3}$$\leq$$\rho_t$$\leq$0.095 fm$^{-3}$ and 0.49 MeV
fm$^{-3}$$\leq$P$_t$$\leq$ 0.59 MeV fm$^{-3}$ for the liquid core-solid crust
transition density and pressure, respectively. The corresponding range of the
proton fraction at this transition density range is found to be
0.029$\leq$x$_{p(t)}$$\leq$0.032.",1401.0090v1
2016-09-26,Effect of Pauli blocking on coherent states of composite bosons,"The quantum nature of elementary bosons can be completely erased by using
coherent states known as Glauber states. Here, we consider composite bosons
(cobosons) made of two fermions and look for the possibility to erase the
bosonic quantum nature of the field and the fermionic quantum nature of its
constituents, when the distribution of the coboson Schmidt decomposition is
either flat like Frenkel excitons, or localized like Wannier excitons. We show
that for Frenkel-like cobosons, complete erasure of the field quantum nature is
possible up to a density which corresponds to a sizable fraction of the number
of fermion-pair states making the coboson at hand. At higher density, the Pauli
exclusion principle between fermionic constituents shows up dramatically. It
induces: (i) the decrease of number-operator eigenvalues down to 1 and the
increase of the number-state second-order correlation function up to 2; (ii)
the disappearance of the usual sharp peak in the coherent-state distribution
and the increase of the coherent-state second-order correlation function up to
2. It also is possible to construct number states and coherent states for
Wannier-like cobosons, but their forms are far more complex. Finally, we show
that Pauli blocking makes the coboson coherent states qualitatively different
from the Anderson's ansatz.",1609.08119v1
2003-08-23,"Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory","For closed-shell systems, the local density approximation (LDA) and the LYP,
BLYP, and B3LYP functionals are shown to be compatible with reference-state
one-particle density-matrix theory, where this recently introduced formalism is
based on Brueckner-orbital theory and an energy functional that includes exact
exchange and a non-universal correlation-energy functional. The method is
demonstrated to reduce to a density functional theory when the
exchange-correlation energy-functional has a simplified form, i.e., its
integrand contains only the coordinates of two electron, say r1 and r2, and it
has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner
and Hartree--Fock orbitals are often very similar, any local exchange
functional that works well with Hartree--Fock theory is a reasonable
approximation with reference-state one-particle density-matrix theory. The LDA
approximation is also a reasonable approximation. However, the Colle--Salvetti
correlation-energy functional, and the LYP variant, are not ideal for the
method, since these are universal functionals. Nevertheless, they appear to
provide reasonable approximations. The B3LYP functional is derived using a
linear combination of two functionals: One is the BLYP functional; the other
uses exact exchange and a correlation-energy functional from the LDA.",0308084v1
2015-01-01,Electronic structure and magnetic properties of $\mathrm{CaCr}\mathrm{O}_3$: The interplay between spin- and orbital-orderings,"The electronic structure and magnetic properties of CaCr$\mathrm{O}_3$ have
been calculated by two methods, including hybrid-exchange density-function
theory and density-functional theory + $U$. The computed densities of states
from both of these methods are in a qualitative agreement with the previous
x-ray spectroscopy. On the other hand, the opening of the band gap separates
them apart. hybrid-exchange density-functional theory always gives a finite
band gap, down to $\sim 1.2$ eV from HSE06 functional, whereas by tuning the
Hubbard-$U$ parameter down to $0.5$ eV, a conducting state with AFM-C (defined
in the text) spin configuration can be achieved. From hybrid density-functional
theory, the computed nearest-neighbouring exchange interaction along the
$c$-axis and in the $ab$-plane are $\sim 4$ meV and $\sim 6$ meV
(anti-ferromagnetic), respectively, which are qualitatively in agreement with
the previous magnetic measurements. These anti-ferromagnetic exchange
interaction, together with the in-plane anti-ferro-orbital ordering will induce
a spin-orbital frustration, which could play a role for the abnormal electronic
properties in CaCrO$_3$. In hybrid-exchange density-functional theory, an
abrupt reduction ($\sim 0.2$ eV) of the majority-spin band gap of the
ferromagnetic state between 60 K and 100 K has been found as lowering
temperature, which shows a strong link to the previous optical conductivity
measurements in [A. C. Komarek, et. al., Phys. Rev. B \textbf{84}, 125114
(2011)]. In sharp contrast, the density-functional theory + $U$ methods
predicted AFM-C state as the lowest AFM state for the crystal structure
measured below 90 K, above which AFM-A is however the lowest. The closely
related concepts including electron-hole liquid and surface-plasmon-mediating
spin-spin interactions have been discussed as well.",1501.00319v4
1996-07-23,Dynamics of compressible edge and bosonization,"We work out the dynamics of the compressible edge of the quantum Hall system
based on the electrostatic model of Chklovskii et al.. We introduce a
generalized version of Wen's hydrodynamic quantization approach to the dynamics
of sharp edge and rederive Aleiner and Glazman's earlier result of multiple
density modes. Bosonic operators of density excitations are used to construct
fermions at the interface of the compressible and incompressible region. We
also analyze the dynamics starting with the second-quantized Hamiltonian in the
lowest Landau level and work out the time development of density operators.
Contrary to the hydrodynamic results, the density modes are strongly coupled.
We argue that the coupling suppresses the propagation of all acoustic modes,
and that the excitations with large wavevectors are subject to decay due to
coupling to the dissipative acoustic modes.A possible correction to the
tunneling density of states is discussed.",9607166v1
2011-02-17,Compaction dynamics of metallic nano-foams: A hydrodynamics simulation study,"The compression of a low-density copper foam was simulated with a radiation,
hydrodynamics code. In one simulation, the foam had a density of $\rho_0 =
1.3407$ g/cm$^3$, 15% the density of copper at standard temperature and
pressure, and was composed of a tangle of standard density cylindrical copper
filaments with a diameter of $4.0\times10^{-7}$ cm. In another simulation, the
foam was a uniform material at the same density. The propagation velocity of
the shock wave ($U_f$) through the foam was measured and compared with
experimental results. The simulations show approximately the same agreement
with experimental results for $U_f$ and agreed with estimates from different
equations of state and simulations using molecular dynamics. Behavior of the
foam ahead of the shock wave is also discussed where the porous nature of the
foam allows for the formation of a vapor precursor.",1102.3719v1
2015-09-28,An explanation for the tiny value of the cosmological constant and the low vacuum energy density,"The paper aims to provide an explanation for the tiny value of the
cosmological constant and the low vacuum energy density to represent the dark
energy. To accomplish this, we will search for a fundamental principle of
symmetry in space-time by means of the elimination of the classical idea of
rest, by including an invariant minimum limit of speed in the subatomic world.
Such a minimum speed, unattainable by particles, represents a preferred
reference frame associated with a background field that breaks down the Lorentz
symmetry. The metric of the flat space-time shall include the presence of a
uniform vacuum energy density, which leads to a negative pressure at
cosmological length scales. Thus, the equation of state for the cosmological
constant [$p$(pressure)$=- \epsilon$ (energy density)] naturally emerges from
such a space-time with an energy barrier of a minimum speed. The tiny values of
the cosmological constant and the vacuum energy density will be successfully
obtained, being in agreement with the observational results of Perlmutter,
Schmidt and Riess.",1510.00595v2
2012-04-02,Calculation of the Structure Properties of a Strange Quark Star in the Presence of Strong Magnetic Field Using a Density Dependent Bag Constant,"In this article we have calculated the structure properties of a strange
quark star in static model in the presence of a strong magnetic field using MIT
bag model with a density dependent bag constant. To parameterize the density
dependence of bag constant, we have used our results for the lowest order
constrained variational calculation of the asymmetric nuclear matter. By
calculating the equation of state of strange quark matter, we have shown that
the pressure of this system increases by increasing both density and magnetic
field. Finally, we have investigated the effect of density dependence of bag
constant on the structure properties of strange quark star.",1204.0325v1
2023-04-18,Coexistence of heterogenous predator-prey systems with density-dependent dispersal,"This paper is concerned with existence, non-existence and uniqueness of
positive (coexistence) steady states to a predator-prey system with
density-dependent dispersal. To overcome the analytical obstacle caused by the
cross-diffusion structure embedded in the density-dependent dispersal, we use a
variable transformation to convert the problem into an elliptic system without
cross-diffusion structure. The transformed system and pre-transformed system
are equivalent in terms of the existence or non-existence of positive
solutions. Then we employ the index theory alongside the method of the
principle eigenvalue to give a nearly complete classification for the existence
and non-existence of positive solutions. Furthermore we show the uniqueness of
positive solutions and characterize the asymptotic profile of solutions for
small or large diffusion rates of species. Our results pinpoint the positive
role of density-dependent dispersal on the population dynamics for the first
time by showing that the density-dependent dispersal is a beneficial strategy
promoting the coexistence of species in the predator-prey system by increasing
the chance of predator's survival.",2304.08739v1
2003-02-20,Electronic structure of rectangular quantum dots,"We study the ground state properties of rectangular quantum dots by using the
spin-density-functional theory and quantum Monte Carlo methods. The dot
geometry is determined by an infinite hard-wall potential to enable comparison
to manufactured, rectangular-shaped quantum dots. We show that the electronic
structure is very sensitive to the deformation, and at realistic sizes the
non-interacting picture determines the general behavior. However, close to the
degenerate points where Hund's rule applies, we find spin-density-wave-like
solutions bracketing the partially polarized states. In the
quasi-one-dimensional limit we find permanent charge-density waves, and at a
sufficiently large deformation or low density, there are strongly localized
stable states with a broken spin-symmetry.",0302410v1
2014-03-20,"Linear-response calculation of the effective Coulomb interaction between closed-shell localized electrons: Cu, Zn, and ZnO","A linear-response method to calculate the effective Coulomb interaction ($U$)
between closed-shell localized electrons is suggested and applied to the $3d$
closed-shell systems (Cu, Zn, and ZnO) based on plane-wave basis
density-functional theory calculations. Since the closed-shell localized states
are far below the Fermi level, large local perturbation potential ($\alpha$)
projected to the localized states is applied to induce purposeful density
response ($\Delta n$). From the $\alpha$, the perturbation potential cost for
density response onset, by which the $\Delta n$ begins to be induced, is
removed. The main screening channel for the effective Coulomb interaction is
the itinerant electrons deoccupied from the perturbed localized states. The Cu,
Zn, and ZnO $3d$ electron binding energies are calculated based on the local
density approximation plus $U$ with the $U$ values calculated from the
linear-response, which are found to be in good agreement with experiments.",1403.5062v1
2003-12-01,Is Cosmic Coincidence a Consequence of a Law of Nature?,"A field theory is proposed where the regular fermionic matter and the dark
fermionic matter are different states of the same ""primordial"" fermion fields.
In regime of the fermion densities typical for normal particle physics, the
primordial fermions split into three families identified with regular fermions.
When fermion energy density becomes comparable with dark energy density, the
theory allows new type of states. The possibility of such Cosmo-Low Energy
Physics (CLEP) states is demonstrated by means of solutions of the field theory
equations describing FRW universe filled by homogeneous scalar field and
uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are
drawn into cosmological expansion by means of dynamically changing their own
parameters. One of the features of the fermions in CLEP state is that in the
late time universe their masses increase as a^{3/2}. The energy density of the
cold dark matter consisting of neutrinos in CLEP state scales as a sort of dark
energy; this cold dark matter possesses negative pressure and for the late time
universe its equation of state approaches that of the cosmological constant.
The total energy density of such universe is less than it would be in the
universe free of fermionic matter at all. The (quintessence) scalar field is
coupled to dark matter but its coupling to regular fermionic matter appears to
be extremely strongly suppressed. The key role in obtaining these results
belongs to a fundamental constraint (which is consequence of the action
principle) that plays the role of a new law of nature.",0312006v5
2022-04-05,Escaping the maze: a statistical sub-grid model for cloud-scale density structures in the interstellar medium,"The interstellar medium (ISM) is a turbulent, highly structured multi-phase
medium. State-of-the-art cosmological simulations of the formation of galactic
discs usually lack the resolution to accurately resolve those multi-phase
structures. However, small-scale density structures play an important role in
the life cycle of the ISM, and determine the fraction of cold, dense gas, the
amount of star formation and the amount of radiation and momentum leakage from
cloud-embedded sources. Here, we derive a $statistical\, model$ to calculate
the unresolved small-scale ISM density structure from coarse-grained,
volume-averaged quantities such as the $gas\, clumping\, factor$,
$\mathcal{C}$, and mean density $\left<\rho\right>_V$. Assuming that the
large-scale ISM density is statistically isotropic, we derive a relation
between the three-dimensional clumping factor, $\mathcal{C}_\rho$, and the
clumping factor of the $4\pi$ column density distribution on the cloud surface,
$\mathcal{C}_\Sigma$, and find $\mathcal{C}_\Sigma=\mathcal{C}_\rho^{2/3}$.
Applying our model to calculate the covering fraction, i.e., the $4\pi$ sky
distribution of optically thick sight-lines around sources inside interstellar
gas clouds, we demonstrate that small-scale density structures lead to
significant differences at fixed physical ISM density. Our model predicts that
gas clumping increases the covering fraction by up to 30 per cent at low ISM
densities compared to a uniform medium. On the other hand, at larger ISM
densities, gas clumping suppresses the covering fraction and leads to increased
scatter such that covering fractions can span a range from 20 to 100 per cent
at fixed ISM density. All data and example code is publicly available at
GitHub.",2204.02053v1
2014-04-14,"Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice","Recently two interesting candidate quantum phases --- the chiral spin density
wave state featuring anomalous quantum Hall effect and the d+id superconductor
--- were proposed for the Hubbard model on the honeycomb lattice at 1/4 doping.
Using a combination of exact diagonalization, density matrix renormalization
group, the variational Monte Carlo method and quantum field theories, we study
the quantum phase diagrams of both the Hubbard model and t-J model on the
honeycomb lattice at 1/4-doping. The main advantage of our approach is the use
of symmetry quantum numbers of ground state wavefunctions on finite size
systems (up to 32 sites) to sharply distinguish different quantum phases. Our
results show that for $1\lesssim U/t< 40$ in the Hubbard model and for $0.1<
J/t<0.80(2)$ in the t-J model, the quantum ground state is either a chiral spin
density wave state or a spin-charge-Chern liquid, but not a d+id
superconductor. However, in the t-J model, upon increasing $J$ the system goes
through a first-order phase transition at $J/t=0.80(2)$ into the d+id
superconductor. Here the spin-charge-Chern liquid state is a new type of
topologically ordered quantum phase with Abelian anyons and fractionalized
excitations. Experimental signatures of these quantum phases, such as tunneling
conductance, are calculated. These results are discussed in the context of
1/4-doped graphene systems and other correlated electronic materials on the
honeycomb lattice.",1404.3452v3
2017-11-30,Frustration-induced internal stresses are responsible for quasilocalized modes in structural glasses,"It has been recently shown [E. Lerner, G. D\""uring, and E. Bouchbinder, Phys.
Rev. Lett. 117, 035501 (2016)] that the non-phononic vibrational modes of
structural glasses at low-frequencies $\omega$ are quasi-localized and follow a
universal density of states $D(\omega)\!\sim\!\omega^4$. Here we show that the
gapless nature of the observed density of states depends on the existence of
internal stresses which generically emerge in glasses due to frustration, thus
elucidating a basic element underlying this universal behavior. Similarly to
jammed particulate packings, low-frequency modes in structural glasses emerge
from a balance between a local elasticity term and an internal stress term in
the dynamical matrix, where the difference between them is orders of magnitude
smaller than their typical magnitude. By artificially reducing the magnitude of
internal stresses in a computer glass former in three dimensions, we show that
a gap is formed in the density of states below which no vibrational modes
exist, thus demonstrating the crucial importance of internal stresses. Finally,
we show that while better annealing the glass upon cooling from the liquid
state significantly reduces its internal stresses, the self-organizational
processes during cooling render the gapless $D(\omega)\!\sim\!\omega^4$ density
of state unaffected.",1711.11263v3
2004-06-14,Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,"A single-photon Fock state has been generated by means of conditional
preparation from a two-photon state emitted in the process of spontaneous
parametric down-conversion. A recently developed high-frequency homodyne
tomography technique has been used to completely characterize the Fock state by
means of a pulse-to-pulse analysis of the detectors' difference photocurrent.
The density matrix elements of the generated state have been retrieved with a
final detection efficiency of about 57%. A comparison has been performed
between the phase-averaged tomographic reconstructions of the Wigner function
as obtained from the measured density-matrix elements and from a direct Abel
transform of the homodyne data. The ability of our system to work at the full
repetition rate of the pulsed laser (82 MHz) substantially simplifies the
detection scheme, allowing for more ``exotic'' quantum states to be generated
and analyzed.",0406090v1
2015-01-13,Bound states of a ferromagnetic wire in a superconductor,"We consider the problem of bound states in strongly anisotropic ferromagnetic
impurities in a superconductor, motivated by recent experiments that claim to
observe Majorana modes at the ends of ferromagnetic wires on a superconducting
substrate [S. Nadj-Perge et al., Science 346, 602 (2014)]. Generalizing the
successful theory of bound states of spherically symmetric impurities, we
consider a wire-like potential using both analytical and numerical approaches.
We find that away from the ends of the wire the bound states form bands with
pronounced van Hove singularities, giving rise to subgap peaks in the local
density of states. For sufficiently strong magnetization of the wire, we show
that this process generically produces a sharp peak at zero energy in the local
density of states near the ends of the wire. This zero-energy peak has
qualitative similarities to the claimed signature of a Majorana mode observed
in the aforementioned experiment.",1501.03149v3
2015-04-24,From the granular Leidenfrost state to buoyancy-driven convection,"Grains inside a vertically vibrated box undergo a transition from a density
inverted and horizontally homogeneous state, referred to as the granular
Leidenfrost state, to a buoyancy-driven convective state. We perform a
simulational study of the precursors of such a transition, and quantify their
dynamics as the bed of grains is progressively fluidized. The transition is
preceded by transient convective states, which increase their correlation time
as the transition point is approached. Increasingly correlated convective flows
lead to density fluctuations, as quantified by the structure factor, that also
shows critical behaviour near the transition point. The amplitude of the
modulations in the vertical velocity field are seen to be best described by a
quintic supercritical amplitude equation with an additive noise term. The
validity of such an amplitude equation, and previously observed collective
semi-periodic oscillations of the bed of grains, suggests a new interpretation
of the transition analogous to a coupled chain of vertically vibrated damped
oscillators. Increasing the size of the container shows metastability of
convective states, as well as an overall invariant critical behaviour close to
the transition.",1504.06426v1
2022-03-31,Shiba states in systems with density of states singularities,"Magnetic impurities placed in the superconductor can lead to emergence of the
Yu-Shiba-Rusinov bound states. Coupling between the impurity and the substrate
depends on density of states (DOS) at the Fermi level and can be tuned by DOS
singularities. In this paper, we study the role of DOS singularities using the
real space Bogoliubov-de Gennes equations for chosen lattice models. To uncover
the role of these singularities (Dirac point, van Hove singularity, or the flat
band), we study honeycomb, kagome, and Lieb lattices. We show that the
properties of the Shiba state strongly depends on the type of lattice.
Nevertheless some behaviors are generic, e.g. dependence of the critical
magnetic coupling on the DOS at the Fermi level. However, the Shiba states
realized in the Lieb lattice exhibit extraordinary properties, which can be
explained by the presence of a few nonequivalent sublattices. Depending on the
location of the magnetic impurity in the chosen sublattice, the value of
critical magnetic coupling $J_\text{c}$ can be reduced or enhanced when the
flat band is located at the Fermi level. In this context, we also present
differences in the local DOS and coherence lengths for different sublattices in
the Lieb lattice.",2203.17108v1
2022-06-07,Possible formation mechanism of multistate gravitational atoms,"The collision of two equilibrium ground state solutions of the
Schr\""odinger-Poisson (SP) system, in orthogonal states, is proposed as a
formation mechanism of mixed state solutions of the SP system with spherical
and first dipolar components. The collisions are simulated by solving
numerically the SP system for two orthogonal states, considering head-on
encounters, and using various mass ratios between the initial configurations
with different head-on momentum. The results indicate that the less massive of
the configurations pinches-off the more massive one, and redistributes its
density along the axis of collision. The averaged in time density of the two
states resembles the distribution of matter of bi-state equilibrium
configurations with monopolar and dipolar contributions.",2206.03407v2
2023-01-31,Density of states and spectral function of a superconductor out of a quantum-critical metal,"We analyze the validity of a quasiparticle description of a superconducting
state at a metallic quantum-critical point (QCP). A normal state at a QCP is a
non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps
out low-energy excitations, except for a sliver of states for non-s-wave gap
symmetry, and at a first glance, should restore a coherent quasiparticle
behavior. We argue that this does not necessarily hold as in some cases the
fermionic self-energy remains singular slightly above the gap edge. This
singularity gives rise to markedly non-BCS behavior of the density of states
and to broadening and eventual vanishing of the quasiparticle peak in the
spectral function. We analyze the set of quantum-critical models with an
effective dynamical 4-fermion interaction, mediated by a gapless boson at a
QCP, $V(\Omega) \propto 1/\Omega^\gamma$. We show that coherent quasiparticle
behavior in a superconducting state holds for $\gamma <1/2$, but breaks down
for larger $\gamma$. We discuss signatures of quasiparticle breakdown and
compare our results with the data.",2301.13679v1
2023-10-17,Excited States in Warm and Hot Dense Matter,"Accurate modeling of warm and hot dense matter is challenging in part due to
the multitude of excited states that must be considered. In thermal density
functional theory, these excited states are averaged over to produce a single,
averaged, thermal ground state. Here we present a variational framework and
model that includes explicit excited states. In this framework an excited state
is defined by a set of effective one-electron occupation factors and the
corresponding energy is defined by the effective one-body energy with an
exchange and correlation term. The variational framework is applied to an
atom-in-plasma model (a generalization of the so-called average atom model).
Comparisons with a density functional theory based average atom model generally
reveal good agreement in the calculated pressure, but the new model also gives
access to the excitation energies and charge state distributions.",2310.11586v1
2021-11-20,Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems,"We study numerically the the charge neutral excitations (magnetorotons) in
fractional quantum Hall systems, concentrating on the two Jain states near
quarter filling, $\nu=2/7$ and $\nu=2/9$, and the $\nu=1/4$ Fermi-liquid state
itself. In contrast to the $\nu=1/3$ states and the Jain states near half
filling, on each of the two Jain states $\nu=2/7$ and $\nu=2/9$ the graviton
spectral densities show two, instead of one, magnetoroton peaks. The
magnetorotons have spin 2 and have opposite chiralities in the $\nu=2/7$ state
and the same chirality in the $\nu=2/9$ state. We also provide a numerical
verification of a sum rule relating the guiding center spin $\bar s$ with the
spectral densities of the stress tensor",2111.10593v1
2023-12-13,"$^{12}$C and $α$-clusters, $0^+$ spectrum, and Hoyle-state candidates in $^{24}$Mg","Background: A recent inelastic alpha-scattering experiment [Phys. Rev. Lett.
129, 102701 (2022)] found $0^+$ resonances in $^{24}$Mg on and above the
$^{12}$C+$^{12}$C break-up threshold. It has been conjectured that the states
have a $^{12}$C+$^{12}$C cluster structure, and play a similar role in
accelerating $^{12}$C+$^{12}$C fusion to the manner in which the Hoyle state
accelerates production of $^{12}$C in massive stars.
  Purpose: We wish to build up a quantitative theoretical basis for the
considerations of the Hoyle-state paradigm, by calculating the distribution of
the $0^+$ states in the shell, as well as in the relevant cluster models.
  Methods: We determine the spectrum of excited $0^+$ states in $^{24}$Mg
nucleus using multiconfigurational dynamical symmetry calculations leading to a
unified description of the quartet (or shell), $^{12}$C+$^{12}$C and
$^{20}$Ne+$^{4}$He cluster configurations.
  Results: The density of $0^+$ states in the quartet spectrum is comparable to
that found in experiment; however, the density of cluster states is
considerably less.
  Conclusions: The recently observed alpha-scattering resonances do not seem to
be simple $^{12}$C+$^{12}$C cluster states, but are more plausibly interpreted
as fragmented cluster states due to coupling to quartet excitations, as
background states.",2312.08318v1
2021-12-26,Generalized Logotropic Models and their Cosmological Constraints,"We propose a new class of cosmological unified dark sector models called
""{\em Generalized Logotropic Models}"". They depend on a free parameter $n$. The
original logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130
(2015)] is a special case of our generalized model corresponding to $n=1$. In
our scenario, the Universe is filled with a single fluid, a generalized
logotropic dark fluid (GLDF), whose pressure $P$ includes higher order
logarithmic terms of the rest-mass density $\rho_m$. The total energy density
$\epsilon$ is the sum of the rest-mass energy density $\rho_m c^2$ and the
internal energy density $u$ which play the role of dark matter energy density
$\epsilon_m$ and dark energy density $\epsilon_{de}$, respectively. We
investigate the cosmological behavior of the generalized logotropic models by
focusing on the evolution of the energy density, scale factor, equation of
state parameter, decceleration parameter and squared speed of sound. Low values
of $n\le 3$ are favored. We also study the asymptotic behavior of the
generalized logotropic models. In particular, we show that the model presents a
phantom behavior and has three distinct ways of evolution depending on the
value of $n$. For $n\le 2$, it leads to a little rip and for $n>2$ to a big
rip. We predict the value of the big rip time as a function of $n$ without any
free (undetermined) parameter.",2112.13318v2
2024-01-04,Hybrid star models in the light of new multi-messenger data,"Recent astrophysical mass inferences of compact stars (CSs) HESS J1731-347
and PSR J0952-0607, with extremely small and large masses respectively, as well
as the measurement of the neutron skin of Ca in the CREX experiment challenge
and constrain the models of dense matter. In this work, we examine the concept
of hybrid stars - objects containing quark cores surrounded by nucleonic
envelopes - as models that account for these new data along with other
(multimessenger) inferences. We employ a family of 81 nucleonic equations of
state (EoSs) based on covariant density functional with variable skewness and
slope of symmetry energy at saturation density and a constant speed-of-sound
EoS for quark matter. For each nucleonic EoS, a family of hybrid star EoS is
generated by varying the transition density from nucleonic to quark matter, the
density jump at the transition, and the speed-of-sound. These models are tested
against the data from GW170817 and J1731-347, which favor low-density soft EoS
and PSR J0592-0607 and J0740+6620, which require high-density stiff EoS. We
then examine the occurrence of twin configurations and quantify the ranges of
masses and radii that they can possess. It is shown that including J1731-347
data favors EoS models which predict low-mass twin stars with masses $M
\lesssim 1.3\,M_{\odot}$ that can be realized if the deconfinement transition
density is low. If combined with a large speed-of-sound in quark matter such
models allow for maximum masses of hybrid stars in the range
$2.0$-$2.6\,M_{\odot}$.",2401.02198v1
2018-12-07,Stochastic dynamics and thermodynamics around a metastable state based on the linear Dean-Kawasaki equation,"The Dean-Kawasaki equation forms the basis of the stochastic density
functional theory (DFT). Here it is demonstrated that the Dean-Kawasaki
equation can be directly linearized in the first approximation of the driving
force due to the free energy functional $F[\rho] $ of an instantaneous density
distribution $\rho$, when we consider small density fluctuations around a
metastable state whose density distribution $\rho^*$ is determined by the
stationary equation $\delta F[\rho]/\delta \rho|_{\rho=\rho^*}=\mu$ with $\mu$
denoting the chemical potential. Our main results regarding the linear
Dean-Kawasaki equation are threefold. First, (i) the corresponding stochastic
thermodynamics has been formulated, showing that the heat dissipated into the
reservoir is negligible on average. Next, (ii) we have developed a field
theoretic treatment combined with the equilibrium DFT, giving an approximate
form of $F[\rho]$ that is related to the equilibrium free energy functional.
Accordingly, (iii) the linear Dean-Kawasaki equation, which has been reduced to
a tractable form expressed by the direct correlation function, allows us to
compare the stochastic dynamics around metastable and equilibrium states,
particularly in the Percus-Yevick hard sphere fluids; we have found that the
metastable density is larger and the effective diffusion constant in the
metastable state is smaller than the equilibrium ones in repulsive fluids.",1812.02951v1
1994-11-10,Collapse and Fragmentation of Cylindrical Magnetized Clouds. II. Simulation with Nested Grid Scheme,"Fragmentation process in a cylindrical magnetized cloud is studied with the
nested grid method. The nested grid scheme use 15 levels of grids with
different spatial resolution overlaid subsequently, which enables us to trace
the evolution from the molecular cloud density $\sim 100 {\rm cm}^{-3}$ to that
of the protostellar disk $\sim 10^{10} {\rm cm} ^{-3}$ or more. Fluctuation
with small amplitude grows by the gravita- tional instability. It forms a disk
perpendicular to the magnetic fields which runs in the direction parallel to
the major axis of the cloud. Matter accrets on to the disk mainly flowing along
the magnetic fields and this makes the column density increase. The radial
inflow, whose velocity is slower than that perpendicular to the disk, is driven
by the increase of the gravity. While the equation of state is isothermal and
magnetic fields are perfectly coupled with the matter, which is realized in the
density range of $\rho \lesssim 10^{10} {\rm cm}^{-3}$, never stops the
contraction. The structure of the contracting disk reaches that of a singular
solution as the density and the column density obey $\rho(r)\propto r^{-2}$ and
$\sigma(r) \propto r^{-1}$, respectively. The magnetic field strength on the
mid-plane is proportional to $\rho(r)^{1/2}$ and further that of the center
($B_c$) evolves as proportional to the square root of the gas density ($\propto
\rho_c^{1/2}$). It is shown that isothermal clouds experience ``run-away''
collapses. The evolution after the equation of state becomes hard is also
discussed.",9411040v1
2010-09-13,Extreme Cosmic-Ray-Dominated-Regions: a new paradigm for high star formation density events in the Universe,"We examine in detail the recent proposal that extreme
Cosmic-Ray-Dominated-Regions (CRDRs) characterize the ISM of galaxies during
events of high-density star formation, fundamentally altering its initial
conditions (Papadopoulos 2010). Solving the coupled chemical and thermal state
equations for dense UV-shielded gas reveals that the large cosmic ray energy
densities in such systems (U_{CR} (few)x(10^3-10^4) U_{CR,Gal}) will indeed
raise the minimum temperature of this phase (where the initial conditions of
star formation are set) from ~10K (as in the Milky Way) to (50-100)K. Moreover
in such extreme CRDRs the gas temperature remains fully decoupled from that of
the dust, with T_{kin} >> T_{dust}, even at high densities (n(H_2)~10^5--10^6
cm^{-3}), quite unlike CRDRs in the Milky Way where T_k T_{dust} when n(H_2) >=
10^5 cm^{-3}.
  These dramatically different star formation initial conditions will: a) boost
the Jeans mass of UV-shielded gas regions by factors of ~10--100 with respect
to those in quiescent or less extreme star forming systems, and b) ""erase"" the
so-called inflection point of the effective equation of state (EOS) of
molecular gas. Both these effects occur across the entire density range of
typical molecular clouds, and may represent {\it a new paradigm for all
high-density star formation in the Universe}, with cosmic rays as the key
driving mechanism, operating efficiently even in the high dust extinction
environments of extreme starbursts...",1009.2496v2
2011-01-22,The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model,"We have studied the extended Hubbard model in the atomic limit. The
Hamiltonian analyzed consists of the effective on-site interaction U and the
intersite density-density interactions Wij (both: nearest-neighbour and
next-nearest-neighbour). The model can be considered as a simple effective
model of charge ordered insulators. The phase diagrams and thermodynamic
properties of this system have been determined within the variational approach,
which treats the on-site interaction term exactly and the intersite
interactions within the mean-field approximation. Our investigation of the
general case taking into account for the first time the effects of
longer-ranged density-density interaction (repulsive and attractive) as well as
possible phase separations shows that, depending on the values of the
interaction parameters and the electron concentration, the system can exhibit
not only several homogeneous charge ordered (CO) phases, but also various phase
separated states (CO-CO and CO-nonordered). One finds that the model considered
exhibits very interesting multicritical behaviours and features, including
among others bicritical, tricritical, critical-end and isolated critical
points.",1101.4287v4
2019-12-10,Accurate effective potential for density amplitude and the corresponding Kohn-Sham exchange-correlation potential calculated from approximate wavefunctions,"Over the past few years it has been pointed out that direct inversion of
accurate but approximate ground state densities leads to Kohn-Sham
exchange-correlation (xc) potentials that can differ significantly from the
exact xc potential of a given system. On the other hand, the corresponding
wavefunction based construction of exchange-correlation potential as done by
Baerends et al. and Staroverov et al. obviates such problems and leads to
potentials that are very close to the true xc potential. In this paper, we
provide an understanding of why the wavefunction based approach gives the
exchange-correlation potential accurately. Our understanding is based on the
work of Levy, Perdew and Sahni (LPS) who gave an equation for the square root
of density (density amplitude) and the expression for the associated effective
potential in the terms of the corresponding wavefunction. We show that even
with the use of approximate wavefunctions the LPS expression gives accurate
effective and exchange-correlation potentials. Based on this we also identify
the source of difference between the potentials obtained from a wavefunction
and those given by the inversion of the associated density. Finally, we suggest
exploring the possibility of obtaining accurate ground-state density from an
approximate wavefunction for a system by making use of the LPS effective
potential.",1912.04520v2
2007-07-24,An HI Threshold for Star Cluster Formation in Tidal Debris,"Super star clusters are young, compact star clusters found in the central
regions of interacting galaxies. Recently, they have also been reported to
preferentially form in certain tidal tails, but not in others. In this paper,
we have used 21 cm HI maps and the Hubble Space Telescope Wide Field Planetary
Camera 2 images of eight tidal tail regions of four merging galaxy pairs to
compare the kiloparsec scale HI distribution with the location of super star
clusters found from the optical images. For most of the tails, we find that
there is an increase in super star cluster density with increasing projected HI
column density, such that the star cluster density is highest when log N(HI) >=
20.6 cm^{-2}, but equal to the background count rate at lower HI column
density. However, for two tails (NGC 4038/39 Pos A and NGC 3921), there is no
significant star cluster population despite the presence of gas at high column
density. This implies that the N(HI) threshold is a necessary but not
sufficient condition for cluster formation. Gas volume density is likely to
provide a more direct criterion for cluster formation, and other factors such
as gas pressure or strength of encounter may also have an influence. Comparison
of HI thresholds needed for formation of different types of stellar structures
await higher resolution HI and optical observations of larger numbers of
interacting galaxies.",0707.3582v1
2012-10-11,Pseudogap state from quantum criticality,"Upon application of an external tuning parameter, a magnetic state can be
driven to a normal metal state at zero temperature. This phenomenon is known as
quantum criticality and leads to fascinating responses in thermodynamics and
transport of the compound. In the standard picture, a single quantum critical
point occurs at zero temperature, which results in a nontrivial critical
behaviour in its vicinity. Here we show that in two dimensions the scenario is
considerably more complex due to the enormous amount of quantum fluctuations.
Instead of the single point separating the antiferromagnet from the normal
metal, we have discovered a broad region between these two phases where the
magnetic order is destroyed but certain areas of the Fermi surface are closed
by a large gap. This gap reflects the formation of a novel quantum state
characterised by a superposition of d-wave superconductivity and a
quadrupole-density wave, id est a state in which an electron quadrupole density
spatially oscillates with a period drastically different from the one of the
original spin-density wave. At moderate temperatures both orders co-exist at
short distances but thermal fluctuations destroy the long-range order. Below a
critical temperature the fluctuations are less essential and superconductivity
becomes stable. This new phenomenon may shed some light on the origin of the
mysterious pseudogap state and of the high-temperature transition into the
superconducting state in cuprates. Our results demonstrate that quantum phase
transitions between antiferromagnets and normal metals in layered materials may
be the proper playground for search of new high temperature superconductors.",1210.3276v2
2022-08-18,Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium,"Non-normalizable states are difficult to interpret in the orthodox quantum
formalism but often occur as solutions to physical constraints in quantum
gravity. We argue that pilot-wave theory gives a straightforward physical
interpretation of non-normalizable quantum states, as the theory requires only
a normalized density of configurations to generate statistical predictions. In
order to better understand such states, we conduct the first study of
non-normalizable solutions of the harmonic oscillator from a pilot-wave
perspective. We show that, contrary to intuitions from orthodox quantum
mechanics, the non-normalizable eigenstates and their superpositions are bound
states in the sense that the velocity field $v_y \to 0$ at large $\pm y$. We
argue that defining a physically meaningful equilibrium density for such states
requires a new notion of equilibrium, named pilot-wave equilibrium, which is a
generalisation of the notion of quantum equilibrium. We define a new
$H$-function $H_{pw}$, and prove that a density in pilot-wave equilibrium
minimises $H_{pw}$, is equivariant, and remains in equilibrium with time. We
prove an $H$-theorem for the coarse-grained $H_{pw}$, under assumptions similar
to those for relaxation to quantum equilibrium. We give an explanation of the
emergence of quantization in pilot-wave theory in terms of instability of
non-normalizable states due to perturbations and environmental interactions.
Lastly, we discuss applications in quantum field theory and quantum gravity,
and implications for pilot-wave theory and quantum foundations in general.",2208.08945v4
1996-03-04,Optical conductivity associated with solitons in the Peierls state as modified by zero-point-motion disorder,"We extend previous work to consider the effect of the soliton on the density
of states and conductivity of quasi-one-dimensional Peierls systems with
quantum lattice fluctuations, modeled by a random static disorder. Two features
have been verified over an order of magnitude variation in the disorder. (1)
The soliton density of states and the leading edges of both the soliton-to-band
and the band-to-band conductivities have universal scaling forms. (2) The
soliton-to-band conductivity has the remarkable feature that the leading edge
is accurately predicted by the joint density of states while the trailing edge
tracks the rigid-lattice conductivity. Or, in other words, disorder dominates
the leading edge, while matrix element effects are predominant for the trailing
edge.",9603019v1
2000-05-10,Theory of the Fano Resonance in the STM Tunneling Density of States due to a Single Kondo Impurity,"The conduction electron density of states nearby single magnetic impurities,
as measured recently by scanning tunneling microscopy (STM), is calculated,
taking into account tunneling into conduction electron states only. The Kondo
effect induces a narrow Fano resonance in the conduction electron density of
states, while scattering off the d-level generates a weakly energy dependent
Friedel oscillation. The line shape varies with the distance between STM tip
and impurity, in qualitative agreement with experiments, but is very sensitive
to details of the band structure. For a Co impurity the experimentally observed
width and shift of the Kondo resonance are in accordance with those obtained
from a combination of band structure and strongly correlated calculations.",0005166v1
2006-07-11,Quasiparticle spectrum of the cuprate BiSrCaCuO: Possible connection to the phase diagram,"We previously introduced [T. Cren et al., Europhys. Lett. 52, 203 (2000)] an
energy-dependant gap function, $\Delta(E)$, that fits the unusual shape of the
quasiparticle (QP) spectrum for both BiSrCaCuO and YBaCuO. A simple
anti-resonance in $\Delta(E)$ accounts for the pronounced QP peaks in the
density of states, at an energy $\Delta_p$, and the dip feature at a higher
energy, $E_{dip}$. Here we go a step further : our gap function is consistent
with the ($T, p$) phase diagram, where $p$ is the carrier density. For large QP
energies ($E >> \Delta_p$), the total spectral gap is $\Delta(E) \simeq
\Delta_p + \Delta_\phi$, where $\Delta_\phi$ is tied to the condensation
energy. From the available data, a simple $p$-dependance of $\Delta_p$ and
$\Delta_\phi$ is found, in particular $\Delta_\phi(p) \simeq 2.3 k_B T_c(p)$.
These two distinct energy scales of the superconducting state are interpreted
by comparing with the normal and pseudogap states. The various forms of the QP
density of states, as well as the spectral function $A(k,E)$, are discussed.",0607281v2
2008-09-25,Shear state of freely evolving granular gases,"Hydrodynamic equations are used to identify the final state reached by a
freely evolving granular gas above but close to its shear instability. The
theory predicts the formation of a two bands shear state with a steady density
profile. There is a modulation between temperature and density profiles as a
consequence of the energy balance, the density fluctuations remaining small,
without producing clustering. Moreover, the time dependence of the velocity
field can be scaled out with the squared root of the average temperature of the
system. The latter follows the Haff law, but with an effective cooling rate
that is smaller than that of the free homogeneous state. The theoretical
predictions are compared with numerical results for inelastic hard disks
obtained by using the direct Monte Carlo simulation method, and a good
agreement is obtained for low inelasticity.",0809.4379v1
2011-12-19,Exact relaxation dynamics of a localized many-body state in the 1D bose gas,"Through an exact method we numerically solve the time evolution of the
density profile for an initially localized state in the one-dimensional bosons
with repulsive short-range interactions. We show that a localized state with a
density notch is constructed by superposing one-hole excitations. The initial
density profile overlaps the plot of the squared amplitude of a dark soliton in
the weak coupling regime. We observe the localized state collapsing into a flat
profile in equilibrium for a large number of particles such as N=1000. The
relaxation time increases as the coupling constant decreases, which suggests
the existence of off-diagonal long-range order. We show a recurrence phenomenon
for a small number of particles such as N=20.",1112.4244v3
2013-03-28,Absence of Bose condensation on lattices with moat bands,"We study hard-core bosons on a class of frustrated lattices with the lowest
Bloch band having a degenerate minimum along a closed contour, the moat, in the
reciprocal space. We show that at small density the ground state of the system
is given by a noncondensed state, which may be viewed as a state of fermions
subject to Chern-Simons gauge field. At fixed density of bosons, such a state
exhibits domains of incompressible liquids. Their fixed densities are given by
fractions of the reciprocal-space area enclosed by the moat.",1303.7272v2
2014-04-28,Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3,"We study the quasiparticle excitations around a single vortex in the
superconducting topological insulator Cu$_{x}$Bi$_{2}$Se$_{3}$, focusing on a
superconducting state with point nodes. Inspired by the recent Knight shift
measurements, we propose two ways to detect the positions of point nodes, using
an explicit formula of the density of states with Kramer-Pesch approximation in
the quasiclassical treatment. The zero-energy local density of states around a
vortex parallel to the $c$-axis has a twofold shape and splits along the nodal
direction with increasing energy; these behaviors can be detected by the
scanning tunneling microscopy. An angular dependence of the density of states
with a rotating magnetic field on the $a$-$b$ plane has deep minima when the
magnetic field is parallel to the directions of point nodes, which can be
detected by angular-resolved heat capacity and thermal conductivity
measurements. All the theoretical predictions are detectable via standard
experimental techniques in magnetic fields.",1404.6874v2
2014-11-26,Nearest neighbor tight binding models with an exact mobility edge in one dimension,"We investigate localization properties in a family of deterministic (i.e. no
disorder) nearest neighbor tight binding models with quasiperiodic onsite
modulation. We prove that this family is self-dual under a generalized duality
transformation. The self-dual condition for this general model turns out to be
a simple closed form function of the model parameters and energy. We introduce
the typical density of states as an order parameter for localization in
quasiperiodic systems. By direct calculations of the inverse participation
ratio and the typical density of states we numerically verify that this
self-dual line indeed defines a mobility edge in energy separating localized
and extended states. Our model is a first example of a nearest neighbor tight
binding model manifesting a mobility edge protected by a duality symmetry. We
propose a realistic experimental scheme to realize our results in atomic
optical lattices and photonic waveguides.",1411.7375v3
2015-03-11,Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi2Se3,"We measure gate-tuned thermoelectric power of mechanically exfoliated Bi2Se3
thin films in the topological insulator regime. The sign of the thermoelectric
power changes across the charge neutrality point as the majority carrier type
switches from electron to hole, consistent with the ambipolar electric field
effect observed in conductivity and Hall effect measurements. Near charge
neutrality point and at low temperatures, the gate dependent thermoelectric
power follows the semiclassical Mott relation using the expected surface state
density of states, but is larger than expected at high electron doping,
possibly reflecting a large density of states in the bulk gap. The
thermoelectric power factor shows significant enhancement near the
electron-hole puddle carrier density ~ 0.5 x 1012 cm-2 per surface at all
temperatures. Together with the expected reduction of lattice thermal
conductivity in low dimensional structures, the results demonstrate that
nanostructuring and Fermi level tuning of three dimensional topological
insulators can be promising routes to realize efficient thermoelectric devices.",1503.03252v1
2017-02-28,Generalized reduction formula for Discrete Wigner functions of multiqubit systems,"Density matrices and Discrete Wigner Functions are equally valid
representations of multiqubit quantum states. For density matrices, the partial
trace operation is used to obtain the quantum state of subsystems, but an
analogous prescription is not available for discrete Wigner Functions. Further,
the discrete Wigner function corresponding to a density matrix is not unique
but depends on the choice of the quantum net used for its reconstruction. In
the present work, we derive a reduction formula for discrete Wigner functions
of a general multiqubit state which works for arbitrary quantum nets. These
results would be useful for the analysis and classification of entangled states
and the study of decoherence purely in a discrete phase space setting and also
in applications to quantum computing",1702.08691v1
2019-05-22,Treating different bonding situations: Revisiting Au-Cu alloys using the random phase approximation,"The ground state equilibrium properties of copper-gold alloys have been
explored with the state of art random phase approximation (RPA). Our estimated
lattice constants agree with the experiment within a mean absolute percentage
error (MAPE) of 1.4 percent. Semi-local functionals such as the generalized
gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) and strongly
constrained and appropriately normed (SCAN) fail to provide accurate bulk
moduli, which indicate their inability to describe the system in a stretched or
compressed state with respect to the equilibrium geometry. We find that the
non-locality present in RPA is able to describe the transition between two
delocalized electron densities (bulk elemental constituents to crystallized
alloys), as required to provide accurate formation energies. Based on our
results, we conclude that it is difficult to find a universal density
functional which can give accurate results for a wide range of properties of
intermetallic alloys. However, RPA can capture different bonding situations,
often better than other density functionals. It gives accurate results for a
wide range of ground state properties for the alloys, generated from metals
with completely filled d-shells.",1905.09348v2
2018-08-15,Spin density wave as a superposition of two magnetic states of opposite chirality and its implications,"A magnetic solid with weak spin frustration tends to adopt a noncollinear
magnetic structure such as cycloidal structure below a certain temperature and
a spin density wave (SDW) slightly above this temperature. The causes for these
observa-tions were explored by studying the magnetic structures of BaYFeO4,
which undergoes an SDW and a cycloidal phase transi-tion below 48 and 36 K,
respectively, in terms of density func-tional theory calculations. We show that
an SDW structure aris-es from a superposition of two magnetic states of
opposite chi-rality, an SDW state precedes a chiral magnetic state due to the
lattice relaxation, and whether an SDW is transversal or longitudinal is
governed by the magnetic anisotropy of magnetic ions.",1808.05044v1
2017-11-07,Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids,"We investigate the implications of integrability for the existence of quantum
disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard
model. We argue that there exist finite energy-density eigenstates that exhibit
QDL behaviour in the sense of J. Stat. Mech. P10010 (2014). These states are
atypical in the sense that their entropy density is smaller than that of
thermal states at the same energy density. Furthermore, we show that thermal
states in a particular temperature window exhibit a weaker form of the QDL
property, in agreement with recent results obtained by strong-coupling
expansion methods in arXiv:1611.02075. This article is part of the themed issue
`Breakdown of ergodicity in quantum systems: from solids to synthetics matter'.",1711.02738v1
2018-10-18,The liquid state of one-dimensional Bose mixtures: a quantum Monte-Carlo study,"By using exact quantum Monte-Carlo methods we calculate the ground-state
properties of the liquid phase in one-dimensional Bose mixtures with contact
interactions. We find that the liquid state can be formed if the ratio of
coupling strengths between inter-species attractive and intraspecies repulsive
interactions exceeds a critical value. As a function of this ratio we determine
the density where the energy per particle has a minimum and the one where the
compressibility diverges, thereby identifying the equilibrium density and the
spinodal point in the phase diagram of the homogeneous liquid. Furthermore, in
the stable liquid state, we calculate the chemical potential, the speed of
sound, as well as structural and coherence properties such as the pair
correlation function, the static structure factor and the one-body density
matrix, thus providing a detailed description of the bulk region in self-bound
droplets.",1810.07950v1
2019-03-14,Non-equilibrium Ionization States Within Galactic Outflows: Explaining Their O VI and N V Column Densities,"We present a suite of one-dimensional spherically-symmetric hydrodynamic
simulations that study the atomic ionization structure of galactic outflows. We
track the ionization state of the outflowing gas with a non-equilibrium atomic
chemistry network that includes photoionization, photo-heating, and ion-by-ion
cooling. Each simulation describes a steady-state outflow that is defined by
its mass and energy input rates, sonic radius, metallicity, and UV flux from
both the host galaxy and meta-galactic background. We find that for a large
range of parameter choices, the ionization state of the material departs
strongly from what it would be in photo-ionization equilibrium, in conflict
with what is commonly assumed in the analysis of observations. In addition,
nearly all the models reproduce the low N V to O VI column density ratios and
the relatively high O VI column densities that are observed.",1903.06183v1
2021-06-25,Surface density-of-states on semi-infinite topological photonic and acoustic crystals,"Iterative Green's function, based on cyclic reduction of block tridiagonal
matrices, has been the ideal algorithm, through tight-binding models, to
compute the surface density-of-states of semi-infinite topological electronic
materials. In this paper, we apply this method to photonic and acoustic
crystals, using finite-element discretizations and a generalized eigenvalue
formulation, to calculate the local density-of-states on a single surface of
semi-infinite lattices. The three-dimensional (3D) examples of gapless
helicoidal surface states in Weyl and Dirac crystals are shown and the
computational cost, convergence and accuracy are analyzed.",2106.13444v1
2022-08-27,Memory efficient Fock-space recursion scheme for computing many-fermion resolvents,"A fundamental roadblock to the exact numerical solution of many-fermion
problems is the exponential growth of the Hilbert space with system size. It
manifests as extreme dynamical memory and computation-time requirements for
simulating many-fermion processes. Here we construct a novel reorganization of
the Hilbert space to establish that the exponential growth of dynamical-memory
requirement is suppressed inversely with system size in our approach.
Consequently, the state-of-the-art resolvent computation can be performed with
substantially less memory. The memory-efficiency does not rely on Hamiltonian
symmetries, sparseness, or boundary conditions and requires no additional
memory to handle long-range density-density interaction and hopping. We provide
examples calculations of interacting fermion ground state energy, the
many-fermion density of states and few-body excitations in interacting ground
states in one and two dimensions.",2208.12936v2
2023-12-30,On the Ground State Quantum Droplet for Large Chemical Potentials,"In the present work we revisit the problem of the quantum droplet in atomic
Bose-Einstein condensates with an eye towards describing its ground state in
the large density, so-called Thomas-Fermi limit. We consider the problem as
being separable into 3 distinct regions: an inner one, where the Thomas-Fermi
approximation is valid, a sharp transition region where the density abruptly
drops towards the (vanishing) background value and an outer region which
asymptotes to the background value. We analyze the spatial extent of each of
these regions, and develop a systematic effective description of the rapid
intermediate transition region. Accordingly, we derive a uniformly valid
description of the ground state that is found to very accurately match our
numerical computations. As an additional application of our considerations, we
show that this formulation allows for an analytical approximation of excited
states such as the (trapped) dark soliton in the large density limit.",2401.00213v2
2016-07-07,"Kondo effect at low electron density and high particle-hole asymmetry in 1D, 2D, and 3D","Using the perturbative scaling and the NRG, we study the characteristic
energy scales in the Kondo impurity problem as a function of the exchange
coupling constant $J$ and the conduction electron density. We discuss the
relation between the impurity binding energy $\Delta E$ and the Kondo
temperature $T_K$. We find that the two are proportional only for large values
of $J$, whereas in the weak-coupling limit the energy gain is quadratic in $J$,
while the Kondo temperature is exponentially small. The exact relation between
the two quantities depends on the detailed form of the density of states of the
band. In the limit of low electron density the Kondo screening is affected by
the strong particle-hole asymmetry due to the presence of the band-edge van
Hove singularities. We consider the cases of 1D, 2D, and 3D tight-binding
lattices with inverse-square-root, step function, and square-root onsets of the
density of states that are characteristic of the respective dimensionalities.
We always find two different regimes depending on whether $T_K$ is higher or
lower than $\mu$, the chemical potential measured from the bottom of the band.
For 2D and 3D, we find a sigmoidal cross-over between the large-$J$ and
small-$J$ asymptotics in $\Delta E$, and a clear separation between $\Delta E$
and $T_K$ for $T_K < \mu$. For 1D, there is in addition a sizable
intermediate-$J$ regime where the Kondo temperature is quadratic in $J$ due to
the diverging density of states at the band edge. Furthermore, we find that in
1D the particle-hole asymmetry leads to a large decrease of $T_K$ compared to
the standard result obtained by approximating the density of states to be
constant (flat-band approximation), while in 3D the opposite is the case; this
is due to the non-trivial interplay of the exchange and potential scattering
renormalization in the presence of particle-hole asymmetry.",1607.01891v2
2011-10-18,Low-energy sub-gap states in multi-channel Majorana wires,"One-dimensional p-wave superconductors are known to harbor Majorana bound
states at their ends. Superconducting wires with a finite width W may have
fermionic subgap states in addition to possible Majorana end states. While they
do not necessarily inhibit the use of Majorana end states for topological
computation, these subgap states can obscure the identification of a
topological phase through a density-of-states measurement. We present two
simple models to describe low-energy fermionic subgap states. If the wire's
width W is much smaller than the superconductor coherence length \xi, the
relevant subgap states are localized near the ends of the wire and cluster near
zero energy, whereas the lowest-energy subgap states are delocalized if $W
\gtrsim \xi$. Notably, the energy of the lowest-lying fermionic subgap state
(if present at all) has a maximum for W ~ \xi.",1110.4062v1
2015-03-18,Determination of stabilizer states,"The determination of many special types of quantum states has been studied
thoroughly, such as the generalized |GHZ> states, |W> states equivalent under
stochastic local operations and classical communication and Dicke states. In
this paper, we are going to study another special entanglement states which is
stabilizer states. The stabilizer states and their subset graph states play an
important role in quantum error correcting codes, multipartite purification and
so on. We show that all n- qubit stabilizer states are uniquely determined
(among arbitrary states, pure or mixed) by their reduced density matrices for
systems which are the supports of n independent generators of the corresponding
stabilizer formalisms.",1503.05421v1
2002-09-10,Lattice QCD Results at Finite Temperature and Density,"Recent lattice results on QCD at finite temperatures and densities are
reviewed. Two new and independent techniques give compatible results for
physical quantities. The phase line separating the hadronic and quark-gluon
plasma phases, the critical endpoint and the equation of state are discussed.",0209101v1
2004-08-17,Nuclear Lattice Simulations with EFT,"This proceedings article is a summary of results from work done in
collaboration with Bugra Borasoy and Thomas Schaefer. We study nuclear and
neutron matter by combining chiral effective field theory with non-perturbative
lattice methods. We present results for hot neutron matter at temperatures 20
to 40 MeV and densities below twice nuclear matter density.",0408027v1
2003-10-21,Special relativity and reduced spin density matrices,"We derive the general formula for Lorentz-transformed spin density matrix. It
is shown that an appropriate Lorentz transformation can prduce totally
unpolarized state out of pure one. Further properties, as depurification by an
arbitrary Lorentz boost and its relation to the localization properties are
also discussed.",0310132v1
2007-11-02,Maximum supercurrent in Josephson junctions with alternating critical current density,"We consider theoretically and numerically magnetic field dependencies of the
maximum supercurrent across Josephson tunnel junctions with spatially
alternating critical current density. We find that two flux-penetration fields
and one-splinter-vortex equilibrium state exist in long junctions.",0711.0294v1
2009-08-18,Quantum condensation in electron-hole bilayers with density imbalance,"We study the two-dimensional spatially separated electron-hole system with
density imbalance at absolute zero temperature. By means of the mean-field
theory, we find that the Fulde-Ferrell state is fairly stabilized by the order
parameter mixing effect.",0908.2492v1
2010-11-22,Exact phase space functional for two-body systems,"The determination of the two-body density functional from its one-body
density is achieved for Moshinsky's harmonium model, using a phase-space
formulation, thereby resolving its phase dilemma. The corresponding sign rules
can equivalently be obtained by minimizing the ground-state energy.",1011.4742v1
2020-11-19,A Practical Introduction to Density Functional Theory,"These lecture notes contain a brief practical introduction to doing density
functional theory calculations for crystals using the open source Quantum
Espresso software. The level is aimed at graduate students who are studying
condensed matter or solid state physics, either theoretical or experimental.",2011.09888v1
2021-11-23,A robust solver for wavefunction-based Density Functional Theory calculations,"A new iterative solver is proposed to efficiently calculate the ground state
electronic structure in Density Functional Theory calculations. This algorithm
is particularly useful for simulating physical systems considered difficult to
converge by standard solvers, in particular metallic systems. The effectiveness
of the proposed algorithm is demonstrated on various applications.",2111.11947v1
2004-08-18,Analytical representations of unified equations of state of neutron-star matter,"Analytical representations are derived for two equations of state (EOSs) of
neutron-star matter: FPS and SLy. Each of these EOSs is unified, that is, it
describes the crust and the core of a neutron star using the same physical
model. Two versions of the EOS parametrization are considered. In the first
one, pressure and mass density are given as functions of the baryon density. In
the second version, pressure, mass density, and baryon density are given as
functions of the pseudo-enthalpy, which makes this representation particularly
useful for 2-D calculations of stationary rotating configurations of neutron
stars.",0408324v2
2003-09-15,The equation of state for two flavor QCD at finite density,"We discuss the equation of state for QCD at non-zero temperature and density.
We present results of a simulation for QCD with 2 flavors of p4-improved
staggered fermions. Derivatives of $\ln {\cal Z}$ with respect to quark
chemical potential $\mu_q$ up to fourth order are calculated, enabling
estimates of the pressure, quark number density and associated susceptibilities
as functions of $\mu_q$ via a Taylor series expansion. We also discuss the
radius of convergence of the expansion as a function of temperature. It is
found that the fluctuations in the quark number density increase in the
vicinity of the phase transition temperature and the susceptibilities start to
develop a pronounced peak as $\mu_q$ is increased. This suggests the presence
of a critical endpoint in the $(T, \mu_q)$ plane.",0309077v1
2006-10-12,Constraining the density dependence of the symmetry energy in the nuclear equation of state using heavy ion beams,"The density dependence of the symmetry energy in the equation of state of
asymmetric nuclear matter (N/Z $>$ 1) is important for understanding the
structure of systems as diverse as the atomic nuclei and neutron stars. Due to
a proper lack of understanding of the basic nucleon-nucleon interaction for
matters that are highly asymmetric and at non-normal nuclear density, this very
important quantity has remained largely unconstrained. Recent studies using
beams from the Cyclotron Institute of Texas A$&$M University, constraining the
density dependence of the symmetry energy, is presented. A dependence of the
form E$_{sym}(\rho)$ = C($\rho/\rho_{o})^{\gamma}$, where C = 31.6 MeV and
$\gamma$ = 0.69, is obtained from the dynamical and statistical model analysis.
Their implications to both astrophysical and nuclear physics studies are
discussed.",0610019v1
1999-07-21,Equation of State of Hypermatter in beta Equilibrium in a Quark Model with Excluded Volume Correction,"We study the effects of the finite size of the baryons on the equation of
state of homogeneous hadronic matter with hyperons. The finite extension of
hadrons is introduced in order to improve the perfomance of field theoretical
models at very high densities, simulating the short-range hard-core repulsive
part of the baryon-baryon potential. We choose the Quark Meson Coupling model
to describe the baryon dynamics because this model provides a density dependent
radius of the bag. In addition we calculate finite size corrections for the
Zimanyi-Moszkowski model in order to make a definite comparison. In both cases
finite size effects are implemented through a Van der Waals like correction in
the normalization of the baryon fields. In this approach we investigate
$\beta$-stable matter in conditions that could be found in the interior of
massive stars. We find that the excluded volume corrections contribute
significantly for densities above twice the symmetric nuclear matter saturation
density, although for the quark model the results strongly depends upon the
equilibrium conditions for the confinement volume immersed in a dense medium.",9907087v1
2020-09-28,Phase diagram of alpha matter with Skyrme-like scalar interaction,"The equation of state and phase diagram of strongly interacting matter
composed of $\alpha$ particles are studied in the mean-field approximation. The
particle interactions are included via a Skyrme-like mean field, containing
both attractive and repulsive terms. The model parameters are found by fitting
known values of binding energy and baryon density in the ground state of
$\alpha$ matter, obtained from microscopic calculations by Clark and Wang.
Thermodynamic quantities of $\alpha$ matter are calculated in the broad domains
of temperature and baryon density, which can be reached in heavy-ion collisions
at intermediate energies. The model predicts both first-order liquid-gas phase
transition and Bose-Einstein condensation of $\alpha$ particles. We present the
profiles of scaled variance, sound velocity and isochoric heat capacity along
the isentropic trajectories of $\alpha$ matter. Strong density fluctuations are
predicted in the vicinity of the critical point at temperature $T_c\approx
14~\textrm{MeV}$ and density $n_c\approx 0.012~\textrm{fm}^{-3}$.",2009.13487v3
2023-05-18,Magnetic catalysis in weakly interacting hyperbolic Dirac materials,"Due to linearly vanishing density of states, emergent massless Dirac
quasiparticle resulting from the free fermion motion on a family of
two-dimensional half-filled bipartite hyperbolic lattices feature dynamic mass
generation through quantum phase transitions only for sufficiently strong
finite-range Coulomb repulsion. As such, strong nearest-neighbor Coulomb
repulsion ($V$) is conducive to the nucleation of a charge-density-wave (CDW)
order with a staggered pattern of average fermionic density between two
sublattices of bipartite hyperbolic lattices. Considering a collection of
spinless fermions (for simplicity), here we show that application of strong
external magnetic fields by virtue of producing a \emph{finite} density of
states near the zero energy triggers the condensation of the CDW order even for
\emph{infinitesimal} $V$. The proposed magnetic catalysis mechanism is
operative for uniform as well as inhomogeneous (bell-shaped) magnetic fields.
We present scaling of the CDW order with the total flux enclosed by hyperbolic
Dirac materials for a wide range of (especially subcritical) $V$.",2305.11174v1
2016-09-30,Cosmological implications of the transition from the false vacuum to the true vacuum state,"We study the cosmology with the running dark energy. The parametrization of
dark energy with the respect to the redshift is derived from the first
principles of quantum mechanics. Energy density of dark energy is obtained from
the quantum process of transition from the false vacuum state to the true
vacuum state. This is the class of the extended interacting $\Lambda$CDM
models. We consider the energy density of dark energy parametrization
$\rho_\text{de}(t)$, which follows from the Breit-Wigner energy distribution
function which is used to model the quantum unstable systems. The idea that
properties of the process of the quantum mechanical decay of unstable states
can help to understand the properties of the observed universe was formulated
by Krauss and Dent and this idea was used in our considerations. In the
cosmological model with the mentioned parametrization there is an energy
transfer between the dark matter and dark energy. In such a evolutional
scenario the universe is starting from the false vacuum state and going to the
true vacuum state of the present day universe. We find that the intermediate
regime during the passage from false to true vacuum states takes place. The
intensity of the analyzed process is measured by a parameter $\alpha$. For the
small value of $\alpha$ ($0<\alpha <0.4$) this intermediate (quantum) regime is
characterized by an oscillatory behavior of the density of dark energy while
the for $\alpha > 0.4$ the density of the dark energy simply jumps down. In
both cases (independent from the parameter $\alpha$) the today value of density
of dark energy is reached at the value of $0.7$. We estimate the cosmological
parameters for this model with visible and dark matter. This model becomes in
good agreement with the astronomical data and is practically indistinguishable
from $\Lambda$CDM model.",1609.09828v2
2016-03-24,Disorder-induced density of states on the surface of a spherical topological insulator,"We consider a topological insulator (TI) of spherical geometry and
numerically investigate the influence of disorder on the density of surface
states. To the clean Hamiltonian we add a surface disorder potential of the
most general hermitian form, $V = V^0(\theta,\phi) + {\bf V}(\theta,\phi) \cdot
{\bf \sigma}$. We expand these four disorder functions in spherical harmonics
and draw the expansion coefficients randomly from a four-dimensional, zero-mean
gaussian distribution. Different strengths and classes of disorder are realized
by specifying the $4 \times 4$ covariance matrix. For each instantiation of the
disorder, we solve for the energy spectrum via exact diagonalization. Then we
compute the disorder-averaged density of states, $\rho(E)$, by averaging over
200,000 different instantiations. Disorder broadens the Landau-level delta
functions of the clean density of states into peaks that decay and merge
together. If the spin-dependent term is dominant, these peaks split due to the
breaking of the degeneracy between time-reversed partner states. Increasing
disorder strength pushes states closer and closer to zero energy (the Dirac
point), resulting in a low-energy density of states that becomes nonzero for
sufficient disorder, typically approaching an energy-independent saturation
value, for most classes of disorder. But for purely spin-dependent disorder
with ${\bf V}$ either entirely out-of-surface or entirely in-surface, we
identify intriguing disorder-induced features in the vicinity of the Dirac
point. In the out-of-surface case, a new peak emerges at zero energy. In the
in-surface case, we see a symmetry-protected zero at zero energy, with
$\rho(E)$ increasing linearly toward nonzero-energy peaks. These striking
features are explained in terms of the breaking (or not) of two chiral
symmetries of the clean Hamiltonian.",1603.07676v1
2006-01-31,Equation of state for isospin asymmetric nuclear matter using Lane potential,"A mean field calculation for obtaining the equation of state (EOS) for
symmetric nuclear matter from a density dependent M3Y interaction supplemented
by a zero-range potential is described. The energy per nucleon is minimized to
obtain the ground state of symmetric nuclear matter. The saturation energy per
nucleon used for nuclear matter calculations is determined from the
co-efficient of the volume term of Bethe-Weizs\""acker mass formula which is
evaluated by fitting the recent experimental and estimated atomic mass excesses
from Audi-Wapstra-Thibault atomic mass table by minimizing the mean square
deviation. The constants of density dependence of the effective interaction are
obtained by reproducing the saturation energy per nucleon and the saturation
density of spin and isospin symmetric cold infinite nuclear matter. The EOS of
symmetric nuclear matter, thus obtained, provide reasonably good estimate of
nuclear incompressibility. Once the consants of density dependence are
determined, EOS for asymmetric nuclear matter is calculated by adding to the
isoscalar part, the isovector component of the M3Y interaction that do not
contribute to the EOS of symmetric nuclear matter. These EOS are then used to
calculate the pressure, the energy density and the velocity of sound in
symmetric as well as isospin asymmetric nuclear matter.",0601098v2
2020-07-13,Radius and equation of state constraints from massive neutron stars and GW190814,"Motivated by the unknown nature of the $2.50-2.67\,M_\odot$ compact object in
the binary merger event GW190814, we study the maximum neutron star mass based
on constraints from low-energy nuclear physics, neutron star tidal
deformabilities from GW170817, and simultaneous mass-radius measurements of PSR
J0030+045 from NICER. Our prior distribution is based on a combination of
nuclear modeling valid in the vicinity of normal nuclear densities together
with the assumption of a maximally stiff equation of state at high densities, a
choice that enables us to probe the connection between observed heavy neutron
stars and the transition density at which conventional nuclear physics models
must break down. We demonstrate that a modification of the highly uncertain
supra-saturation density equation of state beyond 2.64 times normal nuclear
density is required in order for chiral effective field theory models to be
consistent with current neutron star observations and the existence of
$2.6\,M_\odot$ neutron stars. We also show that the existence of very massive
neutron stars strongly impacts the radii of $\sim 2.0\,M_\odot$ neutron stars
(but not necessarily the radii of $1.4\,M_\odot$ neutron stars), which further
motivates future NICER radius measurements of PSR J1614-2230 and PSR
J0740+6620.",2007.06526v3
2020-12-11,Density profile of a self-gravitating polytropic turbulent fluid in the context of ensembles of molecular clouds,"We obtain an equation for the density profile in a self-gravitating
polytropic spherically symmetric turbulent fluid with an equation of state
$p_{\rm gas}\propto \rho^\Gamma$. This is done in the framework of ensembles of
molecular clouds represented by single abstract objects as introduced by Donkov
et al. (2017). The adopted physical picture is appropriate to describe the
conditions near to the cloud core where the equation of state changes from
isothermal (in the outer cloud layers) with $\Gamma=1$ to one of `hard
polytrope' with exponent $\Gamma>1$. On the assumption of steady state, as the
accreting matter passes through all spatial scales, we show that the total
energy per unit mass is an invariant with respect to the fluid flow. The
obtained equation reproduces the Bernoulli equation for the proposed model and
describes the balance of the kinetic, thermal and gravitational energy of a
fluid element. We propose as well a method to obtain approximate solutions in a
power-law form which results in four solutions corresponding to different
density profiles, polytropic exponents and energy balance equations for a fluid
element. One of them, a density profile with slope $-3$ and polytropic exponent
$\Gamma=4/3$, matches with observations and numerical works and, in particular,
leads to a second power-law tail of the density distribution function in dense,
self-gravitating cloud regions.",2012.06252v3
1993-07-19,Density of states and magnetic susceptibilities on the octagonal tiling,"We study electronic properties as a function of the six types of local
environments found in the octagonal tiling. The density of states has six
characteristic forms, although the detailed structure differs from site to site
since no two sites are equivalent in a quasiperiodic tiling. We present the
site-dependent magnetic susceptibility of electrons on this tiling, which also
has six characteristic dependences. We show the existence of a non-local spin
susceptibility, which decays with the square of the distance between sites and
is the quasiperiodic version of Ruderman-Kittel oscillations. These results are
obtained for a tight-binding Hamiltonian with pure hopping.Finally, we
investigate the formation of local magnetic moments when electron-electron
interactions are included.",9307038v1
2000-02-16,Vibrational properties of the one-component $σ$ phase,"A structural model of a one-component $\sigma$-phase crystal has been
constructed by means of molecular dynamics simulation. The phonon dispersion
curves and the vibrational density of states were computed for this model. The
dependence of the vibrational properties on the thermodynamical parameters was
investigated. The vibrational density of states of the $\sigma$-phase structure
is found to be similar to that of a one-component glass with icosahedral local
order. On the basis of this comparison it is concluded that the $\sigma$ phase
can be considered to be a good crystalline reference structure for this glass.",0002243v1
2000-10-04,Measurement of the energy dependence of phase relaxation by single electron tunneling,"Single electron tunneling through a single impurity level is used to probe
the fluctuations of the local density of states in the emitter. The energy
dependence of quasi-particle relaxation in the emitter can be extracted from
the damping of the fluctuations of the local density of states (LDOS). At
larger magnetic fields Zeeman splitting is observed.",0010070v1
2000-12-06,Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory,"The performance of many-body perturbation theory for calculating ground-state
properties is investigated. We present fully numerical results for the electron
gas in three and two dimensions in the framework of the GW approximation. The
overall agreement with very accurate Monte Carlo data is excellent, even for
those ranges of densities for which the GW approach is often supposed to be
unsuitable. The latter seems to be due to the fulfilment of general
conservation rules. These results open further prospects for accurate
calculations of ground-state properties circumventing the limitations of
standard density functional theory.",0012090v1
2003-11-14,Transport through ferromagnet/superconductor interfaces,"The differential resistance of submicron-size ferromagnet/superconductor
interface structures shows asymmetries as a function of the current through the
ferromagnet/superconductor interface. These asymmetries are a consequence of
spin-polarized electron transport from the ferromagnet to the superconductor,
coupled with the Zeeman-splitting of the superconducting quasiparticle density
of states. They are sensitive to the orientation of the magnetization of the
ferromagnet, as the magnetic field required to spin-split the quasiparticle
density of states can be provided by the ferromagnetic element itself.",0311334v2
2002-04-06,Black hole entropy without brick walls,"The properties of the thermal radiation are discussed by using the new
equation of state density motivated by the generalized uncertainty relation in
the quantum gravity. There is no burst at the last stage of the emission of a
Schwarzshild black hole. When the new equation of state density is utilized to
investigate the entropy of a scalar field outside the horizon of a static black
hole, the divergence appearing in the brick wall model is removed, without any
cutoff. The entropy proportional to the horizon area is derived from the
contribution of the vicinity of the horizon.",0204029v2
2005-07-19,Results dealing with the behavior of the integrated density of states of random divergence operators,"In this paper we generalize and improve results proven for acoustic operators
in \cite{jmp,long}. It deals with the behavior of the integrated density of
states of random divergence operators of the form
$H\_\omega=\sum\_{i,j=1}^d\partial\_{x\_{i}}a\_{i,j}(\omega,x)\partial\_{x\_j}$
; on the internal band edges of the spectrum. We propose an application of such
a result to get localization.",0507385v2
2002-04-15,Existence of the density of states for one-dimensional alloy-type potentials with small support,"We study spectral properties of Schr\""odinger operators with random
potentials of alloy type on $L^2(\RR)$ and their restrictions to finite
intervals. A Wegner estimate for non-negative single site potentials with small
support is proven. It implies the existence and local uniform boundedness of
the density of states. Our estimate is valid for all bounded energy intervals.
Wegner estimates play a key role in an existence proof of pure point spectrum.",0204030v1
2008-04-29,Electronic structure of magnetically modulated graphene,"We present a theoretical study of the electronic structure of magnetically
modulated graphene. We consider monolayer graphene in the presence of a
perpendicular magnetic field and a unidirectional weak magnetic modulation. The
density of states and the bandwidth of the Dirac electrons in this system are
determined. We have found magnetic Weiss oscillations in the bandwidth and the
density of states. These oscillations are out of phase and larger in amplitude
than the ones in the electrically modulated graphene. In addition, these
oscillations are in phase and smaller in amplitude to those of magnetically
modulated standard electron gas system.",0804.4583v2
2009-01-06,Wang-Landau simulation for the quasi-one-dimensional Ising model,"We revisit the nature of the quasi-one-dimensional Ising model on the basis
of Wang-Landau simulation. We introduce the density of states in the
two-dimensional energy space corresponding to the intra- and inter-chain
directions. We then analyze the interchain coupling dependence of the specific
heat of the anistropic two-dimensional Ising model in the context of the
density of states, and further discuss the size dependences of the peak
temperature. We also discuss the feature of the phase transition in the
three-dimensional case.",0901.0637v2
2009-10-27,A Heat Kernel Approach to Interest Rate Models,"We construct default-free interest rate models in the spirit of the
well-known Markov funcional models: our focus is analytic tractability of the
models and generality of the approach. We work in the setting of state price
densities and construct models by means of the so called propagation property.
The propagation property can be found implicitly in all of the popular state
price density approaches, in particular heat kernels share the propagation
property (wherefrom we deduced the name of the approach). As a related matter,
an interesting property of heat kernels is presented, too.",0910.5033v1
2014-09-02,On the symmetry of the electronic density in the three-electron parabolic quantum dot,"The structure of the lowest states of a three-electron axially symmetric
parabolic quantum dot in a zero magnetic field is investigated. It is shown
that the electronic density of the triplet states possesses certain approximate
symmetry which is best seen when using Dalitz plots as the visualization tool.
It is demonstrated that the origin of that symmetry is caused by the symmetry
of the potential energy in the vicinity of its minimum. The discovered symmetry
could provide an insight into the problem of the separation of slow and fast
variables in the Schro\""dinger equation for the axially or spherically
symmetric quantum dots.",1409.0613v2
2016-09-17,Effects of electron-impurity scattering on density of states in silicene: impurity bands and band-gap narrowing,"Considering the interband correlation, we present a generalized
multiple-scattering approach of Green's function to investigate the effects of
electron-impurity scattering on the density of states in silicene. The
reduction of energy gaps in the case of relatively high chemical potential and
the transformation of split-off impurity bands into band tails for low chemical
potential are found. The dependency of optical conductivity on the impurity
concentration is also discussed for frequency within the terahertz regime.",1609.05260v1
2016-10-10,The crystalline structure of orthorhombic SrRuO$_3$: Application of hybrid scheme to the density functionals revised for solids,"The crystalline structure of ground-state orthorhombic SrRuO$_3$ is
reproduced by applying hybrid density functional theory scheme to the
functionals based on the revised generalized-gradient approximations for
solid-state calculations. The amount of Hartree-Fock (HF) exchange energy is
varied in the range of $5-20\%$ in order to systematically ascertain the
optimum value of HF mixing which in turn ensures the best correspondence to the
experimental measurements. Such investigation allows to expand the set of tools
that could be used for the efficient theoretical modelling of, for example,
only recently stabilized phases of SrRuO$_3$.",1610.02942v1
2016-10-23,On the change of density of states in two-body interactions,"We derive a general relation in two-body scattering theory that more directly
relates the change of density of states (DDOS) due to interaction to the shape
of the potential. The relation allows us to infer certain global properties of
the DDOS from the global properties of the potential. In particular, we show
that DDOS is negative at all energies and for all partial waves, for potentials
that are more repulsive than $+1/r^2$ everywhere. This behavior represents a
different class of global properties of DDOS from that described by the
Levinson's theorem.",1610.07210v1
2017-02-23,Description of spontaneous photon emission and local density of states in presence of a lossy polaritonic inhomogenous medium,"We provide a description of spontaneous emission in a dispersive and
dissipative linear inhomogeneous medium based on the generalized
Huttner-Barnett model [Phys. Rev. A 46, 4306 (1992)]. Our discussion considers
on an equal footing both the photonic and material fluctuations which are
necessary to preserve unitarity of the quantum evolution. Within this approach
we justify the results obtained in the past using the Langevin noise method
that neglects the removal of photonic fluctuations. We finally discuss the
concept of local density of states (LDOS) in a lossy and dispersive
inhomogeneous environment that provides a basis for theoretical studies of
fluorescent emitters near plasmonic and polaritonic antennas.",1702.07127v1
2017-05-02,Investigation of Defect Modes of Chiral Photonic Crystals,"Some properties of defect modes of cholesteric liquid crystals (CLC) are
presented. It is shown that when the CLC layer is thin the density of states
and emission intensity are maximum for the defect mode, whereas when the CLC
layer is thick, these peaks are observed at the edges of the photonic band gap.
Similarly, when the gain is low, the density of states and emission intensity
are maximum for the defect mode, whereas at high gains these peaks are also
observed at the edges of the photonic band gap. The possibilities of
low-threshold lasing and obtaining high-Q microcavities have been investigated.",1705.02376v1
2011-11-14,Lifshitz tails for matrix-valued Anderson models,"This paper is devoted to the study of Lifshitz tails for a continuous
matrix-valued Anderson-type model $H_{\omega}$ acting on $L^2(\R^d)\otimes
\C^{D}$, for arbitrary $d\geq 1$ and $D\geq 1$. We prove that the integrated
density of states of $H_{\omega}$ has a Lifshitz behavior at the bottom of the
spectrum. We obtain a Lifshitz exponent equal to $-d/2$ and this exponent is
independent of $D$. It shows that the behaviour of the integrated density of
states at the bottom of the spectrum of a quasi-d-dimensional Anderson model is
the same as its behaviour for a d-dimensional Anderson model.",1111.3121v2
2012-04-04,Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators,"We obtain a complete asymptotic expansion of the integrated density of states
of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs to
a wide class of almost-periodic self-adjoint pseudo-differential operators of
order less than 2w. In particular, we obtain such an expansion for magnetic
Schr\""odinger operators with either smooth periodic or generic almost-periodic
coefficients.",1204.1076v1
2013-09-23,Distribution of Entropy of Bardeen Regular Black Hole with Corrected State Density,"We consider corrections to all orders in the Planck length on the quantum
state density, and calculate the statistical entropy of the scalar field on the
background of the Bardeen regular black hole numerically. We obtain the
distribution of entropy which is inside the horizon of black hole and the
contribution of the vicinity of horizon takes a great part of the whole
entropy.",1309.5699v1
2019-03-28,On the continuity of the integrated density of states in the disorder,"Recently, Hislop and Marx studied the dependence of the integrated density of
states on the underlying probability distribution for a class of discrete
random Schr\""odinger operators, and established a quantitative form of
continuity in weak* topology. We develop an alternative approach to the
problem, based on Ky Fan inequalities, and establish a sharp version of the
estimate of Hislop and Marx. We also consider a corresponding problem for
continual random Schr\""odinger operators on $\R^d$.",1903.12222v2
2019-06-11,Collective spin density excitations of fractional quantum Hall states in dilute ultracold Bose atoms,"We have studied collective spin density excitations of fractional quantum
Hall effect (FQHE) in rotating Bose-Einstein condensation for the three filling
fractions of first series of Jain's composite fermion sequences. We have
considered, short-ranged contact interactions between the Bose atoms as well as
long range Coulomb interactions to compare the nature of the spectras with FQHE
of electrons. Using Monte Carlo method for finite but large number of
particles, the lowest order collective modes of spin-reversed sectors is
calculated here, by computing the energy differences of the respective excitons
from the fully polarized ground states.",1906.04917v1
2007-05-11,Quantum Measurement as a Final-State Interaction with a Macroscopic External System,"A small quantum scattering system (the microsystem) is studied in interaction
with a large system (the macrosystem) described by unknown stochastic
variables. The interaction between the two systems is diagonal for the
microsystem in a certain orthonormal basis, and the interaction gives an
imprint on the macrosystem. Moreover, the interaction is assumed to involve
only small transfers of energy and momentum between the two systems (as
compared to typical energies/momenta within the microsystem). The analysis is
carried out within scattering theory. Calculated in the conventional way, the
transition amplitude for the whole system factorizes. The interaction taking
place within the macrosystem is assumed to depend on the stochastic variables
in such a way that, on the average, no particular basis vector state of the
microsystem is favoured. The density matrix is studied in a formalism which
includes generation of the ingoing state and absorption of the final state.
Then the dependence of the final state on the conventional scattering amplitude
for the microsystem is highly non-linear.
  In the thermodynamic limit of the macrosystem, the density matrix of the
ensemble (of microsystem plus macrosystem) develops into a final state which
involves a set of macroscopically distinguishable states, each with the
microsystem in one of the basis vector states and the macrosystem in an
entangled state.
  For an element of the ensemble, i.e., for a single measurement, the result is
instead a random walk, where the microsystem ends up in one of the basis vector
states (reduction of the wave packet).",0705.1649v1
2024-01-04,Dynamic coexistence driven by physiological transitions in microbial communities,"Microbial ecosystems are commonly modeled by fixed interactions between
species in steady exponential growth states. However, microbes often modify
their environments so strongly that they are forced out of the exponential
state into stressed or non-growing states. Such dynamics are typical of
ecological succession in nature and serial-dilution cycles in the laboratory.
Here, we introduce a phenomenological model, the Community State model, to gain
insight into the dynamic coexistence of microbes due to changes in their
physiological states. Our model bypasses specific interactions (e.g., nutrient
starvation, stress, aggregation) that lead to different combinations of
physiological states, referred to collectively as ""community states"", and
modeled by specifying the growth preference of each species along a global
ecological coordinate, taken here to be the total community biomass density. We
identify three key features of such dynamical communities that contrast starkly
with steady-state communities: increased tolerance of community diversity to
fast growth rates of species dominating different community states, enhanced
community stability through staggered dominance of different species in
different community states, and increased requirement on growth dominance for
the inclusion of late-growing species. These features, derived explicitly for
simplified models, are proposed here to be principles aiding the understanding
of complex dynamical communities. Our model shifts the focus of ecosystem
dynamics from bottom-up studies based on idealized inter-species interaction to
top-down studies based on accessible macroscopic observables such as growth
rates and total biomass density, enabling quantitative examination of
community-wide characteristics.",2401.02556v1
2002-04-14,Superconducting charge-ordered states in cuprates,"Motivated by recent neutron scattering and scanning tunneling microscopy
(STM) experiments on cuprate superconductors, we discuss charge-ordered states,
in particular with two-dimensional charge modulation patterns, co-existing with
superconductivity. We extend previous studies of a large-N mean-field
formulation of the t-J model. In addition to bond-centered superconducting
stripe states at low doping, we find checkerboard-modulated superconducting
states which are favorable in an intermediate doping interval. We also analyze
the energy dependence of the Fourier component of the local density of states
at the ordering wavevector for several possible modulation patterns, and
compare with STM results.",0204284v2
2016-09-06,Landau-Zener-Stueckelberg physics with a singular continuum of states,"This work addresses the dynamical quantum problem of a driven discrete energy
level coupled to a semi-infinite continuum whose density of states has a
square-root-type singularity, such as states of a free particle in one
dimension or quasiparticle states in a BCS superconductor. The system dynamics
is strongly affected by the quantum-mechanical repulsion between the discrete
level and the singularity, which gives rise to a bound state, suppresses the
decay into the continuum, and can produce Stueckelberg oscillations. This
quantum coherence effect may limit the performance of mesoscopic
superconducting devices, such as quantum electron turnstile.",1609.01418v2
2002-04-17,Electronic structure of multiquantum giant vortex states in mesoscopic superconducting disks,"We report self-consistent calculations of the microscopic electronic
structure of the so-called giant vortex states. These novel multiquantum vortex
states, detected by recent magnetization measurements on submicron disks, are
qualitatively different from the Abrikosov vortices in the bulk. We find that,
in addition to multiple branches of bound states in the core region, the local
tunneling density of states exhibits Tomasch oscillations due to the
single-particle interference arising from quantum confinement. These features
should be directly observable by scanning tunneling spectroscopy.",0204384v1
2000-03-07,Maximally entangled mixed states in two qubits,"We propose novel mixed states in two qubits, ``maximally entangled mixed
states'', which have a property that the amount of entanglement of these states
cannot be increased further by applying any unitary operations. The property is
proven when the rank of the states is less than 4, and confirmed numerically in
the other general cases. The corresponding entanglement of formation specified
by its eigenvalues gives an upper bound of that for density matrices with same
eigenvalues.",0003023v1
2002-04-18,Calculation of entanglement for continious variable states,"In this paper, we present a general formula for obtaining the reduced density
opeator for any biparticle pure entangled state. Using this formula, we derive,
in a compact form, the explicit formula of the entanglement for any bipartical
pure entangled Gaussian state. In the case of Gaussian states, the criteria of
separabelity can be naturely obtained by the formula. For non-Gaussian states,
we also show the usefulness of the method presented in this paper.",0204098v1
2007-04-04,Vortex state in a Fulde-Ferrell-Larkin-Ovchinnikov superconductor based on the quasiclassical theory,"We investigate the vortex state with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
modulations suggested for a high field phase of CeCoIn_5. On the basis of the
quasiclassical Eilenberger theory, we calculate the three dimensional structure
of pair potentials, internal magnetic fields, paramagnetic moments, and
electronic states, for the s-wave and the d-wave pairings comparatively. The
\pi-phase shift of the pair potential at the FFLO nodal plane or at the vortex
core induces sharp peak states in the local density of states, and enhances the
local paramagnetic moment. We also discuss the NMR spectrum and the neutron
scattering as methods to detect the FFLO structure.",0704.0483v1
2008-09-15,Steady state of Stochastic Sandpile Models,"We study the steady state of the abelian sandpile models with stochastic
toppling rules. The particle addition operators commute with each other, but in
general these operators need not be diagonalizable. We use their abelian
algebra to determine their eigenvalues, and the Jordan block structure. These
are then used to determine the probability of different configurations in the
steady state. We illustrate this procedure by explicitly determining the
numerically exact steady state for a one dimensional example, for systems of
size $\le12$, and also study the density profile in the steady state.",0809.2615v1
2015-01-07,Domain walls in superconductors: Andreev bound states and tunneling features,"Domain walls can be formed in superconductors with a discrete degeneracy of
the ground state, for instance, due to the breaking of time reversal symmetry.
We study all cases where the formation of domain walls is possible in a
tetragonal superconductor with the point group $D_{4h}$. We discuss both
triplet and mixed singlet order parameters. It is found that in all cases the
domain walls support subgap Andreev bound states, whose energies strongly
depend on the direction of semiclassical propagation. The bound state
contribution to the density of quasiparticle states exhibits peculiar features,
which can be observed in tunneling experiments.",1501.01570v2
2015-07-22,Superconductivity Induced Topological Phase Transition at the Edge of Even Denominator Fractional Quantum Hall States,"We show that every even-denominator fractional quantum Hall (FQH) state
possesses at least two robust, topologically distinct gapless edge phases if
charge conservation is broken at the boundary by coupling to a superconductor.
The new edge phase allows for the possibility of a direct coupling between
electrons and emergent neutral fermions of the FQH state. This can potentially
be experimentally probed through geometric resonances in the tunneling density
of states at the edge, providing a probe of fractionalized, yet electrically
neutral, bulk quasiparticles. Other measurable consequences include a charge
$e$ fractional Josephson effect, a charge $e/4q$ quasiparticle blocking effect
in filling fraction $p/2q$ FQH states, and modified edge electron tunneling
exponents.",1507.06305v1
2017-02-13,Implementation of quantum state tomography for time-bin qudits,"Quantum state tomography (QST) is an essential tool for characterizing an
unknown quantum state. Recently, QST has been performed for entangled qudits
based on orbital angular momentum, time-energy uncertainty, and frequency bins.
Here, we propose a QST for time-bin qudits, with which the number of
measurement settings scales linearly with dimension $d$. Using the proposed
scheme, we performed QST for a four-dimensional time-bin maximally entangled
state with 16 measurement settings. We successfully reconstructed the density
matrix of the entangled qudits, with which the average fidelity of the state
was calculated to be 0.950.",1702.03635v1
2018-06-14,Correlation Measurement of an unknown state with Weak Coupling,"Traditionally, quantum state correlation can be obtained with calculations on
a state density matrix already known. Here, we propose a model with which
correlations of unknown quantum states can be obtained. There are no needs of
classical communication in the course of coupling, optimization and complicated
calculations. All we need are weak coupling and ancillary systems. We detail
the model on the state in which particles belong to the different owners. A
concisely example is elaborated in the last part of this paper.",1806.05591v2
2009-12-01,"Pressure-Induced Insulating State in Ba1-xRExIrO3 (RE = Gd, Eu) Single Crystals","BaIrO3 is a novel insulator with coexistent weak ferromagnetism, charge and
spin density wave. Dilute RE doping for Ba induces a metallic state, whereas
application of modest pressure readily restores an insulating state
characterized by a three-order-of-magnitude increase of resistivity. Since
pressure generally increases orbital overlap and broadens energy bands, a
pressure-induced insulating state is not commonplace. The profoundly dissimilar
responses of the ground state to light doping and low hydrostatic pressures
signal an unusual, delicate interplay between structural and electronic degrees
of freedom in BaIrO3.",0912.0227v1
2019-06-24,Communal pairing in spin-imbalanced Fermi gases,"A spin-imbalanced Fermi gas with an attractive contact interaction forms a
superconducting state whose underlying components are superpositions of Cooper
pairs that share minority-spin fermions. This superconducting state includes
correlations between all available fermions, making it energetically favorable
to the Fulde--Ferrell--Larkin--Ovchinnikov superconducting state. The ratio of
the number of up- and down-spin fermions in the instability is set by the ratio
of the up- and down-spin density of states in momentum at the Fermi surfaces,
to fully utilize the accessible fermions. We present analytical and
complementary Diffusion Monte Carlo results for the state.",1906.10227v2
2020-12-22,Tensor-network approach to thermalization in open quantum many-body systems,"We investigate the relaxation dynamics of open non-integrable quantum
many-body systems in the thermodynamic limit by using a tensor-network
formalism. We simulate the Lindblad quantum master equation (LQME) of infinite
systems by making use of the uniform matrix product operators (MPO) as the
ansatz of their density matrices. Furthermore, we establish a method to measure
the thermodynamic equivalence between two states described by the uniform MPOs.
We numerically show that when an initial state of the LQME is a thermal Gibbs
state, a time evolved state is always indistinguishable from a Gibbs state with
a time-dependent effective temperature in the weak-dissipation and
thermodynamic limit.",2012.12274v1
2022-09-07,The Stability of the Quantum Hall State at $ν= 1$ in Bilayer Electron Systems,"The ground states of electrons in two vertically coupled quantum dots in the
presence of an external magnetic field have been studied within the density
functional theory. A phase diagram of the transition to the quantum Hall state
in double quantum dots has been plotted for the Landau level filling factor
$\nu = 1$. It has been shown that the quantum Hall state can be stable for a
zero tunnel splitting. The influence of the impurity potential on the stability
condition for the quantum Hall state has been analyzed.",2209.03429v1
2015-05-27,Unusual A2142 supercluster with a collapsing core: distribution of light and mass,"We study the distribution, masses, and dynamical properties of galaxy groups
in the A2142 supercluster. We analyse the global luminosity density
distribution in the supercluster and divide the supercluster into the
high-density core and the low-density outskirts regions. We find galaxy groups
and filaments in the regions of different global density, calculate their
masses and mass-to-light ratios and analyse their dynamical state with several
1D and 3D statistics. We use the spherical collapse model to study the
dynamical state of the supercluster. We show that in A2142 supercluster groups
and clusters with at least ten member galaxies lie along an almost straight
line forming a 50 Mpc/h long main body of the supercluster. The A2142
supercluster has a very high density core surrounded by lower-density outskirt
regions. The total estimated mass of the supercluster is M_est = 6.2
10^{15}M_sun. More than a half of groups with at least ten member galaxies in
the supercluster lie in the high-density core of the supercluster, centered at
the rich X-ray cluster A2142. Most of the galaxy groups in the core region are
multimodal. In the outskirts of the supercluster, the number of groups is
larger than in the core, and groups are poorer. The orientation of the cluster
A2142 axis follows the orientations of its X-ray substructures and radio halo,
and is aligned along the supercluster axis. The high-density core of the
supercluster with the global density D8 > 17 and perhaps with D8 > 13 may have
reached the turnaround radius and started to collapse. A2142 supercluster with
luminous, collapsing core and straight body is an unusual object among galaxy
superclusters. In the course of the future evolution the supercluster may be
split into several separate systems.",1505.07233v2
2019-12-20,AutoScale: Learning to Scale for Crowd Counting and Localization,"Recent works on crowd counting mainly leverage CNNs to count by regressing
density maps, and have achieved great progress. In the density map, each person
is represented by a Gaussian blob, and the final count is obtained from the
integration of the whole map. However, it is difficult to accurately predict
the density map on dense regions. A major issue is that the density map on
dense regions usually accumulates density values from a number of nearby
Gaussian blobs, yielding different large density values on a small set of
pixels. This makes the density map present variant patterns with significant
pattern shifts and brings a long-tailed distribution of pixel-wise density
values. We propose a simple and effective Learning to Scale (L2S) module, which
automatically scales dense regions into reasonable closeness levels (reflecting
image-plane distance between neighboring people). L2S directly normalizes the
closeness in different patches such that it dynamically separates the
overlapped blobs, decomposes the accumulated values in the ground-truth density
map, and thus alleviates the pattern shifts and long-tailed distribution of
density values. This helps the model to better learn the density map. We also
explore the effectiveness of L2S in localizing people by finding the local
minima of the quantized distance (w.r.t. person location map). To the best of
our knowledge, such a localization method is also novel in localization-based
crowd counting. We further introduce a customized dynamic cross-entropy loss,
significantly improving the localization-based model optimization. Extensive
experiments demonstrate that the proposed framework termed AutoScale improves
upon some state-of-the-art methods in both regression and localization
benchmarks on three crowded datasets and achieves very competitive performance
on two sparse datasets.",1912.09632v4
1996-03-29,Plasmons in simple-metal slabs: a semiclassical approach,"Collective excitations in simple metal systems can be described successfully
in terms of a local one-body excitation operator Q, due to the long range
nature of the coulomb interaction. For the plasmon modes of a simple-metal
slab, momentum expansions of Q are calculated using a variational procedure,
equivalent to a restricted RPA calculation. The dispersion relation and the
density fluctuation for each mode are found in the sudden approximation using
the proper Q operator and the RPA sum-rule formalism. The contribution of the
exchange and correlation energy is estimated using a local density functional.
The positive background is described within a jellium model while the
ground-state electronic density is approximated by a double step profile. The
density fluctuation of the plasmon modes above the plasma frequency form
standing waves across the slab. The spectra below the plasma frequency is
qualitatively different to that of local optics calculations, due to the
appearance of two multipole plasmon modes that shift down the origin of the
$\omega_{+}$ plasmon. The dependence of the results on the width of the slab,
the density of the simple-metal and the surface diffuseness is discussed.
Throughout, we compare our results with previous RPA and TDLDA calculations.",9603184v1
2010-01-04,de Sitter expansion with anisotropic fluid in Bianchi type-I space-time,"Some features of the Bianchi type-I universes in the presence of a fluid that
wields an anisotropic equation of state (EoS) parameter are discussed in the
context of general relativity. The models that exhibit de Sitter volumetric
expansion due to the constant effective energy density (the sum of the energy
density of the fluid and the anisotropy energy density) are of particular
interest. We also introduce two locally rotationally symmetric models, which
exhibit de Sitter volumetric expansion in the presence of a hypothetical fluid
that has been obtained by minimally altering the conventional vacuum energy. In
the first model, the directional EoS parameter on the x axis is assumed to be
-1, while the ones on the other axes and the energy density of the fluid are
allowed to be functions of time. In the second model, the energy density of the
fluid is assumed to be constant, while the directional EoS parameters are
allowed to be functions of time.",1001.0550v2
2013-05-23,A phenomenological model for the description of rotating spokes in HiPIMS discharges,"In the ionization region above circular planar magnetrons well defined
regions of high emissivity are observed, when the discharge is driven in the
HiPIMS regime. Once their mode is stabilized, these structures rotate in the E
x B direction with a constant rotation frequency in the hundreds of kHz range.
A phenomenological model of the phenomenon is developed, in the form of a
system of nonlinear coupled partial differential equations. The system is
solved analytically in a frame co-moving with the structure, and its solution
gives the neutral density and the plasma density once the electron density
shape is imposed. From the balance of the mechanisms of ionization, electron
loss and constant neutral refilling, a steady state configuration in the
rotating frame is achieved for the electron and neutral densities. Therefore,
the spoke experimentally observed can be sustained simply by the combination of
this highly reduced number of phenomena. Finally, a study of the sensitivity of
neutral and plasma densities to the physical parameters is also given.",1305.5354v3
2015-05-31,The density of eigenvalues seen from the soft edge of random matrices in the Gaussian beta-ensembles,"We characterize the phenomenon of ""crowding"" near the largest eigenvalue
$\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian
$\beta$-ensemble of random matrix theory, including in particular the Gaussian
orthogonal ($\beta=1$), unitary ($\beta=2$) and symplectic ($\beta = 4$)
ensembles. We focus on two distinct quantities: (i) the density of states (DOS)
near $\lambda_{\max}$, $\rho_{\rm DOS}(r,N)$, which is the average density of
eigenvalues located at a distance $r$ from $\lambda_{\max}$ (or the density of
eigenvalues seen from $\lambda_{\max}$) and (ii) the probability density
function of the gap between the first two largest eigenvalues, $p_{\rm
GAP}(r,N)$. Using heuristic arguments as well as well numerical simulations, we
generalize our recent exact analytical study of the Hermitian case
(corresponding to $\beta = 2$). We also discuss some applications of these two
quantities to statistical physics models.",1506.00245v1
2015-08-06,Universal Approximation of Edge Density in Large Graphs,"In this paper, we present a novel way to summarize the structure of large
graphs, based on non-parametric estimation of edge density in directed
multigraphs. Following coclustering approach, we use a clustering of the
vertices, with a piecewise constant estimation of the density of the edges
across the clusters, and address the problem of automatically and reliably
inferring the number of clusters, which is the granularity of the coclustering.
We use a model selection technique with data-dependent prior and obtain an
exact evaluation criterion for the posterior probability of edge density
estimation models. We demonstrate, both theoretically and empirically, that our
data-dependent modeling technique is consistent, resilient to noise, valid non
asymptotically and asymptotically behaves as an universal approximator of the
true edge density in directed multigraphs. We evaluate our method using
artificial graphs and present its practical interest on real world graphs. The
method is both robust and scalable. It is able to extract insightful patterns
in the unsupervised learning setting and to provide state of the art accuracy
when used as a preparation step for supervised learning.",1508.01340v1
2017-03-03,Evidence of density waves in single crystalline nanowires of Pyrochlore Iridates,"We present experimental evidence of emergent density wave instability in
single crystalline low dimensional wires of Yittrium based Pyrochlore Iridates.
We demonstrate electric field induced nonlinear hysteretic switching of the
density wave at low temperature, followed by smooth nonlinear conduction at
higher temperature (T > 40 K) in $Y_{2-x}Bi_{x}Ir_{2}O_{7}$ with x = 0 and 0.3.
AC transport measurements reveal the presence of four different collective
relaxation processes which dominate at different temperature scales. There is a
strong coupling of the normal charge carriers with the density wave condensate,
which is reflected in the linear scaling of the dc conductivity with the
collective relaxation rate across a wide range of frequency and temperature
regime. The evidence of density wave in low dimensional single crystals of
Pyrochlore Iridate could be a precursor to the possible experimental
confirmation of the Weyl semimetallic ground state with broken chiral symmetry.",1703.01115v1
2022-04-14,Effective Dynamics of Extended Fermi Gases in the High-Density Regime,"We study the quantum evolution of many-body Fermi gases in three dimensions,
in arbitrarily large domains. We consider both particles with non-relativistic
and with relativistic dispersion. We focus on the high-density regime, in the
semiclassical scaling, and we consider a class of initial data describing
zero-temperature states. In the non-relativistic case we prove that, as the
density goes to infinity, the many-body evolution of the reduced one-particle
density matrix converges to the solution of the time-dependent Hartree
equation, for short macroscopic times. In the case of relativistic dispersion,
we show convergence of the many-body evolution to the relativistic Hartree
equation for all macroscopic times. With respect to previous work, the rate of
convergence does not depend on the total number of particles, but only on the
density: in particular, our result allows us to study the quantum dynamics of
extensive many-body Fermi gases.",2204.07222v2
2023-05-24,Density Functional Theory of Material Design: Fundamentals and Applications -- I,"This article is part-I of a review of density-functional theory (DFT) that is
the most widely used method for calculating electronic structure of materials.
The accuracy and ease of numerical implementation of DFT methods has resulted
in its extensive use for materials design and discovery and has thus ushered in
the new field of computational material science. In this article we start with
an introduction to Schr\""odinger equation and methods of its solutions. After
presenting exact results for some well-known systems, difficulties encountered
in solving the equation for interacting electrons are described. How these
difficulties are handled using the variational principle for the energy to
obtain approximate solutions of the Schr\""odinger equation is discussed. The
resulting Hartree and Hartree-Fock theories are presented along with results
they give for atomic and solid-state systems. We then describe Thomas-Fermi
theory and its extensions which were the initial attempts to formulate
many-electron problem in terms of electronic density of a system. Having
described these theories, we introduce modern density functional theory by
discussing Hohenberg-Kohn theorems that form its foundations. We then go on to
discuss Kohn-Sham formulation of density-functional theory in its exact form.
Next, local density approximation is introduced and solutions of Kohn-Sham
equation for some representative systems, obtained using the local density
approximation, are presented. We end part-I of the review describing the
contents of part-II.",2305.14634v1
2016-04-15,Estimation of low rank density matrices: bounds in Schatten norms and other distances,"Let ${\mathcal S}_m$ be the set of all $m\times m$ density matrices
(Hermitian positively semi-definite matrices of unit trace). Consider a problem
of estimation of an unknown density matrix $\rho\in {\mathcal S}_m$ based on
outcomes of $n$ measurements of observables $X_1,\dots, X_n\in {\mathbb H}_m$
(${\mathbb H}_m$ being the space of $m\times m$ Hermitian matrices) for a
quantum system identically prepared $n$ times in state $\rho.$ Outcomes
$Y_1,\dots, Y_n$ of such measurements could be described by a trace regression
model in which ${\mathbb E}_{\rho}(Y_j|X_j)={\rm tr}(\rho X_j), j=1,\dots, n.$
The design variables $X_1,\dots, X_n$ are often sampled at random from the
uniform distribution in an orthonormal basis $\{E_1,\dots, E_{m^2}\}$ of
${\mathbb H}_m$ (such as Pauli basis). The goal is to estimate the unknown
density matrix $\rho$ based on the data $(X_1,Y_1), \dots, (X_n,Y_n).$ Let $$
\hat Z:=\frac{m^2}{n}\sum_{j=1}^n Y_j X_j $$ and let $\check \rho$ be the
projection of $\hat Z$ onto the convex set ${\mathcal S}_m$ of density
matrices. It is shown that for estimator $\check \rho$ the minimax lower bounds
in classes of low rank density matrices (established earlier) are attained up
logarithmic factors for all Schatten $p$-norm distances, $p\in [1,\infty]$ and
for Bures version of quantum Hellinger distance. Moreover, for a slightly
modified version of estimator $\check \rho$ the same property holds also for
quantum relative entropy (Kullback-Leibler) distance between density matrices.",1604.04600v1
2018-04-25,Exploring the thermal energy contents of the intergalactic medium with the Sunyaev-Zel'dovich effect,"We examine the thermal energy contents of the intergalactic medium (IGM) over
three orders of magnitude in both mass density and gas temperature using
thermal Sunyaev-Zel'dovich effect (tSZE). The analysis is based on {\it Planck}
tSZE map and the cosmic density field, reconstructed for the SDSS DR7 volume
and sampled on a grid of cubic cells of $(1h^{-1}{\rm Mpc})^3$, together with a
matched filter technique employed to maximize the signal-to-noise. Our results
show that the pressure - density relation of the IGM is roughly a power law
given by an adiabatic equation of state, with an indication of steepening at
densities higher than about $10$ times the mean density of the universe. The
implied average gas temperature is $\sim 10^4\,{\rm K}$ in regions of mean
density, $\rho_{\rm m} \sim {\overline\rho}_{\rm m}$, increasing to about
$10^5\,{\rm K}$ for $\rho_{\rm m} \sim 10\,{\overline\rho}_{\rm m}$, and to
$>10^{6}\,{\rm K}$ for $\rho_{\rm m} \sim 100\,{\overline\rho}_{\rm m}$. At a
given density, the thermal energy content of the IGM is also found to be higher
in regions of stronger tidal fields, likely due to shock heating by the
formation of large scale structure and/or feedback from galaxies and AGNs. A
comparison of the results with hydrodynamic simulations suggests that the
current data can already provide interesting constraints on galaxy formation.",1804.09715v1
2005-11-29,"Density Evolution, Thresholds and the Stability Condition for Non-binary LDPC Codes","We derive the density evolution equations for non-binary low-density
parity-check (LDPC) ensembles when transmission takes place over the binary
erasure channel. We introduce ensembles defined with respect to the general
linear group over the binary field. For these ensembles the density evolution
equations can be written compactly. The density evolution for the general
linear group helps us in understanding the density evolution for codes defined
with respect to finite fields. We compute thresholds for different alphabet
sizes for various LDPC ensembles. Surprisingly, the threshold is not a
monotonic function of the alphabet size. We state the stability condition for
non-binary LDPC ensembles over any binary memoryless symmetric channel. We also
give upper bounds on the MAP thresholds for various non-binary ensembles based
on EXIT curves and the area theorem.",0511100v1
2017-08-22,Kinetic theory based force treatment in lattice Boltzmann equation,"In the gas kinetic theory, it showed that the zeroth order of the density
distribution function $f^{(0)}$ and local equilibrium density distribution
function were the Maxwellian distribution $f^{(eq)}(\rho,\emph{\textbf{u}}, T)$
with an external force term, where $\rho$ the fluid density,
$\emph{\textbf{u}}$ the physical velocity and $T$ the temperature, while in the
lattice Boltzmann equation (LBE) method numerous force treatments were proposed
with a discrete density distribution function $f_i$ apparently relaxed to a
given state $f^{(eq)}_i(\rho,\emph{\textbf{u}}^*)$, where the given velocity
$\emph{\textbf{u}}^*$ could be different with $\emph{\textbf{u}}$, and the
Chapman-Enskog analysis showed that $f^{(0)}_i$ and local equilibrium density
distribution function should be $f^{(eq)}_i(\rho,\emph{\textbf{u}}^*)$ in the
literature. In this paper, we start from the kinetic theory and show that the
$f^{(0)}_i$ and local equilibrium density distribution function in LBE should
obey the Maxwellian distribution $f^{(eq)}_i(\rho,\emph{\textbf{u}})$ with
$f_i$ relaxed to $f^{(eq)}_i(\rho,\emph{\textbf{u}}^*)$, which are consistent
with kinetic theory, then the general requirements for the force term are
derived, by which the correct hydrodynamic equations could be recovered at
Navier-Stokes level, and numerical results confirm our theoretical analysis.",1708.06477v1
2020-05-04,"Probing the supersolid order via high-energy scattering: analytical relations among response, density modulation, and superfluid fraction","High-energy scattering spectroscopy is a widely-established technique for
probing the characteristic properties of complex physical systems. Motivated by
the recent observation of long-sought supersolid states in dipolar quantum Bose
gases, I investigate the general relationships existing between the density
contrast, the superfluid fraction, and the response to a high-energy scattering
probe of density-modulated states within a classical-field approach. I focus on
the two extreme regimes of ""shallow"" and ""deep"" supersolids, which are of
particular interest in describing the phase transitions of the supersolid to a
uniform superfluid and an incoherent crystal state, respectively. Using
relevant Ans\""atze for the fields of dipolar supersolid states in these
regimes, I specify and illustrate the scaling laws relating the three
observables. This work was first prompted to develop an intuitive understanding
of a concomitant study based on experiments and mean-field numerical
simulations. Beyond this specific application, this works provides a simple and
general framework to describe density-modulated states, and in particular the
intriguing case of supersolids. It describes key properties characterizing the
supersolid order and highlights new possibilities for probing such properties
based on high-energy scattering response.",2005.01614v3
2023-07-27,Preparation of Entangled Many-Body States with Machine Learning,"Preparation of a target quantum many-body state on quantum simulators is one
of the significant steps in quantum science and technology. With a small number
of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state,
have been prepared, but fundamental difficulties in systems with many qubits
remain, including the Lieb-Robinson bounds for the number of quantum
operations. Here, we provide one algorithm with an implementation of a deep
learning process and achieve to prepare the target ground states with many
qubits. Our strategy is to train a machine-learning model and predict
parameters with many qubits by utilizing a pattern of quantum states from the
corresponding quantum states with small numbers of qubits. For example, we
demonstrate that our algorithm with the Quantum Approximate Optimization Ansatz
can effectively generate the ground state for a 1D XY model with 64 spins. We
also demonstrate that the reduced density operator of two qubits can be
utilized to capture the pattern of quantum many-body states such as correlation
lengths even for quantum critical states.",2307.14627v1
1999-12-14,First-Principles Calculations of Positron Annihilation in Solids,"We present first-principles approaches based on density functional theory for
calculating positron states and annihilation characteristics in condensed
matter. The treatment of the electron-positron correlation effects (the
enhancement of the electron density at the positron with respect to mean-field
density) is shown to play a crucial role when calculating the annihilation
rates. A generalized gradient approximation (GGA) takes the strong
inhomogeneities of the electron density in the ion core region into account and
reproduces well the experimental total annihilation rates (inverses of the
positron lifetimes) by suppressing the rates given by a local density
approximation (LDA). The GGA combined with an electron-state-dependent
enhancement scheme gives a good description for the momentum distributions of
the annihilating positron-electron pairs reproducing accurately the trends
observed in the angular correlation (ACAR) or Doppler broadening measurements
of the annihilation radiation. The combination of the present positron lifetime
and momentum density calculations with the corresponding measurements yields a
unique tool for defect identification. Especially, the investigation of various
vacancy-type defects in semiconductors able to trap positrons will be an
important field for these methods. We will show that the identification of
vacancy-impurity complexes in highly n-Type Si and the study of the SiO$_2$/Si
interface are particularly interesting applications.",9912250v2
2006-02-23,Experimental determination of the symmetry energy of a low density nuclear gas,"Experimental analyses of moderate temperature nuclear gases produced in the
violent collisions of 35 MeV/nucleon$^{64}$Zn projectiles with $^{92}$Mo and
$^{197}$Au target nuclei reveal a large degree of alpha particle clustering at
low densities. For these gases, temperature and density dependent symmetry
energy coefficients have been derived from isoscaling analyses of the yields of
nuclei with A $\leq 4$. At densities of 0.01 to 0.05 times the ground state
density of symmetric nuclear matter, the temperature and density dependent
symmetry energies are 10.7 to 13.5 MeV. These values are much larger than those
obtained in mean field calculations. They are in quite good agreement with
results of a recently proposed Virial Equation of State calculation.",0602023v2
2007-06-09,"Folding model study of the isobaric analog excitation: isovector density dependence, Lane potential and nuclear symmetry energy","A consistent folding model analysis of the ($\Delta S=0, \Delta T=1$) charge
exchange \pn reaction measured with $^{48}$Ca, $^{90}$Zr, $^{120}$Sn and
$^{208}$Pb targets at the proton energies of 35 and 45 MeV is done within a
two-channel coupling formalism. The nuclear ground state densities given by the
Hartree-Fock-Bogoljubov formalism and the density dependent CDM3Y6 interaction
were used as inputs for the folding calculation of the nucleon optical
potential and \pn form factor. To have an accurate isospin dependence of the
interaction, a complex isovector density dependence of the CDM3Y6 interaction
has been carefully calibrated against the microscopic Brueckner-Hatree-Fock
calculation by Jeukenne, Lejeune and Mahaux before being used as folding input.
Since the isovector coupling was used to explicitly link the isovector part of
the nucleon optical potential to the cross section of \pn reaction exciting the
0$^+$ isobaric analog states in $^{48}$Sc, $^{90}$Nb, $^{120}$Sb and
$^{208}$Bi, the newly parameterized isovector density dependence could be well
tested in the folding model analysis of the \pn reaction. The isospin- and
density dependent CDM3Y6 interaction was further used in the Hartree-Fock
calculation of asymmetric nuclear matter, and a realistic estimation of the
nuclear symmetry energy has been made.",0706.1282v1
2016-04-12,Heavy-tailed phase-space distributions beyond Boltzmann-Gibbs and equipartition: Statistics of confined cold atoms,"The Boltzmann-Gibbs density, a central result of equilibrium statistical
mechanics, relates the energy of a system in contact with a thermal bath to its
equilibrium statistics. This relation is lost for non-thermal systems such as
cold atoms in optical lattices, where the heat bath is replaced by the laser
beams of the lattice. We investigate in detail the stationary phase-space
probability for Sisyphus cooling under harmonic confinement. In particular, we
elucidate whether the total energy of the system still describes its stationary
state statistics. We find that this is true for the center part of the
phase-space density for deep lattices, where the Boltzmann-Gibbs density
provides an approximate description. The relation between energy and statistics
also persists for strong confinement and in the limit of high energies, where
the system becomes underdamped. However, the phase-space density now exhibits
heavy power-law tails. In all three cases we find expressions for the leading
order phase-space density and corrections which break the equivalence of
probability and energy and violate energy equipartition. The non-equilibrium
nature of the steady state is confounded by explicit violations of detailed
balance. We complement these analytical results with numerical simulations to
map out the intricate structure of the phase-space density.",1604.03616v1
2019-09-23,Intrinsic Cluster-Shaped Density Waves in Cellular Dynamical Mean-Field Theory,"It is well known that cellular dynamical mean-field theory (CDMFT) leads to
the artificial breaking of translation invariance. In spite of this, it is one
of the most successful methods to treat strongly correlated electrons systems.
Here, we investigate in more detail how this broken translation invariance
manifests itself. This allows to disentangle artificial broken translation
invariance effects from the genuine strongly correlated effects captured by
CDMFT. We report artificial density waves taking the shape of the
cluster---cluster density waves---in all our zero temperature CDMFT solutions,
including pair density waves in the superconducting state. We discuss the
limitations of periodization regarding this phenomenon, and we present
mean-field density-wave models that reproduce CDMFT results at low energy in
the superconducting state. We then discuss how these artificial density waves
help the agreement of CDMFT with high temperature superconducting cuprates
regarding the low-energy spectrum, in particular for subgap structures observed
in tunnelling microscopy. We relate these subgap structures to nodal and
anti-nodal gaps in our results, similar to those observed in photoemission
experiments. This fortuitous agreement suggests that spatial inhomogeneity may
be a key ingredient to explain some features of the low-energy underdoped
spectrum of cuprates with strongly correlated methods. This work deepens our
understanding of CDMFT and clearly identifies signatures of broken translation
invariance in the presence of strong correlations.",1909.10141v3
2020-11-16,"Impacts of density-dependent predation, cannibalism and fishing in a stage-structured population model of the blue crab in Chesapeake Bay","The blue crab (Callinectes sapidus) is a dominant ecological species of high
commercial value. Spawning stock and recruitment of the Chesapeake Bay
population declined by 80% in the 1990s. After severe management actions were
implemented in 2008, female abundance rebounded to pre-1994 levels and
stabilized. The stepwise decline in the early 1990s, followed by a consistently
low level of abundance for 15 y and a jump to high abundance after 2008,
suggested the existence of alternative stable states. Alternatively, high
fishing pressure combined with low recruitment in 1992 could have triggered a
proportional decline in the population, followed by a population increase in
2008 due to rigorous management actions that reduced fishing. We evaluated
these alternatives with a stage-structured dynamic population model using
ordinary differential equations. In addition, stock assessment models assume
that fishing and mortality are independent of density. Hence, we also
investigated the role of density-dependent predation, cannibalism and fishing
in blue crab population dynamics. We conclude that for the blue crab population
in Chesapeake Bay: (1) bistable positive states are not likely with
biologically realistic parameter values; (2) hyperbolic (depensatory) fishing
will not produce extinction at the range of population densities observed in
the bay; and (3) crabs can survive a higher fishing rate under the more
realistic assumption of sigmoidal (density-dependent) predation and cannibalism
than under constant (density-independent) predation and cannibalism. These
collectively indicate that the blue crab population in Chesapeake Bay is
resilient to a range of biotic and abiotic disturbances.",2011.08308v1
2021-03-14,Optical detection of charge-density-wave instability in the non-magnetic kagome metal KV$_3$Sb$_5$,"Coexisting density-wave and superconducting states along with the large
anomalous Hall effect in the absence of local magnetism remain intriguing and
enigmatic features of the AV$_3$Sb$_5$ kagome metals (A = K, Rb, Cs). Here, we
demonstrate via optical spectroscopy and density-functional calculations that
low-energy dynamics of KV$_3$Sb$_5$ is characterized by unconventional
localized carriers, which are strongly renormalized across the density-wave
transition and indicative of electronic correlations. Strong phonon anomalies
are prominent not only below the density-wave transition, but also at high
temperatures, suggesting an intricate interplay of phonons with the underlying
electronic structure. We further propose the star-of-David and tri-hexagon
(inverse star-of-David) configurations for the density-wave order in
KV$_3$Sb$_5$. These configurations are strongly reminiscent of $p$-wave states
expected in the Hubbard model on the kagome lattice at the filling level of the
van Hove singularity. The proximity to this regime should have intriguing and
far-reaching implications for the physics of KV$_3$Sb$_5$ and related
materials.",2103.07912v2
2006-12-16,Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy,"We construct a Laplacian-level meta-generalized gradient approximation
(meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy
density $\tau$ of an electronic ground state of density $n$. This meta-GGA is
designed to recover the fourth-order gradient expansion $\tau^{GE4}$ in the
appropiate slowly-varying limit and the von Weizs\""{a}cker expression
$\tau^{W}=|\nabla n|^2/(8n)$ in the rapidly-varying limit. It is constrained to
satisfy the rigorous lower bound $\tau^{W}(\mathbf{r})\leq\tau(\mathbf{r})$.
Our meta-GGA is typically a strong improvement over the gradient expansion of
$\tau$ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas,
Hooke's atom, one-electron Gaussian density, quasi-two dimensional electron
gas, and nonuniformly-scaled hydrogen atom. We also construct a Laplacian-level
meta-GGA for exchange and correlation by employing our approximate $\tau$ in
the Tao, Perdew, Staroverov and Scuseria (TPSS) meta-GGA density functional.
The Laplacian-level TPSS gives almost the same exchange-correlation enhancement
factors and energies as the full TPSS, suggesting that $\tau$ and $\nabla^2 n$
carry about the same information beyond that carried by $n$ and $\nabla n$. Our
kinetic energy density integrates to an orbital-free kinetic energy functional
that is about as accurate as the fourth-order gradient expansion for many real
densities (with noticeable improvement in molecular atomization energies), but
considerably more accurate for rapidly-varying ones.",0612430v1
2021-05-18,Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition,"In this work we consider the generalized zeta function method to obtain
temperature corrections to the vacuum (Casimir) energy density, at zero
temperature, associated with quantum vacuum fluctuations of a scalar field
subjected to a helix boundary condition and whose modes propagate in
(3+1)-dimensional Euclidean spacetime. We find closed and analytical
expressions for both the two-point heat kernel function and free energy density
in the massive and massless scalar field cases. In particular, for the massless
scalar field case, we also calculate the thermodynamics quantities internal
energy density and entropy density, with their corresponding high- and
low-temperature limits. We show that the temperature correction term in the
free energy density must suffer a finite renormalization, by subtracting the
scalar thermal blackbody radiation contribution, in order to provide the
correct classical limit at high temperatures. We check that, at low
temperature, the entropy density vanishes as the temperature goes to zero, in
accordance with the third law of thermodynamics. We also point out that, at low
temperatures, the dominant term in the free energy and internal energy
densities is the vacuum energy density at zero temperature. Finally, we also
show that the pressure obeys an equation of state.",2105.08220v3
2017-10-18,Collective resonances near zero energy induced by a point defect in bilayer graphene,"Intrinsic defects give rise to scattering processes governing the transport
properties of mesoscopic systems. We investigate analytically and numerically
the local density of states in Bernal stacking bilayer graphene with a point
defect. With Bernal stacking structure, there are two types of lattice sites.
One corresponds to connected sites, where carbon atoms from each layer stack on
top of each other, and the other corresponds to disconnected sites. From our
theoretical study, a picture emerges in which the pronounced zero-energy peak
in the local density of states does not attribute to zero-energy impurity
states associated to two different types of defects but to a collective
phenomenon of the low-energy resonant states induced by the defect. To
corroborate this description, we numerically show that at small system size
$N$, where $N$ is the number of unit cells, the zero-energy peak near the
defect scales as $1/\ln N$ for the quasi-localized zero-energy state and as
$1/N$ for the delocalized zero-energy state. As the system size approaches to
the thermodynamic limit, the former zero-energy peak becomes a power-law
singularity $1/|E|$ in low energies, while the latter is broadened into a
Lorentzian shape. A striking point is that both types of zero-energy peaks
decay as $1/r^2$ away from the defect, manifesting the quasi-localized
character. Based on our results, we propose a general formula for the local
density of states in low-energy and in real space. Our study sheds light on
this fundamental problem of defects.",1710.06584v2
2001-03-01,"The equation of state for almost elastic, smooth, polydisperse granular gases for arbitrary density","Simulation results of dense granular gases with particles of different size
are compared with theoretical predictions concerning the pair-correlation
functions, the collison rate, the energy dissipation, and the mixture pressure.
The effective particle-particle correlation function, which enters the equation
of state in the same way as the correlation function of monodisperse granular
gases, depends only on the total volume fraction and on the dimensionless width
A of the size-distribution function. The ''global equation of state'' is
proposed, which unifies both the dilute and the dense regime.
  The knowledge about a global equation of state is applied to steady-state
situations of granular gases in the gravitational field, where averages over
many snapshots are possible. The numerical results on the density profile agree
perfectly with the predictions based on the global equation of state, for
monodisperse situations. In the bi- or polydisperse cases, segregation occurs
with the heavy particles at the bottom.",0103015v1
2005-09-12,Equation of state for an interacting holographic dark energy model,"We investigate a model of the interacting holographic dark energy with cold
dark matter (CDM). If the holographic energy density decays into CDM, we find
two types of the effective equation of state. In this case we have to use the
effective equations of state ($\omega^{\rm eff}_{\rm \Lambda}$) instead of the
equation of state ($\omega_{\rm \Lambda})$. For a fixed ratio of two energy
densities, their effective equations of state are given by the same negative
constant. Actually, the cosmic anti-friction arisen from the vacuum decay
process may induce the acceleration with $\omega^{\rm eff}_{\rm \Lambda}<-1/3$.
For a variable ratio, their effective equations of state are slightly
different, but they approach the same negative constant in the far future.
Consequently, we show that such an interacting holographic energy model cannot
accommodate a transition from the dark energy with $\omega^{\rm eff}_{\rm
\Lambda}\ge-1$ to the phantom regime with $\omega^{\rm eff}_{\rm \Lambda}<-1$.",0509040v2
2003-08-01,Precise study of the Efimov three-particle spectrum and structure functions within variational approach,"A precise study within variational approach of the basic properties of the
three-particle spectrum and structure functions with Gaussian potential near
the critical coupling constant of interaction where the Efimov effect takes
place is carried out. A method is developed to calculate highly excited states
with very small binding energies, and numerical analysis is carried out for the
ground and three excited energy states. For these states, one-particle density
distributions, formfactors, pair correlation functions, and momentum
distributions are calculated. It is found that the second excited state has
already all the basic features of a level from the infinite Efimov series. An
essential asymmetry is found in the position of energy levels with respect to
the critical constant point. A halo-type structure is revealed in the
one-particle density distributions, and formfactors are shown to have specific
dips of finite depth, the number of dips being equal to the number of the
state. The behaviour of pair correlation functions and momentum distributions
is studied for three-particle states.",0308003v2
2007-12-10,Point contact spectroscopy of Pr$_{2-x}$Ce$_x$CuO$_4$ in high magnetic fields,"We have studied the density of states of the normal state of the
electron-doped superconductor Pr$_{2-x}$Ce$_x$CuO$_4$ at low temperatures and
in magnetic fields up to 31 Tesla using point contact spectroscopy on single
crystals. Our data clearly reveal an anomalous gap in the normal state density
of states. This normal state gap survives even in the highest applied field of
31 T. Our results cast doubt over whether this gap found in electron-doped
cuprates is the analog of the pseudogap in hole-doped cuprates. We have
suggested an alternate origin of the normal state gap, which involves the
effect of disorder and electron correlations at the surface of cuprates.",0712.1614v1
2008-12-04,Quantum correlations of twophoton polarization states in the parametric down-conversion process,"We consider correlation properties of twophoton polarization states in the
parametric down-conversion process. In our description of polarization states
we take into account the simultaneous presence of colored and white noise in
the density matrix. Within the considered model we study the dependence of the
von Neumann entropy on the noise amount in the system and derive the
separability condition for the density matrix of twophoton polarization state,
using Perec-Horodecki criterion and majorization criterion. Then the dependence
of the Bell operator (in CHSH form) on noise is studied. As a result, we give a
condition for determining the presence of quantum correlation states in
experimental measurements of the Bell operator. Finally, we compare our
calculations with experimental data [doi:10.1103/PhysRevA.73.062110] and give a
noise amount estimation in the photon polarization state considered there.",0812.0878v2
2010-02-07,Ground states and dynamics of population-imbalanced Fermi condensates in one dimension,"By using the numerically exact density-matrix renormalization group (DMRG)
approach, we investigate the ground states of harmonically trapped
one-dimensional (1D) fermions with population imbalance and find that the
Larkin-Ovchinnikov (LO) state, which is a condensed state of fermion pairs with
nonzero center-of-mass momentum, is realized for a wide range of parameters.
The phase diagram comprising the two phases of i) an LO state at the trap
center and a balanced condensate at the periphery and ii) an LO state at the
trap center and a pure majority component at the periphery, is obtained. The
reduced two-body density matrix indicates that most of the minority atoms
contribute to the LO-type quasi-condensate. With the time-dependent DMRG, we
also investigate the real-time dynamics of a system of 1D fermions in response
to a spin-flip excitation.",1002.1433v3
2011-06-05,Thermal-assisted Anisotropy and Thermal-driven Instability in the Superfluidity state of Two-Species Polar Fermi Gas,"We study the superfluid state of two-species heteronuclear Fermi gases with
isotropic contact and anisotropic long-range dipolar interactions. By
explicitly taking account of Fock exchange contribution, we derive
self-consistent equations describing the pairing states in the system.
Exploiting the symmetry of the system, we developed an efficient way of solving
the self-consistent equations by exploiting the symmetries. We find that the
temperature tends to increase the anisotropy of the pairing state, which is
rather counterintuitive. We study the anisotropic properties of the system by
examining the angular dependence of the number density distribution, the
excitation spectrum and the pair correlation function. The competing effects of
the contact interaction and the dipolar interaction upon the anisotropy are
revealed. We derive and compute the superfluid mass density $\rho_{ij}$ for the
system. Astonishingly, we find that $\rho_{zz}$ becomes negative above some
certain temperature $T^*$($T<T_c$), signaling some instability of the system.
This suggests that the elusive FFLO state may be observed in experiments, due
to an anisotropic state with a spontaneously generated superflow.",1106.0891v1
2011-09-27,Counting hot/cold spots in quark-gluon plasma,"We study how local fluctuations in the initial states of relativistic
heavy-ion collisions manifest themselves in the correlations between different
orders of harmonic moments of the density profiles, particularly those
involving only odd harmonics which purely arise from initial state
fluctuations. We find the strengths of those correlations are sensitive to the
number of hot and cold spots in the initial states. Hydrodynamic evolution of
the fireball translates initial state geometric anisotropies as well as their
correlations into final state momentum anisotropies and correlations. We
conclude that the measurement of the correlations between different harmonic
moments of final state azimuthal distribution can be employed to quantify the
inhomogeneity of the initial density profiles such as the population of hot and
cold spots that are produced in high energy nuclear collisions.",1109.5961v3
2015-01-16,On the separability criterion of bipartite states with certain non-Hermitian operators,"We construct a density matrix whose elements are written in terms of
expectation values of non-Hermitian operators and their products for arbitrary
dimensional bipartite states. We then show that any expression which involves
matrix elements can be reformulated by the expectation values of these
non-Hermitian operators and vice versa. We consider the condition of pure
states and pure product states and rewrite them in terms of expectation values
and density matrix elements respectively. We utilize expectation values of
these operators to present the condition for separability of ${C}^d \otimes
{C}^d$ bipartite states. With the help of our separability criterion we detect
entanglement in certain classes of higher dimensional bipartite states.",1501.03914v1
2016-09-02,A microscopic model for the magnetic field driven breakdown of the dissipationless state in the integer and fractional quantum Hall effect,"Intra Landau level thermal activation, from localized states in the tail, to
delocalized states above the mobility edge in the same Landau level, explains
the $B_c(T)$ (half width of the dissipationless state) phase diagram for a
number of different quantum Hall samples with widely ranging carrier density,
mobility and disorder. Good agreement is achieved over $2-3$ orders of
magnitude in temperature and magnetic field for a wide range of filling
factors. The Landau level width is found to be independent of magnetic field.
The mobility edge moves, in the case of changing Landau level overlap to
maintain a sample dependent critical density of states at that energy. An
analysis of filling factor $\nu=2/3$ shows that the composite Fermion Landau
levels have exactly the same width as their electron counterparts. An important
ingredient of the model is the Lorentzian broadening with long tails which
provide localized states deep in the gap which are essential in order to
reproduce the robust high temperature $B_c(T)$ phase observed in experiment.",1609.00485v1
2019-12-20,Matrix product state of multi-time correlations,"For an interacting spatio-temporal lattice system we introduce a formal way
of expressing multi-time correlation functions of local observables located at
the same spatial point with a time state, i.e. a statistical distribution of
configurations observed along a time lattice. Such a time state is defined with
respect to a particular equilibrium state that is invariant under space and
time translations. The concept is developed within the Rule 54 reversible
cellular automaton, for which we explicitly construct a matrix product form of
the time state, with matrices that act on the 3-dimensional auxiliary space. We
use the matrix-product state to express equal-space time-dependent
density-density correlation function, which, for special maximum-entropy values
of equilibrium parameters, agrees with the previous results. Additionally, we
obtain an explicit expression for the probabilities of observing all multi-time
configurations, which enables us to study distributions of times between
consecutive excitations and prove the absence of decoupling of timescales in
the Rule 54 model.",1912.09742v2
2004-08-13,"Sample dependence of the structural, vibrational, and electronic properties of a-Si:H: A density-functional-based tight-binding study","The sample dependence of various properties of hydrogenated amorphous silicon
($a$-Si:H) have been studied with 216 silicon atoms and 24 hydrogen atoms using
the density functional based tight binding molecular dynamics simulations. The
Si-Si and Si-H pair correlation functions are independent of preparation
procedure as well as initial conditions, the H-H pair correlation functions are
sample dependent. The distribution of hydrogen atoms in all the samples is
nonuniform and depends upon the preparation procedure as well as the initial
structure from which the hydrogenated amorphous silicon sample is generated.
The Si-Si bond length and Si-Si-Si bond angle distributions are nearly
independent of sample preparation procedure, but Si-H bond length distributions
are sample dependent. The peaks in the vibrational density of states (VDOS) at
high frequencies are in reasonable accord with the experimental results. The
positions of the high frequency peaks are found to be dependent on the local
environment. While the high frequency vibrational modes related to Si-Si bond
vibrations are moderately localized, the vibrational modes related to Si-H bond
vibrations in $a$-Si:H samples are highly localized. In samples generated from
the liquid quench the free energy is smaller, whereas the entropy and specific
heat are larger as compared to that of samples generated by hydrogenation of
pure amorphous silicon samples. The total electronic density of states and
local density of electronic states (LDOS) at Si atom sites are nearly sample
independent, while the LDOS at the H atom sites are dependent on the sample
preparation procedure.",0408309v1
2007-08-22,A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases,"We use hydrodynamics to investigate non-stationary channel flows of freely
cooling dilute granular gases. We focus on the regime where the sound travel
time through the channel is much shorter than the characteristic cooling time
of the gas. As a result, the gas pressure rapidly becomes almost homogeneous,
while the typical Mach number of the flow drops well below unity. Eliminating
the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear
and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates.
This equation describes a broad class of channel flows and, in particular, can
follow the development of the clustering instability from a weakly perturbed
homogeneous cooling state to strongly nonlinear states. If the heat diffusion
is neglected, the reduced equation is exactly soluble, and the solution
develops a finite-time density blowup. The heat diffusion, however, becomes
important near the attempted singularity. It arrests the density blowup and
brings about novel inhomogeneous cooling states (ICSs) of the gas, where the
pressure continues to decay with time, while the density profile becomes
time-independent. Both the density profile of an ICS, and the characteristic
relaxation time towards it are determined by a single dimensionless parameter
that describes the relative role of the inelastic energy loss and heat
diffusion. At large values of this parameter, the intermediate cooling dynamics
proceeds as a competition between low-density regions of the gas. This
competition resembles Ostwald ripening: only one hole survives at the end.",0708.3085v2
2013-01-23,Phase transitions of dense neutron matter with generalized Skyrme interaction to superfluid states with triplet pairing in strong magnetic field,"A generalized non-relativistic Fermi-liquid approach was used to find
analytical formulas for temperatures $T_{c,1}(n,H)$ and $T_{c,2}(n,H)$ (which
are functions nonlinear of density n and linear of magnetic field H) of phase
transitions in spatially uniform dense pure neutron matter from normal to
superfluid states with spin-triplet p-wave pairing (similar to anisotropic
superfluid phases $^3He-A_{1}$ and $^3He-A_{2}$) in steady and homogeneous
strong magnetic field (but $|\mu_{n}| H\ll E_{c}<\varepsilon_{F}(n)$, where
$\mu_{n}$ is the magnetic dipole moment of a neutron, E_{c} is the cutoff
energy and $\varepsilon_{F}(n)$ is the Fermi energy in neutron matter). General
formulas for $T_{c,1,2}(n,H)$ (valid for arbitrary parametrization of the
effective Skyrme interaction in neutron matter) are specified here for
generalized BSk18 parametrization of the Skyrme forces (with additional terms
dependent on density n) on the interval $0.3\ n_{0}<n<n_{c}(BSk18)\approx
2.7952 n_{0}$, where $n_{0}=0.17{fm}^{-3}$ is nuclear density and at critical
density $n_{c}(BSk18)$ triplet superfluidity disappears,
$T_{c,0}(n_{c},H=0)=0$. Expressions for phase transition temperatures
$T_{c,0}(n)< 0.09 MeV$ (at E_{c}=10 MeV) and $T_{c,1,2}(n,H)$ are realistic
non-monotone functions of density n for BSk18 parametrization of the Skyrme
forces (contrary to their monotone increase for all previous BSk
parameterizations). Phase transitions to superfluid states of such type might
occur in liquid outer core of magnetars (strongly magnetized neutron stars).",1301.5528v1
2015-10-24,Spatial modulation of the composition of a binary liquid near a repulsive wall,"When a binary liquid is confined by a strongly repulsive wall, the local
density is depleted near the wall and an interface similar to that between the
liquid and its vapor is formed. This analogy suggests that the composition of
the binary liquid near this interface should exhibit spatial modulation similar
to that near a liquid-vapor interface even if the interactions of the wall with
the two components of the liquid are the same. The Guggenheim adsorption
relation quantifies the concentrations of two components of a binary mixture
near a liquid-vapor interface and qualitatively states that the majority
(minority) component enriches the interface for negative (positive) mixing
energy if the surface tensions of the two components are not very different.
From molecular dynamics simulations of binary mixtures with different
compositions and interactions, we find that the Guggenheim relation is
qualitatively satisfied at wall-induced interfaces for systems with negative
mixing energy at all state points considered. For systems with positive mixing
energy, this relation is found to be qualitatively valid at low densities,
while it is violated at state points with high density where correlations in
the liquid are strong. This observation is validated by a calculation of the
density profiles of the two components of the mixture using density functional
theory with the Ramakrishnan-Yussouff free-energy functional. Possible reasons
for the violation of the Guggenheim relation are discussed.",1510.07113v1
2019-11-08,Study of the phase diagram of the Kitaev-Hubbard chain,"We present a detailed study of the phase diagram of the Kitaev-Hubbard chain,
that is the Kitaev chain in the presence of a nearest-neighbour density-density
interaction, using both analytical techniques as well as DMRG. In the case of a
moderate attractive interaction, the model has the same phases as the
non-interacting chain, a trivial and a topological phase. For repulsive
interactions, the phase diagram is more interesting. Apart from the previously
observed topological, incommensurate and charge density wave phases, we
identify the `excited state charge density wave' phase. In this phase, the
ground state resembles an excited state of an ordinary charge density phase,
but is lower in energy due to the frustrated nature of the model. We find that
the dynamical critical exponent takes the value $z\simeq 1.8$. Interestingly,
this phase only appears for even system sizes, and is sensitive to the chemical
potential on the edges of the chain. For the topological phase, we present an
argument that excludes the presence of a strong zero mode for a large part of
the topological phase. For the remaining region, we study the time dependence
of the edge magnetization (using the bosonic incarnation of the model). These
results further expand the region where a strong zero mode does not occur.",1911.03156v3
2020-08-18,"Equation of State of Hot, Dense Magnesium Derived with First-PrinciplesComputer Simulations","Using two first-principles computer simulation techniques, path integral
Monte-Carlo and density functional theory molecular dynamics, we derive the
equation of state of magnesium in the regime of warm dense matter, with
densities ranging from 0.43 to 86.11~g/cm$^3$~and temperatures from 20,000 K to
$5\times10^8$~K. These conditions are relevant for the interiors of giant
planets and stars as well as for shock compression measurements and inertial
confinement fusion experiments. We study ionization mechanisms and electronic
structure of magnesium as a function of density and temperature. We show that
the L shell electrons 2s and 2p energy bands merge at high density. This
results into a gradual ionization of the L-shell with increasing density and
temperature. In this regard, Mg differs from MgO, which is also reflected in
the shape of its principal shock Hugoniot curve. For Mg, we predict a single
broad pressure-temperature region where the shock compression ratio is
approximately 4.9. Mg thus differs from Si and Al plasma that exhibit two
well-separated compression maxima on the Hugoniot curve for L and K shell
ionizations. Finally we study multiple shocks and effects of preheat and
precompression.",2008.08459v1
2023-10-05,Topological Density Correlations in a Fermi Gas,"A Fermi gas of non-interacting electrons, or ultra-cold fermionic atoms, has
a quantum ground state defined by a region of occupancy in momentum space known
as the Fermi sea. The Euler characteristic $\chi_F$ of the Fermi sea serves to
topologically classify these gapless fermionic states. The topology of a $D$
dimensional Fermi sea is physically encoded in the $D+1$ point equal time
density correlation function. In this work, we first present a simple proof of
this fact by showing that the evaluation of the correlation function can be
formulated in terms of a triangulation of the Fermi sea with a collection of
points, links and triangles and their higher dimensional analogs. We then make
use of the topological $D+1$ point density correlation to reveal universal
structures of the more general $M$ point density correlation functions in a $D$
dimensional Fermi gas. Two experimental methods are proposed for observing
these correlations in $D=2$. In cold atomic gases imaged by quantum gas
microscopy, our analysis supports the feasibility of measuring the third order
density correlation, from which $\chi_F$ can be reliably extracted in systems
with as few as around 100 atoms. For solid-state electron gases, we propose
measuring correlations in the speckle pattern of intensity fluctuations in
nonlinear X-ray scattering experiments.",2310.03737v1
2024-03-05,Listening to the long ringdown: a novel way to pinpoint the equation of state in neutron-star cores,"Multimessenger signals from binary neutron star (BNS) mergers are promising
tools to infer the largely unknown properties of nuclear matter at densities
that are presently inaccessible to laboratory experiments. The gravitational
waves (GWs) emitted by BNS merger remnants, in particular, have the potential
of setting tight constraints on the neutron-star equation of state (EOS) that
would complement those coming from the late inspiral, direct mass-radius
measurements, or ab-initio dense-matter calculations. To explore this
possibility, we perform a representative series of general-relativistic
simulations of BNS systems with EOSs carefully constructed so as to cover
comprehensively the high-density regime of the EOS space. From these
simulations, we identify a novel and tight correlation between the ratio of the
energy and angular-momentum losses in the late-time portion of the post-merger
signal, i.e., the ""long ringdown"", and the properties of the EOS at the highest
pressures and densities in neutron-star cores. When applying this correlation
to post-merger GW signals, we find a significant reduction of the EOS
uncertainty at densities several times the nuclear saturation density, where no
direct constraints are currently available. Hence, the long ringdown has the
potential of providing new and stringent constraints on the state of matter in
neutron stars in general and, in particular, in their cores.",2403.03246v1
2016-11-07,The Electronic States of a Double Carbon Vacancy Defect in Pyrene: A Model Study for Graphene,"The electronic states occurring in a double vacancy defect for graphene
nanoribbons have been calculated in detail based on a pyrene model. Extended ab
initio calculations using the MR configuration interaction (MRCI) method have
been performed to describe in a balanced way the manifold of electronic states
derived from the dangling bonds created by initial removal of two neighboring
carbon atoms from the graphene network. In total, this study took into account
the characterization of 16 electronic states (eight singlets and eight
triplets) considering unrelaxed and relaxed defect structures. The ground state
was found to be of 1Ag character with around 50% closed shell character. The
geometry optimization process leads to the formation of two five-membered rings
in a pentagon octagon pentagon structure. The closed shell character increases
thereby to ~70%, the analysis of unpaired density shows only small
contributions confirming the chemical stability of that entity. For the
unrelaxed structure the first five excited states (3B3g, 3B2u, 3B1u, 3Au and
1Au) are separated from the ground state by less than 2.5 eV. For comparison,
unrestricted density functional theory (DFT) calculations using several types
of functionals have been performed within different symmetry subspaces defined
by the open shell orbitals. Comparison with the MRCI results gave good
agreement in terms of finding the 1Ag state as ground state and in assigning
the lowest excited states. Linear interpolation curves between the unrelaxed
and relaxed defect structures also showed good agreement between the two
classes of methods opening up the possibilities of using extended nanoflakes
for multistate investigations at DFT level.",1611.01916v1
2003-12-19,Status of a self-bound equations of state and analytic solutions in general relativity,"We have obtained a criterion for spherically symmetric and static structures
under hydrostatic equilibrium in general relativity (GR), which states that for
a given value of $\sigma \equiv (P_0/E_0) \equiv $ the ratio of central
pressure to central energy-density], the compaction parameter $u \equiv (M/a)$,
where $M$ is the total mass and $a$ is the radius of the configuration] or the
surface redshift of any regular configuration cannot exceed that of the
corresponding homogeneous density sphere, that is, $u \leq u_h$, where $u_h$ is
the compaction parameter of the homogeneous density sphere. By examining
various exact solutions and surface). On the other hand, configurations having
a finite density on the surface (that is, the self-bound structures) do not
fulfill this criterion. This criterion puts a severe restriction on the static
structures based upon the general relativistic field equations and consequently
on the upper limit of mass, surface and central redshift and other physical
parameters of spherically symmetric and static configurations.",0312516v2
1996-06-06,Bose-Einstein Condensation In Disordered Exclusion Models and Relation to Traffic Flow,"A disordered version of the one dimensional asymmetric exclusion model where
the particle hopping rates are quenched random variables is studied. The steady
state is solved exactly by use of a matrix product. It is shown how the
phenomenon of Bose condensation whereby a finite fraction of the empty sites
are condensed in front of the slowest particle may occur. Above a critical
density of particles a phase transition occurs out of the low density phase
(Bose condensate) to a high density phase. An exponent describing the decrease
of the steady state velocity as the density of particles goes above the
critical value is calculated analytically and shown to depend on the
distribution of hopping rates. The relation to traffic flow models is
discussed.",9606036v1
2003-08-07,Potential energy landscape-based extended van der Waals equation,"The inherent structures ({\it IS}) are the local minima of the potential
energy surface or landscape, $U({\bf r})$, of an {\it N} atom system.
Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the
implications for the equation of state are investigated. It is shown that the
van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$
coefficients, holds on the high-temperature plateau of the averaged {\it IS}
energy. However, an additional ``landscape'' contribution to the pressure is
found at lower $T$. The resulting extended {\it vdW} equation, unlike the
original, is capable of yielding a water-like density anomaly, flat isotherms
in the coexistence region {\it vs} {\it vdW} loops, and several other desirable
features. The plateau energy, the width of the distribution of {\it IS}, and
the ``top of the landscape'' temperature are simulated over a broad reduced
density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the
data yield an explicit equation of state, which is argued to be useful at high
density; it nevertheless reproduces the known values of $a$ and $b$ at the
critical point.",0308142v1
2004-07-23,Nonlinear screening and stopping power in two-dimensional electron gases,"We have used density functional theory to study the nonlinear screening
properties of a two-dimensional (2D) electron gas. In particular, we consider
the screening of an external static point charge of magnitude Z as a function
of the distance of the charge from the plane of the gas. The self-consistent
screening potentials are then used to determine the 2D stopping power in the
low velocity limit based on the momentum transfer cross-section. Calculations
as a function of Z establish the limits of validity of linear and quadratic
response theory calculations, and show that nonlinear screening theory already
provides significant corrections in the case of protons. In contrast to the 3D
situation, we find that the nonlinearly screened potential supports a bound
state even in the high density limit. This behaviour is elucidated with the
derivation of a high density screening theorem which proves that the screening
charge can be calculated perturbatively in the high density limit for arbitrary
dimensions. However, the theorem has particularly interesting implications in
2D where, contrary to expectations, we find that perturbation theory remains
valid even when the perturbing potential supports bound states.",0407638v1
2006-05-09,Spatial variation of the laser fields and electron dynamics at a gas-solid interface,"In the long wavelength domain, typically for wavelengths lambda > 100
angstroms, the laser fields are usually taken as independent of the spatial
coordinate. However, at the gas-solid interface the electron density of the
material and the incident laser fields vary sharply on a scale of few
angstroms. Instead of solving Maxwell equations, we present here a theoretical
model, called Electromagnetic Fields from Electron Density (EMFED), generating
a continuous vector potential from phenomenological relations combining the
unperturbed electron density of the material system, the material constants and
the laws of optics. As an application of this model, we calculate in a time
dependent approach the transition probability and the induced current density
between the last bulk state below the Fermi energy and the first image state of
a Cu(001) metallic surface. These observables are significantly modified by the
spatial variation of the vector potential at the surface. The Coulomb gauge
condition, fullfilled everywhere else, breaks down near the surface. The
difference between the s- and p- polarizations of the laser field partially
unravels this effect.",0605231v1
2007-04-18,Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons,"We employ the formalism of bond currents, expressed in terms of the
nonequilibrium Green functions, to image the charge flow between two sites of
the honeycomb lattice of graphene ribbons of few nanometers width. In sharp
contrast to nonrelativistic electrons, current density profiles of quantum
transport at energies close to the Dirac point in clean zigzag graphene
nanoribbons (ZGNR) differs markedly from the profiles of charge density peaked
at the edges due to zero-energy localized edge states. For transport through
the lowest propagating mode induced by these edge states, edge vacancies do not
affect current density peaked in the center of ZGNR. The long-range potential
of a single impurity acts to reduce local current around it while concurrently
increasing the current density along the zigzag edge, so that ZGNR conductance
remains perfect $G=2e^2/h$.",0704.2419v1
2013-03-22,Role of single-particle and pair condensates in Bose systems with arbitrary intensity of interaction,"We study a superfluid Bose system with single-particle and pair condensates
on the basis of a half-phenomenological theory of a Bose liquid not involving
the weakness of interparticle interaction. The coupled equations describing the
equilibrium state of such system are derived from the variational principle for
entropy. These equations are analyzed at zero temperature both analytically and
numerically. It is shown that the fraction of particles in the single-particle
and pair condensates essentially depends on the total density of the system. At
densities attainable in condensates of alkali-metal atoms, almost all particles
are in the single-particle condensate. The pair condensate fraction grows with
an increasing total density and becomes dominant. It is shown that at density
of liquid helium, the single-particle condensate fraction is less than 10%,
which agrees with experimental data on inelastic neutron scattering, Monte
Carlo calculations and other theoretical predictions. The ground state energy,
pressure, and compressibility are found for the system under consideration. The
spectrum of single-particle excitations is also analyzed.",1303.5539v1
2013-05-27,"On the isotope effects of ZrX2 (X = H, D and T): A First-principles study","Zirconium hydride is an important material for storage of hydrogen isotopes.
Here we report the structural, electronic, vibrational and thermodynamic
properties of ZrH2, ZrD2 and ZrT2 using density functional theory (DFT). The
structural optimization was carried out by the plane-wave based
pseudo-potential method under the generalized gradient approximation (GGA)
scheme. The electronic structure of the ZrH2 compound was illustrated in terms
of the electronic density of states, charge density distribution and the
electron localization function. The phonon dispersion curves, phonon density of
states and thermodynamic properties of ZrX2 (X= H, D, T) compounds were
evaluated based on frozen phonon method. Both the Raman and infrared active
vibrational modes of ZrX2 at {\Gamma}-point were analyzed which showed
significant isotopic effect on ZrX2 compounds. For example, the energy gap
between optical and acoustic modes reduces for ZrT2 than ZrD2 and ZrH2. The
formation energies of ZrX2 compounds, including the ZPE contributions, were
-113.97, -126.50 and -132.04 kJ/(mole of compound) for X = H, D and T,
respectively.",1305.6109v1
2020-07-28,Unraveling liquid polymorphism in silicon driven out-of-equilibrium,"Using nonequilibrium molecular dynamics (NEMD) simulations, we study the
properties of supercooled liquids of Si under shear at T=1060K over a range of
densities encompassing the low-density liquid (LDL) and high-density liquid
(HDL) forms. This enables us to generate nonequilibrium steady-states of the
LDL and HDL polymorphs, that remain stabilized in their liquid forms for as
long as the shear is applied. This is unlike the LDL and HDL forms at rest,
which are metastable under those conditions and, when at rest, rapidly undergo
a transition towards the crystal, i.e. the thermodynamically stable equilibrium
phase. In particular, through a detailed analysis of the structural and
energetic features of the liquids under shear, we identify the range of
densities, as well as the range of shear rates, that give rise to the two
forms. We also show how the competition between shear and tetrahedral order
impacts the two-body entropy in steady-states of Si under shear. These results
open the door to new ways of utilizing shear to stabilize forms that are
metastable at rest and can exhibit unique properties, since, for instance,
experiments on Si have shown that HDL is metallic, with no band gap, while LDL
is semimetallic, with a pseudogap.",2007.13917v1
2016-08-02,Superfluidity of a rarefied gas of electron-hole pairs in a bilayer system,"The conditions of stability of the superfluid phase in double layer systems
with pairing of spatially separated electrons and holes in the low density
limit are studied. The general expression for the collective excitation
spectrum is obtained. It is shown that under increase in the distance $d$
between the layers the minimum emerges in the excitation spectrum. When d
reaches the critical value the superfluid state becomes unstable relative to
the formation of a kind of the Wigner crystal state. The same instability
occurs at fixed d under increase in the density of carries. It is established
that the critical distance and the critical density are related to each other
by the inverse power function. The impact of the impurities on the temperature
of the superfluid transition is investigated. The impact is found weak at the
impurity concentration smaller than the density of the pairs. It is shown that
in the rarefied system the critical temperature T_c = 100 K can be reached.",1608.00898v1
2019-12-11,Dynamics of Open Tight-binding Model,"In this paper, we investigate the open tight-binding model with $N$ sites
coupled to two reservoirs on its edges with the nonequilibrium Green function
method to understand effects of open boundaries. As a result, we obtain an
analytical expression of the electron density in the steady state and in the
transient regime for $N \rightarrow \infty$ and at absolute zero temperature.
From the expression of the electron density in the steady state, we show that
the open boundaries do not affect the qualitative behavior of the electron
density and the phase transition which has been observed for the isolated
tight-binding model also exists in our open case. Using the expression of the
time-dependent electron density, we show that a two-step decay appears in the
relaxation process purely caused by open boundaries. In addition, we show that
the dependence of speed of convergence on boundary coupling strength
qualitatively changes at a certain value of the boundary parameters. This is a
result of special eigenvalues of a non-hermitian matrix whose imaginary parts
do not vanish even in the limit $N \rightarrow \infty$.",1912.05633v1
2021-04-13,Does our universe conform with the existence of a universal maximum energy-density $ρ^{uni}_{max}$ ?,"Recent astronomical observations of high redshift quasars, dark
matter-dominated galaxies, mergers of neutron stars, glitch phenomena in
pulsars, cosmic microwave background and experimental data from hadronic
colliders do not rule out, but they even support the hypothesis that the
energy-density in our universe most likely is upper-limited by
$\rho^{uni}_{max},$ which is predicted to lie between $2$ to $3$ the nuclear
density $\rho_0.$ Quantum fluids in the cores of massive NSs with $\rho \approx
\rho^{uni}_{max}$ reach the maximum compressibility state, where they become
insensitive to further compression by the embedding spacetime and undergo a
phase transition into the purely incompressible gluon-quark superfluid state. A
direct correspondence between the positive energy stored in the embedding
spacetime and the degree of compressibility and superfluidity of the trapped
matter is proposed. In this paper relevant observation signatures that support
the maximum density hypothesis are reviewed, a possible origin of
$\rho^{uni}_{max}$ is proposed and finally the consequences of this scenario on
the spacetime's topology of the universe as well as on the mechanisms
underlying the growth rate and power of the high redshift QSOs are discussed.",2104.06321v1
2023-11-03,Massive neutron stars as mass gap candidates: Exploring equation of state and magnetic field,"The densities in the cores of the neutron stars (NSs) can reach several times
that of the nuclear saturation density. The exact nature of matter at these
densities is still virtually unknown. We consider a number of proposed,
phenomenological relativistic mean-field equations of state to construct
theoretical models of NSs. We find that, based on our selected set of models,
the emergence of exotic matter at these high densities restricts the mass of
NSs to $\simeq 2.2 M_\odot$. However, the presence of magnetic fields and a
model anisotropy significantly increases the star's mass, placing it within the
observational mass gap that separates the heaviest NSs from the lightest black
holes. Therefore, we propose that gravitational wave observations, like
GW190814, and other potential candidates within this mass gap, may actually
represent massive, magnetized NSs.",2311.02169v2
1996-08-02,A note on magnetic-field induced level-density condensation in a two-dimensional electron gas with point scatterers,"The density-of-states (DOS) for a magnetized (B) two-dimensional electron gas
(2DEG) containing point scatterers of arbitrary strengths, concentration
($n_s$) and distribution is analyzed. It is shown from the first principles
that for \(n_s \leq B/\Phi_o \equiv n_B\), the areal density of flux quanta
\(\Phi_o \equiv hc/e\), the DOS retains the extensive degeneracy characteristic
of the Landau levels, but reduced by a factor \((1 - {n_s}/{n_B})\). This
elementary but exact result gives a level condensation for magnetic field \(B >
n_s\Phi_o\), as first noted by Br\'{e}zin {\em et al.}. Its implications for
the Integral Quantum Hall Effect and for Random Matrix Theory are pointed out.",9608005v1
1996-10-14,Density Matrix and Renormalization for Classical Lattice Models,"We review the variational principle in the density matrix renormalization
group (DMRG) method, which maximizes an approximate partition function within a
restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground
state energy. The variational principle is applied to two-dimensional (2D)
classical lattice models, where the density matrix is expressed as a product of
corner transfer matrices. (CTMs) DMRG related fields and future directions of
DMRG are briefly discussed.",9610107v1
1998-02-11,Vortices in Density Wave Systems Subject to Transverse Electric Fields,"In this paper we predict many interesting new properties of vortices in
highly anisotropic density wave systems subject to strong transverse electric
fields. We mainly concentrate on ground state properties. Besides electric
field-induced vortices we consider also thermally activated vortices. A new
type of temperature-driven transition between two different phases of density
waves in strong fields is predicted and several new properties of those phases
are reported.",9802125v2
1999-02-25,Practical Methods for Ab Initio Calculations on Thousands of Atoms,"We describe recent progress in developing practical ab initio methods for
which the computer effort is proportional to the number of atoms: linear
scaling or O(N) methods. It is shown that the locality property of the density
matrix gives a general framework for constructing such methods. We then
describe our scheme, which operates within density functional theory. Efficient
methods for reaching the electronic ground state are summarised, both for
finding the density matrix, and in varying the localised orbitals.",9902343v1
1999-05-12,Nonmonotonic Temperature-dependent Resistance in Low Density 2D Hole Gases,"The low temperature longitudinal resistance-per-square Rxx(T) in ungated
GaAs/AlGaAs quantum wells of high peak hole mobility 1.7x10^6 cm^2/Vs is
metallic for 2D hole density p as low as 3.8x10^9 cm-2. The electronic
contribution to the resistance, R_{el}(T), is a nonmonotonic function of T,
exhibiting thermal activation, R_{el}(T) ~ exp{-E_a/kT}, for kT<<E_F and a
heretofore unnoted decay R_{el}(T) ~ 1/T for k_T>EF. The form of R_{el}(T) is
independent of density, indicating a fundamental relationship between the low
and high T scattering mechanisms in the metallic state.",9905176v1
2001-06-25,Density functional study of the adsorption of K on the Cu(111) surface,"The adsorption of potassium on the Cu(111) surface in a 2x2 pattern has been
simulated with all-electron full-potential density functional calculations. The
top site is found to be the preferred adsorption site, with the other highly
symmetric adsorption sites being nearly degenerate. The bond length from
potassium to the nearest copper atom is computed to be 2.83 Angstrom.
Population analysis and density of states indicate that there is no evidence
for covalent bonding so that the binding mechanism appears to be a metallic
bond.",0106499v1
2001-12-03,Kinetic energy density functionals for non-periodic systems,"Kinetic energy functionals of the electronic density are used to model large
systems in the context of density functional theory, without the need to obtain
electronic wavefunctions. We discuss the problems associated with the
application of widely used kinetic energy functionals to non-periodic systems.
We develop a method that circumvents this difficulty and allows the kinetic
energy to be evaluated entirely in real space. We demonstrate that the method
is efficient [O(N)] and accurate by comparing the results of our real-space
formulation to calculations performed in reciprocal space, and to calculations
using traditional approaches based on electronic states.",0112040v1
2002-01-23,Excitonic condensation in a symmetric electron-hole bilayer,"Using Diffusion Monte Carlo simulations we have investigated the ground state
of a symmetric electron-hole bilayer and determined its phase diagram at T=0.
We find clear evidence of an excitonic condensate, whose stability however is
affected by in-layer electronic correlation. This stabilizes the electron-hole
plasma at large values of the density or inter-layer distance, and the Wigner
crystal at low density and large distance. We have also estimated pair
correlation functions and low order density matrices, to give a microscopic
characterization of correlations, as well as to try and estimate the condensate
fraction.",0201414v1
2002-05-07,A form factor approach to finite temperature correlation functions in $c=1$ CFT,"The excitation spectrum of specific conformal field theories (CFT) with
central charge $c=1$ can be described in terms of quasi-particles with charges
$Q=-p,+1$ and fractional statistics properties. Using the language of Jack
polynomials, we compute form factors of the charge density operator in these
CFTs. We study a form factor expansion for the finite temperature
density-density correlation function, and find that it shows a quick
convergence to the exact result. The low-temperature behavior is recovered from
a form factor with $p+1$ particles, while the high-temperature limit is
recovered from states containing no more than 3 particles.",0205128v1
2003-01-14,Ab-initio determination of the localized/delocalized f-manifold in UPd_2Al_3,"The electronic structure of UPd_2Al_3 is described using the self-interaction
corrected local-spin-density approximation to density functional theory. The
groundstate is found to be characterized by the coexistence of localized (f^2)
and delocalized U f electrons, in agreement with experimental evidence. We
observe significant difference in electronic structure between UPd_2Al_3 and
the previously studied UPt_3 compound. Even though a trend towards localization
exists in UPt_3, the total energies and the density of states at the Fermi
level favor a groundstate with localized f^1, rather than f^2 U ions.",0301215v1
2004-08-12,Exact results for one-dimensional disordered bosons with strong repulsion,"We study one-dimensional incommensurate bosons with strong repulsive
interactions and weak disorder. In analogy to the clean Tonks-Girardeau gas, a
Bose-Fermi mapping expresses this problem in terms of disordered free fermions.
Thereby many known results apply, in particular for the density-density
correlations, the distribution function of the local density of states, and the
complete spectral statistics. We also analyze the bosonic momentum
distribution, and comment on the experimental observability of these
predictions in ultracold atomic gases.",0408289v2
2006-04-18,Density functional theory of freezing for soft interactions in two dimensions,"A density functional theory of two-dimensional freezing is presented for a
soft interaction potential that scales as inverse cube of particle distance.
This repulsive potential between parallel, induced dipoles is realized for
paramagnetic colloids on an interface, which are additionally exposed to an
external magnetic field. An extended modified weighted density approximation
which includes correct triplet correlations in the liquid state is used. The
theoretical prediction of the freezing transition is in good agreement with
experimental and simulation data.",0604422v1
2006-10-26,Pair density functional theory by means of the correlated wave function,"We present a density functional scheme for calculating the pair density (PD)
by means of the correlated wave function. This scheme is free from both of
problems related to PD functional theory, i.e., (a) the need to constrain the
variational principle to $N$-representable PDs and (b) the development of a
kinetic energy functional. By using the correlated wave function, the searching
region for the ground-state PD is substantially extended as compared with our
previous theory[Physica B \textbf{372} (2007), in press]. The variational
principle results in the simultaneous equations that yield the best PD beyond
the previous theory, not to mention the Hartree-Fock approximation.",0610725v1
2005-01-15,Holographic energy density in the Brans-Dicke teory,"We study cosmological applications of the holographic energy density.
Considering the holographic energy density as a dynamical cosmological
constant, we need the Brans-Dicke theory as a dynamical framework instead of
general relativity. In this case we use the Bianchi identity as a consistency
relation to obtain physical solutions. It is shown that the future event
horizon as the IR cutoff provides the dark energy in the Brans-Dicke theory.
Furthermore the role of the Brans-Dicke scalar is clarified in the dark
energy-dominated universe by calculating its equation of state.",0501118v1
1997-03-06,Liquid-Gas Phase Transition in Nuclear Equation of State,"A canonical ensemble model is used to describe a caloric curve of nuclear
liquid-gas phase transition. Allowing a discontinuity in the freeze out density
from one spinodal density to another for a given initial temperature, the
nuclear liquid-gas phase transition can be described as first order. Averaging
over various freeze out densities of all the possible initial temperatures for
a given total reaction energy, the first order characteristics of liquid-gas
phase transition is smeared out to a smooth transition. Two experiments, one at
low beam energy and one at high beam energy show different caloric behaviors
and are discussed.",9703012v1
1998-09-24,Relationships between two--particle overlap functions and the two--body density matrix for many-fermion systems,"Relationships are obtained connecting the two-nucleon overlap function of the
eigenstates in the (A-2) particle system with the asymptotic behavior of the
two-body density matrix for the ground state of the A-particle system.This
makes it possible to calculate the two-body overlap functions, spectroscopic
factors and separation energies on the basis of a realistic two-body density
matrix. The procedure can be used in describing the (e,e'NN) and (\gamma, NN)
reactions where the two--body overlap functions are a key ingredient in the
analysis.",9809076v1
2000-08-23,Density Effect on Hadronization of a Quark Plasma,"The hadronization cross section in a quark plasma at finite temperature and
density is calculated in the framework of Nambu--Jona-lasinio model with
explicit chiral symmetry breaking. In apposition to the familiar temperature
effect, the quark plasma at high density begins to hadronize suddenly. It leads
to a sudden and strong increase of final state pions in relativistic heavy ion
collisions which may be considered as a clear signature of chiral symmetry
restoration.",0008043v1
2002-07-11,Quasi-Local Density Functional Theory and its Application within Extended Thomas-Fermi Approximation,"A generalization of the Density Functional Theory is proposed. The theory
developed leads to single-particle equations of motion with a quasi-local
mean-field operator, which contains a quasi-particle position-dependent
effective mass and a spin-orbit potential. The energy density functional is
constructed using the Extended Thomas-Fermi approximation. Within the framework
of this approach the ground-state properties of the doubly magic nuclei are
considered. The calculations have been performed using the finite-range Gogny
D1S force. The results are compared with the exact Hartree-Fock calculations.",0207029v1
2002-12-18,Spatial structure of a vortex in low density neutron matter,"We study in a fully selfconsistent approach the structure of a vortex in low
density superfluid neutron matter. We determine that the matter density profile
of a vortex shows a significant depletion in the region of the core, a feature
never reported for a vortex state in a Fermi superfluid.",0212072v2
2004-10-26,"Antisymmetrized Green's function approach to $(e,e')$ reactions with a realistic nuclear density","A completely antisymmetrized Green's function approach to the inclusive
quasielastic $(e,e')$ scattering, including a realistic one-body density, is
presented. The single particle Green's function is expanded in terms of the
eigenfunctions of the nonhermitian optical potential. This allows one to treat
final state interactions consistently in the inclusive and in the exclusive
reactions. Nuclear correlations are included in the one-body density. Numerical
results for the response functions of $^{16}$O and $^{40}$Ca are presented and
discussed.",0410103v1
1999-03-19,Reconstructing the density matrix of a spin s through Stern-Gerlach measurements (II),"The density matrix of a spin s is fixed uniquely if the probabilities to
obtain the value s upon measuring n.S are known for 4s(s+1) appropriately
chosen directions n in space. These numbers are just the expectation values of
the density operator in coherent spin states, and they can be determined in an
experiment carried out with a Stern-Gerlach apparatus. Furthermore, the
experimental data can be inverted providing thus a parametrization of the
statistical operator by 4s(s+1) positive parameters.",9903067v1
2008-11-05,Spin resolved energy parametrization of a quasi-one-dimensional electron gas,"By carrying out extensive lattice regularized diffusion Monte Carlo
calculations, we study the spin and density dependence of the ground state
energy for a quasi-one-dimensional electron gas, with harmonic transverse
confinement and long-range $1/r$ interactions. We present a parametrization of
the exchange-correlation energy suitable for spin density functional
calculations, which fulfills exact low and high density limits.",0811.0725v2
2009-01-20,Charge Density Refinement of the Si (111) 7x7 Surface,"We report an experimental refinement of the local charge density at the Si
(111) 7x7 surface utilizing a combination of x-ray and high energy electron
diffraction. By perturbing about a bond-centered pseudoatom model, we find
experimentally that the adatoms are in an anti-bonding state with the atoms
directly below. We are also able to experimentally refine a charge transfer of
0.26(4) e- from each adatom site to the underlying layers. These results are
compared with a full-potential all-electron density functional DFT calculation.",0901.3135v1
2009-08-24,Enhancement in transition temperature and critical current density of CeO0.8F0.2FeAs by yttrium doping,"We report significant enhancement in superconducting properties of yttrium
substituted Ce1-xYxOFFeAs superconductors. The polycrystalline samples were
prepared by two step solid state reaction technique. X-ray diffraction
confirmed tetragonal ZrCuSiAs structure with decrease in both a and c lattice
parameters on increasing yttrium substitution (with fixed F content). With
smaller ion Y in place of Ce, the transition temperature increased by 6 K.
Yttrium doping also lead to higher critical fields as well as stronger inter
and intra-granular current density. The magnetization critical current density
increased by an order of magnitude at 30 K and 1 T magnetic field.",0908.3372v1
2010-03-18,Correlation of the scaling exponent of the diffusivity-density function in viscous liquids with their elastic properties,"Fundamental thermodynamical concepts and a solid-state point defect elastic
model are used to formulate a diffusivity-density scaling function for viscous
liquids. It is proved in a straightforward manner that the scaling exponent
describing the density scaling of the diffusivity, is related with the pressure
derivative of the isothermal bulk modulus.",1003.3559v2
2010-10-19,Coexistence of Superconductivity and Charge Density Wave in SrPt2As2,"SrPt2As2 is a novel arsenide superconductor, which crystallizes in the
CaBe2Ge2-type structure as a different polymorphic form of the ThCr2Si2-type
structure. SrPt2As2 exhibits a charge-density-wave (CDW) ordering at about 470
K and enters into a superconducting state at Tc = 5.2 K. The coexistence of
superconductivity and CDW refers to Peierls instability with a moderately
strong electron-phonon interaction. Thus SrPt2As2 can be viewed as a
nonmagnetic analog of iron-based superconductors, such as doped BaFe2As2, in
which superconductivity emerges in close proximity to spin-density-wave
ordering.",1010.3950v2
2011-08-11,Effective Hamiltonian of Liquid-Vapor Curved Interfaces in Mean Field,"We analyze a one-component simple fluid in a liquid-vapor coexistence state,
which forms an arbitrarily curved interface. By using an approach based on
density functional theory, we obtain an exact and simple expression for the
grand potential at the level of mean field approximation that depends on the
density profile and the short-range interaction potential. By introducing the
step-function approximation for the density profile, and using general
geometric arguments, we expand the grand potential in powers of the principal
curvatures of the surface and find consistency with the Helfrich
phenomenological model in the second order approximation.",1108.2535v1
2011-09-29,Distances of qubit density matrices on Bloch sphere,"We recall the Einstein velocity addition on the open unit ball $\B$ of
$\R^{3}$ and its algebraic structure, called the Einstein gyrogroup. We
establish an isomorphism between the Einstein gyrogroup on $\B$ and the set of
all qubit density matrices representing mixed states endowed with an
appropriate addition. Our main result establishes a relation between the trace
metric for the qubit density matrices and the rapidity metric on the Einstein
gyrogroup $\B$.",1109.6564v1
2011-10-10,Classical Driven Transport in Open Systems with Particle Interactions and General Couplings to Reservoirs,"We study nonequilibrium steady states of lattice gases with nearest-neighbor
interactions that are driven between two reservoirs. Density profiles in these
systems exhibit oscillations close to the reservoirs. We demonstrate that an
approach based on time-dependent density functional theory copes with these
oscillations and predicts phase diagrams of bulk densities to a good
approximation under arbitrary boundary-reservoir couplings. The minimum or
maximum current principles can be applied only for specific bulk-adapted
couplings. We show that they generally fail to give the correct topology of
phase diagrams but can still be useful for getting insight into the mutual
arrangement of different phases.",1110.2198v1
2012-05-28,The holographic quantum effective potential at finite temperature and density,"We develop a formalism that allows the computation of the quantum effective
potential of a scalar order parameter in a class of holographic theories at
finite temperature and charge density. The effective potential is a valuable
tool for studying the ground state of the theory, symmetry breaking patterns
and phase transitions. We derive general formulae for the effective potential
and apply them to determine the phase transition temperature and density in the
scaling region.",1205.6205v1
2012-06-08,Spectral density and metal-insulator phase transition in Mott insulators within RDMFT,"We present a method for calculating the spectrum of periodic solids within
reduced density matrix functional theory. This method is validated by a
detailed comparison of the angular momentum projected spectral density with
that of well established many-body techniques, in all cases finding an
excellent agreement. The physics behind the pressure induced insulator-metal
phase transition in MnO is investigated. The driving mechanism of this
transition is identified as increased crystal field splitting with pressure,
resulting in a charge redistribution between the Mn $e_g$ and $t_2g$ symmetry
projected states.",1206.1712v1
2012-09-26,Exact solutions to the spin-2 Gross-Pitaevskii equations,"We present several exact solutions to the coupled nonlinear Gross-Pitaevskii
equations which describe the motion of the one-dimensional spin-2 Bose-Einstein
condensates. The nonlinear density-density interactions are decoupled by making
use of the properties of Jacobian elliptical functions. The distinct time
factors in each hyperfine state implies a ""Lamor"" procession in these
solutions. Furthermore, exact time-evolving solutions to the time-dependent
Gross-Pitaevskii equations are constructed through the spin-rotational symmetry
of the Hamiltonian. The spin-polarizations and density distributions in the
spin-space are analyzed.",1209.5852v1
2014-12-13,"Aspects of gluon propagation in Landau gauge: spectral densities, and mass scales at finite temperature","We discuss a method to extract the K\""all\'en-Lehmann spectral density of a
particle (be it elementary or bound state) propagator and apply it to compute
gluon spectral densities from lattice data. Furthermore, we also consider the
interpretation of the Landau-gauge gluon propagator at finite temperature as a
massive-type bosonic propagator.",1412.4286v1
2015-02-06,Recent developments at finite density on the lattice,"Some recent developments to handle the numerical sign problem in QCD and
related theories at nonzero density are reviewed. In this contribution I focus
on changing the integration order to soften the severity of the sign problem,
the density of states, and the extension into the complex plane (complex
Langevin dynamics and Lefshetz thimbles).",1502.01850v2
2016-01-01,The shell model Monte Carlo approach to level densities: recent developments and perspectives,"We review recent advances in the shell model Monte Carlo approach for the
microscopic calculation of statistical and collective properties of nuclei. We
discuss applications to the calculation of (i) level densities in nickel
isotopes, implementing a recent method to circumvent the odd-particle sign
problem; (ii) state densities in heavy nuclei; (iii) spin distributions of
nuclear levels; and (iv) finite-temperature quadrupole distributions.",1601.00107v1
2017-05-11,Monitoring Nonadiabatic Avoided Crossing Dynamics in Molecules by Ultrafast X-Ray Diffraction,"We examine time-resolved X-ray diffraction from molecules in the gas phase
which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled
electrons and nuclei. Several contributions to the signal are identified,
representing (in decreasing strength) elastic scattering, contributions of the
electronic coherences created by nonadiabatic couplings in the avoided crossing
regime, and inelastic scattering. The former probes the charge density and
delivers direct information on the evolving molecular geometry. The latter two
contributions are weaker and carry spatial information of the transition charge
densities (off-diagonal elements of the charge-density operator). Simulations
are presented for the nonadiabatic harpooning process in the excited states of
sodium fluoride.",1705.03978v1
2016-11-02,Atomic orbital self-energy and electronegativity,"In this work, atomic calculations were performed within the local-density and
generalized-gradient approximations of exchange and correlation density
functionals within density-functional theory to provide accurate periodic
trends of first ionization energies and electron affinities of the atomic
series from hydrogen to xenon. Electronegativities were determined directly
from Mulliken's formula and were shown to be equivalently calculated rather by
using Slater-Janak's transition state or by calculating the electrostatic
self-energies of the orbitals involved in the transition to ions. Finally,
comparisons were made with other theoretical and experimental results,
including Mulliken-Jaff\'e's electronegativity scale.",1611.01033v1
2017-01-17,Some Theoretical Results Regarding the Polygonal Distribution,"The polygonal distributions are a class of distributions that can be defined
via the mixture of triangular distributions over the unit interval. The class
includes the uniform and trapezoidal distributions, and is an alternative to
the beta distribution. We demonstrate that the polygonal densities are dense in
the class of continuous and concave densities with bounded second derivatives.
Pointwise consistency and Hellinger consistency results for the maximum
likelihood (ML) estimator are obtained. A useful model selection theorem is
stated as well as results for a related distribution that is obtained via the
pointwise square of polygonal density functions.",1701.04512v1
2018-08-21,Density matrix of chaotic quantum systems,"The nonequilibrium dynamics in chaotic quantum systems denies a fully
understanding up to now, even if thermalization in the long-time asymptotic
state has been explained by the eigenstate thermalization hypothesis which
assumes a universal form of the observable matrix elements in the eigenbasis of
Hamiltonian. It was recently proposed that the density matrix elements have
also a universal form, which can be used to understand the nonequilibrium
dynamics at the whole time scale, from the transient regime to the long-time
steady limit. In this paper, we numerically test these assumptions for density
matrix in the models of spins.",1808.06881v2
2020-09-05,Relativistic Strong Scott Conjecture: A Short Proof,"We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic
energy $(c^2p^2+c^4)^{1/2}-c^2$ used already by Chandrasekhar. We study the
behavior of the one-particle ground state density on the length scale $Z^{-1}$
in the limit $Z,c\to\infty$ keeping $Z/c$ fixed. We give a short proof of a
recent result by the authors and Barry Simon showing the convergence of the
density to the relativistic hydrogenic density on this scale.",2009.02474v1
2008-07-04,Intense Terahertz Laser Fields Induced and Manipulated Pseudospin Polarization in Graphene,"We investigate the pseudospin-dependent density-energy relation (whose
differential with respect to energy is density of states) of a monolayer
graphene under intense terahertz laser field by exactly solving the
time-dependent Schr\""{o}dinger equation with help of Floquet's theorem. We find
that psedospin polarization can be induced by a circular polarized terahertz
laser field. The psedospin polarization in K and K$^{\prime}$ valleys can be
exactly opposite sign when the electron densities in these two calleys are
equivalent. Further more, we find that the psedospin polarization can be
manipulated by the strength, frequency, and especially the polarization
orientation of the field.",0807.0667v1
2013-09-13,Transport with ultracold atoms at constant density,"We investigate the transport through a few-level quantum system described by
a Markovian master equation with temperature- and particle-density dependent
chemical potentials. From the corresponding Onsager relations we extract linear
response transport coefficients in analogy to the electronic conductance,
thermal conductance and thermopower. Considering ideal Fermi and Bose gas
reservoirs we observe steady-state currents against the thermal bias as a
result of the non-linearities introduced by the constraint of a constant
particle density in the reservoirs. Most importantly, we find signatures of the
on-set of Bose-Einstein condensation in the transport coefficients.",1309.3488v2
2013-09-24,Alpha-Particle Clustering from Expanding Self-Conjugate Nuclei within the Hartree-Fock-Bogoliubov Approach,"The nuclear equation of state is explored with the constrained HFB approach
for self conjugate nuclei. It is found that beyond a certain low, more or less
universal density, those nuclei spontaneously cluster into A/4 alpha particles
with A the nucleon number. The energy at the threshold density increases
linearly with the number of alpha particles as does the experimental threshold
energy. Taking off the spurious c.o.m. energy of each alpha particle almost
gives agreement between theory and experiment. The implications of these
results with respect to alpha clustering and the nuclear EOS at low density are
discussed.",1309.6104v1
2014-06-20,"""Nodal gap"" induced by the incommensurate diagonal spin density modulation in underdoped high-$T_c$ superconductors","Recently it was revealed that the whole Fermi surface is fully gapped for
several families of underdoped cuprates. The existence of the finite energy gap
along the $d$-wave nodal lines (""nodal gap"") contrasts the common understanding
of the $d$-wave pairing symmetry, which challenges the present theories for the
high-$T_c$ superconductors. Here we propose that the incommensurate diagonal
spin-density-wave order can account for the above experimental observation. The
Fermi surface and the local density of states are also studied. Our results are
in good agreement with many important experiments in high-$T_c$
superconductors.",1406.5408v1
2018-09-24,Partition potential for hydrogen-bonding in formic acid dimers,"The ground-state energy and density of four low-energy conformations of the
formic acid dimer were calculated via Partition Density Functional Theory
(PDFT). The differences between isolated and PDFT monomer densities display
similar deformation patterns for primary and secondary hydrogen bonds among all
four dimers. In contrast, the partition potential shows no transferable
features in the bonding regions. These observations highlight the global
character of the partition potential and the cooperative effect that occurs
when a dimer is bound via more than one hydrogen bond. We also provide
numerical confirmation of the intuitive (but unproven) observation that
fragment deformation energies are larger for systems with larger binding
energies.",1809.08906v1
2023-06-01,Waterlike density anomaly in fermions,"In this work we explore the one-dimensional extended Hubbard model as a fluid
system modelling liquid phases of different densities. This model naturally
displays two length scales of interaction, which are connected with waterlike
anomalies. We analyze the density anomaly as a function of the model
parameters, namely the hopping, on-site and first neighbor interactions. We
show that this anomaly is present for a wide range of model parameters and is
connected to a ground-state liquid-liquid critical point.",2306.01161v2
1997-03-25,Phase Diagram of the Half-Filled Extended Hubbard Model in Two Dimensions,"We consider an extended Hubbard model of interacting fermions on a lattice.
The fermion kinetic energy corresponds to a tight binding Hamiltonian with
nearest neighbour (-t) and next nearest neighbour (t') hopping matrix elements.
In addition to the onsite Hubbard interaction (U) we also consider a nearest
neighbour repulsion (V). We obtain the zero temperature phase diagram of our
model within the Hartree-Fock approximation. We consider ground states having
charge and spin density wave ordering as well as states with orbital
antiferromagnetism or spin nematic order. The latter two states correspond to
particle-hole binding with $d_{x^2-y^2}$ symmetry in the charge and spin
channels respectively. For $t' = 0$, only the charge density wave and spin
density wave states are energetically stable. For non-zero t', we find that
orbital antiferromagnetism (or spin nematic) order is stable over a finite
portion of the phase diagram at weak coupling. This region of stability is seen
to grow with increasing values of t'.",9703213v1
2001-12-13,Various spin-polarization states beyond the maximum-density droplet: a quantum Monte Carlo study,"Using variational quantum Monte Carlo method, the effect of Landau-level
mixing on the lowest-energy--state diagram of small quantum dots is studied in
the magnetic field range where the density of magnetic flux quanta just exceeds
the density of electrons. An accurate analytical many-body wave function is
constructed for various angular momentum and spin states in the lowest Landau
level, and Landau-level mixing is then introduced using a Jastrow factor. The
effect of higher Landau levels is shown to be significant; the transition lines
are shifted considerably towards higher values of magnetic field and certain
lowest-energy states vanish altogether.",0112243v1
2003-12-18,"Spin Density Wave and D-Wave Superconducting Order Parameter ""Coexistence""","We study the properties of a spin-density-wave antiferromagnetic mean-field
ground state with d-wave superconducting (DSC) correlations. This ground state
always gains energy by Cooper pairing. It would fail to superconduct at
half-filling due to the antiferromagnetic gap although its particle-like
excitations would be Bogolyubov-BCS quasiparticles consisting of coherent
mixtures of electrons and holes. More interesting and relevant to the
superconducting cuprates is the case when antiferromagnetic order is turned on
weakly on top of the superconductivity. This would correspond to the onset of
antiferromagnetism at a critical doping. In such a case a small gap
proportional to the weak antiferromagnetic gap opens up for nodal
quasiparticles, and the quasiparticle peak would be discernible. We evaluate
numerically the absorption by nodal quasiparticles and the local density of
states for several ground states with antiferromagnetic and d-wave
superconducting correlations.",0312451v1
2006-04-05,Shot noise in diffusive ferromagnetic metals,"We show that shot noise in a diffusive ferromagnetic wire connected by tunnel
contacts to two ferromagnetic electrodes can probe the intrinsic density of
states and the extrinsic impurity scattering spin-polarization contributions in
the polarization of the wire conductivity. The effect is more pronounced when
the electrodes are perfectly polarized in opposite directions. While in this
case the shot noise has a weak dependence on the impurity scattering
polarization, it is strongly affected by the polarization of the density of
states. For a finite spin-flip scattering rate the shot noise increases well
above the normal state value and can reach the full Poissonian value when the
density of states tends to be perfectly polarized. For the parallel
configuration we find that the shot noise depends on the relative sign of the
intrinsic and the extrinsic polarizations.",0604142v1
2010-01-12,Electron Capture $β$-Decay of $^7$Be Encapsulated in C$_{60}$: Origin of Increased Electron Density at the $^7$Be Nucleus,"We offer a new theoretical interpretation for the effect of enhanced electron
density at $^7$Be nucleus encapsulated in fullerene C$_{60}$. Our {\it{ab
initio}} Hartree-Fock calculations show that electron density at the $^7$Be
nucleus in $^7$Be@C$_{60}$ increase due to {\it{}attractive} effective
potential well generated by the fullerene. The 2$s$ state in the isolated Be
atom turns into 3$s$ state in the joint potential. This new state has higher
energy, and slightly larger amplitude at the Be nucleus than the previous 2$s$
state. Moreover the 3$s$ wave function has additional {\it{}node} appeared at
the distance $r \simeq 5a_B$ from the center. The node imitates repulsion
between the Be electron and the fullerene wall, because the electron has zero
probability to occupy this region. Such imitation of the repulsion by means of
the node in attractive potential has direct physical analogy in the theory of
$\alpha$-$\alpha$ and $N$-$N$ nuclear interactions.",1001.1995v1
2012-09-24,Pair correlation of giant halo nuclei in continuum Skyrme-Hartree-Fock-Bogoliubov theory,"The giant halos predicted in neutron-rich Zr isotopes with $A=124-138$ are
investigated by using the self-consistent continuum Skyrme
Hartree-Fock-Bogoliubov approach, in which the asymptotic behavior of continuum
quasiparticle states is properly treated by the Green's function method. We
study in detail the neutron pair correlation involved in the giant halo by
analyzing the asymptotic exponential tail of the neutron pair condensate (pair
density) in addition to that of the neutron particle density. The neutron
quasiparticle spectra associated with these giant halo nuclei are examined. It
is found that the asymptotic exponential tail of the neutron pair condensate is
dominated by non-resonant continuum quasiparticle states corresponding to the
scattering states with low asymptotic kinetic energy. This is in contrast to
the asymptotic tail of the neutron density, whose main contributions arise from
the resonant quasiparticle states corresponding to the weakly-bound
single-particle orbits and resonance orbits in the Hartree-Fock potential.",1209.5263v1
2012-10-05,Josephson current and density of states in proximity circuits with s+- superconductors,"We study the emergent proximity effect in mesoscopic circuits that involve a
conventional superconductor and an unconventional pnictide superconductor
separated by a diffusive normal or ferromagnetic wire. The focus is placed on
revealing signatures of the proposed s+- state of pnictides from the
proximity-induced density of states and Josephson current. We find analytically
a universal result for the density of states that exhibits both the Thouless
gap at low energies, and peculiar features near the superconducting gap edges
at higher energies. The latter may be used to discriminate between s+- and s++
symmetry scenarios in scanning tunneling spectroscopy experiments. We also
calculate Josephson current-phase relationships for different junction
configurations, which are found to display robust 0-\pi transitions for a wide
range of parameters.",1210.1875v2
2013-02-14,Fluctuating flow angles and anisotropic flow measurements,"Event-by-event fluctuations in the initial density distributions of the
fireballs created in relativistic heavy-ion collisions lead to event-by-event
fluctuations of the final anisotropic flow angles, and density inhomogeneities
in the initial state cause these flow angles to vary with the transverse
momentum of the emitted particles. It is shown that these effects lead to
characteristically different transverse momentum dependencies for anisotropic
flow coefficients extracted from different experimental methods. These
differences can be used to experimentally constrain flow angle fluctuations in
the final state of heavy-ion collisions which, in turn, are sensitive to the
initial state density fluctuations and the shear viscosity of the expanding
fireball medium.",1302.3535v2
2016-06-08,Fast and Extensible Online Multivariate Kernel Density Estimation,"We present xokde++, a state-of-the-art online kernel density estimation
approach that maintains Gaussian mixture models input data streams. The
approach follows state-of-the-art work on online density estimation, but was
redesigned with computational efficiency, numerical robustness, and
extensibility in mind. Our approach produces comparable or better results than
the current state-of-the-art, while achieving significant computational
performance gains and improved numerical stability. The use of diagonal
covariance Gaussian kernels, which further improve performance and stability,
at a small loss of modelling quality, is also explored. Our approach is up to
40 times faster, while requiring 90\% less memory than the closest
state-of-the-art counterpart.",1606.02608v1
2017-05-26,Cross Dimensionality and Emergent Nodal Superconductivity with $p$-orbital Atomic Fermions,"I study cross dimensionality of $p$-orbital atomic fermions loaded in an
optical square lattice with repulsive interactions. The cross-dimensionality
emerges when the transverse tunneling of $p$-orbital fermions is negligible.
With renormalization group analysis, the system is found to support two
dimensional charge, orbital, and spin density wave states with incommensurate
wavevectors. The transition temperatures of these states are controlled by
perturbations near a one dimensional Luttinger liquid fixed point. Considering
transverse tunneling, the cross-dimensionality breaks down and the density wave
(DW) orders become unstable, and I find an unconventional superconducting state
mediated by fluctuation effects. The superconducting gap has an emergent nodal
structure determined by the Fermi momentum, which is tunable by controlling
atomic density. Taking an effective description of the superconducting state,
it is shown that the nodal structure of Cooper pairing can be extracted from
momentum-space radio-frequency spectroscopy in atomic experiments. These
results imply that $p$-orbital fermions could enrich the possibilities of
studying correlated physics in optical lattice quantum emulators beyond the
single-band Fermi Hubbard model.",1705.09686v1
2017-08-08,Pair formation of hard core bosons in flat band systems,"Hard core bosons in a large class of one or two dimensional flat band systems
have an upper critical density, below which the ground states can be described
completely. At the critical density, the ground states are Wigner crystals. If
one adds a particle to the system at the critical density, the ground state and
the low lying multi particle states of the system can be described as a Wigner
crystal with an additional pair of particles. The energy band for the pair is
separated from the rest of the multi-particle spectrum. The proofs use a
Gerschgorin type of argument for block diagonally dominant matrices. In certain
one-dimensional or tree-like structures one can show that the pair is
localised, for example in the chequerboard chain. For this one-dimensional
system with periodic boundary condition the energy band for the pair is flat,
the pair is localised.",1708.02508v3
2020-07-02,"Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene","We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene.
This compliments our earlier analysis of the pairing instabilities. We assume
that near half-filling of either conduction or valence band, the Fermi level is
close to Van Hove points, where the density of states diverges, and study
potential instabilities in the particle-hole channel within a patch model with
two valley degrees of freedom. The hexagonal symmetry of twisted bilayer
graphene allows for either six or twelve Van Hove points. We consider both
cases and find the same two leading candidates for particle-hole order. One is
an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading
inter-valley hopping induces antiferromagnetism between the valleys. The same
state has also been obtained in strong coupling approaches, indicating that
this order is robust. The other is a mixed state with $120^\circ$ complex spin
order and orthogonal complex charge order. In addition, we find a weaker, but
still attractive interaction in nematic channels, and discuss the type of a
nematic order.",2007.00871v2
2020-01-02,Dynamical density and spin response of Fermi arcs and their consequences for Weyl semimetals,"Weyl semimetals exhibit exotic Fermi-arc surface states, which strongly
affect their electromagnetic properties. We derive analytical expressions for
all components of the composite density-spin response tensor for the surfaces
states of a Weyl-semimetal model obtained by closing the band gap in a
topological insulating state and introducing a time-reversal-symmetry-breaking
term. Based on the results, we discuss the electromagnetic susceptibilities,
the current response, and other physical effects arising from the density-spin
response. We find a magnetoelectric effect caused solely by the Fermi arcs. We
also discuss the effect of electron-electron interactions within the random
phase approximation and investigate the dispersion of surface plasmons formed
by Fermi-arc states. Our work is useful for understanding the electromagnetic
and optical properties of the Fermi arcs.",2001.00438v2
2021-09-04,Multi-State Formulation of the Frozen-Density Embedding Quasi-Diabatization Approach,"We present a multi-state implementation of the recently developed FDE-diab
methodology [J. Chem. Phys., 148 (2018), 214104] in the Serenity program. The
new framework extends the original approach such that any number of
charge-localized quasi-diabatic states can be coupled, giving an access to
calculations of ground and excited state spin-density distributions as well as
to excitation energies. We show that it is possible to obtain results similar
to those from correlated wave function approaches such as the complete active
space self-consistent field method at much lower computational effort.
Additionally, we present a series of approximate computational schemes, which
further decrease the overall computational cost and systematically converge to
the full FDE-diab solution. The proposed methodology enables computational
studies on spin-density distributions and related properties for large
molecular systems of biochemical interest.",2109.01877v1
2023-01-09,High-fidelity imaging of a band insulator in a three-dimensional optical lattice clock,"We report on the observation of a high-density, band insulating state in a
three-dimensional optical lattice clock. Filled with a nuclear-spin polarized
degenerate Fermi gas of 87Sr, the 3D lattice has one atom per site in the
ground motional state, thus guarding against frequency shifts due to contact
interactions. At this high density where the average distance between atoms is
comparable to the probe wavelength, standard imaging techniques suffer from
large systematic errors. To spatially probe frequency shifts in the clock and
measure thermodynamic properties of this system, accurate imaging techniques at
high optical depths are required. Using a combination of highly saturated
fluorescence and absorption imaging, we confirm the density distribution in our
3D optical lattice in agreement with a single spin band insulating state.
Combining our clock platform with this high filling fraction opens the door to
studying new classes of long-lived, many-body states arising from dipolar
interactions.",2301.03343v1
2002-05-19,Manifestation of photonic band structure in small clusters of spherical particles,"We study the formation of the photonic band structure in small clusters of
dielectric spheres. The first signs of the band structure, an attribute of an
infinite crystal, can appear for clusters of 5 particles. Density of resonant
states of a cluster of 32 spheres may exhibit a well defined structure similar
to the density of electromagnetic states of the infinite photonic crystal. The
resonant mode structure of finite-size aggregates is shown to be insensitive to
random displacements of particles off the perfect lattice positions as large as
half-radius of the particle. The results were obtained by an efficient
numerical method, which relates the density of resonant states to the the
scattering coefficients of the electromagnetic scattering problem. Generalized
multisphere Mie (GMM) solution was used to obtain scattering matrix elements.
These results are important to miniature photonic crystal design as well as
understanding of light localization in dense random media.",0205393v1
2016-03-21,Model-Independent Inference of Neutron Star Radii from Moment of Inertia Measurements,"A precise moment of inertia measurement for PSR J0737-3039A in the double
pulsar system is expected within the next five years. We present here a new
method of mapping the anticipated measurement of the moment of inertia directly
into the neutron star structure. We determine the maximum and minimum values
possible for the moment of inertia of a neutron star of a given radius based on
physical stability arguments, assuming knowledge of the equation of state only
at densities below the nuclear saturation density. If the equation of state is
trusted up to the nuclear saturation density, we find that a measurement of the
moment of inertia will place absolute bounds on the radius of PSR J0737-3039A
to within $\pm$1 km. The resulting combination of moment of inertia, mass, and
radius measurements for a single source will allow for new, stringent
constraints on the dense-matter equation of state.",1603.06594v2
2006-10-16,Gravitational stability of finite massive bodies,"Jeans instability of finite massive bodies at hydrostatic equilibrium is
studied. Differential equation governing the evolution of infinitesimal
disturbances is derived. We take into account radial inhomogeneity of mass
density and other fluid parameters at the equilibrium state. Dispersion
relation and a simple analytical formula, generalizing the Jeans criterion of
instability, are derived.",0610450v1
1991-10-15,Some Properties of (Non) Critical Strings,"We review some recent developments in string theory, emphasizing the
importance of vacuum instabilities, their relation to the density of states,
and the role of space-time fermions in non-critical string theory. We also
discuss the classical dynamics of two dimensional string theory.",9110041v1
2013-07-25,An application of group expansion to the Anderson-Bernoulli model,"We establish smoothness of the density of states for 1D lattice Schrodinger
operators with potential taking values $\pm\lambda$, for $\lambda$ in a class
of small algebraic numbers and energy $E\in)-2, 2($ suitably restricted away
from $\pm2$.",1307.6867v1
2018-08-28,Formula for The IDS of Periodic Jacobi Matrices,"We prove that on the spectrum the integrated density of states (IDS for
short) of periodic Jacobi matrices is related to the discriminant. The method
is to count the number of generalized zeros of Bloch wave solutions.",1808.09084v2
2010-10-13,Approach to equilbrium in nano-scale systems at finite temperatur,"We study the time evolution of the reduced density matrix of a system of
spin-1/2 particles interacting with an environment of spin-1/2 particles. The
initial state of the composite system is taken to be a product state of a pure
state of the system and a pure state of the environment. The latter pure state
is prepared such that it represents the environment at a given finite
temperature in the canonical ensemble. The state of the composite system
evolves according to the time-dependent Schr{\""{o}}dinger equation, the
interaction creating entanglement between the system and the environment. It is
shown that independent of the strength of the interaction and the initial
temperature of the environment, all the eigenvalues of the reduced density
matrix converge to their stationary values, implying that also the entropy of
the system relaxes to a stationary value. We demonstrate that the difference
between the canonical density matrix and the reduced density matrix in the
stationary state increases as the initial temperature of the environment
decreases. As our numerical simulations are necessarily restricted to a modest
number of spin-1/2 particles ($<36$), but do not rely on time-averaging of
observables nor on the assumption that the coupling between system and
environment is weak, they suggest that the stationary state of the system
directly follows from the time evolution of a pure state of the composite
system, even if the size of the latter cannot be regarded as being close to the
thermodynamic limit.",1010.2646v1
1996-01-24,Axisymmetric circumstellar interaction in supernovae,"Multiwavelength observations of Type II supernovae have shown evidence for
the interaction of supernovae with the dense slow winds from the red supergiant
progenitor stars. Observations of planetary nebulae and the nebula around SN
1987A show that the slow winds from extended stars frequently have an axisymme-
tric structure with a high density in the equatorial plane. We have carried out
numerical calculations of the interaction of a supernova with such an axisymme-
tric density distribution. For small values of the angular density gradient at
the pole, the asymmetry in the interaction shell is greater than, but close to,
that expected from purely radial motion. If the angular density gradient is
above a moderate value, the flow qualitatively changes and a protrusion emerges
along the axis. For a power-law supernova density profile, the flow approaches
a self-similar state in which the protrusion length is $2-4$ times the radius
of the main shell. The critical density gradient is larger for steeper density
profiles of the ejecta. Most of our calculations are axisymmetric, but we have
carried out a 3-dimensional calculation to show that the protrusion is not a
numerical artifact along the symmetry axis. For typical supernova parameters,
the protrusions take $\gtrsim$ several years to develop. The appearance of the
shell with protrusions is similar to that observed in VLBI radio images of the
remnant 41.9 +58 in M82 and, possibly, of SN 1986J. We also considered the
possibility of asymmetric ejecta and found that it had a relatively small
effect on the asymmetry of the interaction region.",9601137v1
2019-08-19,Semi-Local Parameterization of the Electron Localization Function in Second-Order Density Gradients,"The electron localization function (ELF) is a universal measure of electron
localization that allows for, e.g., an effective characterization of physical
bonds in molecular and solid state systems. In the context of the widely used
Kohn-Sham density-functional theory (KS-DFT) and its generalizations, ELF is
given in terms of the single-particle electron density as well as the
non-interacting kinetic energy density (KED) of the KS system. Starting from
the notion of an edge electron gas put forth by Kohn and Mattsson, we here use
an \emph{exactly soluble}, strongly correlated few-electron model of a
harmonically confined electron gas in order to parameterize the
positive-definite non-interacting KS KED in terms of the density and its
reduced second-order gradients. We arrive at a simple, yet generally applicable
functional approximation to ELF expressed in the electron density and its
derivatives. To demonstrate the validity of our approach, we use the obtained
parameterization to perform topological analysis of the bonds in solid Al and
Si, and to study physical and chemical adsorption of graphene on a Ni surface.
We find that while the expression does not provide a quantitatively accurate
approximation of absolute ELF values, the most essential qualitative features
are captured. Hence, the expression is useful in contexts where the electron
density is available, but not the KS orbitals or the KED, and one desires a
qualitative picture of the electron localization that mimics ELF.",1908.06947v1
2005-01-22,Evolution of the structure of amorphous ice - from low-density amorphous (LDA) through high-density amorphous (HDA) to very high-density amorphous (VHDA) ice,"We report results of molecular dynamics simulations of amorphous ice for
pressures up to 22.5 kbar. The high-density amorphous ice (HDA) as prepared by
pressure-induced amorphization of Ih ice at T=80 K is annealed to T=170 K at
various pressures to allow for relaxation. Upon increase of pressure, relaxed
amorphous ice undergoes a pronounced change of structure, ranging from the
low-density amorphous ice (LDA) at p=0, through a continuum of HDA states to
the limiting very high-density amorphous ice (VHDA) regime above 10 kbar. The
main part of the overall structural change takes place within the HDA
megabasin, which includes a variety of structures with quite different local
and medium-range order as well as network topology and spans a broad range of
densities. The VHDA represents the limit to densification by adapting the
hydrogen-bonded network topology, without creating interpenetrating networks.
The connection between structure and metastability of various forms upon
decompression and heating is studied and discussed. We also discuss the analogy
with amorphous and crystalline silica. Finally, some conclusions concerning the
relation between amorphous ice and supercooled water are drawn.",0501543v1
2002-10-25,Electron Mobility in Dense Argon Gas at Several Temperatures,"The mobility $\mu$ of excess electrons in dense Argon gas has been measured
as a function of the applied electric field $E$ and of the gas density N at
several temperatures in the range $142.6<T<200$ K, encompassing the critical
temperature Tc=150.86 K. We report here measurements at densities up to N?7
nm$^{-3}$, close to the critical density, $N_c \approx$ 8.1 nm$^{-3}$, reached
for the isotherm closest to the critical one. At all temperatures, below as
well as above Tc, and up to moderately high densities, the density-normalized
mobility $\mu N$ shows the usual electric field dependence present in a gas
with a Ramsauer-Townsend minimum due to the mainly attractive electron-atom
interaction. mN is constant and field independent for small values of $E,$
shows a maximum for a reduced field $E/N \approx$ 4 mTd, and then decreases
rapidly with the field, approximately proportional to $(E/N)^{-1/2}.$ The
zero-field density-normalized mobility $\mu_0 N, $for all T>$T_c,$ shows the
well known anomalous positive density effect, i.e., m0N increases with
increasing N, confirming previous results obtained for T=300 K and 162.7 K.
Below Tc, however, $\mu_0 N$ does not show the expected anomalous positive
density effect, but it rather features a broad maximum. This appears to be a
crossover behavior between the positive density effect shown for T>Tc and the
small negative effect previously observed for T$\approx$ 90 K. In any case, the
data at all temperatures confirm the interpretation of the anomalous density
effect as being essentially due by the density-dependent quantum shift of the
electron ground state kinetic energy in a disordered medium as a result of
multiple scattering (MS) processes, although other MS processes do influence
the outcome of the experiment.",0210104v1
2018-10-18,Optimization of highly excited matrix product states with an application to vibrational spectroscopy,"Configuration-interaction-type calculations on electronic and vibrational
structure are often the method of choice for the reliable approximation of
many-particle wave functions and energies. The exponential scaling, however,
limits their application range. An efficient approximation to the full
configuration interaction solution can be obtained with the density matrix
renormalization group (DMRG) algorithm without a restriction to a predefined
excitation level. In a standard DMRG implementation, however, excited states
are calculated with a ground-state optimization in the space orthogonal to all
lower lying wave function solutions. A trivial parallelization is therefore not
possible and the calculation of highly excited states becomes prohibitively
expensive, especially in regions with a high density of states. Here, we
introduce two variants of the density matrix renormalization group algorithm
that allow us to target directly specific energy regions and therefore highly
excited states. The first one, based on shift-and-invert techniques, is
particularly efficient for low-lying states, but is not stable in regions with
a high density of states. The second one, based on the folded auxiliary
operator, is less efficient, but more accurate in targeting high-energy states.
We apply the algorithm to the solution of the nuclear Schroedinger equation,
but emphasize that it can be applied to the diagonalization of general
Hamiltonians as well, such as the electronic Coulomb Hamiltonian to address
X-ray spectra. In combination with several root-homing algorithms and a
stochastic sampling of the determinant space, excited states of interest can be
adequately tracked and analyzed during the optimization. We demonstrate that we
can accurately calculate prominent spectral features of large molecules such as
the sarcosyn-glycine dipeptide.",1810.08044v2
1997-07-02,The structure of galaxy clusters in different cosmologies,"We investigate the internal structure of clusters of galaxies in
high-resolution N-body simulations of 4 different cosmologies. There is a
higher proportion of disordered clusters in critical-density than in
low-density universes, although the structure of relaxed clusters is very
similar in each. Crude measures of substructure, such as the shift in the
position of the centre-of-mass as the density threshold is varied, can
distinguish the two in a sample of just 20 or so clusters; it is harder to
differentiate between clusters in open and flat models with the same density
parameter. Most clusters are in a quasi-steady state within the virial radius
and are well-described by the density profile of Navarro, Frenk & White (1995).",9707018v1
2004-02-03,Probing the Evolution of the Dark Energy Density with Future Supernova Surveys,"The time dependence of the dark energy density can be an important clue to
the nature of dark energy in the universe. We show that future supernova data
from dedicated telescopes (such as SNAP), when combined with data of nearby
supernovae, can be used to determine how the dark energy density $\rho_X(z)$
depends on redshift, if $\rho_X(z)$ is not too close to a constant. For
quantitative comparison, we have done an extensive study of a number of dark
energy models. Based on these models we have simulated data sets in order to
show that we can indeed reconstruct the correct sign of the time dependence of
the dark energy density, outside of a degeneracy region centered on $1+w_0 =
-w_1 z_{max}/3$ (where $z_{max}$ is the maximum redshift of the survey, e.g.,
$z_{max}=1.7$ for SNAP). We emphasize that, given the same data, one can obtain
much more information about the dark energy density directly (and its time
dependence) than about its equation of state.",0402080v1
2006-12-05,The Phase Transition of Dark Energy,"Considering that the universe is filled with the nonrelativistic matter and
dark energy and each component is respectively satisfied with its conservation
condition in the absence of their interaction, we give the change rate of the
fractional density and the density of dark energy from the conservation
condition. It is clear that the fractional density of dark energy will
monotonously increase and gradually become the dominating contribution to the
universe as the redshift becomes low. Combining the evolutional trend of the
state equation of dark energy and the change rate of the density of dark energy
we find that the density of dark energy will decrease up to a minimum and
whereafter it will increase again as the redshift becomes low. This can be
regarded as the phase transition of dark energy from the quintessence phase to
the phantom phase.",0612113v1
2008-09-26,Isomorphic classical molecular dynamics model for an excess electron in a supercritical fluid,"Ring polymer molecular dynamics (RPMD) is used to directly simulate the
dynamics of an excess electron in a supercritical fluid over a broad range of
densities. The accuracy of the RPMD model is tested against numerically exact
path integral statistics through the use of analytical continuation techniques.
At low fluid densities, the RPMD model substantially underestimates the
contribution of delocalized states to the dynamics of the excess electron.
However, with increasing solvent density, the RPMD model improves, nearly
satisfying analytical continuation constraints at densities approaching those
of typical liquids. In the high density regime, quantum dispersion
substantially decreases the self-diffusion of the solvated electron.
  In this regime where the dynamics of the electron is strongly coupled to the
dynamics of the atoms in the fluid, trajectories that can reveal diffusive
motion of the electron are long in comparison to $\beta\hbar$.",0809.4522v1
2010-07-09,Dynamical properties of nuclear and stellar matter and the symmetry energy,"The effects of density dependence of the symmetry energy on the collective
modes and dynamical instabilities of cold and warm nuclear and stellar matter
are studied in the framework of relativistic mean-field hadron models. The
existence of the collective isovector and possibly an isoscalar collective mode
above saturation density is discussed. It is shown that soft equations of state
do not allow for a high density isoscalar collective mode, however, if the
symmetry energy is hard enough an isovector mode will not disappear at high
densities. The crust-core transition density and pressure are obtained as a
function of temperature for $\beta$-equilibrium matter with and without
neutrino trapping. An estimation of the size of the clusters formed in the
non-homogeneous phase as well as the corresponding growth rates and
distillation effect is made. It is shown that cluster sizes increase with
temperature, that the distillation effect close to the inner edge of the
crust-core transition is very sensitive to the symmetry energy, and that,
within a dynamical instability calculation, the pasta phase exists in warm
compact stars up to 10 - 12 MeV.",1007.1564v1
2016-10-24,Violation of f-sum Rule with Generalized Kinetic Energy,"Motivated by the normal state of the cuprates in which the f-sum rule
increases faster than a linear function of the particle density, we derive a
conductivity sum rule for a system in which the kinetic energy operator in the
Hamiltonian is a general function of the momentum squared. Such a kinetic
energy arises in scale invariant theories and can be derived within the context
of holography. Our derivation of the f-sum rule is based on the gauge couplings
of a non-local Lagrangian in which the kinetic operator is a fractional
Laplacian of order $\alpha$. We find that the f-sum rule in this case deviates
from the standard linear dependence on the particle density. We find two
regimes. At high temperatures and low densities, the sum rule is proportional
to $nT^{\frac{\alpha-1}{\alpha}}$ where $T$ is the temperature. At low
temperatures and high densities, the sum rule is proportional to
$n^{1+\frac{2(\alpha-1)}{d}}$ with $d$ being the number of spatial dimensions.
The result in the low temperature and high density limit, when $\alpha < 1$,
can be used to qualitatively explain the behavior of the effective number of
charge carriers in the cuprates at various doping concentrations.",1610.07621v1
2018-04-12,Constraints on the nuclear symmetry energy and its density slope from the α decay process,"We study the impact of the nuclear symmetry energy and its density dependence
on the {\alpha}-decay process. Within the frame work of the performed cluster
model and the energy density formalism, we use different parameterizations of
the Skyrme energy density functionals that yield different equations of state
EOSs. Each EOS is characterized by a particular symmetry-energy coefficient
(asym) and a corresponding density-slope parameters L. The stepwise trends of
the neutron (proton) skin thickness of the involved nuclei with both asym and L
do not clarify the obtained oscillating behaviors of the {\alpha}-decay
half-life T{\alpha} with them. We find that the change of the skin thickness
after {\alpha}-decay satisfactory explains these behaviors. The presented
results provide constrains on asym centered around an optimum value asym= 32
MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate
larger reduction of the proton-skin thickness and less increase in the
neutron-skin thickness after an {\alpha}-decay, yield minimum calculated
half-life with the same extracted value of the {\alpha}-preformation factor
inside the parent nucleus.",1804.04336v1
2019-11-05,Resonant low-energy electron attachment to O\(_{2}\) impurities in dense neon gas,"We report measurements of resonant low-energy electron attachment to O\(_2\)
molecular impurities in neon gas in the temperature range \(46.5\,\mbox{K}\le
T\le 101\,\mbox{K}\). The reduced attachment frequency \(\nu_A/N\) shows a well
defined peak as a function of the gas density \(N\) when the electron energy is
resonant with the 4th vibrational level of O\(_2^-\). For \(46.5\,\mbox{K}\le
T\le 48.4\,\)K a second peak has been detected at a much higher density, which
is due to the formation of ions in the 5th vibrational level. The temperature
dependence of the first peak position can be explained within an ionic bubble
model by computing the electron excess free energy as a function of \(T\) and
\(N\). The peak shape is rationalized by taking into account the density
dependent shift of the electron energy distribution function and the density of
states of excess electrons in a disordered medium, and by assuming that
electrons sample the gas density over a region of the order of the ionic bubble
radius.",1911.01707v1
2020-03-14,Generalized hydrodynamic limit for the box-ball system,"We deduce a generalized hydrodynamic limit for the box-ball system, which
explains how the densities of solitons of different sizes evolve asymptotically
under Euler space-time scaling. To describe the limiting soliton flow, we
introduce a continuous state-space analogue of the soliton decomposition of
Ferrari, Nguyen, Rolla and Wang (cf. the original work of Takahashi and
Satsuma), namely we relate the densities of solitons of given sizes in space to
corresponding densities on a scale of 'effective distances', where the dynamics
are linear. For smooth initial conditions, we further show that the resulting
evolution of the soliton densities in space can alternatively be characterised
by a partial differential equation, which naturally links the time-derivatives
of the soliton densities and the 'effective speeds' of solitons locally.",2003.06526v2
2020-06-24,Optical spectra of 2D monolayers from time-dependent density functional theory,"The optical spectra of two-dimensional (2D) periodic systems provide a
challenge for time-dependent density-functional theory (TDDFT) because of the
large excitonic effects in these materials. In this work we explore how
accurately these spectra can be described within a pure Kohn-Sham
time-dependent density-functional framework, i.e., a framework in which no
theory beyond Kohn-Sham density-functional theory, such as $GW$, is required to
correct the Kohn-Sham gap. To achieve this goal we adapted a recent approach we
developed for the optical spectra of 3D systems [Cavo, Berger, Romaniello,
Phys. Rev. B 101, 115109 (2020)] to those of 2D systems. Our approach relies on
the link between the exchange-correlation kernel of TDDFT and the derivative
discontinuity of ground-state density-functional theory, which guarantees a
correct quasi-particle gap, and on a generalization of the polarization
functional [Berger, Phys. Rev. Lett., 115, 137402 (2015)], which describes the
excitonic effects. We applied our approach to two prototypical 2D monolayers,
$h$-BN and MoS$_2$. We find that our protocol gives a qualitative good
description of the optical spectrum of $h$-BN, whereas improvements are needed
for MoS$_2$ to describe the intensity of the excitonic peaks.",2006.14065v1
2020-12-26,"Structural, Elastic and Electronic Properties of $SmFeO_3$ using Density Functional Theory","We perform first principles simulations for the structural, elastic and
electronic properties of orthorhombic samarium orthoferrite $SmFeO_3$ within
the framework of density functional theory. A number of different density
functionals, such as local density approximation, generalized gradient
approximation, Hubbard interaction modified functional, modified
Becke$-$Johnson approximation and Heyd$-$Scuseria$-$Ernzerhof hybrid functional
have been used to model the exact electron exchange-correlation. We estimate
the energy of the ground state for different magnetic configurations of
$SmFeO_3$. The crystal structure of $SmFeO_3$ is characterized in terms of the
lattice parameters, atomic positions, relevant ionic radii, bond lengths and
bond angles. The stability of the $SmFeO_3$ orthorhombic structure is simulated
in terms of its elastic properties. For the electronic structure simulations,
we provide estimates based on density functionals with varying degrees of
computational complexities in the Jacob's ladder.",2012.13715v1
1999-06-08,A Composite Fermion Hofstader Problem: Partially Polarized Density Wave States in the 2/5 FQHE,"It is well-known that the 2/5 state is unpolarized at zero Zeeman energy,
while it is fully polarized at large Zeeman energies. A novel state with
charge/spin density wave order for Composite Fermions is proposed to exist at
intermediate values of the Zeeman coupling for 2/5. This state has half the
maximum possible polarization, and can be extended to other incompressible
fractions. A Hartree-Fock calculation based on the new approach for all
fractional quantum Hall states developed by R.Shankar and the author is used to
demonstrate the stability of this state to single-particle excitations, and
compute gaps. We compare our results with a very recent experiment which shows
direct evidence for the existence of such a state, and also with more indirect
evidence from past experiments.",9906110v2
2014-07-23,Topological Pair-Density-Wave Superconducting States,"We show that the pair-density-wave (PDW) superconducting state emergent in
extended Heisenberg-Hubbard models in two-leg ladders is topological in the
presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at
an open boundary and at a junction with a uniform $d$-wave one-dimensional
superconductor. Similarly to a conventional finite-momentum paired state, the
order parameter of the PDW state is a charge-$2e$ field with finite momentum.
However, the order parameter here is a {\it quartic} electron operator and
conventional mean-field theory cannot be applied to study this state. We use
bosonization to show that the 1D PDW state has a MZM at a boundary. This
superconducting state is an exotic topological phase supporting Majorana
fermions with finite-momentum pairing fields and charge-$4e$ superconductivity.",1407.6358v3
2023-04-24,Fractional quantum anomalous Hall states in twisted bilayer MoTe$_2$ and WSe$_2$,"We demonstrate via exact diagonalization that AA-stacked TMD homobilayers
host fractional quantum anomalous Hall (FQAH) states with fractionally
quantized Hall conductance at fractional fillings $n=\frac{1}{3},\,
\frac{2}{3}$ and zero magnetic field. While both states are most robust at
angles near $\theta\approx 2^{\circ}$, the $n=\frac{1}{3}$ state gives way to a
charge density wave with increasing twist angle whereas the $n=\frac{2}{3}$
state survives across a much broader range of twist angles. We show that the
competition between FQAH states and charge density wave or metallic phases is
primarily controlled by the wavefunctions and dispersion of the underlying
Chern band, respectively. Additionally, Ising ferromagnetism is found across a
broad range of fillings where the system is insulating or metallic alike. The
spin gap is enhanced at filling fractions where integer and fractional quantum
anomalous Hall states are formed.",2304.12261v3
2013-11-20,Asymptotic equivalence of quantum state tomography and noisy matrix completion,"Matrix completion and quantum tomography are two unrelated research areas
with great current interest in many modern scientific studies. This paper
investigates the statistical relationship between trace regression in matrix
completion and quantum state tomography in quantum physics and quantum
information science. As quantum state tomography and trace regression share the
common goal of recovering an unknown matrix, it is nature to put them in the Le
Cam paradigm for statistical comparison. Regarding the two types of matrix
inference problems as two statistical experiments, we establish their
asymptotic equivalence in terms of deficiency distance. The equivalence study
motivates us to introduce a new trace regression model. The asymptotic
equivalence provides a sound statistical foundation for applying matrix
completion methods to quantum state tomography. We investigate the asymptotic
equivalence for sparse density matrices and low rank density matrices and
demonstrate that sparsity and low rank are not necessarily helpful for
achieving the asymptotic equivalence of quantum state tomography and trace
regression. In particular, we show that popular Pauli measurements are bad for
establishing the asymptotic equivalence for sparse density matrices and low
rank density matrices.",1311.4976v1
1995-07-12,Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices,"A direct and exact method for calculating the density of states for systems
with localized potentials is presented. The method is based on explicit
inversion of the operator $E-H$. The operator is written in the discrete
variable representation of the Hamiltonian, and the Toeplitz property of the
asymptotic part of the obtained {\it infinite} matrix is used. Thus, the
problem is reduced to the inversion of a {\it finite} matrix.",9507039v1
1995-07-20,Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics,"Asymptotical behavior of the distribution function of local density of states
(LDOS) in disordered metallic samples is studied with making use of the
supersymmetric $\sigma$--model approach, in combination with the saddle--point
method. The LDOS distribution is found to have the logarithmically normal
asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D
sample, the result is confirmed by the exact solution. In 2D case a perfect
agreement with an earlier renormalization group calculation is found. In 3D the
found asymptotics is of somewhat different type: $P(\rho)\sim
\exp(-\mbox{const}\,|\ln^3\rho|)$.",9507082v1
1996-01-31,Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States,"We present two novel approaches to establish the local density of states as
an order parameter field for the Anderson transition problem. We first
demonstrate for 2D quantum Hall systems the validity of conformal scaling
relations which are characteristic of order parameter fields. Second we show
the equivalence between the critical statistics of eigenvectors of the
Hamiltonian and of the transfer matrix, respectively. Based on this equivalence
we obtain the order parameter exponent $\alpha_0\approx 3.4$ for 3D quantum
Hall systems.",9601152v2
1996-04-09,Density Matrix Renormalization Group Applied to the Ground State of the XY-Spin-Peierls System,"We use the density matrix renormalization group (DMRG) to map out the ground
state of a XY-spin chain coupled to dispersionless phonons of frequency $%
\omega $. We confirm the existence of a critical spin-phonon coupling $% \alpha
_c\propto \omega ^{0.7}$ for the onset of the spin gap bearing the signature of
a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover
when the spin-Peierls gap $\Delta $ is of order $% \omega $. In the classical
regime, $\Delta >\omega $, the mean-field parameters are strongly renormalized
by non-adiabatic corrections. This is the first application of the DMRG to
phonons.",9604054v1
1996-08-04,Charged Many-Electron -- Single Hole Complexes in a Double Quantum Well near a Metal Plate,"It has been shown that the presence of a metal plate near a double quantum
well with spatially separated electron and hole layers may lead to a drastic
reconstruction of the system state with the formation of stable charged
complexes of several electrons bound to a spatially separated hole. Complexes
of both the Fermi and the Bose statistics may coexist in the ground state and
their relative densities may be changed with the change of the electron and
hole densities. The stability of the charged complexes may be increased by an
external magnetic field perpendicular to the layers plane.",9608012v1
1997-01-22,Extended Impurity Potential in a d_{x^2-y^2} Superconductor,"We investigate the role of a finite potential range of a nonmagnetic impurity
for the local density of states in a d_{x^2-y^2} superconductor. Impurity
induced subgap resonances are modified by the appearance of further scattering
channels beyond the $s$--wave scattering limit. The structure of the local
density of states (DOS) in the vicinity of the impurity is significantly
enhanced and therefore improves the possibility for observing the
characteristic anisotropic spatial modulation of the local DOS in a d_{x^2-y^2}
superconductor by scanning tunneling microscopy.",9701170v1
1997-02-10,Comment on ``Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids'',"In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have
calculated the electron density of states (DOS) for tunneling into a repulsive
Luttinger liquid close to the location of an impurity. The result of their
calculation is a DOS which is enhanced with respect to the pure system, and
moreover diverging for not too strong repulsion. In this Comment we intend to
show that OF's calculation suffers from a subtle flaw which, being corrected,
results into a DOS not only vanishing at zero frequency but in fact suppressed
in comparison with the DOS of a pure Luttinger liquid.",9702080v1
1997-03-03,Density of States of an Electron in a Gaussian Random Potential for (4-epsilon)-dimensional Space,"The density of states for the Schroedinger equation with a Gaussian random
potential is calculated in a space of dimension d=4-epsilon in the entire
energy range including the vicinity of a mobility edge. Leading terms in
1/epsilon are taken into account for N \sim 1 (N is an order of perturbation
theory) while all powers of 1/epsilon are essential for N>>1 with calculation
of the expansion coefficients in the leading order in N.",9703032v1
1997-08-27,Leduc-Righi effect in superconductors with nontrivial density of states,"Increasing of electronic thermal conductivity of superconductor in the model
with nontrivial density of states was considered. The electronic thermal
conductivity K(T) of SC in the presence of external magnetic field was
investigated. It was shown that if symmetrical part of quasiparticle scattering
rate less than cyclotron energy observed mechanism of increasing K(T) can be
separated from connected with asymmetric electronic scattering effects another
one.",9708203v3
1997-10-17,"Gauge Fields, Mode Mixing and Local Density of States in a Quantum Point Contact","It is shown that the elimination of the discrete transverse motion in a
waveguide of arbitrary shape may be described in terms of a non-abelian gauge
field for the longitudinal dynamics. This allows for an exact treatment of the
scattering between different modes by eliminating the gauge field at the
expense of a non-diagonal matrix of local subband energies. The method is
applied to calculate the local density of states (LDOS) in a quantum point
contact. Contrary to the total conductance which is well described by an
adiabatic approximation, mode mixing turns out to play a crucial role for local
properties like the LDOS.",9710174v1
1999-10-04,Numerical studies of the vibrational isocoordinate rule in chalcogenide glasses,"Many properties of alloyed chalcogenide glasses can be closely correlated
with the average coordination of these compounds. This is the case, for
example, of the ultrasonic constants, dilatometric softening temperature and
the vibrational densities of states. What is striking, however, is that these
properties are nevertheless almost independent of the composition at given
average coordination. Here, we report on some numerical verification of this
experimental rule as applied to vibrational density of states.",9910032v1
2000-05-04,Scissors mode in a superfluid Fermi gas,"We evaluate the frequencies of scissors modes for density and concentration
fluctuations in a vapour of fermionic atoms placed in two hyperfine levels
inside a spherical harmonic trap. Both the superfluid and the normal state are
considered, with inclusion of the interactions at the random-phase level. Two
main results are obtained: (i) the transition to the superfluid state is
signalled by the disappearance of soft transverse modes of the normal fluid in
the collisionless regime and (ii) the eigenfrequency of the density
fluctuations in the superfluid coincides with that of the normal fluid in the
collisional regime. The latter property is related to the opening of the gap in
the single-pair spectrum.",0005098v1
2001-04-10,Low-energy vibrational density of states of plasticized poly(methyl methacrylate),"The low-energy vibrational density of states (VDOS)of hydrogenated or
deuterated poly(methyl methacrylate)(PMMA)plasticized by dibutyl phtalate (DBP)
is determined by inelastic neutron scattering.From experiment, it is equal to
the sum of the ones of the PMMA and DBP components.However, a partition of the
total low-energy VDOS among PMMA and DBP was observed.Contrary to Raman
scattering, neutron scattering does not show enhancement of the boson peak due
to plasticization.",0104168v1
2002-05-02,A single polymer chain as an organic quantum wire: optical evidence of a purely 1D density of states,"The excitonic luminescence of an isolated polydiacetylene polymer chain in
its monomer matrix is studied by micro-photoluminescence. These chains behave
as perfect 1D semiconducting wires with the expected 1/$\sqrt{E}$ density of
states between 5 and 50 K. The temperature dependence of the homogeneous width
is explained by interaction with longitudinal acoustic phonons of the crystal
in the range of temperature explored. The optical phonons of the chain which
are involved in the vibronic transitions are found to have coherence times
ranging from 300 to 600 fs.",0205047v1
2002-07-15,A Supersymmetry approach to billiards with randomly distributed scatterers,"The density of states for a chaotic billiard with randomly distributed
point-like scatterers is calculated, doubly averaged over the positions of the
impurities and the shape of the billiard. Truncating the billiard Hamiltonian
to a N x N matrix, an explicit analytic expression is obtained for the case of
broken time-reversal symmetry, depending on rank N of the matrix, number L of
scatterers, and strength of the scattering potential. In the strong coupling
limit a discontinuous change is observed in the density of states as soon as L
exceeds N.",0207351v1
2003-10-18,Variational Monte Carlo study of the ground state properties and vacancy formation energy of solid para-H2 using a shadow wave function,"A Shadow Wave Function (SWF) is employed along with Variational Monte Carlo
techniques to describe the ground state properties of solid molecular
para-hydrogen. The study has been extended to densities below the equilibrium
value, to obtain a parameterization of the SWF useful for the description of
inhomogeneous phases. We also present an estimate of the vacancy formation
energy as a function of the density, and discuss the importance of relaxation
effects near the vacant site.",0310437v1
2003-12-17,The effect of nonmagnetic impurities on the local density of states in s-wave superconductors,"We study the effect of nonmagnetic impurities on the local density of states
(LDOS) in s-wave superconductors. The quasiclassical equations of
superconductivity are solved selfconsistently to show how LDOS evolves with
impurity concentration. The spatially averaged zero-energy LDOS is a linear
function of magnetic induction in low fields, N(E=0)=cB/H_{c2}, for all
impurity concentration. The constant of proportionality ""c"" depends weakly on
the electron mean free path. We present numerical data for differential
conductance and spatial profile of zero-energy LDOS which can help in
estimating the mean free path through the LDOS measurement.",0312420v1
2005-01-21,Density of states anomalies in hybrid superconductor-ferromagnet-normal metal structures,"The results of calculations of the spatially-resolved density of states (DoS)
in an S(F/N) bilayer are presented (S is a superconductor, F is a metallic
ferromagnet, N is a normal metal) within quasiclassical theory in the dirty
limit. Analytical solutions are obtained in the case of thin F, N layers which
demonstrate the peculiar features of DoS in this system. The dependencies of
the minigap and the DoS peak positions on the exchange energy and parameters of
the layers are studied numerically",0501514v1
2005-10-23,Density of states of disordered systems with a finite correlation length,"We consider a semiclassical formulation for the density of states (DOS) of
disordered systems in any dimension. We show that this formulation becomes very
accurate when the correlation length of the disorder potential is large. The
disorder potential does not need to be smooth and is not limited to the
perturbative regime, where the disorder is small. The DOS is expressed in terms
of a convolution of the disorder distribution function and the non-disordered
DOS. We apply this formalism to evaluate the broadening of Landau levels and to
calculate the specific heat in disordered systems.",0510617v2
2006-02-02,Inhomogeneity effects in oxygen doped HgBa$_2$CuO$_{4}$,"We theoretically investigate inhomogeneity effects on the charges, electric
field gradients and site-projected densities of states in
HgBa$_2$CuO$_{4+\delta}$. We find pronounced differences in the doping-induced
number of holes at different atomic sites. The contributions of these sites to
the density of states in the vicinity of the Fermi level are peaked at the same
energy, but vary in magnitude by up to 70 percent and have different energy
dependence. Due to this energy dependence the role of the intrinsic
inhomogeneities for superconductivity strongly depends on the energy and
character of the quasiparticle mediating the Cooper pairing. Our results can
explain the origin of doping-induced effects observed either by local or
macroscopic experimental probes.",0602047v1
1992-05-27,Thermal history of the string universe,"Thermal history of the string universe based on the Brandenberger and Vafa's
scenario is examined. The analysis thereby provides a theoretical foundation of
the string universe scenario. Especially the picture of the initial oscillating
phase is shown to be natural from the thermodynamical point of view. A new tool
is employed to evaluate the multi state density of the string gas. This
analysis points out that the well-known functional form of the multi state
density is not applicable for the important region $T \leq T_H$, and derives a
correct form of it.",9205096v1
2003-12-10,A variational problem for the spatial segregation of reaction--diffusion systems,"In this paper we study a class of stationary states for reaction--diffusion
systems of $k\geq 3$ densities having disjoint supports. For a class of
segregation states governed by a variational principle we prove existence and
provide conditions for uniqueness. Some qualitative properties and the local
regularity both of the densities and of their free boundaries are established
in the more general context of a functional class characterized by differential
inequalities.",0312210v1
2005-10-17,Wegner estimate and the density of states of some indefinite alloy type Schroedinger Operators,"We study Schroedinger operators with a random potential of alloy type. The
single site potentials are allowed to change sign. For a certain class of them
we prove a Wegner estimate. This is a key ingredient in an existence proof of
pure point spectrum of the considered random Schroedinger operators. Our
estimate is valid for all bounded energy intervals and all space dimensions and
implies the existence of the density of states.",0510062v1
2006-06-26,"Aperiodic order, integrated density of states and the continuous algebras of John von Neumann","Lenz and Stollmann recently proved the existence of the integrated density of
states in the sense of uniform convergence of the distributions for certain
operators with aperiodic order. The goal of this paper is to establish a
relation between aperiodic order, uniform spectral convergence and the
continuous algebras invented by John von Neumann. We illustrate the technique
by proving the uniform spectral convergence for random Schodinger operators on
lattices with finite site probabilities, percolation Hamiltonians and for the
pattern-invariant operators of self-similar graphs.",0606061v1
1999-10-08,Characterization of the State of Hydrogen,"Fermionic path integral Monte Carlo simulations have been applied to study
the equilibrium properties of the hydrogen and deuterium in the density and
temperature range of 1.6 < rs < 14.0 and 5000K < T < 167000K. We use this
technique to determine the phase diagram by identifying the plasma, the
molecular, atomic and metallic regime. We explain how one can identify the
phases in the path integral formalism and discuss the state of hydrogen for 5
points in the temperature-density plane. Further we will provide arguments for
the nature of the transitions between the regimes.",9910010v1
2006-01-10,Dynamics of Open Bosonic Quantum Systems in Coherent State Representation,"We consider the problem of decoherence and relaxation of open bosonic quantum
systems from a perspective alternative to the standard master equation or
quantum trajectories approaches. Our method is based on the dynamics of
expectation values of observables evaluated in a coherent state representation.
We examine a model of a quantum nonlinear oscillator with a density-density
interaction with a collection of environmental oscillators at finite
temperature. We derive the exact solution for dynamics of observables and
demonstrate a consistent perturbation approach.",0601063v1
2007-06-28,Semiclassical Density of States for the Quantum Asymmetric Top,"In the quantization of a rotating rigid body, a {\it top,} one is concerned
with the Hamiltonian operator $L_\alpha=\alpha_0^2 L_x^2 + \alpha_1^2 L_y^2 +
\alpha_2^2 L_z^2,$ where $\alpha_0 < \alpha_1 <\alpha_2.$ An explicit formula
is known for the eigenvalues of $L_\alpha$ in the case of the spherical top
($\alpha_1 = \alpha_2 = \alpha_3$) and symmetrical top ($\alpha_1 = \alpha_2
\neq \alpha_3$) \cite{LL}. However, for the asymmetrical top, no such explicit
expression exists, and the study of the spectrum is much more complex. In this
paper, we compute the semiclassical density of states for the eigenvalues of
the family of operators $L_\alpha=\alpha_0^2 L_x^2 + \alpha_1^2 L_y^2 +
\alpha_2^2 L_z^2$ for any $\alpha_0 < \alpha_1 <\alpha_2$.",0706.4127v1
2007-07-14,Weiss oscillations in the electronic structure of modulated graphene,"We present a theoretical study of the electronic structure of modulated
graphene in the presence of a perpendicular magnetic field. The density of
states and the bandwidth for the Dirac electrons in this system are determined.
The appearance of unusual Weiss oscillations in the bandwidth and density of
states is the main focus of this work.",0707.2152v2
2008-05-13,Tracing the equation of state and the density of cosmological constant along z,"We investigate the equation of state w(z) in a non-parametric form using the
latest compilations of distance luminosity from SNe Ia at high z. We combine
the inverse problem approach with a Monte Carlo to scan the space of priors. On
the light of these high redshift supernova data sets, we reconstruct w(z). A
comparison between a sample including the latest results at z>1 and a sample
without those results show the improvement achieved by observations of very
high z supernovae. We present the prospects to measure the variation of dark
energy density along z by this method.",0805.1929v1
2008-10-08,On the density of states and extinction mean free path of waves in random media: Dispersion relations and sum rules,"We establish a fundamental relationship between the averaged density of
states and the extinction mean free path of wave propagating in random media.
  From the principle of causality and the Kramers-Kronig relations, we show
that both quantities are connected by dispersion relations and are constrained
by a frequency sum rule. The results are valid under very general conditions
and should be helpful in the analysis of measurements of wave transport through
complex systems and in the design of randomly or periodically structured
materials with specific transport properties.",0810.1411v1
2008-10-22,Suppression of light propagation in a medium made of randomly arranged dielectric spheres,"Light propagation in a medium made of densely packed dielectric spheres is
investigated by using a rigorous diffraction theory. It is shown that a
substantial suppression of the local density of states occurs in spectral
domains where the single constituents exhibit Mie resonances. The local density
of states decreases exponentially at the pertinent frequencies with a linearly
increasing spatial extension of the aggregated spheres. It is shown that a
self-sustaining random arrangement of core-shell spheres shows the same
fundamental characteristics. Such approach offers a path towards easy to
fabricate photonic materials with omnidirectional gaps that may find use in
various applications.",0810.4080v1
2009-03-16,Coupled-cluster theory of a gas of strongly-interacting fermions in the dilute limit,"We study the ground-state properties of a dilute gas of strongly-interacting
fermions in the framework of the coupled-cluster expansion (CCE). We
demonstrate that properties such as universality, opening of a gap in the
excitation spectrum and applicability of s-wave approximations appear naturally
in the CCE approach. In the zero-density limit, we show that the ground-state
energy density depends on only one parameter which in turn may depend at most
on the spatial dimensionality of the system.",0903.2786v1
2009-04-30,Neutron Stars and the High Density Equation of State,"One of the key ingredients to understand the properties of neutrons stars is
the equation of state at finite densities far beyond nuclear saturation.
Investigating the phase structure of quark matter that might be realized in the
core of NS inspires theory and observation. We discuss recent results of our
work to point out our view on challenges and possibilities in this evolving
field by means of a few examples.",0904.4729v1
2010-03-18,Simple model of the density of states in 1D photonic crystal,"In this paper, we present a simple, yet versatile, analytical model of
one-dimensional photonic crystal (1D PC). In our theoretical model, we take
into account direction of propagation and therefore do not neglect anisotropic
nature of photonic crystals. We derive analytical expressions for mode spectrum
and density of states in 1D photonic crystal. With those formulas, we obtain
mode spectrum characteristics, which depict formation of photonic band gap and
reveal properties of photonic crystals.",1003.3524v1
2010-04-17,Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrodinger operators,"We prove the complete asymptotic expansion of the integrated density of
states of a Schrodinger operator H = -\Delta + b acting in R^d when the
potential b is either smooth periodic, or generic quasi-periodic (finite linear
combination of exponentials), or belongs to a wide class of almost-periodic
functions.",1004.2939v2
2010-09-28,"General, combinatorial formula for the density of states: insights into the energy equipartition principle and the theory of phase transitions","A completely new approach to the problem of energy distribution in
statistical mechanics is developed that results in a general, combinatorial
formula for the density of states. Relying on the approach the energy
equipartition principle is reexamined and a new perspective on the theory of
phase transitions (as resulting from nontrivial patterns of energy distribution
characterized by the well-defined classes of forbidden microstates) is given.",1009.5534v2
2010-12-29,Modification of the Radiation of a Luminescent dye embedded in a finite one-dimensional Photonic Crystal,"A numerical modeling of the radiation emitted from a Luminescent dye embedded
in a finite one-dimensional photonic crystal is presented. The Photonic Band
Structure and the Photonic Density of States are derived using classical
electromagnetic approach, and the Finite Difference Time-Domain formalism is
used to calculate the electromagnetic field distribution. It is found that the
periodic modulation provides an effective way to control the Spontaneous
Emission under certain circumstances. We find the conditions where a large
amount of light can be enhanced on the vicinity of a photonic band edge due to
the presence of a high density of states.
  This phenomena opens the possibility to design new Lasers sources.",1012.5988v1
2011-03-14,Half-Metallicity of Wurtzite NiO and ZnO/NiO (0001) Interface: First Principles Simulation,"First principles calculations based on density functional theory are
performed to investigate the structural, electronic and magnetic properties of
wurtzite ZnO/NiO (0001) interface. By using DFT+U method we discover that the
half-metallic behavior of wurtzite NiO (w-NiO) retains in the ZnO/NiO (0001)
interface. Through analyses of density of state, charge population and magnetic
moments, we find the half-metallicity is weakened around the interface but
interface effect is quite localized. More over the interface system keeps a
ferromagnetic ground state as bulk w-NiO does. Based on the simulations of
epitaxial growth case, w-NiO is predicted to be a promising candidate of
electrode for the injection of spin polarized currents.",1103.2602v1
2011-04-20,Scanning emitter lifetime imaging microscopy for spontaneous emission control,"We report an experimental technique to map and exploit the local density of
optical states of arbitrary planar nano-photonic structures. The method relies
on positioning a spontaneous emitter attached to a scanning probe
deterministically and reversibly with respect to its photonic environment while
measuring its lifetime. We demonstrate the method by imaging the enhancement of
the local density of optical states around metal nanowires. By
nano-positioning, the decay rate of a pointlike source of fluorescence can be
reversibly and repeatedly changed by a factor of two by coupling it to the
guided plasmonic mode of the wire.",1104.4073v1
2011-12-06,Distance dependence of the local density of states in the near field of a disordered plasmonic film,"We measure the statistical distribution of the photonic local density of
states in the near field of a semi-continuous gold film. By varying the
distance between the measurement plane and the film, we show that near-field
confined modes play a major role in the width of the distribution. Numerical
simulations in good agreement with experiments allow us to point out the
influence of non-radiative decay channels at short distance.",1112.1310v3
2011-12-23,Electronic properties of disclinated nanostructured cylinder,"The electronic structure of nanocylinder without and with a small
perturbation is investigated with the help of calculation of the local density
of states. A continuum gauge field-theory model is used for this purpose. In
this model, Dirac equation is solved on a curved surface. The local density of
states is calculated from its solution. The case of 2 heptagonal defects is
considered. This paper is an extension of our previous work [1] where one
heptagonal and one pentagonal defects in hexagonal graphene network were
compared. The metallization for the perturbed cylinder structure is found.",1112.5577v1
2012-07-22,"Harper operators, Fermi curves, and Picard-Fuchs equations","This paper is a continuation of the work on the spectral problem of Harper
operator using algebraic geometry. We continue to discuss the local monodromy
of algebraic Fermi curves based on Picard-Lefschetz formula. The density of
states over approximating components of Fermi curves satisfies a Picard-Fuchs
equation. By the property of Landen transformation, the density of states has a
Lambert series as the quarter period. A $q$-expansion of the energy level can
be derived from a mirror map as in the B-model.",1207.5197v2
2013-06-03,Non-Bunch-Davies Anisotropy,"We introduce a generic mechanism that can extend the effects of relic
anisotropies at the beginning of inflation to relatively much shorter scales in
density perturbations. This is induced by non-Bunch-Davies states of the
quantum fluctuations, and can show up in the non-oscillatory components of the
density perturbations. This mechanism works for general forms of anisotropies,
and, to illustrate it, we use an example of relic vector field. The detailed
scale-dependence of these anisotropies can be used to probe the initial quantum
state of our universe.",1306.0609v1
2013-07-02,The density of states of graphene underneath a metal electrode and its correlation with the contact resistivity,"The density of states (DOS) of graphene underneath a metal is estimated
through a quantum capacitance measurement of the metal/graphene/SiO2/n+-Si
contact structure fabricated by a resist-free metal deposition process.
Graphene underneath Au maintains a linear DOS - energy relationship except near
the Dirac point, whereas the DOS of graphene underneath Ni is broken and
largely enhanced around the Dirac point, resulting in only a slight modulation
of the Fermi energy. Moreover, the DOS of graphene in the contact structure is
correlated with the contact resistivity measured using devices fabricated by
the resist-free process.",1307.0690v1
2014-10-18,Interacting Particles in Disordered Flashing Ratchets,"We study, using Monte Carlo simulations, the steady state properties of a
system of particles interacting via hard core exclusion and moving in a
discrete flashing disordered ratchet potential. Quenched disorder is introduced
by breaking the periodicity of the ratchet potential through changing shape of
the potential across randomly chosen but fixed periods. We show that the
effects of quenched disorder can be broadly classified as strong or weak with
qualitatively different behaviour of the steady state particle flux as a
function of overall particle density. We further show that most of the effects
including a density driven nonequilibrium phase transition observed can be
understood by constructing an effective asymmetric simple exclusion process
(ASEP) with quenched disorder in the hop rates.",1410.4981v1
2016-01-12,Persistence of energy-dependent localization in the Anderson-Hubbard model with increasing system size and doping,"Non-interacting systems with bounded disorder have been shown to exhibit
sharp density of states peaks at the band edge which coincide with an energy
range of abruptly suppressed localization. Recent work has shown that these
features also occur in the presence of on-site interactions in ensembles of
two-site Anderson-Hubbard systems at half filling. Here we demonstrate that
this effect in interacting systems persists away from half filling, and
moreover that energy regions with suppressed localization continue to appear in
ensembles of larger systems despite a loss of sharp features in the density of
states.",1601.03010v1
2016-02-01,Transition in fluctuation behaviour of normal liquids under high pressures,"We explore the behaviour of the inverse reduced density fluctuations and the
isobaric expansion coefficient using {\alpha},{\omega}-dibromoalkanes as an
example. Two different states are revealed far from the critical point: the
region of exponentially decaying fluctuations near the coexistence curve and
the state with longer correlations under sufficiently high pressures. The
crossing of the isotherms of the isobaric expansion coefficient occurs within
the PVT range of the mentioned transition. We discuss the interplay of this
crossing with the changes in molecular packing structure connected with the
analysed function of the density, which represents inverse reduced volume
fluctuations.",1602.00526v1
2019-11-19,Oscillations arising when switching on/off a discontinuous magnetic field,"In the present paper, we theoretically study the effect of density of state
variation on the phenomena in the discontinuous magnetic field. Special
attention is paid to the transient processes when the magnetic field is
switched on (off). The difference in the density of states for the free 2D
electron gas and the electron gas on under the magnetic field can lead to the
occurrence of the electrostatic potential. Considering the transient phenomena
of magnetic field switching, we obtain oscillating behavior of the
electrostatic potential. The analysis includes two limit cases when the
oscillation frequency of the electrostatic potential is low relative to the
cyclotron frequency and when they are of the same order.",1911.08578v1
2016-12-30,Cracking of Charged Polytropes with Generalized Polytropic Equation of State,"We discuss the occurrence of cracking in charged anisotropic polytropes with
generalized polytropic equation of state through two different assumptions; (i)
by carrying out local density perturbations under conformally flat condition
(ii) by perturbing anisotropy, polytropic index and charge parameters. For this
purpose, we consider two different definitions of polytropes exist in
literature. We conclude that under local density perturbations scheme cracking
does not appears in both types of polytropes and stable configuration are
observed, while with second kind of perturbation cracking appears in both types
of polytropes under certain conditions.",1701.04686v1
2018-03-22,Hyperbolic Blockade: Suppression of the Photonic Density of States and the Spontaneous Emission Rate at the Interface with Conducting Medium,"Surface scattering of free electrons strongly modifies the electromagnetic
response near the interface. Due to the inherent anisotropy of the surface
scattering that necessarily reverses the normal the interface component of the
electron velocity while its tangential component may remain the same, a thin
layer near a high-quality interface shows strong dielectric anisotropy. The
formation of the resulting hyperbolic dispersion layers near the
metal-dielectric interface strongly modifies the local density of states, and
leads to orders of magnitude changes in all associated phenomena.",1803.08191v1
2017-10-17,Ergodicity of the LLR method for the Density of States,"The LLR method is a novel algorithm that enables us to evaluate the density
of states in lattice gauge theory. We present our study of the ergodicity
properties of the LLR algorithm for the model of Yang Mills SU(3). We show that
the use of the replica exchange method alleviates significantly the topological
freeze-out that severely affects other algorithms.",1710.06250v1
2018-09-06,QCD at high density: Equation of state for nuclear collisions and neutron stars,"A unified chiral mean field approach is presented for QCD thermodynamics in a
wide range of temperatures and densities. The model simultaneously gives a
satisfactory description of lattice QCD thermodynamics and fulfills nuclear
matter and astrophysical constraints. The resulting equation of state can be
incorporated in relativistic fluid-dynamical simulations of heavy-ion
collisions and neutron stars mergers. Access to different regions of the QCD
phase diagram can be obtained in simulations of heavy-ion data and observations
of neutron star mergers.",1809.02000v1
2020-11-09,Sharp Bounds for the Integrated Density of States of a Strongly Disordered 1D Anderson-Bernoulli Model,"In this article we give upper and lower bounds for the integrated density of
states (IDS) of the 1D discrete Anderson-Bernoulli model when the disorder is
strong enough to separate the two spectral bands. These bounds are uniform on
the disorder and hold over the whole spectrum. They show the existence of a
sequence of energies in which the value of the IDS can be given explicitly and
does not depend on the disorder parameter.",2011.04756v2
2023-04-30,Absolute continuity of the integrated density of states in the localized regime,"We establish the absolute continuity of the integrated density of states
(IDS) for quasi-periodic Schr\""odinger operators with a large trigonometric
potential and Diophantine frequency. This partially solves Eliasson's open
problem in 2002. Furthermore, this result can be extended to a class of
quasi-periodic long-range operators on $\ell^2(\Z^d)$. Our proof is based on
stratified quantitative almost reducibility results of dual cocycles.
Specifically, we prove that a generic analytic one-parameter family of
cocycles, sufficiently close to constant coefficients, is reducible except for
a zero Hausdorff dimension set of parameters. This result affirms Eliasson's
conjecture in 2017.",2305.00457v2
2023-07-21,The $\mathfrak S_k$-circular limit of random tensor flattenings,"The tensor flattenings appear naturally in quantum information when one
produces a density matrix by partially tracing the degrees of freedom of a pure
quantum state. In this paper, we study the joint $^*$-distribution of the
flattenings of large random tensors under mild assumptions, in the sense of
free probability theory. We show the convergence toward an operator-valued
circular system with amalgamation on permutation group algebras for which we
describe the covariance structure. As an application we describe the law of
large random density matrix of bosonic quantum states.",2307.11439v1
2019-02-05,A new equation of state for dense hydrogen-helium mixtures,"We present a new equation of state (EOS) for dense hydrogen/helium mixtures
which covers a range of densities from $10^{-8}$ to $10^6$ g.cm$^{-3}$,
pressures from $10^{-9}$ to $10^{13}$ GPa and temperatures from $10^{2}$ to
$10^{8}$ K. The calculations combine the EOS of Saumon, Chabrier & vanHorn
(1995) in the low density, low temperature molecular/atomic domain, the EOS of
Chabrier & Potekhin (1998) in the high-density, high-temperature fully ionized
domain, the limits of which differ for H and He, and ab initio quantum
molecular dynamics (QMD) calculations in the intermediate density and
temperature regime, characteristic of pressure dissociation and ionization. The
EOS for the H/He mixture is based on the so-called additive volume law and thus
does not take into account the interactions between the two species. A major
improvement of the present calculations over existing ones is that we calculate
the entropy over the entire density-temperature domain, a necessary quantity
for stellar or planetary evolution calculations. The EOS results are compared
with existing experimental data, namely Hugoniot shock experiments for pure H
and He, and with first principle numerical simulations for both the single
elements and the mixture. This new EOS covers a wide range of physical and
astrophysical conditions, from jovian planets to solar-type stars, and recovers
the existing relativistic EOS at very high densities, in the domains of white
dwarfs and neutron stars.",1902.01852v1
2022-08-02,Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals,"Dynamic density functional theory (DDFT) is a promising approach for
predicting the structural evolution of a drying suspension containing one or
more types of colloidal particles. The assumed free-energy functional is a key
component of DDFT that dictates the thermodynamics of the model and, in turn,
the density flux due to a concentration gradient. In this work, we compare
several commonly used free-energy functionals for drying hard-sphere
suspensions including local-density approximations based on the ideal-gas,
virial, and Boubl\'{i}k-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of
state as well as a weighted-density approximation based on fundamental measure
theory (FMT). To determine the accuracy of each functional, we model one- and
two-component hard-sphere suspensions in a drying film with varied initial
heights and compositions, and we compare the DDFT-predicted volume-fraction
profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately
predicts the structure of the one-component suspensions even at high
concentrations and when significant density gradients develop, but the virial
and BMCSL equations of state provide reasonable approximations for smaller
concentrations at a reduced computational cost. In the two-component
suspensions, FMT and BMCSL are similar to each other but modestly overpredict
the extent of stratification by size compared to BD simulations. This work
provides helpful guidance for selecting thermodynamic models for soft materials
in nonequilibrium processes such as solvent drying, solvent freezing, and
sedimentation.",2208.01528v1
2022-11-21,Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons,"We assess the accuracy of common hybrid exchange-correlation (XC) functionals
(PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within Kohn-Sham density functional
theory (KS-DFT) for the harmonically perturbed electron gas at parameters
relevant for the challenging conditions of warm dense matter. Generated by
laser-induced compression and heating in the laboratory, warm dense matter is a
state of matter that also occurs in white dwarfs and planetary interiors. We
consider both weak and strong degrees of density inhomogeneity induced by the
external field at various wavenumbers. We perform an error analysis by
comparing to exact quantum Monte-Carlo results. In the case of a weak
perturbation, we report the static linear density response function and the
static XC kernel at a metallic density for both the degenerate ground-state
limit and for partial degeneracy at the electronic Fermi temperature. Overall,
we observe an improvement in the density response for partial degeneracy when
the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used compared to the
previously reported results for the PBE, PBEsol, LDA, AM05, and SCAN
functionals; B3LYP, on the other hand, does not perform well for the considered
system. Together with the reduction of self-interaction errors, this seems to
be the rationale behind the relative success of the HSE03 functional for the
description of the experimental data on aluminum and liquid ammonia at WDM
conditions.",2211.11688v1
2002-09-06,Quantum theory of bilayer quantum Hall smectics,"Mean-field theory predicts that bilayer quantum Hall systems at odd integer
total filling factors can have stripe ground states in which the top Landau
level is occupied alternately by electrons in one of the two layers. We report
on an analysis of the properties of these states based on a coupled Luttinger
liquid description that is able to account for quantum fluctuations of
charge-density and position along each stripe edge. The soft modes associated
with the broken symmetries of the stripe state lead to an unusual coupled
Luttinger liquid system with strongly enhanced low-temperature heat capacity
and strongly suppressed low-energy tunneling density of states. We assess the
importance of the intralayer and interlayer back-scattering terms in the
microscopic Hamiltonian, which are absent in the Luttinger liquid description,
by employing a perturbative renormalization group approach which re-scales time
and length along but not transverse to the stripes. With interlayer
back-scattering interactions present the Luttinger liquid states are unstable
either to an incompressible striped state that has spontaneous interlayer phase
coherence and a sizable charge gap even at relatively large layer separations,
or to Wigner crystal states. Our quantitative estimates of the gaps produced by
back-scattering interactions are summarized in Fig. [phase_diagram] by a
schematic phase diagram intended to represent predicted experimental findings
in very high mobility bilayer systems at dilution refrigerator temperatures as
a function of layer separation and bilayer density balance.",0209173v1
2012-10-10,Exotic Ground States of Directional Pair Potentials via Collective-Density Variables,"Collective-density variables have proved to be a useful tool in the
prediction and manipulation of how spatial patterns form in the classical
many-body problem. Previous work has employed properties of collective-density
variables along with a robust numerical optimization technique to find the
classical ground states of many-particle systems subject to radial pair
potentials in one, two and three dimensions. That work led to the
identification of ordered and disordered classical ground states. In this
paper, we extend these collective-coordinate studies by investigating the
ground states of directional pair potentials in two dimensions. Our study
focuses on directional potentials whose Fourier representations are non-zero on
compact sets that are symmetric with respect to the origin and zero everywhere
else. We choose to focus on one representative set which has exotic
ground-state properties: two circles whose centers are separated by some fixed
distance. We obtain ground states for this ""two-circle"" potential that display
large void regions in the disordered regime. As more degrees of freedom are
constrained the ground states exhibit a collapse of dimensionality
characterized by the emergence of filamentary structures and linear chains.
This collapse of dimensionality has not been observed before in related
studies.",1210.3071v1
2014-05-05,Zero-energy bound state at the interface between an $s$-wave superconductor and a disordered normal metal with repulsive electron-electron interactions,"In recent years, there has been a renewed interest in the proximity effect
due to its role in the realization of topological superconductivity. Here, we
study a superconductor--normal metal proximity system with repulsive
electron-electron interactions in the normal layer. It is known that in the
absence of disorder or normal reflection at the superconductor--normal metal
interface, a zero-energy bound state forms and is localized to the interface
[Fauchere et al., Phys. Rev. Lett. 82, 3336 (1999)]. Using the quasiclassical
theory of superconductivity, we investigate the low-energy behavior of the
density of states in the presence of finite disorder and an interfacial
barrier. We find that as the mean free path is decreased, the zero-energy peak
in the density of states is broadened and reduced. In the quasiballistic limit,
the bound state eliminates the minigap pertinent to a noninteracting normal
layer and a distinct peak is observed. When the mean free path becomes
comparable to the normal layer width, the zero-energy peak is strongly
suppressed and the minigap begins to develop. In the diffusive limit, the
minigap is fully restored and all signatures of the bound state are eliminated.
We find that an interfacial potential barrier does not change the functional
form of the density of states peak but does shift this peak away from zero
energy.",1405.0918v2
2000-09-22,Iterative algorithm for reconstruction of entangled states,"An iterative algorithm for the reconstruction of an unknown quantum state
from the results of incompatible measurements is proposed. It consists of
Expectation-Maximization step followed by a unitary transformation of the
eigenbasis of the density matrix. The procedure has been applied to the
reconstruction of the entangled pair of photons.",0009093v2
2003-04-13,Entanglement of Formation for a Class of Quantum States,"Entanglement of formation for a class of higher dimensional quantum mixed
states is studied in terms of a generalized formula of concurrence for
$N$-dimensional quantum systems. As applications, the entanglement of formation
for a class of $16\times 16$ density matrices are calculated.",0304095v1
2014-09-19,"Correlations in the low-density Fermi gas: Fermi-Liquid state, Dimerization, and BCS Pairing","We present ground state calculations for low-density Fermi gases described by
two model interactions, an attractive square-well potential and a Lennard-Jones
potential, of varying strength. We use the optimized Fermi-Hypernetted Chain
integral equation method which has been proved to provide, in the density
regimes of interest here, an accuracy better than one percent. We first examine
the low-density expansion of the energy and compare with the exact answer by
Huang and Yang (H. Huang and C. N. Yang, {\em Phys. Rev.\/} {\bf 105}, 767
(1957)). It is shown that a locally correlated wave function of the
Jastrow-Feenberg type does not recover the quadratic term in the expansion of
the energy in powers of $\a0\KF$, where $\a0$ is the vacuum $s$-wave scattering
length and $\KF$ the Fermi wave number. The problem is cured by adding
second-order perturbation corrections in a correlated basis. Going to higher
densities and/or more strongly coupled systems, we encounter an instability of
the normal state of the system which is characterized by a divergence of the
{\em in-medium\/} scattering length. We interpret this divergence as a
phonon-exchange driven dimerization of the system, similar to what one has at
zero density when the vacuum scattering length $\a0$ diverges. We then study,
in the stable regime, the superfluid gap and its dependence on the density and
the interaction strength. We identify two different corrections to low-density
expansions: One is medium corrections to the pairing interaction, and the other
one finite-range corrections. We show that the most important finite-range
corrections are a direct manifestation of the many-body nature of the system.",1409.5649v2
2004-10-07,Integral equations for simple fluids in a general reference functional approach,"The integral equations for the correlation functions of an inhomogeneous
fluid mixture are derived using a functional Taylor expansion of the free
energy around an inhomogeneous equilibrium distribution. The system of
equations is closed by the introduction of a reference functional for the
correlations beyond second order in the density difference from the equilibrium
distribution. Explicit expressions are obtained for energies required to insert
particles of the fluid mixture into the inhomogeneous system. The approach is
illustrated by the determination of the equation of state of a simple,
truncated Lennard--Jones fluid and the analysis of the behavior of this fluid
near a hard wall. The wall--fluid integral equation exhibits complete drying
and the corresponding coexisting densities are in good agreement with those
obtained from the standard (Maxwell) construction applied to the bulk fluid.
Self--consistency of the approach is examined by analyzing the
virial/compressibility routes to the equation of state and the Gibbs--Duhem
relation for the bulk fluid, and the contact density sum rule and the Gibbs
adsorption equation for the hard wall problem. For the bulk fluid, we find good
self--consistency for stable states outside the critical region. For the hard
wall problem, the Gibbs adsorption equation is fulfilled very well near phase
coexistence where the adsorption is large.For the contact density sum rule, we
find some deviationsnear coexistence due to a slight disagreement between the
coexisting density for the gas phase obtained from the Maxwell construction and
from complete drying at the hard wall.",0410185v1
2016-03-15,Particle Gaussian Mixture (PGM) Filters,"Recursive estimation of nonlinear dynamical systems is an important problem
that arises in several engineering applications. Consistent and accurate
propagation of uncertainties is important to ensuring good estimation
performance. It is well known that the posterior state estimates in nonlinear
problems may assume non-Gaussian multimodal densities. In the past, Gaussian
mixture filters and particle filters were introduced to handle non-Gaussianity
and nonlinearity. However, these methods have seen only limited success as most
mixture filters attempt to fix the number of mixture modes during estimation
process, and the particle filters suffer from the curse of dimensionality. In
this paper, we propose a particle based Gaussian mixture filtering approach for
the general nonlinear estimation problem that is free of the particle depletion
problem inherent to most particle filters. We employ an ensemble of randomly
sampled states for the propagation of state probability density. A Gaussian
mixture model of the propagated uncertainty is then recovered by clustering the
ensemble. The posterior density is obtained subsequently through a Kalman
measurement update of the mixture modes. We prove the weak convergence of the
PGM density to the true filter density assuming exponential forgetting of
initial conditions by the true filter. The estimation performance of the
proposed filtering approach is demonstrated through several test cases.",1603.04510v1
2006-01-07,Another convex combination of product states for the separable Werner state,"In this paper, we write down the separable Werner state in a two-qubit system
explicitly as a convex combination of product states, which is different from
the convex combination obtained by Wootters' method. The Werner state in a
two-qubit system has a single real parameter and varies from inseparable state
to separable state according to the value of its parameter. We derive a hidden
variable model that is induced by our decomposed form for the separable Werner
state. From our explicit form of the convex combination of product states, we
understand the following: The critical point of the parameter for separability
of the Werner state comes from positivity of local density operators of the
qubits.",0601044v2
2021-07-15,Multipolar nematic state of nonmagnetic FeSe based on the DFT+$U$,"Clarifying the origin of nematic state in FeSe is one of urgent problems in
the field of iron-based superconductivity. Motivated by the discovery of a
nematic solution in the density-functional theory implemented by on-site
Coulomb interaction (DFT+$U$) [npj Quantum Mater. \textbf{5}, 50 (2020)], we
reexamine the $U$ dependence of electronic states in the nonmagnetic normal
state of FeSe and perform full multipolar analyses for the nematic state. We
find that with increasing $U$ the normal state experiences a topological change
in the Fermi surfaces before the emergence of a nematic ground state. The
resulting nematic ground state is a multipolar state having both
antiferrohexadecapoles in the $E$ representation and ferromultipoles in the
$B_2$ representation on each Fe site. Cooperative coupling between the $E$ and
the $B_2$ multipoles in the local coordinate with the $D_{2d}$ point group will
play an important role in the formation of the $d_{xz},~d_{yz}$
orbital-splitting nematic state not only in FeSe, but also in other iron
pnictides.",2107.07244v3
2013-04-25,Toward computability of trace distance discord,"It is known that a reliable geometric quantifier of discord-like correlations
can be built by employing the so-called trace distance. This is used to measure
how far the state under investigation is from the closest ""classical-quantum""
one. To date, the explicit calculation of this indicator for two qubits was
accomplished only for states such that the reduced density matrix of the
measured party is maximally mixed, a class that includes Bell-diagonal states.
Here, we first reduce the required optimization for a general two-qubit state
to the minimization of an explicit two-variable function. Using this framework,
we show next that the minimum can be analytically worked out in a number of
relevant cases including quantum-classical and X states. This provides an
explicit and compact expression for the trace distance discord of an arbitrary
state belonging to either of these important classes of density matrices.",1304.6879v2
2015-02-25,Scanning tunneling microscopy study of the possible topological surface states in BiTeCl,"Recently, the non-centrosymmetric bismuth tellurohalides such as BiTeCl are
being studied as possible candidates of topological insulators. While some
photoemission studies showed that BiTeCl is an inversion asymmetric topological
insulator, others showed that it is a normal semiconductor with Rashba
splitting. Meanwhile, first-principle calculationsfailed to confirm the
existence of topological surface states in BiTeCl so far. Therefore, the
topological nature of BiTeCl requires further investigation. Here we report low
temperature scanning tunneling microscopy study on the surface states of BiTeCl
single crystals. On the tellurium-terminated surfaces with low defect density,
strong evidences for topological surface states are found in the quasi-particle
interference patterns generated by the scattering of these states, both in the
anisotropy of the scattering vectors and the fast decay of the interference
near step edges. Meanwhile, on samples with much higher defect densities, we
observed surface states that behave differently. Our results help to resolve
the current controversy on the topological nature of BiTeCl.",1502.07080v1
2015-06-10,Baryon Number Fluctuations from a Crossover Equation of State Compared to Heavy-Ion Collision Measurements in the Beam Energy Range $\sqrt{s_{NN}}$ = 7.7 to 200 GeV,"Fluctuations of the proton number distribution in central Au-Au collisions
have been measured by the STAR collaboration in a beam energy scan at the
Relativistic Heavy Ion Collider (RHIC). The motivation is a search for evidence
of a critical point in the equation of state. It was found that the skewness
and kurtosis display an interesting energy dependence. We compare these
measurements to an equation of state which smoothly interpolates between an
excluded volume hadron resonance gas at low energy density to a perturbative
plasma of quarks and gluons at high energy density. This crossover equation of
state agrees very well with the lattice QCD equation of state. The crossover
equation of state can reproduce the data if the fluctuations are frozen at a
temperature significantly lower than the average chemical freeze-out.",1506.03408v1
2016-10-07,The Role of Interaction in the Pairing of Two Spin-orbit Coupled Fermions,"We investigate the role of a repulsive s-wave interaction in the two-body
problem in the presence of spin orbit couplings, motivated by current interests
in exploring exotic superfluid phases in spin-orbit coupled Fermi gases. For
weak spin orbit coupling where the density of states is not significantly
altered, we analytically show that the high-energy states become more important
in determining the binding energy when the interaction strength decreases.
Consequently, tuning the interaction gives rise to a rich ground state
behavior, including a zigzag of the ground state momentum or inducing
transitions among the meta-stable states. By exactly solving the two-body
problem for a spin-orbit coupled Fermi mixture, we demonstrate that our
analysis can also apply to the case when the density of states is significantly
modified by the spin-orbit coupling. Our findings pave the way for
understanding and controlling the paring of fermions in the presence of spin
orbit couplings.",1610.02927v2
2016-08-30,Conditions for entanglement purification with general two-qubit states,"We present the convergence study of a recurrence entanglement purification
protocol using arbitrary two-qubit initial states. The protocol is based on a
rank two projector in the Bell basis which serves as a two-qubit operation
replacing the usual controlled-NOT gate. We show that the whole space of
two-qubit density matrices is mapped onto an invariant subspace characterized
by seven real parameters. By analyzing this type of density matrices we are
able to find general conditions for entanglement purification in the form of
two inequalities between pairs of diagonal elements and pairs of coherences. We
show that purifiable initial states do not necessary require a fidelity larger
than one half with respect to any maximally entangled pure state. Furthermore,
we find a family of states parametrized by their concurrence that can be
perfectly converted into a Bell state in just one step of the protocol with
probability proportional to the square of the concurrence.",1608.08585v1
2018-01-22,Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems,"For a class of typical states, the real-time and real-space dynamics of
non-equilibrium density profiles has been recently studied for integrable
models, i.e. the spin-1/2 XXZ chain [PRB 95, 035155 (2017)] and the
Fermi-Hubbard chain [PRE 96, 020105 (2017)]. It has been found that the
non-equilibrium dynamics agrees with linear response theory. Moreover, in the
regime of strong interactions, clear signatures of diffusion have been
observed. However, this diffusive behavior strongly depends on the choice of
the initial state and disappears for untypical states without internal
randomness. In the present work, we address the question whether or not the
above findings persist for non-integrable models. As a first step, we study the
spin-1/2 XXZ chain, where integrability can be broken due to an additional
next-nearest neighbor interaction. Furthermore, we analyze the differences of
typical and untypical initial states on the basis of their entanglement and
their local density of states.",1801.07031v1
2019-01-08,A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states,"With a two step optimization method of entanglement witness, we analytically
propose a set of necessary and sufficient entanglement criteria for four qubit
symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set
contains four criteria. Two of them are linear with density matrix elements.
The other two criteria are nonlinear with density matrix elements. The
criterion set has a nest structure. A proper subset of the criteria is
necessary and sufficient for the entanglement of a proper subset of the states.
We illustrate the nest structure of criterion set with the general Werner state
set and its superset the highly symmetric GHZ diagonal state set, they are
subsets of the symmetric GHZ diagonal state set.",1901.02312v1
2021-02-15,Spin-Dependent Transport Through a Colloidal Quantum Dot: The Role of Exchange Interactions,"The study of charge and spin transport through semiconductor quantum dots is
experiencing a renaissance due to recent advances in nano-fabrication and the
realization of quantum dots as candidates for quantum computing. In this work,
we combine atomistic electronic structure calculations with quantum master
equation methods to study the transport of electrons and holes through strongly
confined quantum dots coupled to two leads with a voltage bias. We find that a
competition between the energy spacing between the two lowest quasiparticle
energy levels and the strength of the exchange interaction determines the spin
states of the lowest two quasiparticle energy levels. Specifically, the low
density of electron states results in a spin singlet being the lowest energy
two-electron state whereas, in contrast, the high density of states and
significant exchange interaction results in a spin triplet being the lowest
energy two-hole state. The exchange interaction is also responsible for spin
blockades in transport properties, which could persist up to temperatures as
high as 77K for strongly confined colloidal quantum dots from our calculations.
Lastly, we relate these findings to the preparation and manipulation of singlet
and triplet spin qubit states in quantum dots using voltage biases.",2102.07778v1
2023-04-02,Generalized hypergeometric coherent states for special functions: mathematical and physical properties,"In continuation of our previous works J. Phys. A: Math. Gen. 35, 9355-9365
(2002), J. Phys. A: Math. Gen. 38, 7851 (2005) and Eur. Phys. J. D 72, 172
(2018), we investigate a class of generalized coherent states for associated
Jacobi polynomials and hypergeometric functions, satisfying the resolution of
the identity with respect to a weight function expressed in terms of Meijer's
G-function. We extend the state Hilbert space of the constructed states and
discuss the property of the reproducing kernel and its analytical expansion.
Further, we provide the expectation values of observables relevant to this
quantum model. We also perform the quantization of the complex plane, compute
and analyze the probability density and the temporal stability in these states.
Using the completeness relation provided by the coherent states, we achieve the
thermodynamic analysis in the diagonal $P$-representation of the density
operator.",2305.02194v1
2021-12-08,Unusual Dynamical Properties of Disordered Polaritons in Micocavities,"The strong light-matter interaction in microcavities gives rise to intriguing
phenomena, such as cavity-mediated transport that can potentially overcome the
Anderson localization. Yet, an accurate theoretical treatment is challenging as
the matter (e.g.,molecules) are subject to large energetic disorder. In this
article, we develop the Green's function solution to the Fano-Anderson model
and use the exact analytical solution to quantify the effects of energetic
disorder on the spectral and transport properties in microcavities. Starting
from microscopic equation of motions, we derive an effective non-Hermitian
Hamiltonian and predict a set of scaling laws: (i) The complex eigen-energies
of the effective Hamiltonian exhibit an exceptional point, which leads to
underdamped coherent dynamics in the weak disorder regime, where the decay rate
increases with disorder, and overdamped incoherent dynamics in the strong
disorder regime, where the slow decay rate decreases with disorder. (ii) The
total density of states of disordered ensembles can be exactly partitioned into
the cavity, bright-state and dark-state local density of states, which are
determined by the complex eigen solutions and can be measured via spectroscopy.
(iii) The cavity-mediated relaxation and transport dynamics are intimately
related such that the energy-resolved relaxation and transport rates are
proportional to the cavity local density of states. The ratio of the disorder
averaged relaxation and transport rates equals the molecule number, which can
be interpreted as a result of a quantum random walk. (iv) A turnover in the
rates as a function of disorder or molecule density can be explained in terms
of the overlap of the disorder distribution function and the cavity local
density of states. These findings reveal the significant impact of the dark
states on the transport properties of disordered ensembles in cavities.",2112.04060v2
2010-01-29,Vortex structures and zero energy states in the BCS-to-BEC evolution of p-wave resonant Fermi gases,"Multiply quantized vortices in the BCS-to-BEC evolution of p-wave resonant
Fermi gases are investigated theoretically. The vortex structure and the
low-energy quasiparticle states are discussed, based on the self-consistent
calculations of the Bogoliubov-de Gennes and gap equations. We reveal the
direct relation between the macroscopic structure of vortices, such as particle
densities, and the low-lying quasiparticle state. In addition, the net angular
momentum for multiply quantized vortices with a vorticity $\kappa$ is found to
be expressed by a simple equation, which reflects the chirality of the Cooper
pairing. Hence, the observation of the particle density depletion and the
measurement of the angular momentum will provide the information on the
core-bound state and $p$-wave superfluidity. Moreover, the details on the zero
energy Majorana state are discussed in the vicinity of the BCS-to-BEC
evolution. It is demonstrated numerically that the zero energy Majorana state
appears in the weak coupling BCS limit only when the vortex winding number is
odd. There exist the $\kappa$ branches of the core bound states for a vortex
state with vorticity $\kappa$, whereas only one of them can be the zero energy.
This zero energy state vanishes at the BCS-BEC topological phase transition,
because of interference between the core-bound and edge-bound states.",1001.5325v2
2022-12-22,Separability and entanglement of resonating valence-bond states,"We investigate separability and entanglement of Rokhsar-Kivelson (RK) states
and resonating valence-bond (RVB) states. These states play a prominent role in
condensed matter physics, as they can describe quantum spin liquids and quantum
critical states of matter, depending on their underlying lattices. For dimer RK
states on arbitrary tileable graphs, we prove the exact separability of the
reduced density matrix of $k$ disconnected subsystems, implying the absence of
bipartite and multipartite entanglement between the subsystems. For more
general RK states with local constraints, we argue separability in the
thermodynamic limit, and show that any local RK state has zero logarithmic
negativity, even if the density matrix is not exactly separable. In the case of
adjacent subsystems, we find an exact expression for the logarithmic negativity
in terms of partition functions of the underlying statistical model. For RVB
states, we show separability for disconnected subsystems up to exponentially
small terms in the distance $d$ between the subsystems, and that the
logarithmic negativity is exponentially suppressed with $d$. We argue that
separability does hold in the scaling limit, even for arbitrarily small ratio
$d/L$, where $L$ is the characteristic size of the subsystems. Our results hold
for arbitrary lattices, and encompass a large class of RK and RVB states, which
include certain gapped quantum spin liquids and gapless quantum critical
systems.",2212.11740v3
2015-04-26,Highway Traffic State Estimation with Mixed Connected and Conventional Vehicles,"A macroscopic model-based approach for estimation of the traffic state,
specifically of the (total) density and flow of vehicles, is developed for the
case of ""mixed"" traffic, i.e., traffic comprising both ordinary and connected
vehicles. The development relies on the following realistic assumptions: (i)
The density and flow of connected vehicles are known at the (local or central)
traffic monitoring and control unit on the basis of their regularly reported
positions, and (ii) the average speed of conventional vehicles is roughly equal
to the average speed of connected vehicles. Thus, complete traffic state
estimation (for arbitrarily selected segments in the network) may be achieved
by merely estimating the percentage of connected vehicles with respect to the
total number of vehicles. A model is derived, which describes the dynamics of
the percentage of connected vehicles, utilizing only well-known conservation
law equations that describe the dynamics of the density of connected vehicles
and of the total density of all vehicles. Based on this model, which is a
linear time-varying system, an estimation algorithm for the percentage of
connected vehicles is developed employing a Kalman filter. The estimation
methodology is validated through simulations using a second-order macroscopic
traffic flow model as ground truth for the traffic state. The approach calls
for a minimum of spot sensor-based total flow measurements {according to a
variety of possible location configurations.",1504.06879v1
2023-11-30,Structure in the speed of sound: from neutron stars to heavy-ion collisions,"From the observation of both heavy neutron stars and light ones with small
radii, one anticipates a steep rise in the speed of sound of nuclear matter as
a function of baryon density up to values close to the causal limit. A question
follows whether such behavior of the speed of sound in neutron-rich matter is
compatible with the equation of state extracted from low-energy heavy-ion
collisions. In this work, we consider a family of neutron star equations of
state characterized by a steep rise in the speed of sound, and use the symmetry
energy expansion to obtain equations of state applicable to the
almost-symmetric nuclear matter created in heavy-ion collisions. We then
compare collective flow data from low-energy heavy-ion experiments with results
of simulations obtained using the hadronic transport code SMASH with the
mean-field potential reproducing the density-dependence of the speed of sound.
We show that equations of state featuring a peak in the speed of sound squared
occurring at densities between 2-3 times the saturation density of normal
nuclear matter, producing neutron stars of nearly M_max~2.5 M_Sun, are
consistent with heavy-ion collision data.",2311.18819v2
2016-07-29,An investigation of nonclassical properties of light using an optical tomogram,"By analyzing the optical tomogram of a linear superposition of coherent
states, we show that distinctive signatures of the macroscopic superposition
states are displayed directly in the optical tomograms of the states. We also
study the effect of decoherence on the optical tomograms of the macroscopic
superposition states. Since the wave packet fractional revivals are associated
with the generation of macroscopic superposition states, these signatures help
in visualizing the revivals and fractional revivals occurring in a nonlinear
medium directly in the optical tomogram of the time-evolved state. We found
that the optical tomogram of the time-evolved state at the instants of
fractional revivals show structures with sinusoidal strands. Using a class of
initial superposed wave packets evolving in the Kerr-like medium, we further
show that the condition for the occurrence of fractional revival phenomenon
depends on the number of wave packets composing the initial superposition
state. In the case of a two-mode electromagnetic field, we investigate the
entanglement of the state directly using the optical tomogram. We have shown
that the signatures of entanglement can be observed directly in the single-mode
optical tomogram of the state without reconstructing the density matrix of the
system. We also analyze the effect of decoherence on the optical tomograms of
the entangled states. Further, we examine the optical tomograms of the
entangled states generated using a beam splitter with a Kerr medium placed into
one of its input modes. We have found the signatures of entanglement in the
optical tomogram for the entangled states generated at the instants of two- and
three-subpacket fractional revival times.",1607.08752v1
2006-03-29,Dynamical age of the universe as a constraint on the parametrization of dark energy equation of state,"The dynamical age of the universe depends upon the rate of the expansion of
the universe, which explicitly involves the dark energy equation of state
parameter $w(z)$. Consequently, the evolution of $w(z)$ has a direct imprint on
the age of the universe. We have shown that the dynamical age of the universe
as derived from CMB data can be used as an authentic criterion, being
independent of the priors like the present value of the Hubble constant $H_{0}$
and the cosmological density parameter $\Omega_{M}^{0}$, to constrain the range
of admissible values of $w$ for quiessence models and to test the physically
viable parametrizations of the equation of state $w(z) $ in kinessence models.
An upper bound on variation of dark energy density is derived and a relation
between cosmological density parameters and the transition redshift is
established.",0603786v4
1998-04-01,Relaxation in a perfect funnel,"We have exactly solved the relaxational dynamics of a model protein which
possesses a kinetically perfect funnel-like energy landscape. We find that the
dependence of the relaxation time, $\tau$, on the density of states (DOS) and
the energy level spacing distributions of the model displays several main types
of behavior depending on the temperature $T$. This allows us to identify
possible generic features of the relaxation. For some ranges of $T$, $\tau$ is
insensitive to the density of states; for intermediate values of $T$ it depends
on the energy level spacing distribution rather than on the DOS directly, and
it becomes gradually more dependent on DOS with increasing temperature;
finally, the relaxation can also be determined exclusively by the presence of a
deep gap in the energy spectrum rather than by the detailed features of the
density of states. We found that the behavior of $\tau$ crucially depends on
the degeneracy of the energy spectrum. For the special case of exponentially
increasing degeneracy, we were able to identify a characteristic temperature
which roughly separates the relaxational regimes controlled by energetics and
by entropy, respectively. Finally, the validity of our theory is discussed when
roughness of energy landscape is added.",9804006v1
2015-12-21,The EOS of neutron matter and the effect of $Λ$ hyperons to neutron star structure,"The structure of neutron stars is determined by the equation of state of the
matter inside the star, which relies on the knowledge of nuclear interactions.
While radii of neutron stars mostly depend on the equation of state of neutron
matter at nuclear densities, their maximum mass can be drastically affected by
the appearance of hyperons at higher densities in the inner core of the star.
We summarize recent quantum Monte Carlo results on the calculation of the
equation of state of neutron matter at nuclear and higher densities. We report
about the development of realistic hyperon-nucleon interactions based on the
available experimental data for light- and medium-heavy hypernuclei and on the
effect of $\Lambda$ hyperons to the neutron star structure.",1512.06832v1
2018-09-10,Effect of van-Hove singularities in single-walled carbon nanotube leads on transport through double quantum dot system,"The double quantum dot system with single-walled metallic armchair carbon
nanotube leads has been studied using Non-equilibrium Green function in the
Keldysh formalism. The effect of relative spacing between the energy levels of
the dots, interdot tunneling matrix-element, interdot Coulomb interaction and
van-Hove singularities in density of states characteristics of
quasi-one-dimensional carbon nanotube leads on the conductance of the double
quantum dot system has been studied. The conductance and dot occupancies are
calculated at finite temperature. It is observed that the density of states of
the carbon nanotube leads play a significant role in determining the
conductance profile. In particular, whenever the chemical potential of the
isolated double quantum dot system is aligned with the position of a van-Hove
singularity in the density of states of armchair carbon nanotube leads, the
height of the corresponding conductance peak falls considerably. It is further
observed that the suppression in the heights of the alternate peaks depends on
the relative positions of the energy levels of the dots and their magnitude of
separation.",1809.03379v1
1996-02-17,The Nuclear Level Density and the Determination of Thermonuclear Rates for Astrophysics,"The prediction of cross sections for nuclei far off stability is crucial in
the field of nuclear astrophysics. In recent calculations the nuclear level
density -- as an important ingredient to the statistical model
(Hauser-Feshbach) -- has shown the highest uncertainties. We present a global
parametrization of nuclear level densities based on the back-shifted Fermi-Gas
formalism. Employment of an energy-dependent level density parameter $a$ and
microscopic corrections from a recent FRDM mass formula by M\""oller et al.\
leads to a highly improved fit of level densities at the neutron-separation
energy in the mass range $20\le A \le 245$. The importance of using proper
microscopic corrections from mass formulae is emphasized. The resulting level
description is well suited for astrophysical applications.
  The level density can also provide clues to the applicability of the
statistical model which is only correct for a high density of excited states.
Using the above description one can derive a ``map'' for the applicability of
the model for reactions of stable and unstable nuclei with neutral and charged
particles.",9602087v1
2001-06-06,Formation Of Quark Matter In Neutron Stars,"At very large densities and/or temperatures a quark-hadron phase transition
is expected to take place. Simulations of QCD on lattice at zero baryon density
indicate that the transition occurs at $T_c \sim 150-170$ MeV. The calculations
indicate that transition is likely to be second order or a cross over
phenomenon. Although the lattice simulations have not given any indication on
when the transition occurs at nonzero baryon density, the transition is
expected to occur around the densities of few times nuclear matter density.
Also, there is a strong reason to believe that the quark matter formed after
the phase transition is in colour superconducting phase. The matter densities
in the interior of neutron stars are expected to be several times the nuclear
matter density and therefore the neutron star cores may possibly consist of
quark matter. One then expects that this quark matter is formed during the
collapse of supernova. Starting with the assumption that the quark matter, when
formed consists of predominantly u and d quarks, we consider the evolution of
strange quarks by weak interactions in the present work. The reaction rates and
time required to reach the chemical equilibrium are computed here. Our
calculations show that the chemical equilibrium is reached in about $10^{-7}$
seconds. Further more during and immediately after the equilibration process
enormous amount of energy is released and copious numbers of neutrinos are
produced. We show that for reasonable models of nuclear equations of state the
amount of energy released could be as high as $10^{53}$ ergs and as many as
$10^{58}$ neutrinos may be emitted during the quark matter formation.",0106012v1
2015-03-04,Reilly's type inequality for the Laplacian associated to a density related with shrinkers for MCF,"Let $(\bar{M},<,>,e^\psi)$ be a Riemannian manifold with a density, and let
$M$ be a closed $n$-dimensional submanifold of $\bar{M}$ with the induced
metric and density. We give an upper bound on the first eigenvalue $\lambda_1$
of the closed eigenvalue problem for $\Delta_\psi$ (the Laplacian on $M$
associated to the density) in terms of the average of the norm of the vector
${\vec{H}}_{{\psi}} + {\bar \nabla}$ with respect to the volume form induced by
the density, where ${\vec{H}}_{{\psi}}$ is the mean curvature of $M$ associated
to the density $e^\psi$.
  When $\bar{M}=\Bbb R^{n+k}$ or $\bar{M}=S^{n+k-1}$, the equality between
$\lambda_1$ and its bound implies that $e^\psi$ is a Gaussian density ($\psi(x)
= \frac{C}{2} |x|^2$, $C<0$), and $M$ is a shrinker for the mean curvature flow
(MCF) on $\Bbb R^{n+k}$.
  We prove also that $\lambda_1 =-C$ on the standard shrinker torus of
revolution.
  Based on this and on the Yau's conjecture on the first eigenvalue of minimal
submanifolds of $S^n$, we conjecture that the equality $\lambda_1=-C$ is true
for all the shrinkers of MCF in $\mathbb{R}^{n+k}$.",1503.01332v3
2022-07-30,Impact of Symmetry Energy on Sound Speed and Spinodal Decomposition in Dense Neutron-Rich Matter,"Using a meta model for nuclear Equation of State (EOS) with its parameters
constrained by astrophysical observations and terrestrial nuclear experiments,
we examine effects of nuclear EOS especially its symmetry energy \esym term on
the speed of sound squared $C^2_s(\rho)$ and the critical density $\rho_t$
where $C^2_s(\rho_t)$ vanishes (indicating the onset of spinodal decomposition)
in both dense neutron-rich nucleonic matter relevant for relativistic heavy-ion
collisions and the cold $n+p+e+\mu$ matter in neutron stars at
$\beta$-equilibrium. Unlike in nucleonic matter with fixed values of the
isospin asymmetry $\delta$, in neutron stars with a density dependent isospin
profile $\delta(\rho)$ determined consistently by the $\beta$ equilibrium and
charge neutrality conditions, the $C^2_s(\rho)$ almost always show a peak and
then vanishes at $\rho_t$. The latter strongly depends on the high-density
behavior of \esym if the skewness parameter $J_0$ characterizing the stiffness
of high-density symmetric nuclear matter (SNM) EOS is not too far above its
currently known most probable value of about $-190$ MeV inferred from recent
Bayesian analyses of neutron star observables. Moreover, in the case of having
a super-soft \esym that is decreasing with increasing density above about twice
the saturation density of nuclear matter, the $\rho_t$ is significantly lower
than the density where the \esym vanishes (indicating the onset of
isospin-separation instability and pure neutron matter formation) in neutron
star cores.",2208.00321v2
2010-01-26,Symmetry breaking in a localized interacting binary BEC in a bi-chromatic optical lattice,"By direct numerical simulation of the time-dependent Gross-Pitaevskii
equation using the split-step Fourier spectral method we study different
aspects of the localization of a cigar-shaped interacting binary
(two-component) Bose-Einstein condensate (BEC) in a one-dimensional
bi-chromatic quasi-periodic optical-lattice potential, as used in a recent
experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)].
We consider two types of localized states: (i) when both localized components
have a maximum of density at the origin x=0, and (ii) when the first component
has a maximum of density and the second a minimum of density at x=0. In the
non-interacting case the density profiles are symmetric around x=0. We
numerically study the breakdown of this symmetry due to inter-species and
intra-species interaction acting on the two components. Where possible, we have
compared the numerical results with a time-dependent variational analysis. We
also demonstrate the stability of the localized symmetry-broken BEC states
under small perturbation.",1001.4667v1
2016-04-26,Multiband effects and the possible Dirac states in LaAgSb$_2$,"Here we report the possible signature of Dirac fermions in the
magnetoresistance, Hall resistivity and magnetothermopower of LaAgSb$_2$. The
opposite sign between Hall resistivity and Seebeck coefficient indicates the
multiband effect. Electronic structure calculation reveals the existence of the
linear bands and the parabolic bands crossing the Fermi level. The large linear
magnetoresistance was attributed to the quantum limit of the possible Dirac
fermions or the breakdown of weak-field magnetotransport at the charge density
wave phase transition. Analysis of Hall resistivity using two-band model
reveals that Dirac holes which dominate the electronic transport have much
higher mobility and larger density than conventional electrons. Magnetic field
suppresses the apparent Hall carrier density, and also induces the sign change
of the Seebeck coefficient from negative to positive. These effects are
possibly attributed to the magnetic field suppression of the density of states
at the Fermi level originating from the quantum limit of the possible Dirac
holes.",1604.07819v1
2022-04-13,Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States,"We present the conceptual and technical background required to describe and
understand the correlations and fluctuations of the empirical density and
current of steady-state diffusion processes on all time scales -- observables
central to statistical mechanics and thermodynamics on the level of individual
trajectories. We focus on the important and non-trivial effect of a spatial
coarse graining. Making use of a generalized time-reversal symmetry we provide
deeper insight about the physical meaning of fluctuations of the coarse-grained
empirical density and current, and explain why a systematic variation of the
coarse-graining scale offers an efficient method to infer bounds on a system's
dissipation. Moreover, we discuss emerging symmetries in the statistics of the
empirical density and current, and the statistics in the central-limit regime.
More broadly our work promotes the application of stochastic calculus as a
powerful direct alternative to Feynman-Kac theory and path-integral methods.",2204.06553v4
2002-09-23,Transverse acoustic nature of the excess of vibrational states in vitreous silica,"We present a numerical simulation study of the density-dependence (rho = 2.2
- 4.0 g/cm^3) of the high-energy collective dynamics in vitreous silica at
mesoscopic wavevectors (Q = 1 - 18 nm^-1). The density-dependence of the
longitudinal and transverse current spectra provides evidence that the excess
modes observed in the density of states of this and many other glasses, i.e.
the Boson Peak, arises from the high-Q limit of the quasi-transverse acoustic
branch. This conclusion emerges from the comparison of the numerical results
with the experimentally observed energy-shift and intensity variation of the
Boson Peak with increasing density.",0209519v2
2003-03-04,More examples of structure formation in the Lemaitre-Tolman model,"In continuing our earlier research, we find the formulae needed to determine
the arbitrary functions in the Lemaitre-Tolman model when the evolution
proceeds from a given initial velocity distribution to a final state that is
determined either by a density distribution or by a velocity distribution. In
each case the initial and final distributions uniquely determine the L-T model
that evolves between them, and the sign of the energy-function is determined by
a simple inequality. We also show how the final density profile can be more
accurately fitted to observational data than was done in our previous paper. We
work out new numerical examples of the evolution: the creation of a galaxy
cluster out of different velocity distributions, reflecting the current data on
temperature anisotropies of CMB, the creation of the same out of different
density distributions, and the creation of a void. The void in its present
state is surrounded by a nonsingular wall of high density.",0303016v2
1998-10-29,Dynamical structure of the chiral QCD vacuum in the zero modes enhancement quantum model,"Using the effective potential approach for composite operators we have
formulated the quantum model of the QCD vacuum. It is based on the existence
and importance of the nonperturbative $q^{-4}$-type dynamical, topologically
nontrivial excitations of the gluon field configuration. The QCD vacuum is
found stable since the vacuum energy density has no imaginary part. Moreover, a
possible ground (stationary) state of the nonperturbative Yang-Mills (quenched
QCD) vacuum is discovered. The vacuum energy density at stationary state
depends on a scale at which nonperturbative effects become important. The quark
part of the vacuum energy density depends in addition on the constant of
integration of the corresponding Schwinger-Dyson equation. The value of the
above mentioned scale is determined from the bounds for the pion decay constant
in the chiral limit. Our value for the chiral QCD vacuum energy density is one
order of magnitude bigger than the instanton based models can provide while a
fair agreement with recent phenomenological and lattice results for the chiral
condensate is obtained.",9810516v2
2009-11-29,Nuclear constraints on the core-crust transition density and pressure of neutron stars,"Using the equation of state of asymmetric nuclear matter that has been
recently constrained by the isospin diffusion data from intermediate-energy
heavy ion collisions, we have studied the transition density and pressure at
the inner edge of neutron star crusts, and they are found to be 0.040 fm^{-3}
<= \rho_{t}<= 0.065 fm^{-3} and 0.01 MeV/fm^{3} <= P_{t} <= 0.26 MeV/fm^{3},
respectively, in both the dynamical and thermodynamical approaches. We have
further found that the widely used parabolic approximation to the equation of
state of asymmetric nuclear matter gives significantly higher values of
core-crust transition density and pressure, especially for stiff symmetry
energies. With these newly determined transition density and pressure, we have
obtained an improved relation between the mass and radius of neutron stars
based on the observed minimum crustal fraction of the total moment of inertia
for Vela pulsar.",0911.5470v1
2012-12-31,Hadron-Quark Crossover and Massive Hybrid Stars,"On the basis of the percolation picture from the hadronic phase with hyperons
to the quark phase with strangeness, we construct a new equation of state (EOS)
with the pressure interpolated as a function of the baryon density. The maximum
mass of neutron stars can exceed $2M_{\odot}$ if the following two conditions
are satisfied; (i) the crossover from the hadronic matter to the quark matter
takes place at around three times the normal nuclear matter density, and (ii)
the quark matter is strongly interacting in the crossover region and has stiff
equation of state. This is in contrast to the conventional approach assuming
the first order phase transition in which the EOS becomes always soft due to
the presence of the quark matter at high density. Although the choice of the
hadronic EOS does not affect the above conclusion on the maximum mass, the
three-body force among nucleons and hyperons plays an essential role for the
onset of the hyperon mixing and the cooling of neutron stars.",1212.6803v2
2013-09-17,Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study,"We present dynamical density functional theory results for the time evolution
of the density distribution of a sedimenting model two-dimensional binary
mixture of colloids. The interplay between the bulk phase behaviour of the
mixture, its interfacial properties at the confining walls, and the
gravitational field gives rise to a rich variety of equilibrium and
non-equilibrium morphologies. In the fluid state, the system exhibits both
liquid-liquid and gas-liquid phase separation. As the system sediments, the
phase separation significantly affects the dynamics and we explore situations
where the final state is a coexistence of up to three different phases. Solving
the dynamical equations in two-dimensions, we find that in certain situations
the final density profiles of the two species have a symmetry that is different
from that of the external potentials, which is perhaps surprising, given the
statistical mechanics origin of the theory. The paper concludes with a
discussion on this.",1309.4326v1
2003-03-11,Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder,"The fate of the current carrying states of a quantum Hall system is
considered in the situation when the disorder strength is increased and the
transition from the quantum Hall liquid to the Hall insulator takes place. We
investigate a two-dimensional lattice model with spatially correlated disorder
potentials and calculate the density of states and the localization length
either by using a recursive Green function method or by direct diagonalization
in connection with the procedure of level statistics. From the knowledge of the
energy and disorder dependence of the localization length and the density of
states (DOS) of the corresponding Landau bands, the movement of the current
carrying states in the disorder--energy and disorder--filling-factor plane can
be traced by tuning the disorder strength.
  We show results for all sub-bands, particularly the traces of the Chern and
anti-Chern states as well as the peak positions of the DOS. For small disorder
strength $W$ we recover the well known weak levitation of the critical states,
but we also reveal, for larger $W$, the strong levitation of these states
across the Landau gaps without merging. We find the behavior to be similar for
exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our
study resolves the discrepancies of previously published work in demonstrating
the conflicting results to be only special cases of a general lattice model
with spatially correlated disorder potentials.
  To test whether the mixing between consecutive Landau bands is the origin of
the observed floating, we truncate the Hilbert space of our model Hamiltonian
and calculate the behavior of the current carrying states under these
restricted conditions.",0303191v1
2021-01-14,Entanglement of formation and monogamy of multi-party quantum entanglement,"We provide a sufficient condition for the monogamy inequality of multi-party
quantum entanglement of arbitrary dimensions in terms of entanglement of
formation. Based on the classical-classical-quantum(ccq) states whose quantum
parts are obtained from the two-party reduced density matrices of a three-party
quantum state, we show the additivity of the mutual information of the ccq
states guarantees the monogamy inequality of the three-party pure state in
terms of EoF. After illustrating the result with some examples, we generalize
our result of three-party systems into any multi-party systems of arbitrary
dimensions.",2101.05590v1
2021-01-27,QCD Equation of State at Finite Chemical Potentials for Relativistic Nuclear Collisions,"We review the equation of state of QCD matter at finite densities. We discuss
the construction of the equation of state with net baryon number, electric
charge, and strangeness using the results of lattice QCD simulations and hadron
resonance gas models. Its application to the hydrodynamic analyses of
relativistic nuclear collisions suggests that the interplay of multiple
conserved charges is important in the quantitative understanding of the dense
nuclear matter created at lower beam energies. Several different models of the
QCD equation of state are discussed for comparison.",2101.11591v1
2005-06-13,The maximum density droplet to lower density droplet transition in quantum dots,"We show that, Landau level mixing in two-dimensional quantum dot wave
functions can be taken into account very effectively by multiplying the exact
lowest Landau level wave functions by a Jastrow factor which is optimized by
variance minimization. The comparison between exact diagonalization and fixed
phase diffusion Monte Carlo results suggests that the phase of the many-body
wave functions are not affected much by Landau level mixing. We apply these
wave functions to study the transition from the maximum density droplet state
(incipient integer quantum Hall state with angular momentum L=N(N-1)/2) to
lower density droplet states (L>N(N-1)/2).",0506295v1
2011-07-08,Decision Based Uncertainty Propagation Using Adaptive Gaussian Mixtures,"Given a decision process based on the approximate probability density
function returned by a data assimilation algorithm, an interaction level
between the decision making level and the data assimilation level is designed
to incorporate the information held by the decision maker into the data
assimilation process. Here the information held by the decision maker is a loss
function at a decision time which maps the state space onto real numbers which
represent the threat associated with different possible outcomes or states. The
new probability density function obtained will address the region of interest,
the area in the state space with the highest threat, and will provide overall a
better approximation to the true conditional probability density function
within it. The approximation used for the probability density function is a
Gaussian mixture and a numerical example is presented to illustrate the
concept.",1107.1546v1
2008-11-26,Equation of state for dense supernova matter,"We provide an equation of state for high density supernova matter by applying
a momentum-dependent effective interaction. We focus on the study of the
equation of state of high-density and high-temperature nuclear matter
containing leptons (electrons and neutrinos) under the chemical equilibrium
condition. The conditions of charge neutrality and equilibrium under
$\beta$-decay process lead first to the evaluation of the lepton fractions and
afterwards the evaluation of internal energy, pressure, entropy and in total to
the equation of state of hot nuclear matter for various isothermal cases.
Thermal effects on the properties and equation of state of nuclear matter are
evaluated and analyzed in the framework of the proposed effective interaction
model. Since supernova matter is characterized by a constant entropy we also
present the thermodynamic properties for isentropic case. Special attention is
dedicated to the study of the contribution of the components of $\beta$-stable
nuclear matter to the entropy per particle, a quantity of great interest for
the study of structure and collapse of supernova.",0811.4232v2
2019-04-25,Dense matter equation of state and neutron star properties from nuclear theory and experiment,"The equation of state of dense matter determines the structure of neutron
stars, their typical radii, and maximum masses. Recent improvements in
theoretical modeling of nuclear forces from the low-energy effective field
theory of QCD has led to tighter constraints on the equation of state of
neutron-rich matter at and somewhat above the densities of atomic nuclei, while
the equation of state and composition of matter at high densities remains
largely uncertain and open to a multitude of theoretical speculations. In the
present work we review the latest advances in microscopic modeling of the
nuclear equation of state and demonstrate how to consistently include also
empirical nuclear data into a Bayesian posterior probability distribution for
the model parameters. Derived bulk neutron star properties such as radii,
moments of inertia, and tidal deformabilities are computed, and we discuss as
well the limitations of our modeling.",1904.11449v1
1998-01-13,Quantum inseparability as local pseudomixture,"We show how to decompose any density matrix of the simplest binary composite
systems, whether separable or not, in terms of only product vectors. We
determine for all cases the minimal number of product vectors needed for such a
decomposition. Separable states correspond to mixing from one to four pure
product states. Inseparable states can be described as pseudomixtures of four
or five pure product states, and can be made separable by mixing them with one
or two pure product states.",9801024v1
2000-06-13,A necessary and sufficient criterion for multipartite separable states,"We present a necessary and sufficient condition for the separability of
multipartite quantum states, this criterion also tells us how to write a
multipartite separable state as a convex sum of separable pure states. To work
out this criterion, we need to solve a set of equations, actually it is easy to
solve these quations analytically if the density matrix of the given quantum
state has few nonzero eigenvalues.",0006058v3
2004-05-11,Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states,"Off-diagonal geometric phases have been developed in order to provide
information of the geometry of paths that connect noninterfering quantal
states. We propose a kinematic approach to off-diagonal geometric phases for
pure and mixed states. We further extend the mixed state concept proposed in
[Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The
first and second order off-diagonal geometric phases are analyzed for unitarily
evolving pairs of pseudopure states.",0405048v2
2008-08-11,Boundary states and edge currents for free fermions,"We calculate the ground state current densities for 2+1 dimensional free
fermion theories with local, translationally invariant boundary states.
Deformations of the bulk wave functions close to the edge and boundary states
both may cause edge current divergencies, which have to cancel in realistic
systems. This yields restrictions on the parameters of quantum field theories
which can arise as low energy limits of solid state systems. Some degree of
Lorentz invariance for boosts parallel to the boundary can be recovered, when
the cutoff is removed.",0808.1497v2
2013-10-31,Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases,"We study the superconducting state in the presence of spin-orbital coupling
and the Zeeman field. It is found that a phase transition from the
Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state
occurs upon increasing the spin-orbital coupling. The nature of this
topological phase transition and its critical property are investigated
numerically. Physical properties of topological superconducting phase are also
explored. Moreover, the local density of states is calculated, through which
the topological feature may be tested experimentally.",1310.8562v3
2008-07-07,Trapping and cooling fermionic atoms into the Mott and Néel states,"We perform a theoretical study of a fermionic gas with two hyperfine states
confined to an optical lattice. We derive a generic state diagram as a function
of interaction strength, particle number, and confining potential. We discuss
the central density, the double occupancy and their derivatives as probes for
the Mott state, connecting our findings to the recent experiment of J\""ordens
et al. Using entropic arguments we compare two different strategies to reach
the antiferromagnetic state in the presence of a trapping potential.",0807.0790v3
2023-05-11,SPT phases for mixed states in one dimension,"This study explores the specific structure of 1D SPT phases with $G\times H$
symmetry ($G, H$ are finite non-Abelian groups) and constructs an order
parameter. We demonstrate that this order parameter can comprehensively
describe this specific structure. Utilizing this order parameter, we prove that
when the SPT phase theory of symmetry $G$ is extended to mixed states, if the
density matrix is treated as a pure SPT state with $G\times G$ symmetry, the
Hermiticity and positive semi-definiteness ensure that the SPT phase of the
mixed state is similarly described by $H^2(G)$. Finally, we propose that under
this perspective, the SPT phase of time-reversal symmetry no longer exists in
mixed states.",2305.06589v2
2018-06-20,Quantifying How Density Gradients and Front Curvature Affect Carbon Detonation Strength During Type Ia Supernovae,"Accurately reproducing the physics behind the detonations of Type Ia
supernovae and the resultant nucleosynthetic yields is important for
interpreting observations of spectra and remnants. The scales of the processes
involved span orders of magnitudes, making the problem computationally
impossible to ever fully resolve in full star simulations in the present and
near future. In the lower density regions of the star, the curvature of the
detonation front will slow the detonation, affecting the production of
intermediate mass elements. We find that shock strengthening due to the density
gradient present in the outer layers of the progenitor is essential for
understanding the nucleosynthesis there, with burning extending well below the
density at which a steady-state detonation is extinct. We show that a complete
reaction network is not sufficient to obtain physical detonations at high
densities and modest resolution due to numerical mixing at the unresolved
reaction front. At low densities, below 6$\times$10$^{5}$ g cm$^{-3}$, it is
possible to achieve high enough resolution to separate the shock and the
reaction region,and the abundance structure predicted by fully resolved
quasi-steady-state calculations is obtained. For our best current benchmark
yields, we utilize a method in which the unresolved portion of Lagrangian
histories are reconstructed based on fully resolved quasi-steady-state
detonation calculations. These computations demonstrate that under-resolved
simulations agree approximately, $\sim$10\% in post-shock values of
temperature, pressure, density, and abundances, with expected detonation
structures sufficiently far from the under-resolved region, but that there is
still room for some improvement in the treatment of subgrid reactions in the
hydrodynamics to before better than 1$\%$ can be achieved at all densities.",1806.07820v1
2015-10-28,"Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study","Motivated by the realization of hard-wall boundary conditions in experiments
with ultracold atoms, we investigate the ground-state properties of spin-1/2
fermions with attractive interactions in a one-dimensional box. We use lattice
Monte Carlo methods to determine essential quantities like the energy, which we
compute as a function of coupling strength and particle number in the regime
from few to many particles. Many-fermion systems bound by hard walls display
non-trivial density profiles characterized by so-called Friedel oscillations
(which are similar to those observed in harmonic traps). In non-interacting
systems, the characteristic length scale of the oscillations is set by (2
kF)^(-1), where kF is the Fermi momentum, while repulsive interactions tend to
generate Wigner-crystal oscillations of period (4 kF)^(-1). Based on the
non-interacting result, we find a remarkably simple parametrization of the
density profiles of the attractively interacting case, which we generalize to
the one-body density matrix. While the total momentum is not a conserved
quantity in the presence of hard walls, the magnitude of the momentum does
provide a good quantum number. We are therefore able to provide a detailed
characterization of the (quasi-)momentum distribution, which displays rather
robust discontinuity at the Fermi surface. In addition, we determine the
spatially varying on-site density-density correlation, which in turn yields
Tan's contact density and, upon integration, Tan's contact. As is well known,
the latter fully determines the short-range correlations and plays a crucial
role in a multitude of equilibrium and non-equilibrium sum rules.",1510.08503v2
2002-03-06,Fine-structure diagnostics of neutral carbon toward HE 0515-4414,"New high-resolution high signal-to-noise spectra of the $z=1.15$ damped Lyman
$\alpha$ (DLA) system toward the quasi-stellar object HE 0515-4414 reveal
absorption lines of the multiplets 2 and 3 in \ion{C}{i}. The resonance lines
are seen in two components with total column densities of $\log N=13.79\pm0.01$
and $\log N=13.36\pm0.01$, respectively. The comparision of theoretical
calculations of the relative fine-structure population with the ratios of the
observed column densities suggests that the \ion{C}{i} absorbing medium is
either very dense or exposed to very intense UV radiation. The upper limit on
the local UV energy density is 100 times the galactic UV energy density, while
the upper limit on the \ion{H}{i} number density is 110 cm$^{-3}$. The
excitation temperatures of the ground state fine-structure levels of $T=15.7$
and $T=11.1$ K, respectively, are consistent with the temperature-redshift
relation predicted by the standard Friedmann cosmology. The cosmic microwave
background radiation (CMBR) is only a minor source of the observed
fine-structure excitation.",0203086v1
2005-11-07,Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps,"Two-component Fermi gases with tunable repulsive or attractive interactions
inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest
laboratory realizations of strongly correlated Luttiger and Luther-Emery
liquids under confinement. We present a microscopic Kohn-Sham
density-functional theory of these systems, with specific attention to a gas on
the approach to a confinement-induced Feshbach resonance. The theory employs
the one-dimensional Gaudin-Yang model as the reference system and transfers the
appropriate Q1D ground-state correlations to the confined inhomogeneous gas
{\it via} a suitable local-density approximation to the exchange and
correlation energy functional. Quantitative understanding of the role of the
interactions in the bulk shell structure of the axial density profile is
thereby achieved. While repulsive intercomponent interactions depress the
amplitude of the shell structure of the noninteracting gas, attractive
interactions stabilize atomic-density waves through spin pairing. These should
be clearly observable in atomic clouds containing of the order of up to a
hundred atoms.",0511158v1
2007-03-07,Effects of diagonal disorder on Charge Density Wave and Superconductivity in local pair systems,"We analyse the influence of diagonal disorder (random site energy) on Charge
Density Wave (CDW) and Superconductivity (SS) in local pair systems which are
described by the model of hard core charged bosons on a lattice. This problem
was previously studied within the mean field approximation for the case of half
filled band (n = 1). Here we extend that investigation to the case of arbitrary
particle concentration (0 < n < 2) and examine the phase diagrams of the model
and the behaviour of superfluid density as a function of n and the increasing
disorder. Depending on the strength of random on-site energies, the intersite
density-density repulsion and the concentration the model can exhibit several
various phases, including homogeneous phases: CDW, SS and Bose-glass (NO) as
well as the phase separated states: CDW-SS, CDW-NO and particle droplets. The
obtained results for SS phase are in qualitative agreement with the available
Monte Carlo calculations for two dimensional lattice. Also, in a definite range
of parameters the system exhibits the phenomena which we call a disorder
induced superconductivity and a disorder induced charge ordering.",0703180v1
2004-01-08,Spectra and waiting-time densities in firing resonant and nonresonant neurons,"The response of a neural cell to an external stimulus can follow one of the
two patterns: Nonresonant neurons monotonously relax to the resting state after
excitation while resonant ones show subthreshold oscillations. We investigate
how do these subthreshold properties of neurons affect their suprathreshold
response. Vice versa we ask: Can we distinguish between both types of neuronal
dynamics using suprathreshold spike trains? The dynamics of neurons is given by
stochastic FitzHugh-Nagumo and Morris-Lecar models with either having a focus
or a node as the stable fixpoint. We determine numerically the spectral power
density as well as the interspike interval density in response to a random
(noise-like) signals. We show that the information about the type of dynamics
obtained from power spectra is of limited validity. In contrast, the interspike
interval density gives a very sensitive instrument for the diagnostics of
whether the dynamics has resonant or nonresonant properties. For the latter
value we formulate a fit formula and use it to reconstruct theoretically the
spectral power density, which coincides with the numerically obtained spectra.
We underline that the renewal theory is applicable to analysis of
suprathreshold responses even of resonant neurons.",0401013v2
2007-08-15,Alignment and Precession of a Black Hole with a Warped Accretion Disc,"We consider the shape of an accretion disc whose outer regions are misaligned
with the spin axis of a central black hole and calculate the steady state form
of the warped disc in the case where the viscosity and surface densities are
power laws in the distance from the central black hole. We discuss the shape of
the resulting disc in both the frame of the black hole and that of the outer
disc. We note that some parts of the disc and also any companion star maybe
shadowed from the central regions by the warp. We compute the torque on the
black hole caused by the Lense-Thirring precession and hence compute the
alignment and precession timescales. We generalise the case with viscosity and
hence surface density independent of radius to more realistic density
distributions for which the surface density is a decreasing function of radius.
We find that the alignment timescale does not change greatly but the precession
timescale is more sensitive. We also determine the effect on this timescale if
we truncate the disc. For a given truncation radius, the the timescales are
less affected for more sharply falling density distributions.",0708.2034v1
2012-10-15,Ground state properties and excitation spectrum of a two dimensional gas of bosonic dipoles,"We present a quantum Monte Carlo study of two-dimensional dipolar Bose gases
in the limit of zero temperature. The analysis is mainly focused on the
anisotropy effects induced in the homogeneous gas when the polarization angle
with respect to the plane is changed. We restrict our study to the regime where
the dipolar interaction is strictly repulsive, although the strength of the
pair repulsion depends on the vector interparticle distance. Our results show
that the effect of the anisotropy in the energy per particle scales with the
gas parameter at low densities as expected, and that this scaling is preserved
for all polarization angles even at the largest densities considered here. We
also evaluate the excitation spectrum of the dipolar Bose gas in the context of
the Feynman approximation and compare the results obtained with the Bogoliubov
ones. As expected, we find that these two approximations agree at very low
densities, while they start to deviate from each other as the density
increases. For the largest densities studied, we observe a significant
influence of the anisotropy of the dipole-dipole interaction in the excitation
spectrum.",1210.3969v1
2016-06-09,Out of equilibrium density dynamics of a quenched fermionic system,"Using a Luttinger liquid theory we investigate the time evolution of the
particle density of a one-dimensional fermionic system with open boundaries and
subject to a finite duration quench of the inter-particle interaction. We
provide analytical and asymptotic solutions to the unitary time evolution of
the system, showing that both switching on and switching off the quench ramp
create light-cone perturbations in the density. The post-quench dynamics is
strongly affected by the interference between these two perturbations. In
particular, we find that the discrepancy between the time-dependent density and
the one obtained by a generalized Gibbs ensemble picture vanishes with an
oscillatory behavior as a function of the quench duration, with local minima
corresponding to a perfect overlap of the two light-cone perturbations. For
adiabatic quenches, we also obtain a similar behavior in the approach of the
generalized Gibbs ensemble density towards the one associated with the ground
state of the final Hamiltonian.",1606.02997v1
2016-10-01,Current-Density Functional Theory for the superconductor,"We present the current-density functional theory for the superconductor
immersed in the magnetic field. The order parameter of the superconducting
state, transverse component of the paramagnetic current-density, and electron
density are chosen as basic variables that uniquely determine the equilibrium
properties of the system. In order to construct this theory, the development of
the approximate form of the exchange-correlation (xc) energy functional is
indispensable as well as the derivation of the effective single-particle
equation which makes it possible to reproduce the equilibrium densities
mentioned above. The rigorous expression of the xc-energy functional is derived
using the technique of the coupling-constant integration. Furthermore, the
approximate form of the xc energy functional is proposed such that the energy
gap resulting from the effective single-particle equation is consistent with
the attractive interaction energy of the system.",1610.00109v1
2016-10-18,The Density-Potential Mapping in Quantum Dynamics,"This work studies in detail the possibility of defining a one-to-one mapping
from charge densities as obtained by the time-dependent Schr\""odinger equation
to external potentials. Such a mapping is provided by the Runge-Gross theorem
and lies at the very core of time-dependent density functional theory. After
introducing the necessary mathematical concepts, the usual mapping ""there"" -
from potentials to wave functions as solutions to the Schr\""odinger equation -
is revisited paying special attention to Sobolev regularity. This is
scrutinised further when the question of functional differentiability of the
solution with respect to the potential arises, a concept related to linear
response theory. Finally, after a brief introduction to general density
functional theory, the mapping ""back again"" - from densities to potentials
thereby inverting the Schr\""odinger equation for a fixed initial state - is
defined. Apart from utilising the original Runge-Gross proof this is achieved
through a fixed-point procedure. Both approaches give rise to mathematical
issues, previously unresolved, which however could be dealt with to some extent
within the framework at hand.",1610.05552v1
2018-04-19,Primordial Mass and Density Segregation in a Young Molecular Cloud,"We analyse the geometry of the Pipe Nebula, drawn by the distribution
($Q$-spatial parameter) and hierarchy ($\Lambda$ spatial segregation) of column
density peaks previously detected and catalogued. By analysing the mass and
volume density of the cores, we determine that both variables shown to be
spatially segregated and with a high degree of substructure. Given the early
evolutionary state of the Pipe Nebula, our results suggest that both, mass and
volume-density segregations, may be primordial, in the sense of appearing in
the early phases of the chain of physical mechanisms which conform the
cluster-formation process. We also propose that volume density, and not mass,
is the parameter that most clearly determines the initial spatial distribution
of pre-stellar cores.",1804.06961v1
2020-07-07,Hierarchical nucleation in deep neural networks,"Deep convolutional networks (DCNs) learn meaningful representations where
data that share the same abstract characteristics are positioned closer and
closer. Understanding these representations and how they are generated is of
unquestioned practical and theoretical interest. In this work we study the
evolution of the probability density of the ImageNet dataset across the hidden
layers in some state-of-the-art DCNs. We find that the initial layers generate
a unimodal probability density getting rid of any structure irrelevant for
classification. In subsequent layers density peaks arise in a hierarchical
fashion that mirrors the semantic hierarchy of the concepts. Density peaks
corresponding to single categories appear only close to the output and via a
very sharp transition which resembles the nucleation process of a heterogeneous
liquid. This process leaves a footprint in the probability density of the
output layer where the topography of the peaks allows reconstructing the
semantic relationships of the categories.",2007.03506v2
2019-02-27,Establishing the Dark Matter Relic Density in an Era of Particle Decays,"If the early universe is dominated by an energy density which evolves other
than radiation-like the normal Hubble-temperature relation $H\propto T^2$ is
broken and dark matter relic density calculations in this era can be
significantly different. We first highlight that for a population of states
$\phi$ sourcing an initial expansion rate of the form $H\propto T^{2+n/2}$ for
$n\geq-4$, during the period of appreciable $\phi$ decays the evolution
transitions to $H\propto T^4$. The decays of $\phi$ imply a source of entropy
production in the thermal bath which alters the Boltzmann equations and impacts
the dark matter relic abundance. We show that the form of the initial expansion
rate leaves a lasting imprint on relic densities established while $H\propto
T^4$ since the value of the exponent $n$ changes the temperature evolution of
the thermal bath. In particular, a dark matter relic density set via freeze-in
or non-thermal production is highly sensitive to the temperature dependance of
the initial expansion rate. This work generalises earlier studies which assumed
initial expansion rates due to matter or kination domination.",1902.10746v2
2019-07-08,Metric Cartesian mechanics of nonlocal energies with tensor internal tensions modifies Navier-Stokes dynamics,"We introduce the gauge-invariant vector dynamics of continuous inertial
densities through the metric formalism for extended mechanical charges. Ricci
scalar density is related to invariant sum of inertial and gravitational mass
densities of nonlocal matter-extension. Such a Cartesian continuum of
gravitating inertial densities is self-governed by internal tensor tensions
toward a static equilibrium state with a Euclidean material 3-space under the
equivalence of inertial and gravitational densities of extended masses.
External forces and local frictions transform the self-dynamics of an
elementary closed continuum into a forced motion of still adaptive energy
flows, where high-order space-time derivatives can provide non-Newtonian
self-accelerations. If such tensor inertial feedback with the inverse constant
of Cavendish 1/G is justified by measurements for the modified Navier-Stokes
equation, the Newton empty space model should be replaced by the Cartesian
matter-extension for the non-local macroscopic world.",1907.03580v1
2023-01-28,Towards a liquid-state theory for active matter,"In equilibrium, the collective behaviour of particles interacting via steep,
short-ranged potentials is well captured by the virial expansion of the free
energy at low density. Here, we extend this approach beyond equilibrium to the
case of active matter with self-propelled particles. Given that active systems
do not admit any free-energy description in general, our aim is to build the
dynamics of the coarse-grained density from first principles without any
equilibrium assumption. Starting from microscopic equations of motion, we
obtain the hierarchy of density correlations, which we close with an ansatz for
the two-point density valid in the dilute regime at small activity. This
closure yields the nonlinear dynamics of the one-point density, with
hydrodynamic coefficients depending explicitly on microscopic interactions, by
analogy with the equilibrium virial expansion. This dynamics admits a spinodal
instability for purely repulsive interactions, a signature of motility-induced
phase separation. Therefore, although our approach should be restricted to
dilute, weakly-active systems a priori, it actually captures the features of a
broader class of active matter.",2301.12155v2
2023-07-21,Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory,"The phenomena of superconductivity and charge density waves are observed in
close vicinity in many strongly correlated materials. Increasing evidence from
experiments and numerical simulations suggests both phenomena can also occur in
an intertwined manner, where the superconducting order parameter is coupled to
the electronic density. Employing density matrix renormalization group
simulations, we investigate the nature of such an intertwined state of matter
stabilized in the phase diagram of the elementary $t$-$t^\prime$-$U$ Hubbard
model in the strong coupling regime. Remarkably, the condensate of Cooper pairs
is shown to be fragmented in the presence of a charge density wave where more
than one pairing wave function is macroscopically occupied. Moreover, we
provide conclusive evidence that the macroscopic wave functions of the
superconducting fragments are well-described by soliton solutions of a
Ginzburg-Landau equation in a periodic potential constituted by the charge
density wave. In the presence of an orbital magnetic field, the order
parameters are gauge invariant, and superconducting vortices are pinned between
the stripes. This intertwined Ginzburg-Landau theory is proposed as an
effective low-energy description of the stripe fragmented superconductor.",2307.11820v1
2004-08-16,A model of phase fluctuations in a lattice d-wave superconductor: application to the Cooper pair charge-density-wave in underdoped cuprates,"We introduce and study an XY-type model of thermal and quantum phase
fluctuations in a two-dimensional correlated lattice d-wave superconductor
based on the QED3 effective theory of high temperature superconductors. General
features of and selected results obtained within this model were reported
earlier in an abbreviated format (Z. Tesanovic, cond-mat/0405235). The model is
geared toward describing not only the long distance but also the intermediate
lengthscale physics of underdoped cuprates. In particular, we elucidate the
dynamical origin and investigate specific features of the Cooper pair
charge-density-wave (CPCDW), which we argue is the state behind the periodic
charge density modulation discovered in recent STM experiments. We illustrate
how Mott-Hubbard correlations near half-filling suppress superfluid density and
favor an incompressible state which breaks translational symmetry of the atomic
lattice. We show how the formation of the CPCDW in such a strongly quantum
fluctuating superconductor can be understood as an Abrikosov-Hofstadter problem
in a type-II dual superconductor, with the role of the dual magnetic field
played by the electron density. The resulting Abrikosov lattice of dual
vortices translates into the periodic modulation of the Bogoliubov-deGennes gap
function and the electronic density. We compute detailed signatures of various
Abrikosov-Hofstadter dual vortex arrays in the single-particle local tunneling
density of states. A 4x4 checkerboard-type modulation pattern naturally arises
as an energetically favored ground state at and near the x = 1/8 doping and
produces good agreement with experimental observations.",0408344v4
2007-04-05,A density tensor hierarchy for open system dynamics: retrieving the noise,"We introduce a density tensor hierarchy for open system dynamics, that
recovers information about fluctuations lost in passing to the reduced density
matrix. For the case of fluctuations arising from a classical probability
distribution, the hierarchy is formed from expectations of products of pure
state density matrix elements, and can be compactly summarized by a simple
generating function. For the case of quantum fluctuations arising when a
quantum system interacts with a quantum environment in an overall pure state,
the corresponding hierarchy is defined as the environmental trace of products
of system matrix elements of the full density matrix. Only the lowest member of
the quantum noise hierarchy is directly experimentally measurable. The unit
trace and idempotence properties of the pure state density matrix imply descent
relations for the tensor hierarchies, that relate the order $n$ tensor, under
contraction of appropriate pairs of tensor indices, to the order $n-1$ tensor.
As examples to illustrate the classical probability distribution formalism, we
consider a quantum system evolving by It\^o stochastic and by jump process
Schr\""odinger equations. As examples to illustrate the corresponding trace
formalism in the quantum fluctuation case, we consider collisional Brownian
motion of an infinite mass Brownian particle, and the weak coupling Born-Markov
master equation. In different specializations, the latter gives the hierarchies
generalizing the quantum optical master equation and the Caldeira--Leggett
master equation. As a further application of the density tensor, we contrast
stochastic Schr\""odinger equations that reduce and that do not reduce the state
vector, and discuss why a quantum system coupled to a quantum environment
behaves like the latter.",0704.0796v4
2022-09-23,Accreting neutron stars from the nuclear energy-density functional theory. II. Equation of state and global properties,"The accretion of matter onto the surface of a neutron star in a low-mass
X-ray binary triggers X-ray bursts, whose ashes are buried and further
processed thus altering the composition and the properties of the stellar
crust. In this second paper of a series, the impact of accretion on the
equation of state and on the global properties of neutron stars is studied in
the framework of the nuclear energy-density functional theory. Considering
ashes made of $^{56}$Fe, we calculated the equations of state using the same
Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21,
as those already employed for determining the crustal heating in our previous
study for the same ashes. All regions of accreting neutron stars were treated
in a unified and thermodynamically consistent way. With these equations of
state, we determined the mass, radius, moment of inertia, and tidal
deformability of accreted neutron stars and compared with catalyzed neutron
stars for which unified equations of state based on the same functionals are
available. The equation of state of accreted neutron stars is found to be
significantly stiffer than that of catalyzed matter, with an adiabatic index
$\Gamma \approx 4/3$ throughout the crust. For this reason, accreting neutron
stars have larger radii. However, their crustal moment of inertia and their
tidal deformability are hardly changed provided density discontinuities at the
interface between adjacent crustal layers are properly taken into account. The
enhancement of the stiffness of the equation of state of accreting neutron
stars is mainly a consequence of nuclear shell effects, thus confirming the
importance of a quantum treatment as stressed in our first study. With our
previous calculations of crustal heating using the same functionals, we have
thus obtained consistent microscopic inputs for simulations of accreting
neutron stars.",2209.11457v1
2000-06-24,Resolving the Structure of Cold Dark Matter Halos II,"We study the effects of mass and force resolution on the density profiles of
galaxy-size Cold Dark Matter (CDM) halos in a flat, low-density cosmological
model with vacuum energy. We show thatalthough increasing the mass and force
resolution allows us to probe deeper into the inner halo regions, it does not
lead to steeper inner density profiles. Instead, the halo profiles converge at
scales larger than four times the formal resolution or the radius containing
more than 200 particles, whichever is larger. In the simulations presented in
this paper, we are able to probe density profile of a relaxed isolated
galaxy-size halo at scales r=(0.005-1)r_vir. We find that the density
distribution can be well approximated by the profile suggested by Moore etal
(1998): rho= x^{-1.5}(1+x^{1.5})^-1, where x=r/r_s and r_s is the
characteristic radius. The analytical profile proposed by Navarro et al. (1996)
rho= x^{-1}(1+x)^-2, also provides a good fit, with the same relative errors of
about 10% for radii larger than 1% of the virial radius. Both analytical
profiles fit equally well because for high-concentration galaxy-size halos the
differences between these profiles become significant only at scales well below
0.01r_vir. We also find that halos of similar mass may have somewhat different
parameters (characteristic radius, maximum rotation velocity, etc.) and shapes
of their density profiles. We associate this scatter in properties with
differences in halo merger histories and the amount of substructure present in
the analyzed halos.",0006343v2
2021-11-10,Magnetic fields in star formation: a complete compilation of all the DCF estimations,"The Davis-Chandrasekhar-Fermi (DCF) method provides an indirect way to
estimate the magnetic field strength from statistics of magnetic field
orientations. We compile all the previous DCF estimations from polarized dust
emission observations and re-calculate the magnetic field strength of the
selected samples with the new DCF correction factors in Liu et al. (2021). We
find the magnetic field scales with the volume density as $B \propto n^{0.57}$.
However, the estimated power-law index of the observed $B-n$ relation has large
uncertainties and may not be comparable to the $B-n$ relation of theoretical
models. A clear trend of decreasing magnetic viral parameter (i.e., increasing
mass-to-flux ratio in units of critical value) with increasing column density
is found in the sample, which suggests the magnetic field dominates the gravity
at lower densities but cannot compete with the gravity at higher densities.
This finding also indicates that the magnetic flux is dissipated at higher
column densities due to ambipolar diffusion or magnetic recennection, and the
accumulation of mass at higher densities may be by mass flows along the
magnetic field lines. Both sub-Alfv\'{e}nic and super-Alfv\'{e}nic states are
found in the sample, with the average state being approximately
trans-Alfv\'{e}nic.",2111.05836v2
2022-11-03,Spin-orbit and exchange proximity couplings in graphene/1T-TaS$_2$ heterostructure triggered by a charge density wave,"Proximity-induced fine features and spin-textures of the electronic bands in
graphene-based van der Waals heterostructures can be explored from the point of
tailoring a twist angle. Here we study spin-orbit coupling and exchange
coupling engineering of graphene states in the proximity of 1T-TaS$_2$ not
triggering the twist, but a charge density wave in 1T-TaS$_2$-a realistic
low-temperature phase. Using density functional theory and effective model we
found that the emergence of the charge density wave in 1T-TaS$_2$ significantly
enhances Rashba spin-orbit splitting in graphene and tilts the spin texture by
a significant Rashba angle-in a very similar way as in the conventional
twist-angle scenarios. Moreover, the partially filled Ta $d$-band in the charge
density wave phase leads to the spontaneous emergence of the in-plane magnetic
order that transgresses via proximity from 1T-TaS$_2$ to graphene, hence,
simultaneously superimposing along the spin-orbit also the exchange coupling
proximity effect. To describe this intricate proximity landscape we have
developed an effective model Hamiltonian and provided a minimal set of
parameters that excellently reproduces all the spectral features predicted by
the first-principles calculations. Conceptually, the charge density wave
provides a highly interesting knob to control the fine features of electronic
states and to tailor the superimposed proximity effects-a sort of twistronics
without twist.",2211.02153v2
2023-05-05,Single-particle-exact density functional theory,"We introduce 'single-particle-exact density functional theory' (1pEx-DFT), a
novel density functional approach that represents all single-particle
contributions to the energy with exact functionals. Here, we parameterize
interaction energy functionals by utilizing two new schemes for constructing
density matrices from 'participation numbers' of the single-particle states of
quantum many-body systems. These participation numbers play the role of the
variational variables akin to the particle densities in standard orbital-free
density functional theory. We minimize the total energies with the help of
evolutionary algorithms and obtain ground-state energies that are typically
accurate at the one-percent level for our proof-of-principle simulations that
comprise interacting Fermi gases as well as the electronic structure of atoms
and ions, with and without relativistic corrections. We thereby illustrate the
ingredients and practical features of 1pEx-DFT and reveal its potential of
becoming an accurate, scalable, and transferable technology for simulating
mesoscopic quantum many-body systems.",2305.03233v2
2021-09-15,Charge density wave breakdown in a heterostructure with electron-phonon coupling,"Understanding the influence of vibrational degrees of freedom on transport
through a heterostructure poses considerable theoretical and numerical
challenges. In this work, we use the density-matrix renormalization group
(DMRG) method together with local basis optimization (LBO) to study the
half-filled Holstein model in the presence of a linear potential, either
isolated or coupled to tight-binding leads. In both cases, we observe a decay
of charge-density-wave (CDW) states at a sufficiently strong potential
strength. Local basis optimization selects the most important linear
combinations of local oscillator states to span the local phonon space. These
states are referred to as optimal modes. We show that many of these local
optimal modes are needed to capture the dynamics of the decay, that the most
significant optimal mode on the initially occupied sites remains well described
by a coherent-state typical for small polarons, and that those on the initially
empty sites deviate from the coherent-state form. Additionally, we compute the
current through the structure in the metallic regime as a function of voltage.
For small voltages, we reproduce results for the Luttinger parameters. As the
voltage is increased, the effect of larger electron-phonon coupling strengths
becomes prominent. Further, the most significant optimal mode remains almost
unchanged when going from the ground state to the current-carrying state in the
metallic regime.",2109.07197v2
2019-12-16,Alpha-particle condensation: a nuclear quantum phase transition,"When the density of a nuclear system is decreased, homogeneous states undergo
the so-called Mott transition towards clusterised states, e.g. alpha
clustering, both in nuclei and in nuclear matter. Here we investigate such a
quantum phase transition (QPT) by using microscopic energy density functional
(EDF) calculations both with the relativistic and the Gogny approaches on the
diluted $^{16}$O nucleus. The evolution of the corresponding single-particle
spectrum under dilution is studied, and a Mott-like transition is predicted at
about 1/3 of the saturation density. Complementary approaches are used in order
to understand this QPT. A study of spatial localisation properties as a
function of the density allows to derive a value of the Mott density in
agreement with the one obtained by fully microscopic calculations in $^{16}$O
and in nuclear matter. Moreover a study of the spontaneous symmetry breaking of
the rotational group in $^{16}$O, down to the discrete tetrahedral one,
provides further insight on the features displayed by the single-particle
spectrum obtained within the EDF approach.The content of the tetrahedrally
deformed A-nucleon product state in terms of spherical particle-hole
configurations is investigated. Finally a study of quartet condensation and the
corresponding macroscopic QPT is undertaken in infinite matter.",1912.07318v1
2022-01-01,"First-principles insights into the mechanical, optoelectronic, thermophysical, and lattice dynamical properties of binary topological semimetal BaGa2","In the present study we have investigated the structural properties,
electronic band dispersion, elastic constants, acoustic behavior, phonon
spectrum, optical properties, and a number of thermophysical parameters of
binary topological semimetal BaGa2 in details via first-principles calculations
using the density functional theory (DFT) based formalisms. The electronic band
structure and density of states calculations with spin orbit coupling reveal
semimetallic nature with clear topological signature. The minimum thermal
conductivities and anisotropies of the compound are calculated. The elastic
constants, phonon dispersion calculations show that the compound under study is
both mechanically and dynamically stable. Comprehensive study of elastic
constants and moduli shows that BaGa2 possesses fairly isotropic mechanical
properties, reasonably good machinability, low Debye temperature and melting
point. The chemical bonding in BaG2 is interpreted via the electronic energy
density of states, electron density distribution, elastic properties and
Mulliken bond population analysis. The compound possesses both ionic and
covalent bondings. The reflectivity spectra show strong anisotropy with respect
to polarization of the incident electric field in the visible to
mid-ultraviolet regions. High reflectivity over wide spectral range makes BaGa2
suitable as a reflecting material. BaGa2 is also an efficient absorber of
ultraviolet radiation. Furthermore, the refractive index is quite high in the
infrared to visible range. All the energy dependent optical parameters show
metallic features and are in complete accord with the underlying bulk
electronic density of states calculations. Most of the results presented in
this study are novel and should serve as useful reference for future study.",2201.00172v1
1997-03-17,Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics,"Density-functional theory is applied to compute the ground-state energies of
quantum hard-sphere solids. The modified weighted-density approximation is used
to map both the Bose and the Fermi solid onto a corresponding uniform Bose
liquid, assuming negligible exchange for the Fermi solid. The required
liquid-state input data are obtained from a paired phonon analysis and the
Feynman approximation, connecting the static structure factor and the linear
response function. The Fermi liquid is treated by the Wu-Feenberg cluster
expansion, which approximately accounts for the effects of antisymmetry.
Liquid-solid transitions for both systems are obtained with no adjustment of
input data. Limited quantitative agreement with simulation indicates a need for
further improvement of the liquid-state input through practical alternatives to
the Feynman approximation.",9703165v1
2004-12-21,Energy lowering of current-carrying single-particle states in open-shell atoms due to an exchange-correlation vector potential,"Current-density-functional theory is used to perturbatively calculate
single-particle energies of open-shell atoms prepared in a current-carrying
state. We focus on the highest occupied such energy, because its negative is,
in principle, the exact ionization energy. A variety of different density
functionals and calculational schemes are compared with each other and
experiment. When the atom is prepared in a current-carrying state, a
current-dependent exchange-correlation functional is found to slightly lower
the single-particle energy of the current-carrying orbital, as compared to a
calculation using standard (current independent) density functionals for the
same system. The current-dependent terms in the exchange-correlation functional
thus provide additional stabilization of the current-carrying state.",0412133v1
2007-08-19,Quantum Energy Inequalities for the Non-Minimally Coupled Scalar Field,"In this paper we discuss local averages of the energy density for the
non-minimally coupled scalar quantum field, extending a previous investigation
of the classical field. By an explicit example, we show that such averages are
unbounded from below on the class of Hadamard states. This contrasts with the
minimally coupled field, which obeys a state-independent lower bound known as a
Quantum Energy Inequality (QEI). Nonetheless, we derive a generalised QEI for
the non-minimally coupled scalar field, in which the lower bound is permitted
to be state-dependent. This result applies to general globally hyperbolic
curved spacetimes for coupling constants in the range $0<\xi\leq 1/4$. We
analyse the state-dependence of our QEI in four-dimensional Minkowski space and
show that it is a nontrivial restriction on the averaged energy density in the
sense that the lower bound is of lower order, in energetic terms, than the
averaged energy density itself.",0708.2450v2
2008-10-22,Remarks on monopole charge properties within the Generalized Coherent State Model,"The Generalized Coherent State Model, proposed previously for a unified
description of magnetic and electric collective properties of nuclear systems,
is used to study the ground state band charge density as well as the E0
transitions from $0^+_{\beta}$ to $0^+_g$. The influence of the nuclear
deformation and of angular momentum projection on the charge density is
investigated. The monopole transition amplitude has been calculated for ten
nuclei. The results are compared with some previous theoretical studies and
with the available experimental data. Our results concerning angular momentum
projection are consistent with those of previous microscopic calculations for
the ground state density. The calculations for the E0 transitions agree quite
well with the experimental data. Issues like how the shape transitions or shape
coexistence are reflected in the $\rho(E0)$ behavior are also addressed.",0810.4073v1
2011-07-29,Electronic structure of fluorides: general trends for ground and excited state properties,"The electronic structure of fluorite crystals are studied by means of density
functional theory within the local density approximation for the exchange
correlation energy. The ground-state electronic properties, which have been
calculated for the cubic structures $CaF_{2}$,$SrF_{2}$, $BaF_{2}$, $CdF_{2}$,
$HgF_{2}$, $\beta $-$PbF_{2}$, using a plane waves expansion of the wave
functions, show good comparison with existing experimental data and previous
theoretical results. The electronic density of states at the gap region for all
the compounds and their energy-band structure have been calculated and compared
with the existing data in the literature. General trends for the ground-state
parameters, the electronic energy-bands and transition energies for all the
fluorides considered are given and discussed in details. Moreover, for the
first time results for $HgF_{2}$ have been presented.",1107.5962v1
2012-09-02,Global classical solutions to the two-dimensional compressible Navier-Stokes equations in $\mathbb{R}^2$,"In this paper, we prove the global well-posedness of the classical solution
to the 2D Cauchy problem of the compressible Navier-Stokes equations with
arbitrarily large initial data when the shear viscosity $\mu$ is a positive
constant and the bulk viscosity $\l(\r)=\r^\b$ with $\b>\frac43$. Here the
initial density keeps a non-vacuum states $\bar\rho>0$ at far fields and our
results generalize the ones by Vaigant-Kazhikhov [41] for the periodic problem
and by Jiu-Wang-Xin [26] and Huang-Li [8] for the Cauchy problem with vacuum
states $\bar\rho=0$ at far fields. It shows that the solution will not develop
the vacuum states in any finite time provided the initial density is uniformly
away from vacuum. And the results also hold true when the initial data contains
vacuum states in a subset of $\mathbb{R}^2$ and the natural compatibility
conditions are satisfied. Some new weighted estimates are obtained to establish
the upper bound of the density.",1209.0157v1
2014-07-24,Dirac-screening stabilized surface-state transport in a topological insulator,"We report magnetotransport studies on a gated strained HgTe device. This
material is a threedimensional topological insulator and exclusively shows
surface state transport. Remarkably, the Landau level dispersion and the
accuracy of the Hall quantization remain unchanged over a wide density range
($3 \times 10^{11} cm^{-2} < n < 1 \times 10^{12} cm^{-2}$). This implies that
even at large carrier densities the transport is surface state dominated, where
bulk transport would have been expected to coexist already. Moreover, the
density dependence of the Dirac-type quantum Hall effect allows to identify the
contributions from the individual surfaces. A $k \cdot p$ model can describe
the experiments, but only when assuming a steep band bending across the regions
where the topological surface states are contained. This steep potential
originates from the specific screening properties of Dirac systems and causes
the gate voltage to influence the position of the Dirac points rather than that
of the Fermi level.",1407.6537v1
2016-01-20,Electronic spin-triplet nematic with a twist,"We analyze a model of itinerant electrons interacting through a quadrupole
density-density repulsion in three dimensions. At the mean field level, the
interaction drives a continuous Pomeranchuk instability towards $d$-wave,
spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation
and spatial rotational symmetries. This order results in spin antisymmetric,
elliptical deformations of the Fermi surfaces of up and down spins. We show
that the effects of quantum fluctuations are similar to those in metallic
ferromagnets, rendering the nematic transition first-order at low temperatures.
Using the fermionic quantum order-by-disorder approach to self-consistently
calculate fluctuations around possible modulated states, we show that the
first-order transition is pre-empted by the formation of a nematic state that
is intertwined with a helical modulation in spin space. Such a state is closely
related to $d$-wave bond density wave order in square-lattice systems.
Moreover, we show that it may coexist with a modulated, $p$-wave
superconducting state.",1601.05414v2
2016-11-07,Quantum-disentangled liquid in the half-filled Hubbard model,"We investigate the existence of quantum disentangled liquid (QDL) states in
the half-filled Hubbard model on bipartite lattices. In the one dimensional
case we employ a combination of integrability and strong coupling expansion
methods to argue that there are indeed finite energy-density eigenstates that
exhibit QDL behaviour in the sense of J. Stat. Mech. P10010 (2014). The states
exhibiting the QDL property are atypical in the sense that while their entropy
density is non-zero, it is smaller than that of thermal states at the same
energy density. We argue that for U >> t these latter thermal states exhibit a
weaker form of the QDL property, which carries over to the higher dimensional
case.",1611.02075v3
2023-02-10,Charge Density Wave Order in Superconducting Topological Insulator Nbx-Bi2Se3,"Spontaneously broken symmetry in the ground state of Bi-based topological
materials can lead to promising Topological superconductors, such as Cu-Bi2Se3,
Sr-Bi2Se3 and Nb-Bi2Se3. In recent studies, coexistence of multiple Fermi
surface features and superconductivity was found in Nb-Bi2Se3. However, the
resultant mutliple Fermi surface--charge density wave has not been
experimentally reported yet. In this paper, we report possible evidence of
co-occurence of a charge density wave (CDW) ground state and a superconducting
(SC) ground state in Nb intercalated Bi2Se3. An intercalation induced Periodic
Lattice Distortion appears to help stabilize the CDW state, possibly assisting
in the formation of 1D chains and rendering electronic and phonon anisotropy to
this intriguing system.",2302.05227v1
2023-06-26,Quantum phases and spectrum of collective modes in a spin-1 BEC with spin-orbital-angular-momentum coupling,"Motivated by the recent experiments [Chen et al., Phys. Rev. Lett 121, 113204
(2018), Chen et al., Phys. Rev. Lett. 121, 250401 (2018)], we investigate the
low-lying excitation spectrum of the ground-state phases of
spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 condensates.At
vanishing detuning, a ferromagnetic SOAM-coupled spin-1 BEC can have two
ground-state phases, namely coreless and polar-core vortex states, whereas an
antiferromagnetic BEC supports only polar-core vortex solution. The angular
momentum per particle, longitudinal magnetization, and excitation frequencies
display discontinuities across the phase boundary between the coreless vortex
and polar-core vortex phases. The low-lying excitation spectrum evaluated by
solving the Bogoliubov-de-Gennes equations is marked by avoided crossings and
hence the hybridization of the spin and density channels. The spectrum is
further confirmed by the dynamical evolution of the ground state subjected to a
perturbation suitable to excite a density or a spin mode and a variational
analysis for the density-breathing mode.",2306.14669v2
2009-07-14,Violation of non-interacting $\cal V$-representability of the exact solutions of the Schrödinger equation for a two-electron quantum dot in a homogeneous magnetic field,"We have shown by using the exact solutions for the two-electron system in a
parabolic confinement and a homogeneous magnetic field [ M.Taut, J Phys.A{\bf
27}, 1045 (1994) ] that both exact densities (charge- and the paramagnetic
current density) can be non-interacting $\cal V$-representable (NIVR) only in a
few special cases, or equivalently, that an exact Kohn-Sham (KS) system does
not always exist. All those states at non-zero $B$ can be NIVR, which are
continuously connected to the singlet or triplet ground states at B=0. In more
detail, for singlets (total orbital angular momentum $M_L$ is even) both
densities can be NIVR if the vorticity of the exact solution vanishes. For
$M_L=0$ this is trivially guaranteed because the paramagnetic current density
vanishes. The vorticity based on the exact solutions for the higher $|M_L|$
does not vanish, in particular for small r. In the limit $r \to 0$ this can
even be shown analytically. For triplets ($M_L$ is odd) and if we assume
circular symmetry for the KS system (the same symmetry as the real system) then
only the exact states with $|M_L|= 1$ can be NIVR with KS states having angular
momenta $m_1=0$ and $|m_2|=1$. Without specification of the symmetry of the KS
system the condition for NIVR is that the small-r-exponents of the KS states
are 0 and 1.",0907.2383v1
2017-06-05,Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States,"Study of an N qubit mixed symmetric separable states is a long standing
challenging problem as there exist no unique separability criterion. In this
regard, we take up the N-qubit mixed symmetric separable states for a detailed
study as these states are of experimental importance and offer elegant
mathematical analysis since the dimension of the Hilbert space reduces from 2^N
to N + 1. Since there exists a one to one correspondence between spin-j system
and an N-qubit symmetric state, we employ Fano statistical tensor parameters
for the parametrization of spin density matrix. Further, we use geometric
multiaxial representation(MAR) of density matrix to characterize the mixed
symmetric separable states. Since separability problem is NP hard, we choose to
study it in the continuum limit where mixed symmetric separable states are
characterized by the P-distribution function \lambda(\theta; \phi). We show
that the N-qubit mixed symmetric separable state can be visualized as a
uniaxial system if the distribution function is independent of \theta and \phi.
We further choose distribution function to be the most general positive
function on a sphere and observe that the statistical tensor parameters
characterizing the N-qubit symmetric system are the expansion coefficients of
the distribution function. As an example for the discrete case, we investigate
the MAR of a uniformly weighted two qubit mixed symmetric separable state. We
also observe that there exists a correspondence between separability and
classicality of states.",1706.01198v1
2022-10-03,Exploring postselection-induced quantum phenomena with time-bidirectional state formalism,"Here we present the time-bidirectional state formalism (TBSF) unifying in a
general manner the standard quantum mechanical formalism with no postselection
and the time-symmetrized two-state (density) vector formalism, which deals with
postselected states. In the proposed approach, a quantum particle's state,
called a time-bidirectional state, is equivalent to a joined state of two
particles propagating in opposite time directions. For a general
time-bidirectional state, we derive outcome probabilities of generalized
measurements, as well as mean and weak values of Hermitian observables. We also
show how the obtained expressions reduce to known ones in the special cases of
no postselection and generalized two-state (density) vectors. Then we develop
tomography protocols based on mutually unbiased bases and a symmetric
informationally complete positive operator-valued measure, allowing
experimental reconstruction of an unknown single qubit time-bidirectional
state. Finally, we employ the developed techniques for tracking of a qubit's
time-reversal journey in a quantum teleportation protocol realized with a
cloud-accessible noisy superconducting quantum processor. The obtained results
justify an existence of a postselection-induced qubit's proper time-arrow,
which is different from the time-arrow of a classical observer, and demonstrate
capabilities of the TBSF for exploring quantum phenomena brought forth by a
postselection in the presence of noise.",2210.01583v2
2006-08-31,The Integrated Density of States for Random Schroedinger Operators,"We survey some aspects of the theory of the integrated density of states
(IDS) of random Schroedinger operators. The first part motivates the problem
and introduces the relevant models as well as quantities of interest. The proof
of the existence of this interesting quantity, the IDS, is discussed in the
second section. One central topic of this survey is the asymptotic behavior of
the integrated density of states at the boundary of the spectrum. In
particular, we are interested in Lifshitz tails and the occurrence of a
classical and a quantum regime. In the last section we discuss regularity
properties of the IDS. Our emphasis is on the discussion of fundamental
problems and central ideas to handle them. Finally, we discuss further
developments and problems of current research.",0608066v1
2010-04-06,Anion height dependence of Tc and density of states in iron based superconductors,"Systematic ab initio LDA calculations were performed for all the typical
representatives of recently discovered class of iron based high-temperature
superconductors: REOFe(As,P) (RE=La,Ce,Nd,Sm,Tb), Ba2Fe2As, (Sr,Ca)FFeAs,
Sr4Sc2O6Fe2P2, LiFeAs and Fe(Se,Te). Non-monotonic behavior of total density of
states at the Fermi level is observed as a function of anion height relative to
Fe layer with maximum at about Dz_a~1.37A, attributed to changing Fe - As
(P,Se,Te) hybridization. This leads to a similar dependence of superconducting
transition temperature Tc as observed in the experiments. The fit of this
dependence to elementary BCS theory produces semiquantitative agreement with
experimental data for Tc for the whole class of iron based superconductors. The
similar fit to Allen - Dynes formula underestimates Tc in the vicinity of the
maximum, signifying the possible importance of non - phonon pairing in this
region. These results unambiguously demonstrate that the main effect of Tc
variation between different types of iron based superconductors is due to the
corresponding variation of the density of states at the Fermi level.",1004.0801v1
2015-07-15,Energy dependence of localization with interactions and disorder: The generalized inverse participation ratio of an ensemble of two-site Anderson-Hubbard systems,"After Anderson's prediction of disorder-induced insulating behavior,
extensive work found no singularities in the density of states of localized
systems. However, Johri and Bhatt recently uncovered the existence of a
non-analyticity in the density of states near the band edge of non-interacting
systems with bounded disorder, in an energy range outside that captured by
previous work. Moreover, this feature marks the boundary of an energy range in
which the localization is sharply suppressed. Given strong current interest in
the effect of interactions on disordered systems, we explore here the effect of
a Hubbard $U$ interaction on this behavior. We find that in ensembles of small
systems a cusp in the density of states persists and continues to be associated
with a sharp suppression of the localization. We explore the origins of this
behavior and discuss its connection with many-body localization.",1507.04289v1
2018-10-31,The density of states of 1D random band matrices via a supersymmetric transfer operator,"Recently, T. and M. Shcherbina proved a pointwise semicircle law for the
density of states of one-dimensional Gaussian band matrices of large bandwidth.
The main step of their proof is a new method to study the spectral properties
of non-self-adjoint operators in the semiclassical regime. The method is
applied to a transfer operator constructed from the supersymmetric integral
representation for the density of states.
  We present a simpler proof of a slightly upgraded version of the semicircle
law, which requires only standard semiclassical arguments and some peculiar
elementary computations. The simplification is due to the use of supersymmetry,
which manifests itself in the commutation between the transfer operator and a
family of transformations of superspace, and was applied earlier in the context
of band matrices by Constantinescu. Other versions of this supersymmetry have
been a crucial ingredient in the study of the localization--delocalization
transition by theoretical physicists.",1810.13150v2
2019-08-08,"The Pauli and $\text{Lévy-Leblond}$ Equations, and the Spin Current Density","We review the literature on the Pauli equation and its current density,
discussing the progression from the original phenomenological version of Pauli
to its derivation by $\text{L\'{e}vy-Leblond}$ from a linearization of the
$\text{Schr\""{o}dinger}$ equation. It was established conclusively by
$\text{L\'{e}vy-Leblond}$'s work that the spin of a spin-1/2 particle such as
an electron is non-relativistic in nature, contrary to what was often stated
following Dirac's derivation of a relativistic wave equation, and his
subsequent demonstration that Pauli's spin interaction term appeared in the
non-relativistic limit. In this limit, the Gordon decomposition of the
associated probability current density was found to contain a spin-dependent
term. Such a term does not follow, however, from the usual derivation of the
current density from the Pauli equation, although various physically motivated
but otherwise ad hoc explanations were put forward to account for it. We
comment on the only exception to these of which we are aware implying the spin
term in the current was in fact non-relativistic in nature. However, the
earlier work of $\text{L\'{e}vy-Leblond}$ had already shown, with no additional
assumptions, that this term was a prominent feature of the current density
derived from his equation. Hence, just as with the spin itself, the spin
current was non-relativistic, claims to the contrary notwithstanding. We
present a somewhat simplified derivation of the $\text{L\'{e}vy-Leblond}$
equation and its current density, commenting on possibilities for experimental
work that might indicate measurable consequences of the spin term in the
current density.",1908.03276v2
2015-11-04,The power of being positive: Robust state estimation made possible by quantum mechanics,"We study the problem of quantum-state tomography under the assumption that
the state of the system is close to pure. In this context, an efficient
measurements that one typically formulates uniquely identify a pure state from
within the set of other pure states. In general such measurements are not
robust in the presence of measurement noise and other imperfections, and
therefore are less practical for tomography. We argue here that state
tomography experiments should instead be done using measurements that can
distinguish a pure state from {\em any} other quantum state, of any rank. We
show that such nontrivial measurements follows from the physical constraint
that the density matrix is positive semidefinite and prove that these
measurements yield a robust estimation of the state. We assert that one can
implement such tomography relatively simply by measuring only a few random
orthonormal bases; our conjecture is supported by numerical evidence. These
results are generalized for estimation of states close to bounded-rank.",1511.01433v2
2024-01-26,Concurrence distribution in excited states of the 1D spin-1/2 transverse field XY model: two different regions,"We investigate the variation of concurrence in a spin-1/2 transverse field XY
chain system in an excited state. Initially, we precisely solve the eigenvalue
problem of the system Hamiltonian using the fermionization technique.
Subsequently, we calculate the concurrence between nearest-neighbor pairs of
spins in all excited states with higher energy than the ground state. Below the
factorized field, denoted as $h_f=\sqrt{J^2-(J \delta)^2}$, we find no pairwise
entanglement between nearest neighbors in excited states. At the factorized
field, corresponding to a factorized state, we observe weak concurrence in very
low energy states. Beyond $h_f$, the concurrence strengthens, entangling all
excited states. The density of entangled states peaks at the center of the
excited spectrum. Additionally, the distribution of concurrence reveals that
the midpoint of the non-zero concurrence range harbors the most entangled
excited states.",2401.15057v1
1996-01-05,Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field,"We develop a method to compute shakeup effects on photoluminescence from a
strong magnetic field induced two-dimensional Wigner crystal. Only localized
holes are considered. Our method treats the lattice electrons and the tunneling
electron on an equal footing, and uses a quantum-mechanical calculation of the
collective modes that does not depend in any way on a harmonic approximation.
We find that shakeup produces a series of sidebands that may be identified with
maxima in the collective mode density of states, and definitively distinguishes
the crystal state from a liquid state in the absence of electron-hole
interaction. In the presence of electron-hole interaction, sidebands also
appear in the liquid state coming from short-range density fluctuations around
the hole. However, the sidebands in the liquid state and the crystal state have
different qualitative behaviors. We also find a shift in the main luminescence
peak, that is associated with lattice relaxation in the vicinity of a vacancy.
The relationship of the shakeup spectrum with previous mean-field calculations
is discussed.",9601017v1
2003-07-16,Layered ferromagnet-superconductor structures: the $π$ state and proximity effects,"We investigate clean mutilayered structures of the SFS and SFSFS type, (where
the S layer is intrinsically superconducting and the F layer is ferromagnetic)
through numerical solution of the self-consistent Bogoliubov-de Gennes
equations for these systems. We obtain results for the pair amplitude, the
local density of states, and the local magnetic moment. We find that as a
function of the thickness $d_F$ of the magnetic layers separating adjacent
superconductors, the ground state energy varies periodically between two stable
states. The first state is an ordinary ""0-state"", in which the order parameter
has a phase difference of zero between consecutive S layers, and the second is
a ""$\pi$-state"", where the sign alternates, corresponding to a phase difference
of $\pi$ between adjacent S layers. This behavior can be understood from simple
arguments. The density of states and the local magnetic moment reflect also
this periodicity.",0307397v1
2003-07-23,Electronic States in Two-Dimensional Triangular Cobalt Oxides: Role of Electronic Correlation,"We obtain the electronic states and structures of two-dimensional cobalt
oxides, Na$_{x}$CoO$_{2}$ (x=0, 0.35, 0.5 and 0.75) by utilizing the
full-potential linear muffin-tin orbitals (FP-LMTO) methods, from which some
essential electronic interaction parameters are estimated: the bare on-site
Coulomb interaction of cobalt U$_{dd}$=7.5 eV renormalizes to 5 eV for x=0.35,
the $pd$ hybridizations t$_{pd\sigma}$ and t$_{pd\pi}$ are -1.40 and 0.70 eV,
respectively. The density of states at E$_{F}$ decreases from 6-7 states/eV in
the local density approximation (LDA) to about 1.0 states/eV in the LDA+U
scheme. The role of the intercalation of water molecules and the microscopic
mechanism of the superconductivity in Na$_{0.35}$CoO$_{2}$$\cdot$mH$_{2}$O is
discussed.",0307560v2
2008-05-22,Entanglement of Valence-Bond-Solid on an Arbitrary Graph,"The Affleck-Kennedy-Lieb-Tasaki (AKLT) spin interacting model can be defined
on an arbitrary graph. We explain the construction of the AKLT Hamiltonian.
Given certain conditions, the ground state is unique and known as the
Valence-Bond-Solid (VBS) state. It can be used in measurement-based quantum
computation as a resource state instead of the cluster state. We study the VBS
ground state on an arbitrary connected graph. The graph is cut into two
disconnected parts: the block and the environment. We study the entanglement
between these two parts and prove that many eigenvalues of the density matrix
of the block are zero. We describe a subspace of eigenvectors of the density
matrix corresponding to non-zero eigenvalues. The subspace is the degenerate
ground states of some Hamiltonian which we call the block Hamiltonian.",0805.3542v2
2008-08-21,Fully Gapped Superconducting State Based on a High Normal State Quasiparticle Density of States in Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ Single Crystals,"We report the specific heat (SH) measurements on single crystals of hole
doped $FeAs$-based superconductor $Ba_{0.6}K_{0.4}Fe_2As_2$. It is found that
the electronic SH coefficient $\gamma_e(T)$ is not temperature dependent and
increases almost linearly with the magnetic field in low temperature region.
These point to a fully gapped superconducting state. Surprisingly the sharp SH
anomaly $\Delta C/T|_{T_c}$ reaches a value of 98 $mJ/mol K^2$ suggesting a
very high normal state quasiparticle density of states ($\gamma_n \approx 63
mJ/mol K^2$). A detailed analysis reveals that the $\gamma_e(T)$ cannot be
fitted with a single gap of s-wave symmetry due to the presence of a hump in
the middle temperature region. However, our data indicate that the dominant
part of the superconducting condensate is induced by an s-wave gap with the
magnitude of about 6 meV.",0808.2941v1
2012-12-16,Stimulated Emission of Radiation in a Single Mode for both Resonance and Non-resonance for Various Initial Photon Distributions,"This paper reexamines the results of Cummings in which the quantum mechanical
two-level-system (TLS) interacts with the electromagnetic field with various
initial distributions and extends that work for both resonant and non-resonant
to times large enough to display multiple photon echoes. The results presented
here include the initial pure coherent state, the field whose initial density
matrix is the Gaussian superposition of coherent states (blackbody radiation)
and density matrices of the field represented by various combinations of mixed
coherent and thermal states with and without squeezing This paper provides, in
addition to the matrix elements to the various states, both the algebraic and
graphical representation for the first order correlation function G=<E+E-> for
resonance and non-resonance. It is found that in all case, the application of
non-resonance leads to oscillations in the first order correlation which was
thought only to apply for the coherent state even for the case of the pure
thermal state.",1212.3752v4
2018-11-30,Half-metallicity of Mn2VAl ferrimagnet revealed by resonant inelastic soft x-ray scattering under magnetic field,"Detailed information on the electronic states of both V and Mn 3d electrons
in the ferrimagnet Mn2VAl is obtained by the bulk sensitive resonant inelastic
soft x-ray scattering (SX-RIXS) excited with the circularly polarized light
under an external magnetic field for the first time. The results under the V
L-edge excitation have revealed the negligible partial density of states (PDOS)
of the V 3d states around the Fermi energy as well as their rather localized
character. Under the Mn L-edge excitation, on the other hand, the spectra are
dominated by fluorescence with clear magnetic circular dichroism with
noticeable excitation photon energy dependence. Compared with the theoretical
prediction of the RIXS spectra based on the density-functional-theory band
structure calculation, an itinerant, spin-dependent character of the Mn 3d
states and decays of the Mn 2p core states are confirmed in consistence with
the half-metallicity of the Mn 3d states.",1811.12600v1
2019-11-05,Floquet boundary states in AB-stacked graphite,"We report on the effect of laser illumination with circularly polarized light
on the electronic structure of AB-stacked graphite samples. By using Floquet
theory in combination with Green's function techniques, we find that the
polarized light induces band-gap openings at the Floquet zone edge
$\hbar\Omega/2$, bridged by chiral boundary states. These states propagate
mainly along the borders of the constituting layers as evidenced by the
time-averaged local density of states and the probability current density in
several geometries. Semianalytic calculations of the Chern number suggest that
these states are of topological nature, similar to those found in illuminated
2D samples like monolayer and bilayer graphene. These states are promising
candidates for the realization of a three-dimensional version of the quantum
Hall effect for Floquet systems.",1911.02144v2
2022-06-30,Effect of configuration mixing on quadrupole and octupole collective states of transitional nuclei,"A model is presented that simultaneously describes shape coexistence and
quadrupole and octupole collective excitations within a theoretical framework
based on the nuclear density functional theory and the interacting boson model.
An optimal interacting-boson Hamiltonian that incorporates the configuration
mixing between normal and intruder states, as well as the octupole degrees of
freedom, is identified by means of self-consistent mean-field calculations
using a universal energy density functional and a pairing interaction, with
constraints on the triaxial quadrupole and the axially-symmetric quadrupole and
octupole shape degrees of freedom. An illustrative application to the
transitional nuclei $^{72}$Ge, $^{74}$Se, $^{74}$Kr, and $^{76}$Kr shows that
the inclusion of the intruder states and the configuration mixing significantly
lower the energy levels of the excited $0^+$ states, and that the predicted
low-lying positive-parity states are characterized by the strong admixture of
nearly spherical, weakly deformed oblate, and strongly deformed prolate shapes.
The low-lying negative-parity states are shown to be dominated by the deformed
intruder configurations.",2206.15184v2
2001-07-30,Martingale Models for Quantum State Reduction,"Stochastic models for quantum state reduction give rise to statistical laws
that are in most respects in agreement with those of quantum measurement
theory. Here we examine the correspondence of the two theories in detail,
making a systematic use of the methods of martingale theory. An analysis is
carried out to determine the magnitude of the fluctuations experienced by the
expectation of the observable during the course of the reduction process and an
upper bound is established for the ensemble average of the greatest
fluctuations incurred. We consider the general projection postulate of L\""uders
applicable in the case of a possibly degenerate eigenvalue spectrum, and derive
this result rigorously from the underlying stochastic dynamics for state
reduction in the case of both a pure and a mixed initial state. We also analyse
the associated Lindblad equation for the evolution of the density matrix, and
obtain an exact time-dependent solution for the state reduction that explicitly
exhibits the transition from a general initial density matrix to the L\""uders
density matrix. Finally, we apply Girsanov's theorem to derive a set of simple
formulae for the dynamics of the state in terms of a family of geometric
Brownian motions, thereby constructing an explicit unravelling of the Lindblad
equation.",0107153v1
2016-10-04,Equation of State for Nucleonic and Hyperonic Neutron Stars with Mass and Radius Constraints,"We obtain a new equation of state for the nucleonic and hyperonic inner core
of neutron stars that fulfills the 2$M_{\odot}$ observations as well as the
recent determinations of stellar radii below 13 km. The nucleonic equation of
state is obtained from a new parametrization of the FSU2 relativistic
mean-field functional that satisfies these latest astrophysical constraints
and, at the same time, reproduces the properties of nuclear matter and finite
nuclei while fulfilling the restrictions on high-density matter deduced from
heavy-ion collisions. On the one hand, the equation of state of neutron star
matter is softened around saturation density, which increases the compactness
of canonical neutron stars leading to stellar radii below 13 km. On the other
hand, the equation of state is stiff enough at higher densities to fulfill the
2$M_{\odot}$ limit. By a slight modification of the parametrization, we also
find that the constraints of 2$M_{\odot}$ neutron stars with radii around 13 km
are satisfied when hyperons are considered. The inclusion of the high magnetic
fields present in magnetars further stiffens the equation of state. Hyperonic
magnetars with magnetic fields in the surface of $ \sim 10^{15}$ G and with
values of $\sim 10^{18}$ G in the interior can reach maximum masses of
2$M_{\odot}$ with radii in the 12-13 km range.",1610.00919v2
2021-09-10,Band gap analysis and carrier localization in cation-disordered ZnGeN$_2$,"Cation site disorder provides a degree of freedom in the growth of ternary
nitrides for tuning the technologically relevant properties of a material
system. For example, the band gap of ZnGeN$_2$ changes when the ordering of the
structure deviates from that of its ground state. By combining the perspectives
of carrier localization and defect states, we analyze the impact of different
degrees of disordering on electronic properties in ZnGeN$_2$, addressing a gap
in current studies which focus on dilute or fully disordered systems. The
present study demonstrates changes in the density of states and localization of
carriers in ZnGeN$_2$ calculated using band gap-corrected density functional
theory and hybrid calculations on partially disordered supercells generated
using the Monte Carlo method. We use localization and density of states to
discuss the ill-defined nature of a band gap in a disordered material,
comparing multiple definitions of the energy gap in the context of theory and
experiment. Decreasing the order parameter results in a large reduction of the
band gap in disordered cases. The reduction in band gap is due in part to
isolated, localized states that form above the valence band continuum and are
associated with nitrogen coordinated by more zinc than germanium. The
prevalence of defect states in all but the perfectly ordered structure creates
challenges for incorporating disordered ZnGeN$_2$ into optical devices, but the
localization associated with these defects provides insight into mechanisms of
electron/hole recombination in the material.",2109.05062v2
2021-09-16,Density Functional Equation of State and Its Application to the Phenomenology of Heavy-Ion Collisions,"We present a mean-field model of the dense nuclear matter equation of state
designed for use in computationally demanding hadronic transport simulations.
Our approach, based on the relativistic Landau Fermi-liquid theory, allows us
to construct a family of equations of state spanning a wide range of possible
bulk properties of dense QCD matter. We implement the developed model in the
hadronic transport code SMASH, and show that the resulting dynamic behavior
reproduces theoretical expectations for the thermodynamic properties of the
system based on the underlying equation of state. In particular, we show that
pair distribution functions calculated from hadronic transport simulation data
are consistent with theoretical expectations based on the second-order cumulant
ratio, and can be used as a signature of crossing the phase diagram in the
vicinity of a critical point. We additionally present a novel method that may
enable a measurement of the speed of sound and its derivative with respect to
the baryon number density in heavy-ion collisions. Application of our approach
to available experimental data implies that the derivative of the speed of
sound is non-monotonic in systems created in collisions at intermediate to low
energies, which in turn may be connected to non-trivial features in the
underlying equation of state.",2109.08105v1
1993-04-08,"Coulomb Gaps in a Strong Magnetic Field, S.-R","We report on a study of interaction effects in the tunneling
density-of-states of a disordered two-dimensional electron gas in the strong
magnetic field limit where only the lowest Landau level is occupied.
Interactions in the presence of disorder are accounted for by performing
finite-size self-consistent Hartree-Fock calculations. We find evidence for the
formation of a pseudo-gap with a tunneling density-of-states which vanishes at
the Fermi energy.",9304012v1
1995-01-08,Superconductivity of Carriers Doped into the Static Charge Density Wave State in 2-Dimensional Square Lattice,"On the purpose of studying the effect of long-range Coulomb-interaction in
strongly correlated electronic systems we bring in as its representative the
nearest-neighbor repulsion ($v$) in addition to the on-site repulsion ($u$) and
shall investigate the possibility of the superconducting transition of carriers
doped into the charge-density wave (CDW) state expected for $v\,>\,u/4$ in
2-dimensional square lattice. We shall see that strongly correlated hopping
processes of doped carriers make the systems superconducting. The favored
superconducting phase is of extended s-wave symmetry, and $T_{c} \sim$100K is
shown to easily be attained near the half-filling.",9501023v1
1996-02-04,Zero--Bias Anomaly in Finite Size Systems,"The small energy anomaly in the single particle density of states of
disordered interacting systems is studied for the zero dimensional case. This
anomaly interpolates between the non--perturbative Coulomb blockade and the
perturbative limit, the latter being an extension of the Altshuler--Aronov zero
bias anomaly at d=0. Coupling of the zero dimensional system to a dissipative
environment leads to an effective screening of the interaction and a
modification of the density of states.",9602015v1
1997-02-26,Thermoelectric Effect in High-$T_c$ Superconductors: the Role of Density of States Fluctuations,"We study the effect of the density of states (DOS) fluctuations on the
thermoelectric coefficient of superconductor above critical temperature. It is
shown that in the isotropic case it is the DOS contribution which gives rise to
the leading correction to thermoelectric coefficient in spite of previous
results where the only Aslamazov-Larkin term was taken into account. This
conclusion is valid for an arbitrary impurity concentration.",9702228v1
2000-08-16,Density of states for dirty d-wave superconductors: A unified and dual approach for different types of disorder,"A two-parameter field theoretical representation is given of a 2-dimensional
dirty d-wave superconductor that interpolates between the Gaussian limit of
uncorrelated weak disorder and the unitary limit of a dilute concentration of
resonant scatterers. It is argued that a duality holds between these two
regimes from which follows that a linearly vanishing density of states in the
Gaussian limit transforms into a diverging one in the unitary limit arbitrarily
close to the Fermi energy.",0008241v1
2000-11-10,"An efficient, multiple range random walk algorithm to calculate the density of states","We present a new Monte Carlo algorithm that produces results of high accuracy
with reduced simulational effort. Independent random walks are performed
(concurrently or serially) in different, restricted ranges of energy, and the
resultant density of states is modified continuously to produce locally flat
histograms. This method permits us to directly access the free energy and
entropy, is independent of temperature, and is efficient for the study of both
1st order and 2nd order phase transitions. It should also be useful for the
study of complex systems with a rough energy landscape.",0011174v1
2004-02-03,Crossover of conductance and local density of states in a single-channel disordered quantum wire,"The probability distribution of the mesoscopic local density of states (LDOS)
for a single-channel disordered quantum wire with chiral symmetry is computed
in two different geometries. An approximate ansatz is proposed to describe the
crossover of the probability distributions for the conductance and LDOS between
the chiral and standard symmetry classes of a single-channel disordered quantum
wire. The accuracy of this ansatz is discussed by comparison with a
large-deviation ansatz introduced by Schomerus and Titov in Phys. Rev. B
\textbf{67}, 100201(R) (2003).",0402073v2
2004-10-27,Ground state properties of a dilute homogeneous Bose gas of hard disks in two dimensions,"The energy and structure of a dilute hard-disks Bose gas are studied in the
framework of a variational many-body approach based on a Jastrow correlated
ground state wave function. The asymptotic behaviors of the radial distribution
function and the one-body density matrix are analyzed after solving the Euler
equation obtained by a free minimization of the hypernetted chain energy
functional. Our results show important deviations from those of the available
low density expansions, already at gas parameter values $x\sim 0.001$. The
condensate fraction in 2D is also computed and found generally lower than the
3D one at the same $x$.",0410690v1
2005-08-26,Fluctuations of local density of states and C0 speckle correlations are equal,"We establish a conceptual relation between the fluctuations of the local
density of states (LDOS) and intensity correlations in speckle patterns
resulting from multiple scattering of waves in random media. We show that among
known types of speckle correlations (C1, C2, C3, and C0) only C0 contributes to
LDOS fluctuations in the infinite medium. We propose to exploit the equivalence
of LDOS fluctuations and C0 intensity correlation as a `selection rule' for
scattering processes contributing to C0.",0508641v2
2005-10-19,Excitonic pairing between nodal fermions,"We study excitonic pairing in nodal fermion systems characterized by a
vanishing quasiparticle density of states at the pointlike Fermi surface and a
concomitant lack of screening for long-range interactions. By solving the gap
equation for the excitonic order parameter, we obtain a critical value of the
interaction strength for a variety of power-law interactions and densities of
states. We compute the free energy and analyze possible phase transitions, thus
shedding further light on the unusual pairing properties of this peculiar class
of strongly correlated systems.",0510519v3
2006-03-09,Test of cold denaturation mechanism for proteins as a function of water's structure,"In a recent paper [PRL 91, 138103 (2003)] a new mechanism to explain the cold
denaturation of proteins, based on the loss of local low-density water
structure, has been proposed. In the present paper this mechanism is tested by
means of full atom numerical simulations. In good agreement with this proposal,
cold denaturation resulting in the unfolded state was found at the High Density
Liquid (HDL) state of water, at which the amount of open tetragonal hydrogen
bonds decreases at cooling.",0603240v1
2006-05-31,Correlation effects in the density of states of annealed GaMnAs,"We report on an experimental study of low temperature tunnelling in hybrid
NbTiN/GaMnAs structures. The conductance measurements display a root mean
square V dependence, consistent with the opening of a correlation gap in the
density of states of GaMnAs. Our experiment shows that low temperature
annealing is a direct empirical tool that modifies the correlation gap and thus
the electron-electron interaction. Consistent with previous results on
boron-doped silicon we find, as a function of voltage, a transition across the
phase boundary delimiting the direct and exchange correlation regime.",0605753v2
2004-05-05,On big rip singularities,"In this comment we discuss big rip singularities occurring in typical phantom
models by violation of the weak energy condition. After that, we compare them
with future late-time singularities arising in models where the scale factor
ends in a constant value and there is no violation of the strong energy
condition. In phantom models the equation of state is well defined along the
whole evolution, even at the big rip. However, both the pressure and the energy
density of the phantom field diverge. In contrast, in the second kind of model
the equation of state is not defined at the big rip because the pressure bursts
at a finite value of the energy density.",0405020v1
2005-12-15,The general solution for relativistic spherical shells,"The general exact solution of the Einstein-matter field equations describing
spherically symmetric shells satisfying an equation of state in closed form is
discussed under general assumptions of physical reasonableness. The solutions
split into two classes: a class of ""astro-physically interesting"" solutions
describing ""ordinary"" matter with positive density and pressure, and a class of
""phantom-like"" solutions with positive density but negative active
gravitational mass, which can also be of interest in several ""very strong
fields"" regimes. Known results on linear-barotropic equations of state are
recovered as particular cases.",0512089v1
2000-11-17,Dibaryons as canonically quantized biskyrmions,"The characteristic feature of the ground state configuration of the Skyrme
model description of nuclei is the absence of recognizable individual nucleons.
The ground state of the skyrmion with baryon number 2 is axially symmetric, and
is well approximated by a simple rational map, which represents a direct
generalization of Skyrme's hedgehog ansatz for the nucleon. If the Lagrangian
density is canonically quantized this configuration may support excitations
that lie close and possible below the threshold for pion decay, and therefore
describe dibaryons. The quantum corrections stabilize these solutions, the mass
density of which have the correct exponential fall off at large distances.",0011063v1
2003-10-08,Proton-nucleus elastic scattering and the equation of state of nuclear matter,"We calculate differential cross sections for proton-nucleus elastic
scattering by using a Glauber theory in the optical limit approximation and
nucleon distributions that can be obtained in the framework of macroscopic
nuclear models in a way dependent on the equation of state of uniform nuclear
matter near the saturation density. We find that the peak angle calculated for
unstable neutron-rich nuclei in the small momentum transfer regime increases as
the parameter L characterizing the density dependence of the symmetry energy
decreases. This is a feature associated with the L dependence of the predicted
matter radii.",0310026v1
1997-07-10,On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3,"Recently I quantized an elastica with Bernoulli-Euler functional in
two-dimensional space using the modified KdV hierarchy. In this article, I will
quantize a Willmore surface, or equivalently a surface with the Polyakov
extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation.
In other words, I show that the density of state of the partition function for
the quantized Willmore surface is expressed by volume of a subspace of the
moduli of the MNV equation.",9707007v1
2007-06-22,Filtering and estimation in stochastic volatility models with rationally distributed disturbances,"This paper deals with the filtering problem for a class of discrete time
stochastic volatility models in which the disturbances have rational
probability density functions. This includes the Cauchy distributions and
Student t-distributions with odd number of degrees of freedom. Using state
space realizations to represent the rational probability density functions we
are able to solve the filtering problem exactly. However the size of the
involved state space matrices grows exponentially with each time step of the
filter. Therefore we use stochastically balanced truncation techniques to
approximate the high order rational functions involved. In a simulation study
we show the applicability of this approach. In addition a simple method of
moments estimator is derived.",0706.3335v1
2007-10-03,The Student ensemble of correlation matrices: eigenvalue spectrum and Kullback-Leibler entropy,"We study a new ensemble of random correlation matrices related to
multivariate Student (or more generally elliptic) random variables. We
establish the exact density of states of empirical correlation matrices that
generalizes the Marcenko-Pastur result. The comparison between the theoretical
density of states in the Student case and empirical financial data is
surprisingly good, even if we are still able to detect systematic deviations.
Finally, we compute explicitely the Kullback-Leibler entropies of empirical
Student matrices, which are found to be independent of the true correlation
matrix, as in the Gaussian case. We provide numerically exact values for these
Kullback-Leibler entropies.",0710.0802v1
2007-11-27,Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling,"We show that the integrated density of states of the almost Mathieu operator
is absolutely continuous if and only if the coupling is non-critical. We deduce
for subcritical coupling that the spectrum is purely absolutely continuous for
almost every phase, settling the measure-theoretical case of Problem 6 of Barry
Simon's list of Schr\""odinger operator problems for the twenty-first century.",0711.4291v1
2008-08-07,Density of states near a vortex core in ferromagnetic superconductors: Application to STM measurements,"We investigate numerically the local density of states (LDOS) in the vicinity
of a vortex core in a ferromagnetic superconductor. Specifically, we
investigate how the LDOS is affected by the relative weight of the spin bands
in terms of the superconducting pairing, and we also examine the effect of
different pairing symmetries for the superconducting order parameter. Our
findings are directly related to scanning tunneling microscopy measurements and
may thus be highly useful to clarify details of the superconducting pairing in
recently discovered ferromagnetic superconductors.",0808.0983v1
2008-09-23,Spiky density of states in large complex Al-Mn phases,"First-principle electronic structure calculations have been performed in
crystalline complex phases mu-Al4Mn and lambda-Al4Mn using the TB-LMTO method.
These atomic structures, related to quasicrystalline structures, contain about
560 atoms in a large hexagonal unit cell. One of the main characteristic of
their density of states is the presence of fine peaks the so-called ""spiky
structure"". From multiple-scattering calculations in real space, we show that
these fine peaks are not artifacts in ab-initio calculations, since they result
from a specific localization of electrons by atomic clusters of different
length scales.",0809.3993v1
2009-06-25,Lipkin translational-symmetry restoration in the mean-field and energy-density-functional methods,"Based on the 1960 idea of Lipkin, the minimization of energy of a
symmetry-restored mean-field state is equivalent to the minimization of a
corrected energy of a symmetry-broken state with the Peierls-Yoccoz mass. It is
interesting to note that the ""unphysical"" Peierls-Yoccoz mass, and not the true
mass, appears in the Lipkin projected energy. The Peierls-Yoccoz mass can be
easily calculated from the energy and overlap kernels, which allows for a
systematic, albeit approximate, restoration of translational symmetry within
the energy-density formalism. Analogous methods can also be implemented for all
other broken symmetries.",0906.4763v1
2009-08-14,Negative Impurity Magnetic Susceptibility and Heat Capacity in a Kondo Model with Narrow Peaks in the Local Density of Electron States,"Temperature dependencies of the impurity magnetic susceptibility, entropy,
and heat capacity have been obtained by the method of numerical renormalization
group and exact diagonalization for the Kondo model with peaks in the electron
density of states near the Fermi energy (in particular, with logarithmic Van
Hove singularities). It is shown that these quantities can be {\it negative}. A
new effect has been predicted (which, in principle, can be observed
experimentally), namely, the decrease in the magnetic susceptibility and heat
capacity of a nonmagnetic sample upon the addition of magnetic impurities into
it.",0908.2040v1
2010-08-11,Local quasiparticle density of states of superconducting SmFeAsO$1-x$F$x$ single crystals: Evidence for spin-mediated pairing,"We probe the local quasiparticles density-of-states in micron-sized
SmFeAsO$_{1-x}$F$_{x}$ single-crystals by means of Scanning Tunnelling
Spectroscopy. Spectral features resemble those of cuprates, particularly a
dip-hump-like structure developed at energies larger than the gap that can be
ascribed to the coupling of quasiparticles to a collective mode, quite likely a
resonant spin mode. The energy of the collective mode revealed in our study
decreases when the pairing strength increases. Our findings support
spin-fluctuation-mediated pairing in pnictides.",1008.2019v1
2010-09-14,Optical amplification enhancement in photonic crystals,"Improving and controlling the efficiency of a gain medium is one of the most
challenging problems of laser research. By measuring the gain length in an opal
based photonic crystal doped with laser dye, we demonstrate that optical
amplification is more than twenty-fold enhanced along the Gamma-K symmetry
directions of the face centered cubic photonic crystal. These results are
theoretically explained by directional variations of the density of states,
providing a quantitative connection between density of the states and light
amplification.",1009.2708v1
2011-02-01,Density of states anomalies in multichannel quantum wires,"We reformulate the Tomonaga--Luttinger liquid theory for
quasi-one-dimensional Fermion systems with many subbands across the Fermi
energy. Our theory enables us to obtain a rigorous expression of the local
density of states (LDOS) for general multichannel quantum wires, describing how
the power-law anomalies of LDOS depend on inter- and intra-subbands couplings
as well as the Fermi velocity of each band. The resulting formula for the
exponents is valid in the case of both bulk contact and edge contact, and thus
plays a fundamental role in the physical properties of multicomponent
Tomonaga--Luttinger liquid systems.",1102.0101v1
2011-03-17,Thermodynamic properties of separable square-wave potentials,"Exact analytic solutions to the Schr\""odinger equation for an electron moving
in three dimensional potentials have been studied. These solutions can
correspond to metals, semiconductors, or insulators. We show that there is an
efficient method to calculate the electron density of states for this class of
potentials. From the density of states, the temperature dependence of
thermodynamic properties such as the chemical potential and the specific heat
were determined. Ten thousand cubic separable potentials were considered. This
data makes it possible to identify trends in how the form of the potential is
related to the thermodynamic properties of a material.",1103.3463v2
2011-04-07,Vacuum fluctuations in a supersymmetric model in FRW spacetime,"We study a noninteracting supersymmetric model in an expanding FRW spacetime.
A soft supersymmetry breaking induces a nonzero contribution to the vacuum
energy density. A short distance cutoff of the order of Planck length provides
a scale for the vacuum energy density comparable with the observed cosmological
constant. Assuming the presence of a dark energy substance in addition to the
vacuum fluctuations of the field an effective equation of state is derived in a
selfconsistent approach. The effective equation of state is sensitive to the
choice of the cut-off but no fine tuning is needed.",1104.1349v1
2012-08-13,Density Waves Instability and a Skyrmion Lattice on the Surface of Strong Topological Insulators,"In this work we analyze the instability conditions for spin-density-waves
(SDW) formation on the surface of strong topological insulators. We find that
for a certain range of Fermi-energies and strength of interactions the SDW
state is favored compared to the unmagnetized and the uniform-magnetization
states. We also find that the SDW are of spiral nature and for a certain range
of parameters a Skyrmion-lattice may form on the surface. We show that this
phase may have a non trivial Chern-number even in the absence of an external
magnetic field.",1208.2576v1
2012-11-26,Correlation effects in disordered conductors with spin accumulation,"We consider the effect of electron-electron interaction on the density of
states of disordered paramagnetic conductor in the presence of spin
accumulation and magnetic field. We show that interaction correction to
electron density of states of the paramagnet may exhibit singularities at
energies corresponding to the difference between chemical potentials of
electrons with opposite spins. We also discuss correlation effects on
conductivity in metallic as well as in hopping regimes and show that spin
accumulation leads to the negative magnetoconductivity.",1211.5943v1
2014-01-29,Investigating Dirty Crossover through Fidelity Susceptibility and Density of States,"We investigate the BCS-BEC crossover in an ultracold atomic gas in the
presence of disorder. The disorder is incorporated in the mean-field formalism
through Gaussian fluctuations. We observe evolution to an asymmetric line-shape
of fidelity susceptibility as a function of interaction coupling with
increasing disorder strength which may point to an impending quantum phase
transition. The asymmetric line-shape is further analyzed using the statistical
tools of skewness and kurtosis. We extend our analysis to density of states
(DOS) for a better understanding of the crossover in the disordered
environment.",1401.7459v1
2014-08-20,Vortex Core Structure in Multilayered Rashba Superconductors,"We numerically study the electronic structure of a single vortex in two
dimensional superconducting bilayer systems within the range of the mean-field
theory. The lack of local inversion symmetry in the system is taken into
account through the layer dependent Rashba spin-orbit coupling. The spatial
profiles of the pair potential and the local quasiparticle density of states
are calculated in the clean spin-singlet superconductor on the basis of the
quasiclassical theory. In particular, we discuss the characteristic core
structure in the pair-density wave state, which is spatially modulated exotic
superconducting phase in a high magnetic field.",1408.4550v1
2015-01-05,Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators,"We show H\""older continuity for the integrated density of states of a
quasi-periodic Jacobi operator with analytic coefficients, in the regime of
positive Lyapunov exponent and with a strong Diophantine condition on the
frequency. In particular, when the coefficients are trigonometric polynomials
we express the H\""older exponent in terms of the degrees of the coefficients.",1501.01028v2
2015-01-22,Collective enhancement of nuclear state densities by the shell model Monte Carlo approach,"The shell model Monte Carlo (SMMC) approach allows for the microscopic
calculation of statistical and collective properties of heavy nuclei using the
framework of the configuration-interaction shell model in very large model
spaces. We present recent applications of the SMMC method to the calculation of
state densities and their collective enhancement factors in rare-earth nuclei.",1501.05525v1
2015-04-19,A semi empirical expression of the virial coefficients for hard sphere fluids at all density,"We propose a new semi empirical expression of the virial coefficients for a
hard sphere fluid which is valid in the disordered phase over the whole density
range. The results are in good agreement with the numerical data and better
than those of the well-known Carnahan & Starling equation of state in the
domain of validity of the later; moreover this new expression accounts for the
singularity which is required for the equation of state at the close random
packing limit.",1504.08353v2
2016-03-23,Ground state phase diagram of Gaussian-Core bosons in two dimensions,"The ground state of a two-dimensional (2D) system of Bose particles of spin
zero, interacting via a repulsive Gaussian-Core potential, has been
investigated by means of Quantum Monte Carlo simulations. The quantum phase
diagram is qualitatively identical to that of 2D Yukawa bosons. While the
system is a fluid at all densities for weak coupling, in the strong coupling
regime it transitions upon compression from a low density superfluid to a
crystal, and then into a reentrant superfluid phase. No evidence of a
(supersolid) cluster crystal phase is seen.",1603.07270v2
2016-07-27,Role of Optical Density of States in Two-mode Optomechanical Cooling,"Dynamical back-action cooling of phonons in optomechanical systems having one
optical mode is well studied. Systems with two optical modes have the potential
to reach significantly higher cooling rate through resonant enhancement of both
pump and scattered light. Here we experimentally investigate the role of dual
optical densities of states on optomechanical cooling, and the deviation from
theory caused by thermal locking to the pump laser. Using this, we demonstrate
a room temperature system operating very close to the strong coupling regime,
where saturation of cooling is anticipated.",1607.07921v1
2016-10-19,Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks,"We show that a generic element of a space of limit-periodic CMV operators has
zero-measure Cantor spectrum. We also prove a Craig--Simon type theorem for the
density of states measure associated with a stochastic family of CMV matrices
and use our construction from the first part to prove that the Craig--Simon
result is optimal in general. We discuss applications of these results to a
quantum walk model where the coins are arranged according to a limit-periodic
sequence. The key ingredient in these results is a new formula which may be
viewed as a relationship between the density of states measure of a CMV matrix
and its Schur function.",1610.06159v1
2019-05-02,Stability properties of the steady state for the isentropic compressible Navier-Stokes equations with density dependent viscosity in bounded intervals,"We prove existence and asymptotic stability of the stationary solution for
the compressible Navier-Stokes equations for isentropic gas dynamics with a
density dependent diffusion in a bounded interval. We present the necessary
conditions to be imposed on the boundary data which ensure existence and
uniqueness of the steady state, and we subsequent investigate its stability
properties by means of the construction of a suitable Lyapunov functional for
the system. The Saint-Venant system, modeling the dynamics of a shallow
compressible fluid, fits into this general framework.",1905.00770v3
2010-05-18,Neutron drip line and the equation of state of nuclear matter,"We investigate how the neutron drip line is related to the density dependence
of the symmetry energy, by using a macroscopic nuclear model that allows us to
calculate nuclear masses in a way dependent on the equation of state of
asymmetric nuclear matter. The neutron drip line obtained from these masses is
shown to appreciably shift to a neutron-rich side in a nuclear chart as the
density derivative of the symmetry energy increases. Such shift is clearly seen
for light nuclei, a feature coming mainly from the surface property of
neutron-rich nuclei.",1005.3183v1
2009-12-07,Dynamical phase transition of a 1D transport process including death,"Motivated by biological aspects related to fungus growth, we consider the
competition of growth and corrosion. We study a modification of the totally
asymmetric exclusion process, including the probabilities of injection $\alpha$
and death of the last particle $\delta$. The system presents a phase transition
at $\delta_c(\alpha)$, where the average position of the last particle $<L>$
grows as $\sqrt{t}$. For $\delta>\delta_c$, a non equilibrium stationary state
exists while for $\delta<\delta_c$ the asymptotic state presents a low density
and max current phases. We discuss the scaling of the density and current
profiles for parallel and sequential updates.",0912.1290v2
2009-12-09,Experimental Probing of Photonic Density of States in Hyperbolic Metamaterial,"In the metamaterial with hyperbolic dispersion (an array of silver nanowires
in alumina membrane) we have observed six-fold reduction of the emission
life-time of dye deposited onto the metamaterials surface. This serves as the
evidence of the earlier predicted high density of photonic states in hyperbolic
metamaterials.",0912.1785v1
2016-05-05,On the ground state energy of the inhomogeneous Bose gas,"Within the self-consistent Hartree-Fock approximation, an explicit expression
for the ground state energy of inhomogeneous Bose gas is derived as a
functional of the inhomogeneous density of the Bose-Einstein condensate. The
results obtained are based on existence of the off-diagonal long-range order in
the single-particle density matrix for systems with a Bose-Einstein condensate.
This makes it possible to avoid the use of anomalous averages. The explicit
form of the kinetic energy, which differs from one in the Gross-Pitaevski
approach, is found. This form is valid beyond the Hartree-Fock approximation
and can be applied for arbitrary strong interparticle interaction.",1605.02696v1
2016-12-15,Doping-dependent magnetization plateaus of a coupled spin-electron chain: exact results,"A coupled spin-electron chain composed of localized Ising spins and mobile
electrons is exactly solved in an external magnetic field within the
transfer-matrix method. The ground-state phase diagram involves in total seven
different ground states, which differ in the number of mobile electrons per
unit cell and the respective spin arrangements. A rigorous analysis of the
low-temperature magnetization process reveals doping-dependent magnetization
plateaus, which may be tuned through the density of mobile electrons. It is
demonstrated that the fractional value of the electron density is responsible
for an enhanced magnetocaloric effect due to an annealed bond disorder of the
mobile electrons.",1612.04968v1
2017-11-09,Density of States under non-local interactions III. N-particle Bernoulli--Anderson model,"Following [7,8], we analyze regularity properties of single-site probability
distributions of the random potential and of the Integrated Density of States
(IDS) in the Anderson models with infinite-range interactions and arbitrary
nontrivial probability distributions of the site potentials. In the present
work, we study $2$-particle Anderson Hamiltonians on a lattice and prove
spectral and strong dynamical localization at low energies, with exponentially
decaying eigenfunctions, for a class of site potentials featuring a power-law
decay.",1711.03326v1
2017-12-08,Linear magnetoresistance in the charge density wave state of quasi-two-dimensional rare-earth tritellurides,"We report measurements of the magnetoresistance in the charge density wave
(CDW) state of rare-earth tritellurides, namely TbTe$_3$ and HoTe$_3$. The
magnetic field dependence of magnetoresistance exhibits a temperature dependent
crossover between a conventional quadratic law at high $T$ and low $B$ and an
unusual linear dependence at low $T$ and high $B$. We present a quite general
model to explain the linear magnetoresistance taking into account the strong
scattering of quasiparticles on CDW fluctuations in the vicinity of ""hot spots""
of the Fermi surface (FS) where the FS reconstruction is the strongest.",1712.02971v1
2020-04-23,Cutoff Dependence and Complexity of the CFT$_2$ Ground State,"We present the vacuum of a two-dimensional conformal field theory (CFT$_2$)
as a network of Wilson lines in $SL(2,\mathbb{R}) \times SL(2,\mathbb{R})$
Chern-Simons theory, which is conventionally used to study gravity in
three-dimensional anti-de Sitter space (AdS$_3$). The position and shape of the
network encode the cutoff scale at which the ground state density operator is
defined. A general argument suggests identifying the `density of complexity' of
this network with the extrinsic curvature of the cutoff surface in AdS$_3$,
which by the Gauss-Bonnet theorem agrees with the holographic Complexity =
Volume proposal.",2004.11377v1
2020-04-24,Separability criteria based on Bloch representation of density matrices,"We study separability criteria in multipartite quantum systems of arbitrary
dimensions by using the Bloch representation of density matrices. We first
derive the norms of the correlation tensors and obtain the necessary conditions
for separability under partition of tripartite and four-partite quantum states.
Moreover, based on the norms of the correlation tensors,we obtain the
separability criteria by matrix method. Using detailed examples, our results
are seen to be able to detect more entangled states than previous studies.
Finally, necessary conditions of separability for multipartite systems are
given under arbitrary partition.",2004.11525v1
2020-05-07,Universal properties of maximum-mass neutron stars: a new tool to explore superdense matter,"I have demonstrated the existence of a tight correlation between the mass,
radius, central density, and pressure of maximum-mass neutron stars modeled
using diverse baryonic equations of state. A possible explanation for these
correlations is provided. Simple analytic forms of such correlations are
suggested and compared with observational constraints on the maximum mass of
neutron stars and their radii. This gives a valuable tool to constrain maximum
pressure and density that could be reached in stable neutron stars, assuming
their equation of state is baryonic.",2005.03549v2
2022-01-29,Vortex pair annihilation in arrays of photon cavities,"We investigate theoretically the evolution of the vortex number in an array
of photon condensates that is brought from an incoherent low density state to a
coherent high density state by a sudden change in the pumping laser intensity.
We analyze how the recombination of vortices and antivortices depends on the
system parameters such as the coefficients for emission and absorption of
photons by the dye molecules, the rate of tunneling between the cavities, the
photon loss rate and the number of photons in the condensate.",2201.12530v1
2022-01-31,Ground state energy of the low density Bose gas with three-body interactions,"We consider the low density Bose gas in the thermodynamic limit with a
three-body interaction potential. We prove that the leading order of the ground
state energy of the system is determined completely in terms of the scattering
energy of the interaction potential. The corresponding result for two-body
interactions was proved in seminal papers of Dyson (1957) and Lieb--Yngvason
(1998).",2201.13440v3
2022-08-02,On asymptotic expansions of the density of states for Poisson distributed random Schrödinger operators,"We study expectation values of matrix elements for boundary values of the
resolvent as well as the density of states for a random Schr\""odinger operator
with potential distributed according to a Poisson process. Asymptotic
expansions for these quantities in the limit of small disorder are derived.
Explicit estimates for the expansion coefficients are given and we show that
their infinite volume limits are in fact finite as the spectral parameter
approaches the spectrum of the free Laplacian.",2208.01578v2
2022-08-09,"And again, about lasing threshold, light localization, and density of states","We investigated numerically the relationship between the lasing threshold,
the density of states (DOS), and field localization in 1D photonic crystals
(PC) for off-axis laser action. The angular dependence of the corresponding
quantities for the two polarizations was obtained, and it was shown that the
relationship between the threshold and DOS is complex, especially near the
Brewster angle in the case of p-polarization. A strong correlation between the
ratio of thresholds and localizations of the two edge modes was found for
s-polarization. The results of this work can be used for optimizing lasers
based on one-dimensional PCs, both for normal and off-axis lasing.",2208.04792v1
2022-10-20,Asymptotic behaviors of the integrated density of states for random Schrödinger operators associated with Gibbs Point Processes,"The asymptotic behaviors of the integrated density of states $N(\lambda)$ of
Schr\""odinger operators with nonpositive potentials associated with Gibbs point
processes are studied. It is shown that for some Gibbs point processes, the
leading terms of $N(\lambda)$ as $\lambda\downarrow-\infty$ coincide with that
for a Poisson point process, which is known. Moreover, for some Gibbs point
processes corresponding to pairwise interactions, the leading terms of
$N(\lambda)$ as $\lambda\downarrow-\infty$ are determined, which are different
from that for a Poisson point process.",2210.11381v1
2022-11-02,Anderson Hamiltonians with singular potentials,"We construct random Schr\""odinger operators, called Anderson Hamiltonians,
with Dirichlet and Neumann boundary conditions for a fairly general class of
singular random potentials on bounded domains. Furthermore, we construct the
integrated density of states of these Anderson Hamiltonians, and we relate the
Lifschitz tails (the asymptotics of the left tails of the integrated density of
states) to the left tails of the principal eigenvalues.",2211.01199v2
2023-02-03,Spectral Theorems for Generalized Weyl Nodes with Impurities in a Magnetic Field,"We prove a few spectral theorems for the density of states of a Weyl node
with arbitrary topology. We show that the density of extended states of a Weyl
node with random impurity potentials remains gapless in the presence of a
magnetic field. Therefore, a magnetic field precludes Anderson localization in
Weyl semi-metals, when inter-node transitions are suppressed for smooth enough
potentials. We also provide a rigorous quantum mechanical proof of the chiral
magnetic effect for arbitrary topology of a Weyl node.",2302.02955v2
2023-09-19,Computation of 3D Band Structure and Density of States (DOS) of 14 Face Centered Cubic (FCC) Crystals using Pseudopotentials,"Electronic properties of materials are crucial to their ability to function
in a wide range of applications, from electronics and energy production to
structural materials and biomedicine. Computational methods are crucial in
understanding these properties before developing the materials. Based on
techniques from Cohen-Bergstresser and Monkhorst-Pack, we developed a computer
program to calculate the electronic structure and density of the state of 14
fcc crystals.",2309.10459v1
2024-02-08,Ground state energy of the low density Bose gas with two-body and three-body interactions,"In the present paper we study the low density Bose gas in the thermodynamic
limit interacting via two-body and three-body interaction potentials. We prove
that the leading order of the ground state energy is entirely characterised by
both the scattering length of the two-body potential and the scattering energy
of the three-body potential. The corresponding result for two-body interactions
was proven in seminal papers of Dyson (1957) and of Lieb-Yngvason (1998), and
the result for three-body interactions was proven by Nam-Ricaud-Triay
(arXiv:2201.13440). The present result resolves a conjecture of
Nam--Ricaud--Triay (arXiv:2202.1396).",2402.05646v1
1997-06-12,Effects of two dimensional plasmons on the tunneling density of states,"We show that gapless plasmons lead to a universal
$(\delta\nu(\epsilon)/\nu\propto |\epsilon|/E_F)$ correction to the tunneling
density of states of a clean two dimensional Coulomb interacting electron gas.
We also discuss a counterpart of this effect in the ""composite fermion metal""
which forms in the presence of a quantizing perpendicular magnetic field
corresponding to the half-filled Landau level. We argue that the latter
phenomenon might be relevant for deviations from a simple scaling observed by
A.Chang et al in the tunneling $I-V$ characteristics of Quantum Hall liquids.",9706129v2
2003-09-12,Effective Random Matrix Theory description of chaotic Andreev billiards,"An effective random matrix theory description is developed for the universal
gap fluctuations and the ensemble averaged density of states of chaotic Andreev
billiards for finite Ehrenfest time. It yields a very good agreement with the
numerical calculation for Sinai-Andreev billiards. A systematic linear decrease
of the mean field gap with increasing Ehrenfest time $\tau_E$ is observed but
its derivative with respect to $\tau_E$ is in between two competing theoretical
predictions and close to that of the recent numerical calculations for Andreev
map. The exponential tail of the density of states is interpreted
semi-classically.",0309306v2
2003-11-04,Vacuum-field Rabi oscillations in atomically doped carbon nanotubes,"We report a strictly non-exponential spontaneous decay dynamics of an excited
two-level atom placed inside or at different distances outside a carbon
nanotube. This is the result of strong non-Markovian memory effects arising
from the rapid frequency variation of the photonic density of states near the
nanotube. The system exhibits vacuum-field Rabi oscillations when the atom is
close enough to the nanotube surface and the atomic transition frequency is in
the vicinity of the resonance of the photonic density of states.",0311065v2
2005-08-24,A new approach to strongly correlated disorder,"Problems involving disordered systems are usually analyzed for systems with
random disorder. However, there are many systems in which the main disorder
involves clusters with correlated differences between their properties and
those of the average system. A new approximation, the average trace
approximation, is proposed for calculating the diagonal elements of the Green
function, and hence the density of states, in such systems. As an example,
application of the method to a simple cubic array of harmonic oscillators shows
that correlation in the disorder leads to a peak in the low frequency density
of states, a result confirmed by computer simulations.",0508571v1
2006-07-07,Ab Initio Study on Electronic Structure of ZrB12 under High Hydrostatic Pressure,"Using projector augmented wave approach within the generalized gradient
approximation, we have studied the structural property and electronic structure
of ZrB12. The calculated lattice constants and bulk modulus are in good
agreement with the available experimental values. A detailed study of the
electronic structure and the charge-density redistribution reveals the features
of strong covalent B-B and weak covalent Zr-B bondings in ZrB12. The states at
the Fermi level mainly come from the $\sigma$-$p_{y}$ and $\pi$-$p_{z}$
orbitals of boron atoms, which are slightly hybridized with the
$t_{2g}$-$d_{xz}$ and $t_{2g}$-$d_{yz}$ orbitals of Zr atoms. As the increased
hydrostatic pressure on ZrB12, the total density of states at the Fermi level
decreases.",0607183v1
2006-10-22,Density of States Extracted from Modified Recursion Relations,"We evaluate the density of states (DOS) associated with tridiagonal symmetric
Hamiltonian matrices and study the effect of perturbation on one of its
entries. Analysis is carried out by studying the resulting three-term recursion
relation and the corresponding orthogonal polynomials of the first and second
kind. We found closed form expressions for the new DOS in terms of the original
one when perturbation affects a single diagonal or off-diagonal site or a
combination of both. The projected DOS is also calculated numerically and its
relation to the average DOS is explored both analytically and numerically.",0610604v1
2007-02-19,Quantum Monte Carlo simulation of spin-polarized H,"The ground-state properties of spin polarized hydrogen H$\downarrow$ are
obtained by means of diffusion Monte Carlo calculations. Using the most
accurate to date ab initio H$\downarrow$-H$\downarrow$ interatomic potential we
have studied its gas phase, from the very dilute regime until densities above
its freezing point. At very small densities, the equation of state of the gas
is very well described in terms of the gas parameter $\rho a^3$, with $a$ the
s-wave scattering length. The solid phase has also been studied up to high
pressures. The gas-solid phase transition occurs at a pressure of 173 bar, a
much higher value than suggested by previous approximate descriptions.",0702442v1
2006-09-27,Effective Theories of Dense and Very Dense Matter,"In these lectures we discuss the uses of effective field theory in studying
dense hadronic matter. We focus on two regimes in the phase diagram. At low
baryon density nucleons can be described as non-relativistic point particles
interacting via short range forces. Interesting effects arise because of the
large nucleon-nucleon scattering length. At very large density QCD matter can
be described in terms of quarks and gluons. Unusual many body effects arise
because of long range gluons fields, and because of the way color and flavor
get entangled in the superconducting state.",0609075v1
2007-06-27,Effect of a single impurity on the local density of states in monolayer and bilayer graphene,"We use the T-matrix approximation to analyze the effect of a localized
impurity on the local density of states in mono- and bilayer graphene. For
monolayer graphene the Friedel oscillations generated by intranodal scattering
obey an inverse-square law, while the internodal ones obey an inverse law. In
the Fourier transform this translates into a filled circle of high intensity in
the center of the Brillouin zone, and empty circular contours around its
corners. For bilayer graphene both types of oscillations obey an inverse law.",0706.4111v3
2011-06-03,Relaxations and rheology near jamming,"We determine the form of the complex shear modulus $G^*$ in soft sphere
packings near jamming. Viscoelastic response at finite frequency is closely
tied to a packing's intrinsic relaxational modes, which are distinct from the
vibrational modes of undamped packings. We demonstrate and explain the
appearance of an anomalous excess of slowly relaxing modes near jamming,
reflected in a diverging relaxational density of states. From the density of
states, we derive the dependence of $G^*$ on frequency and distance to the
jamming transition, which is confirmed by numerics.",1106.0714v2
2013-07-14,"Density of states for GUE, GOE, and interpolating ensembles through supersymmetric approach","We use the supersymmetric formalism to derive an integral formula for the
density of states of the Gaussian Orthogonal Ensemble, and then apply
saddle-point analysis to give a new derivation of the 1/N-correction to
Wigner's law. This extends the work of Disertori on the Gaussian Unitary
Ensemble. We also apply our method to the interpolating ensembles of
Mehta--Pandey.",1307.3698v3
1995-10-02,Unitary Random-Matrix Ensemble with Governable Level Confinement,"A family of unitary $\alpha$-Ensembles of random matrices with governable
confinement potential $V(x) ~ |x|^\alpha$ is studied employing exact results of
the theory of non-classical orthogonal polynomials. The density of levels,
two-point kernel, locally rescaled two-level cluster function and smoothed
connected correlations between the density of eigenvalues are calculated for
strong ($\alpha > 1$) and border ($\alpha = 1$) level confinement. It is shown
that the density of states is a smooth function for $\alpha > 1$, and has a
well-pronounced peak at the band center for $\alpha <= 1$. The case of border
level confinement associated with transition point $\alpha = 1$ is reduced to
the exactly solvable Pollaczek random-matrix ensemble. Unlike the density of
states, all the two-point correlators remain (after proper rescaling) to be
universal down to and including $\alpha = 1$.",9510001v1
2001-03-08,Non-Fermi liquid behaviour and superconductivity in the dissipative model,"We study an exactly-solvable model which shows a zero-temperature transition
from a non-Fermi liquid to a Fermi liquid as a function of particle density.
The quantum critical point separating these two states is not associated with
the usual ordering transition of a bosonic degree of freedom. We analyze the
properties of this critical point in terms of an effective density of states,
and we use this concept to generalize this transition to a class of related
quantum critical points. We study the superconducting instability of the
low-density (non-Fermi liquid) regime and we show that it has an enhanced pair
susceptibility relative to the Fermi liquid. We comment on the applicability of
our results to low-carrier density superconductors.",0103191v1
2004-06-23,Phase slip in a superfluid Fermi gas near a Feshbach resonance,"In this paper, we study the properties of a phase slip in a superfluid Fermi
gas near a Feshbach resonance. The phase slip can be generated by the phase
imprinting method. Below the superfluid transition temperature, it appears as a
dip in the density profile, and becomes more pronounced when the temperature is
lowered. Therefore the phase slip can provide a direct evidence of the
superfluid state. The condensation energy of the superfluid state can be
extracted from the density profile of the phase slip, due to the unitary
properties of the Fermi gas near the resonance. The width of the phase slip is
proportional to the square root of the difference between the transition
temperature and the temperature. The signature of the phase slip in the density
profile becomes more robust across the BCS-BEC crossover.",0406542v2
2006-03-09,Optimal design of spatial distribution networks,"We consider the problem of constructing public facilities, such as hospitals,
airports, or malls, in a country with a non-uniform population density, such
that the average distance from a person's home to the nearest facility is
minimized. Approximate analytic arguments suggest that the optimal distribution
of facilities should have a density that increases with population density, but
does so slower than linearly, as the two-thirds power. This result is confirmed
numerically for the particular case of the United States with recent population
data using two independent methods, one a straightforward regression analysis,
the other based on density dependent map projections. We also consider
strategies for linking the facilities to form a spatial network, such as a
network of flights between airports, so that the combined cost of maintenance
of and travel on the network is minimized. We show specific examples of such
optimal networks for the case of the United States.",0603278v1
2007-12-08,Electronic structure of copper intercalated transition metal dichalcogenides: First-principles calculations,"We report first principles calculations, within density functional theory, of
copper intercalated titanium diselenides, CuxTiSe2, for values of x ranging
from 0 to 0.11. The effect of intercalation on the energy bands and densities
of states of the host material is studied in order to better understand the
cause of the superconductivity that was recently observed in these structures.
We find that charge transfer from the copper atoms to the metal dichalcogenide
host layers causes a gradual reduction in the number of holes in the otherwise
semi-metallic pristine TiSe2, thus suppressing the charge density wave
transition at low temperatures, and a corresponding increase in the density of
states at the Fermi level. These effects are probably what drive the
superconducting transition in the intercalated systems.",0712.1304v2
2007-12-17,Neutron matter at low density and the unitary limit,"Neutron matter at low density is studied within the hole-line expansion.
Calculations are performed in the range of Fermi momentum $k_F$ between 0.4 and
0.8 fm$^{-1}$. It is found that the Equation of State is determined by the
$^1S_0$ channel only, the three-body forces contribution is quite small, the
effect of the single particle potential is negligible and the three hole-line
contribution is below 5% of the total energy and indeed vanishing small at the
lowest densities. Despite the unitary limit is actually never reached, the
total energy stays very close to one half of the free gas value throughout the
considered density range. A rank one separable representation of the bare NN
interaction, which reproduces the physical scattering length and effective
range, gives results almost indistinguishable from the full Brueckner G-matrix
calculations with a realistic force. The extension of the calculations below
$k_F = 0.4$ fm$^{-1}$ does not indicate any pathological behavior of the
neutron Equation of State.",0712.2662v1
2013-10-02,Evolution of electron-boson spectral density in the underdoped region of Bi_2Sr_{2-x}La_xCuO_6,"We use a maximum entropy technique to obtain the electron-boson spectral
density from optical scattering rate data across the underdoped region of the
Bi_2Sr_{2-x}La_xCuO_6 (Bi-2201) phase diagram. Our method involves a
generalization of previous work which explicitly include finite temperature and
the opening of a pseudogap which modifies the electronic structure. We find
that the mass enhancement factor \lambda associated with the electron-boson
spectral density increases monotonically with reduced doping and closer
proximity to the Mott antiferromagnetic insulating state. This observation is
consistent with increased coupling to the spin fluctuations. At the same time
the system has reduced metallicity because of increased pseudogap effects which
we model with a reduced effective density of states around the Fermi energy
with the range of the modifications in energy set by the pseudogap scale.",1310.0692v1
2015-04-27,Fractional Wigner crystal in the helical Luttinger liquid,"The properties of the strongly interacting edge states of two dimensional
topological insulators in the presence of two particle backscattering are
investigated. We find an anomalous behavior of the density-density correlation
functions, which show oscillations that are neither of Friedel nor of Wigner
type: they instead represent a Wigner crystal of fermions of fractional charge
e/2, with e the electron charge. By studying the Fermi operator, we show that
the state characterized by such fractional oscillations still bears the
signatures of spin momentum locking. Finally, we compare the spin-spin
correlation functions and the density-density correlation functions to argue
that the fractional Wigner crystal is characterized by a non trivial spin
texture.",1504.07143v1
2016-07-04,Insights into Phase Transitions and Entanglement from Density Functional Theory,"Density functional theory has made great success in solid state physics,
quantum chemistry and in computational material sciences. In this work we show
that density functional theory could shed light on phase transitions and
entanglement at finite temperatures. Specifically, we show that the equilibrium
state of an interacting quantum many-body system which is in thermal
equilibrium with a heat bath at a fixed temperature is a universal functional
of the first derivatives of the free energy with respect to temperature and
other control parameters respectively. This insight from density functional
theory enables us to express the average value of any physical observable and
any entanglement measure as a universal functional of the first derivatives of
the free energy with respect to temperature and other control parameters. Since
phase transitions are marked by the nonanalytic behavior of free energy with
respect to control parameters, the physical quantities and entanglement
measures may present nonanalytic behavior at critical point inherited from
their dependence on the first derivative of free energy. We use an
experimentally realizable model to demonstrate the idea. These results give new
insights for phase transitions and provide new profound connections between
entanglement and phase transition in interacting quantum many-body physics.",1607.00734v1
2018-02-27,Linear response time-dependent density functional theory of the Hubbard dimer,"The asymmetric Hubbard dimer is used to study the density-dependence of the
exact frequency-dependent kernel of linear-response time-dependent density
functional theory. The exact form of the kernel is given, and the limitations
of the adiabatic approximation utilizing the exact ground-state functional are
shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and
relative oscillator strengths are defined appropriately. The method of Casida
for extracting oscillator strengths from a frequency-dependent kernel is
demonstrated to yield the exact result with this kernel. An unambiguous way of
labelling the nature of excitations is given. The fluctuation-dissipation
theorem is proven for the ground-state exchange-correlation energy. The
distinction between weak and strong correlation is shown to depend on the ratio
of interaction to asymmetry. A simple interpolation between carefully defined
weak-correlation and strong-correlation regimes yields a density-functional
approximation for the kernel that gives accurate transition frequencies for
both the single and double excitations, including charge-transfer excitations.
Many exact results, limits, and expansions about those limits are given in the
appendices.",1802.09988v2
2018-04-25,"Stability of a topological insulator: interactions, disorder and parity of Kramers doublets","We study stability of multiple conducting edge states in a topological
insulator against all multi-particle perturbations allowed by the time-reversal
symmetry. We model a system as a multi-channel Luttinger liquid, where the
number of channels equals the number of Kramers doublets at the edge. We show
that in the clean system with N Kramers doublets there always exist relevant
perturbations (either of superconducting or charge density wave character)
which always open (N-1) gaps. In the charge density wave regime, (N-1) edge
states get localised. The single remaining gapless mode describes sliding of
'Wigner crystal' like structure. Disorder introduces multi-particle
backscattering processes. While the single-particle backscattering turns out to
be irrelevant, the two-particle process may localise this gapless, in
translation invariant system, mode. Our main result is that an interacting
system with N Kramers doublets at the edge may be either a trivial insulator or
a topological insulator for N=1 or 2, depending on density-density repulsion
parameters whereas any higher number N>2 of doublets gets fully localised by
the disorder pinning irrespective of the parity issue.",1804.09675v1
2019-05-15,Crowd Density Estimation using Novel Feature Descriptor,"Crowd density estimation is an important task for crowd monitoring. Many
efforts have been done to automate the process of estimating crowd density from
images and videos. Despite series of efforts, it remains a challenging task. In
this paper, we proposes a new texture feature-based approach for the estimation
of crowd density based on Completed Local Binary Pattern (CLBP). We first
divide the image into blocks and then re-divide the blocks into cells. For each
cell, we compute CLBP and then concatenate them to describe the texture of the
corresponding block. We then train a multi-class Support Vector Machine (SVM)
classifier, which classifies each block of image into one of four categories,
i.e. Very Low, Low, Medium, and High. We evaluate our technique on the PETS
2009 dataset, and from the experiments, we show to achieve 95% accuracy for the
proposed descriptor. We also compare other state-of-the-art texture descriptors
and from the experimental results, we show that our proposed method outperforms
other state-of-the-art methods.",1905.05891v1
2015-12-24,Basic variables to be reproduced in the first-principles theory for superconductors: Fluctuation of the particle number,"We show that the diagonal elements of the second-order reduced density matrix
(RDM2) can be chosen as basic variables for describing the superconducting
state, instead of the off-diagonal elements of the RDM2 that are usually
adopted as basic variables in the density functional scheme. The diagonal
elements of the RDM2 are called pair-density (PD), which is explicitly related
to the fluctuation of the particle number of the system. In this paper, we
argue that the fluctuation of the particle number can become an indication of
the superconducting state, and that the density functional scheme in which the
PD is chosen as a basic variable would be a promising first-principles theory
for superconductors.",1512.07775v1
2017-06-22,Investigation on nickel ferrite nanowire device exhibiting negative differential resistance $-$ a first-principles investigation,"The electronic property of NiFe$_2$O$_4$ nanowire device is investigated
through nonequilibrium Green's functions (NEGF) in combination with density
functional theory (DFT). The electronic transport properties of NiFe$_2$O$_4$
nanowire are studied in terms of density of states, transmission spectrum and
$I{-}V$ characteristics. The density of states gets modified with the applied
bias voltage across NiFe$_2$O$_4$ nanowire device, the density of charge is
observed both in the valence band and in the conduction band on increasing the
bias voltage. The transmission spectrum of NiFe$_2$O$_4$ nanowire device gives
the insights on the transition of electrons at different energy intervals. The
findings of the present work suggest that NiFe$_2$O$_4$ nanowire device can be
used as negative differential resistance (NDR) device and its NDR property can
be tuned with the bias voltage, which may be used in microwave device, memory
devices and in fast switching devices.",1706.10148v1
2018-10-24,A systematic study of the local minima in L(S)DA+U,"We have performed a systematic study of the emergence of meta-stable states
in density functional theory plus Hubbard U (DFT+U ) simulations of NiO, CoO,
FeO. Particular attention is given to the spin-polarization of the
exchange-correlation functional and the double counting term, and the role of
the spin-orbit coupling. The method of occupation matrix control is extended to
use constrained random density matrices to map out the local minima in the
total energy landscape. The extended scheme, random density matrix control, is
successfully benchmarked against UO2, one of the most investigated systems in
the field. When applied to the transition metal oxides it yields several meta-
stable states which are well-characterized by their local spin and orbital
moments. We find that the addition of spin-orbit coupling helps the simulations
to converge to the global high-spin energy minimum. The random density matrix
control scheme combined with LDA+U yields accurate magnetic moments for all the
studied AFM transition metal oxides.",1810.10393v1
2020-05-06,Mechanical and Vibrational Properties of Three-Dimensional Dimer Packings Near the Jamming Transition,"We comprehensively study mechanical and vibrational properties of dimer
packings in three-dimensional space with particular attention on critical
scaling behaviors near the jamming transition. First, we confirm the dependence
of the packing fraction at the transition on the aspect ratio, the isostatic
contact number at the transition, and the scaling dependence of the excess
contact number on the excess density. Second, we study the elastic moduli, bulk
and shear moduli, and establish power-law scaling of them. Finally, we study
the vibrational density of states and its characteristic frequency. The
vibrational density of states shows two plateaus in the lower- and
higher-frequency regions, which are characterized by rotational and
translational vibrational modes, respectively. The onset frequency of the
lower-frequency plateau scales linearly to the square root of excess density.
The scaling laws in the mechanical and vibrational properties are consistent
between two- and three-dimensional dimers, and they are identical to those in
spheres.",2005.02598v2
2021-06-18,A model-agnostic analysis of hybrid stars with reactive interfaces,"We study hybrid stars considering the effects on stellar stability of the
hadron-quark conversion speed at the sharp interface. The equation of state is
constructed by combining a model-agnostic hadronic description with a constant
speed of sound model for quark matter. We show that current LIGO/Virgo, NICER,
low-density nuclear and high-density perturbative QCD constraints can be
satisfied in two scenarios, with low and high transition pressures. If the
conversion speed at the interface is slow, a new class of dynamically stable
hybrid objects is possible and very stiff hadronic equations of state cannot be
discarded. Densities tens of times larger than the nuclear saturation density
are possible at the center of these objects. We discuss possible formation
mechanisms for the new class of hybrid stars and smoking guns for their
observational identification.",2106.10380v3
2021-11-27,Semi-analytical calculation of the trajectory of relativistic nuclear collisions in the QCD phase diagram,"We extend a semi-analytical model that includes the finite nuclear thickness
to calculate the energy density $\epsilon(t)$ and conserved-charge densities
including the net-baryon density $n_{\rm _B}(t)$ produced at
mid-spacetime-rapidity in central Au+Au collisions. Assuming the formation of a
quark-gluon plasma with an ideal gas equation of state of either quantum or
Boltzmann statistics or with a lattice QCD-based equation of state, we extract
the temperature $T$ and chemical potentials $\mu_{\rm _B}$, $\mu_{\rm _Q}$ and
$\mu_{\rm _S}$ as functions of time. This then allows us to semi-analytically
calculate the $T-\mu_{\rm _B}$ trajectory of relativistic nuclear collisions in
the QCD phase diagram, which should benefit the studies of high density physics
including the search for the critical end point. This model is also useful for
exploring the trajectories in the more general $T-\mu_{\rm _B}-\mu_{\rm
_Q}-\mu_{\rm _S}$ QCD phase space.",2111.13932v3
2022-05-03,Cosmological evolution with negative energy densities,"For general number of spatial dimensions we investigate the cosmological
dynamics driven by a cosmological constant and by a source with barotropic
equation of state. It is assumed that for both those sources the energy density
can be either positive or negative. Exact solutions of the cosmological
equations are provided for flat models. For models with curved space and with
zero cosmological constant the general solutions are expressed in terms of the
hypergeometric function. The qualitative evolution is described for all values
of the equation of state parameter. We specify the values of that parameter and
the combinations of the signs for the cosmological constant and matter energy
density for which the cosmological dynamics is nonsingular. An example is
considered with positive cosmological constant and negative matter energy
density induced by the polarization of the hyperbolic vacuum.",2205.01619v3
2022-06-28,Thermal properties of structurally balanced systems on classical random graphs,"The dynamics of social relations and the possibility of reaching the state of
structural balance (Heider balance) under the influence of the temperature
modeling the social noise level are discussed for interacting actors occupying
nodes of classical random graphs. Depending on the graph density $D$, either a
smooth cross-over or a first-order phase transition from a balanced to an
imbalanced state of the system is observed with an increase of the thermal
noise level. The minimal graph density $D_\text{min}$ for which the first-order
phase transition can be observed decreases with system size $N$ as
$D_\text{min}\propto N^{-0.58(1)}$. For graph densities $D>D_\text{min}$ the
reduced critical temperature $T_c^\star=T_c/T_c(D=1)$ increases with the graph
density as $T_c^\star\propto D^{1.719(6)}$ independently of the system size
$N$.",2206.14226v2
2022-08-02,Response of the chiral soliton lattice to spin polarized currents,"Spin polarized currents originate a spin-transfer torque that enables the
manipulation of magnetic textures. Here we theoretically study the effect of a
spin-polarized current on the magnetic texture corresponding to a chiral
soliton lattice in a monoaxial helimagnet under a transverse magnetic field. At
sufficiently small current density the chiral soliton lattice reaches a steady
motion state with a velocity proportional to the intensity of the applied
current, the mobility being independent of the density of solitons and the
magnetic field. This motion is accompanied with a small conical distortion of
the chiral soliton lattice. At large current density the spin-transfer torque
destabilizes the chiral soliton lattice, driving the system to a ferromagnetic
state parallel to the magnetic field. We analyze how the deformation of the
chiral soliton lattice depends on the applied current density. The destruction
of the chiral soliton lattice under current could serve as a possible erasure
mechanisms for spintronic applications.",2208.01768v1
2024-02-09,Real-time Dynamics of the Schwinger Model as an Open Quantum System with Neural Density Operators,"Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon
Plasma are computationally difficult to perform due to the large dimension of
the space of density matrices. This work develops machine learning algorithms
to overcome this difficulty by approximating exact quantum states with neural
network parametrisations, specifically Neural Density Operators. As a proof of
principle demonstration in a QCD-like theory, the approach is applied to solve
the Lindblad master equation in the 1+1d lattice Schwinger Model as an open
quantum system. Neural Density Operators enable the study of in-medium dynamics
on large lattice volumes, where multiple-string interactions and their effects
on string-breaking and recombination phenomena can be studied. Thermal
properties of the system at equilibrium can also be probed with these methods
by variationally constructing the steady state of the Lindblad master equation.
Scaling of this approach with system size is studied, and numerical
demonstrations on up to 32 spatial lattice sites and with up to 3 interacting
strings are performed.",2402.06607v1
2021-09-25,"Inverse mass cascade in dark matter flow and effects on halo deformation, energy, size, and density profiles","Inverse mass cascade is a key feature of the intermediate statistically
steady state for self-gravitating collisionless dark matter flow (SG-CFD). This
paper focus on effects of mass cascade on halo energy, momentum, dispersion,
size, and density. Halo with fast mass accretion has an expanding core. Mass
cascade forms a new layer of mass that deforms the original halo and induces
nonzero radial flow (outwards in core and inwards in outer regions). The
inward/outward flow leads to an extra length scale (scale radius) that is not
present in isothermal profile. Halo concentration c=3.5 can be derived for fast
growing halos. For cusp-core controversy, a double-power-law density is
proposed as a result of nonzero radial flow. The inner/outer density are
controlled by halo deformation rate and halo growth, respectively. The slower
deformation at center, the steeper density. For fast growing halos, radial flow
at center is simply Hubble flow that leads to the existence of central core.
Mass cascade leads to nonzero halo surface energy/tension and radial flow that
enhances dispersion in outer region. An effective exponent of gravity
$n_e$=-1.3 (not -1) is obtained due to halo surface energy. Halo size follows a
geometric Brownian motion and lognormal distribution. Brownian motion of
particles in evolving halos leads to Fokker-Planck equations for particle
distribution that is dependent on the radial and osmotic flow. Complete
solutions of particle distribution are presented based on a simple model of
osmotic flow. The proposed model agrees with N-body simulation for various halo
group sizes. With reference pressure/density defined at center, equation of
state can be established for relative pressure/density. Pressure, density, and
dispersion at halo center are presented. The core size $x_c$ is obtained where
Hubble flow is dominant. Simple closures are proposed for self-consistent halo
density.",2109.12244v2
2001-02-06,RXTE Observations of Hercules X-1 During the July 1998 Short-high State,"We present RXTE monitoring of the eclipsing X-ray binary Hercules X-1
conducted over the short-high state of July 1998. This was one of the last
major short-high states before the source entered an anomalous low-state of
activity. A comparison with previous epochs finds no evidence for special
behavior during these observations. We determine orbital and pulsar spin
periods to facilitate measurements period derivatives during the subsequent
anomalous low state and during the next epoch of high-state activity.
Spectrally, the decay of the short-high state and concurrent pre-eclipse dips
are consistent with obscuration of a central X-ray source by a cloud of
non-uniform column density. The standard model of a warped accretion disk of
finite vertical scale height fits the characteristics of this absorber well.
Pre-eclipse dips have durations a factor of a few longer than the
characteristic durations of dips during main-high states. Pulse profile
structure increases in complexity towards the tail of the short-high state
suggesting changes in accretion curtain geometry.",0102100v1
2023-12-16,Evidence of sharp transitions between octahedral and capped trigonal prism states of the solvation shell of Fe$^{+3}$(aq),"The structure of the solvation shell of aqueous Fe$^{+3}$ ion has been a
subject of controversy due to discrepancies between experiments and different
levels of theory. We address this issue by performing simulations for a wide
range of ion concentrations, using various empirical potential energy
functions, as well as density functional theory calculations of selected
configurations. The solvation shell undergoes abrupt transitions between two
states: an octahedral (OH) state with 6-fold coordination, and a capped
trigonal prism (CTP) state with 7-fold coordination. The lifetime of these
states is concentration dependent. In dilute $\mathrm{FeCl_3}$ solutions, the
lifetime of the two states is similar ($\approx 1$ ns). However, the lifetime
of the OH state increases with ion concentration, while that of the CTP state
decreases slightly. When a uniform negative background charge is used instead
of explicit counterions, the lifetime of the OH state is greatly overestimated.
These findings underscore the need for further experimental measurements as
well as high-level simulations over sufficiently long timescales and low
concentration.",2312.10471v2
2019-11-07,The emergence of cooperativity accompanying vitrification: Insights from density fluctuation dynamics,"We discuss the emergence and growth of the cooperativity accompanying
vitrification based on the density fluctuation dynamics for fragile
glass-forming liquids. (i) The relaxation of density fluctuations proceeds by
the particle (density) exchange process, and is diffusive; that is, the
allowable kinetic paths are strongly restricted by the local conservation law.
(ii) In normal liquid states, this exchange process is less cooperative, and
the diffusion coefficient of density fluctuations $D_c$ is given as $D_c\sim
\lambda^2/\tau_\alpha$, where $\lambda$ is the particle size and $\tau_\alpha$
is the structural relaxation time. On the other hand, in supercooled states the
restriction on the kinetic path is more severe with increasing the degree of
supercooling, which makes the exchange process more cooperative, resulting in
$D_c \sim \xi_{\rm d}^2/\tau_\alpha$ with $\xi_{\rm d}$ being the cooperative
length scale. (iii) The molecular dynamics simulation results show that the
self-diffusion coefficient of the tagged particle, $D_s$, almost coincides with
$D_c$, suggesting that the collective density diffusion and the particle
diffusion closely share the same mechanism: in normal states $D_s$ determines
$D_c$, but vice versa in supercooled states. This immediately leads to the idea
that the breakdown of the Stokes-Einstein relation is not the anomaly in the
single-particle dynamics but reflects the increase in the cooperativity in the
density diffusion at the length scale of $\xi_{\rm d}$.",1911.02802v1
2003-09-08,On the Quantum Density of States and Partitioning an Integer,"This paper exploits the connection between the quantum many-particle density
of states and the partitioning of an integer in number theory. For $N$ bosons
in a one dimensional harmonic oscillator potential, it is well known that the
asymptotic (N -> infinity) density of states is identical to the
Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of
integers. We show that the same statistical mechanics technique for the density
of states of bosons in a power-law spectrum yields the partitioning formula for
p^s(n), the latter being the number of partitions of n into a sum of s-th
powers of a set of integers. By making an appropriate modification of the
statistical technique, we are also able to obtain d^s(n) for distinct
partitions. We find that the distinct square partitions d^2(n) show pronounced
oscillations as a function of n about the smooth curve derived by us. The
origin of these oscillations from the quantum point of view is discussed. After
deriving the Erdos-Lehner formula for restricted partitions for the $s=1$ case
by our method, we generalize it to obtain a new formula for distinct restricted
partitions.",0309020v1
2011-10-26,Thermoelectric transport properties of an apparent Fermi liquid: Relation to an analytic anomaly in the density of states and application to hole-doped delafossites,"Through the motivation of the recent discovery of dispersionless regions in
the band structure of the delafossites, a model density of states of free
fermions including a discontinuity as analytical anomaly is studied. The
resulting temperature dependence of the chemical potential is obtained both
exactly and by different approximation schemes which are then discussed
thoroughly. This includes the introduction of an approximation of the
polylogarithm difference which is capable of accessing a parameter range
neither covered by Sommerfeld expansion nor by Boltzmann approximation. It is
found that the Fermi temperature and several other temperature scales may be
very low, giving rise to experimentally observable behaviours differing from
the one described by Fermi liquid theory. In particular, two kinds of apparent
Fermi liquid behaviour emerge at intermediate temperatures. This behaviour is
related to recent transport data reported for CuCr(1-x)MgxO2 [A. Maignan et.
al, Solid State Commun. 149, 962 (2009)] and CuRh(1-x)MgxO2 [A. Maignan et. al,
Phys. Rev. B 80, 115103 (2009)] by means of the temperature independent
correlation functions ratio approximation. In this way an effective density of
states as well as the effective charge carrier density of these materials are
determined. Furthermore, conclusions about the specific heat of the latter
material are drawn which presents particular effects of the analytical anomaly.",1110.5735v2
1998-01-21,Density fluctuations and phase separation in a traffic flow model,"Within the Nagel-Schreckenberg traffic flow model we consider the transition
from the free flow regime to the jammed regime. We introduce a method of
analyzing the data which is based on the local density distribution. This
analyzes allows us to determine the phase diagram and to examine the separation
of the system into a coexisting free flow phase and a jammed phase above the
transition. The investigation of the steady state structure factor yields that
the decomposition in this phase coexistence regime is driven by density
fluctuations, provided they exceed a critical wavelength.",9801220v1
2013-11-14,Spectral densities from the lattice,"We discuss a method to extract the K\""all\'{e}n-Lehmann spectral density of a
particle (be it elementary or bound state) propagator by means of 4d lattice
data. We employ a linear regularization strategy, commonly known as the
Tikhonov method with Morozov discrepancy principle. An important virtue over
the popular maximum entropy method is the possibility to also probe unphysical
spectral densities, as, for example, of a confined gluon. We apply our proposal
to the SU(3) glue sector.",1311.3643v1
2015-11-19,Equilibrium sampling of hard spheres up to the jamming density and beyond,"We implement and optimize a particle-swap Monte-Carlo algorithm that allows
us to thermalize a polydisperse system of hard spheres up to
unprecedentedly-large volume fractions, where \revise{previous} algorithms and
experiments fail to equilibrate. We show that no glass singularity intervenes
before the jamming density, which we independently determine through two
distinct non-equilibrium protocols. We demonstrate that equilibrium fluid and
non-equilibrium jammed states can have the same density, showing that the
jamming transition cannot be the end-point of the fluid branch.",1511.06182v2
2020-04-07,Nonlinear Electronic Density Response in Warm Dense Matter,"Warm dense matter (WDM)---an extreme state with high temperatures and
densities that occurs e.g. in astrophysical objects---constitutes one of the
most active fields in plasma physics and materials science. These conditions
can be realized in the lab by shock compression or laser excitation, and the
most accurate experimental diagnostics is achieved with lasers and free
electron lasers which is theoretically modeled using linear response theory.
Here, we present first \textit{ab initio} path integral Monte Carlo results for
the nonlinear density response of correlated electrons in WDM and show that for
many situations of experimental relevance nonlinear effects cannot be
neglected.",2004.03229v1
2023-01-18,Locally uniform random permutations with large increasing subsequences,"We investigate the maximal size of an increasing subset among points randomly
sampled from certain probability densities. Kerov and Vershik's celebrated
result states that the largest increasing subset among $N$ uniformly random
points on $[0,1]^2$ has size asymptotically $2\sqrt{N}$. More generally, the
order $\Theta(\sqrt{N})$ still holds if the sampling density is continuous. In
this paper we exhibit two sufficient conditions on the density to obtain a
growth rate equivalent to any given power of $N$ greater than $\sqrt{N}$, up to
logarithmic factors. Our proofs use methods of slicing the unit square into
appropriate grids, and investigating sampled points appearing in each box.",2301.07658v1
2000-10-18,Gravitational Lensing Statistics as a Probe of Dark Energy,"By using the comoving distance, we derive an analytic expression for the
optical depth of gravitational lensing, which depends on the redshift to the
source and the cosmological model characterized by the cosmic mass density
parameter $\Omega_m$, the dark energy density parameter $\Omega_x$ and its
equation of state $\omega_x = p_x/\rho_x$. It is shown that, the larger the
dark energy density is and the more negative its pressure is, the higher the
gravitational lensing probability is. This fact can provide an independent
constraint for dark energy.",0010351v1
1992-10-23,Static Response Function for Longitudinal and Transverse Excitations in Superfluid Helium,"The sum rule formalism is used to evaluate rigorous bounds for the density
and current static response functions in superfluid helium at zero temperature.
Both lower and upper bounds are considered. The bounds are expressed in terms
of ground state properties (density and current correlation funtions) and of
the interatomic potential. The results for the density static response
significantly improve the Feynman approximation and turn out to be close to the
experimental (neutron scattering) data. A quantitative prediction for the
transverse current response is given. The role of one-phonon and multi-particle
excitations in the longitudinal and transverse channels is discussed.
(Phys.Rev.B, in press)",9210021v1
1995-11-16,Analytic Formulations of the Density Matrix Renormalization Group,"We present two new analytic formulations of the Density Matrix
Renormalization Group Method. In these formulations we combine the block
renormalization group (BRG) procedure with Variational and Fokker-Planck
methods. The BRG method is used to reduce the lattice size while the latter are
used to construct approximate target states to compute the block density
matrix. We apply our DMRG methods to the Ising Model in a transverse field (ITF
model) and compute several of its critical properties which are then compared
with the old BRG results.",9511083v1
1997-11-08,Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem,"We apply the density matrix renormalization group (DMRG) method to a
non-equilibrium problem: the asymmetric exclusion process in one dimension. We
study the stationary state of the process to calculate the particle density
profile (one-point function). We show that, even with a small number of
retained bases, the DMRG calculation is in excellent agreement with the exact
solution obtained by the matrix-product-ansatz approach.",9711072v1
1998-11-07,Quantum Field Theory of the Pinned Density Wave,"A model is discussed in which an electric field induces quantum nucleation of
soliton-antisoliton pairs in a pinned charge or spin density wave. Coulomb
blockade prevents pair creation until the electric field exceeds a sharp
threshold value, which can be much smaller than the classical depinning field.
We calculate the vacuum state energy and expectation value of the phase, which
is treated as a quantum scalar field. We find that the phase can also be much
smaller, below threshold, than predicted by classical ``sliding'' density wave
models.",9811103v1
1999-06-14,Temperature and density extrapolations in canonical ensemble Monte Carlo simulations,"We show how to use the multiple histogram method to combine canonical
ensemble Monte Carlo simulations made at different temperatures and densities.
The method can be applied to study systems of particles with arbitrary
interaction potential and to compute the thermodynamic properties over a range
of temperatures and densities. The calculation of the Helmholtz free energy
relative to some thermodynamic reference state enables us to study phase
coexistence properties. We test the method on the Lennard-Jones fluids for
which many results are available.",9906202v1
2003-08-14,Exchange-correlation vector potentials and vorticity-dependent exchange-correlation energy densities in two-dimensional systems,"We present a new approach how to calculate the scalar exchange-correlation
potentials and the vector exchange-correlation potentials from current-carrying
ground states of two-dimensional quantum dots. From these exchange-correlation
potentials we derive exchange-correlation energy densities and examine their
vorticity (or current) dependence. Compared with parameterizations of
current-induced effects in literature we find an increased significance of
corrections due to paramagnetic current densities.",0308269v1
2004-06-02,Onset of Interlayer Phase Coherence in a Bilayer Two-Dimensional Electron System: Effect of Layer Density Imbalance,"Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer
phase coherence in bilayer two-dimensional electron systems at total Landau
level filling factor $\nu_T = 1$. We find that the phase boundary between the
interlayer phase coherent state and the weakly-coupled compressible phase moves
to larger layer separations as the electron density distribution in the bilayer
is imbalanced. The critical layer separation increases quadratically with layer
density difference.",0406067v1
2003-01-27,"Lattice QCD at non-vanishing density: phase diagram, equation of state","We propose a method to study lattice QCD at non-vanishing temperature (T) and
chemical potential (\mu). We use n_f=2+1 dynamical staggered quarks with
semi-realistic masses on L_t=4 lattices. The critical endpoint (E) of QCD on
the Re(\mu)-T plane is located. We calculate the pressure (p), the energy
density (\epsilon) and the baryon density (n_B) of QCD at non-vanishing T and
\mu.",0301027v1
2000-08-23,Sigma Decay at Finite Temperature and Density,"Sigma decay and its relation with chiral phase transition are discussed at
finite temperature and density in the framework of the Nambu-Jona-Lasinio
model. The decay rate for the process sigma -> 2 pions to first order in a
1/N_c expansion is calculated as a function of temperature T and baryon density
n_b. In particular, only when the chiral phase transition happens around the
tricritical point, the sigma decay results in a non-thermal enhancement of
pions in the final state distributions in relativistic heavy ion collisions.",0008041v1
2001-10-21,Charged kaon condensation in high density quark matter,"We show that at asymptotically high densities the ``color-flavor-locked +
neutral kaon condensate'' phase of QCD develops a {\it charged} kaon condensate
through the Coleman-Weinberg mechanism. At densities achievable in neutron
stars a charged kaon condensate forms only for some (natural) values of the low
energy constants describing the low-lying excitations of the ground state.",0110049v2
2008-04-24,High-field Current-carrying Capacity of Semiconducting Carbon Nanotubes,"It is shown that current saturation in semiconducting carbon nanotubes is
indistinguishable from metallic nanotubes if the carrier density is above a
critical value determined by the bandgap and the LO phonon energy. This feature
stems from the higher number of current-carrying states in the semiconducting
tubes due to the van-Hove singularity at the band-edge. Above this critical
carrier density, the ensemble saturation velocity at high-fields is found to be
independent of the bandgap, but strongly dependent on the carrier density,
explaining recent observations.",0804.3997v2
2008-10-19,Stellar matter with a strong magnetic field within density-dependent relativistic models,"The effect of strong magnetic fields on the equation of state (EoS) for
compact stars described with density-dependent relativistic hadronic models is
studied. A comparison with other mean-field relativistic models is done. It is
shown that the largest differences between models occur for low densities, and
that the magnetic field affects the crust properties of a star, namely its
extension.",0810.3390v1
2009-04-24,Phase diagram of imbalanced strongly interacting fermions on a one-dimensional optical lattice,"We show that the Hubbard Hamiltonian with particle-assisted tunneling rates
--recently proposed to model a fermionic mixture near a broad Feshbach
resonance-- displays a ground state phase diagram with superfluid, insulating,
and phase separated regimes. In the latter case, when the populations are
balanced the two phases coexist in microscopic antiferromagnetic domains.
Macroscopic phase segregation into a high-density superfluid of molecules, and
a low-density Fermi liquid of single atoms appears in the density profile above
a critical polarization p_c.",0904.3892v2
2009-10-08,Complete subgraphs in multipartite graphs,"Turan's Theorem states that every graph of a certain edge density contains a
complete graph $K^k$ and describes the unique extremal graphs. We give a
similar Theorem for l-partite graphs. For large l, we find the minimal edge
density $d^k_l$, such that every $\ell$-partite graph whose parts have pairwise
edge density greater than $d^k_l$ contains a $K^k$. It turns out that
$d^k_l=(k-2)/(k-1)$ for large enough l. We also describe the structure of the
extremal graphs.
  For the case of triangles we show that $d^3_{13}=1/2$, disproving a
conjecture by Bondy, Shen, Thomasse and Thomassen.",0910.1447v1
2010-01-04,Rare-earth impurities in Co$_2$MnSi: an opportunity to improve Half-Metallicity at finite temperatures,"We analyse the effects of doping Holmium impurities into the full-Heusler
ferromagnetic alloy Co$_2$MnSi. Experimental results, as well as theoretical
calculations within Density Functional Theory in the ""Local Density
Approximation plus Hubbard U"" framework show that the holmium moment is aligned
antiparallely to that of the transition metal atoms. According to the
electronic structure calculations, substituting Ho on Co sites introduces a
finite density of states in the minority spin gap, while substitution on the Mn
sites preserves the half-metallic character.",1001.0480v1
2011-12-22,Electric field effect on superconductivity at complex oxide interfaces,"We examine the enhancement of the interfacial superconductivity between
LaAlO$_{3}$ and SrTiO$_{3}$ by an effective electric field. Through the
breaking of inversion symmetry at the interface, we show that a term coupling
the superfluid density and an electric field can augment the superconductivity
transition temperature. Microscopically, we show that an electric field can
also produce changes in the carrier density by relating the measured
capacitance to the density of states. Through the electron-phonon induced
interaction in bulk SrTiO$_{3}$, we estimate the transition temperature.",1112.5466v2
2012-06-07,Nuclear Level Densities in the Constant-Spacing Model,"A new method to calculate level densities for non-interacting Fermions within
the constant-spacing model with a finite number of states is developed. We show
that asymptotically (for large numbers of particles or holes) the densities
have Gaussian form. We improve on the Gaussian distribution by using analytical
expressions for moments higher than the second. Comparison with numerical
results shows that the resulting sixth-moment approximation is excellent except
near the boundaries of the spectra and works globally for all particle/hole
numbers and all excitation energies.",1206.1542v2
2012-08-14,Threading dislocation densities in semiconductor crystals: a geometric approach,"In this letter, we introduce a geometric model to explain the origin of the
observed shallow levels in semiconductors threaded by a dislocation density. We
show that a uniform distribution of screw dislocations acts as an effective
uniform magnetic field which yields bound states for a spin-half quantum
particle, even in the presence of a repulsive Coulomb-like potential. This
introduces energy levels within the band gap, increasing the carrier
concentration in the region threaded by the dislocation density and adding
additional recombination paths other than the near band-edge recombination.",1208.2851v1
2013-12-03,Developments in lattice QCD for matter at high temperature and density,"A brief overview of the QCD phase diagram at nonzero temperature and density
is provided. It is explained why standard lattice QCD techniques are not
immediately applicable for its determination, due to the sign problem. We then
discuss a selection of recent lattice approaches that attempt to evade the sign
problem and classify them according to the underlying principle: constrained
simulations (density of states, histograms), holomorphicity (complex Langevin,
Lefschetz thimbles), partial summations (clusters, subsets, bags) and change in
integration order (strong coupling, dual formulations).",1312.0968v2
2014-04-16,Derivation of the Fick's Law for the Lorentz Model in a low density regime,"We consider the Lorentz model in a slab with two mass reservoirs at the
boundaries. We show that, in a low density regime, there exists a unique
stationary solution for the microscopic dynamics which converges to the
stationary solution of the heat equation, namely to the linear profile of the
density. In the same regime the macroscopic current in the stationary state is
given by the Fick's law, with the diffusion coefficient determined by the
Green-Kubo formula.",1404.4186v2
2014-10-23,Conductivity anisotropy helps to reveal the microscopic structure of a density wave at imperfect nesting,"Superconductivity or metallic state may coexist with density wave ordering at
imperfect nesting of the Fermi surface. In addition to the macroscopic spatial
phase separation, there are, at least, two possible microscopic structures of
such coexistence: (i) the soliton-wall phase and (ii) the ungapped
Fermi-surface pockets. We show that the conductivity anisotropy allows to
distinguish between these two microscopic density-wave structures. The results
obtained may help to analyze the experimental observations in layered organic
metals (TMTSF)$_{2}$PF$_{6}$, (TMTSF)$_{2}$ClO$_{4}$, $\alpha
$-(BEDT-TTF)$_{2}$KHg(SCN)$_{4}$ and in other compounds.",1410.6314v1
2017-08-18,Ultra-Sparse Non-Binary LDPC Codes for Probabilistic Amplitude Shaping,"This work shows how non-binary low-density parity-check codes over GF($2^p$)
can be combined with probabilistic amplitude shaping (PAS) (B\""ocherer, et al.,
2015), which combines forward-error correction with non-uniform signaling for
power-efficient communication. Ultra-sparse low-density parity-check codes over
GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary
LDPC codes at a spectral efficiency of 1.5 bits per channel use and a
blocklength of 576 bits. The simulation results are compared to finite length
coding bounds and complemented by density evolution analysis.",1708.05558v1
2017-08-30,Matrix product solution of a left-permeable two-species asymmetric exclusion process,"We study a two-species partially asymmetric exclusion process where the left
boundary is permeable for the `slower' species but the right boundary is not.
We find a matrix product solution for the stationary state, and the exact
stationary phase diagram for the densities and currents. By calculating the
density of each species at the boundaries, we find further structure in the
stationary phases. In particular, we find that the slower species can reach and
accumulate at the far boundary, even in phases where the bulk density of these
particles approaches zero.",1708.09153v2
2010-05-04,Pair Density Wave correlations in the Kondo-Heisenberg Model,"We show, using density matrix renormalization group calculations complemented
by field theoretic arguments, that the spin gapped phase of the one dimensional
Kondo-Heisenberg model exhibits quasi-long range superconducting correlations
{\it only} at a non-zero momentum. The local correlations in this phase
resemble those of the pair density wave state which was recently proposed to
describe the phenomenology of the striped ordered high temperature
superconductor {La$_{2-x}$Ba$_x$% CuO$_4$}, in which the spin, charge, and
superconducting orders are strongly intertwined.",1005.0623v2
2018-08-01,Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo,"Galilean invariance is usually violated in self-consistent mean-field
calculations that employ effective density-dependent nuclear forces. We present
a novel approach, based on variational quantum Monte Carlo techniques, suitable
to preserve this symmetry and assess the effect of its violation, seldom
attempted in the past. To this aim, we generalize the linear optimization
method to encompass the density-dependence of effective Hamiltonians, and study
$^4$He, $^{16}$O, and $^{40}$Ca ground-state properties employing the Gogny
interaction.",1808.00518v2
2020-09-08,The BCS Energy Gap at Low Density,"We show that the energy gap for the BCS gap equation is $ \Xi = \mu \left( 8
e^{-2} + o(1)\right) \exp\left( \frac{\pi}{2\sqrt{\mu} a}\right) $ in the low
density limit $\mu \to 0$. Together with the similar result for the critical
temperature [arXiv:0803.3324] this shows that, in the low density limit, the
ratio of the energy gap and critical temperature is a universal constant
independent of the interaction potential $V$. The results hold for a class of
potentials with negative scattering length $a$ and no bound states.",2009.03701v1
2009-12-03,Infrared and electronic Raman response of coexisting d-wave density wave and d-wave superconductivity,"We present mean-field calculations for the in-plane optical conductivity, the
superfluid density, and the electronic Raman susceptibility in quasi
two-dimensional systems possessing a ground state with two competing order
parameters: d-wave density wave (dDW) and d-wave superconductor (dSC). In the
coexisting dDW+dSC phase we calculate the frequency dependence of these
correlation functions in the presence of impurity scattering in the unitary
limit, relevant to zinc-doped cuprate superconductors.",0912.0564v2
2016-08-04,Improved Separability Criteria Based on Bloch Representation of Density Matrices,"The correlation matrices or tensors in the Bloch representation of density
matrices are encoded with entanglement properties. In this paper, based on the
Bloch representation of density matrices, we give some new separability
criteria for bipartite and multipartite quantum states. Theoretical analysis
and some examples show that the proposed criteria can be more efficient than
the previous related criteria.",1608.01547v2
2020-04-06,Quantum Inspired Word Representation and Computation,"Word meaning has different aspects, while the existing word representation
""compresses"" these aspects into a single vector, and it needs further analysis
to recover the information in different dimensions. Inspired by quantum
probability, we represent words as density matrices, which are inherently
capable of representing mixed states. The experiment shows that the density
matrix representation can effectively capture different aspects of word meaning
while maintaining comparable reliability with the vector representation.
Furthermore, we propose a novel method to combine the coherent summation and
incoherent summation in the computation of both vectors and density matrices.
It achieves consistent improvement on word analogy task.",2004.02705v2
2020-11-07,A Strong Baseline for Crowd Counting and Unsupervised People Localization,"In this paper, we explore a strong baseline for crowd counting and an
unsupervised people localization algorithm based on estimated density maps.
Firstly, existing methods achieve state-of-the-art performance based on
different backbones and kinds of training tricks. We collect different
backbones and training tricks and evaluate the impact of changing them and
develop an efficient pipeline for crowd counting, which decreases MAE and RMSE
significantly on multiple datasets. We also propose a clustering algorithm
named isolated KMeans to locate the heads in density maps. This method can
divide the density maps into subregions and find the centers under local count
constraints without training any parameter and can be integrated with existing
methods easily.",2011.03725v1
2021-02-06,Translation Invariant Bipolarons and Charge Density Waves in High-Temperature Superconductors,"A correlation is established between the theories of superconductivity based
on the concept of charge density waves (CDW) and the translation invariant (TI)
bipolaron theory. It is shown that CDW are originated from TI-bipolaron states
in the pseudogap phase due to Kohn anomaly and form a pair density wave (PDW)
for wave vectors corresponding to nesting. Emerging in the pseudogap phase, CDW
coexist with superconductivity at temperatures below that of superconducting
transition while their wave amplitudes decrease as a Bose condensate is formed
from TI-bipolarons, vanishing at zero temperature.",2103.00494v2
2022-05-12,Global Strong Solutions to Density-Dependent Viscosity Navier-Stokes Equations in 3D Exterior Domains,"The nonhomogeneous Navier-Stokes equations with density-dependent viscosity
is studied in three-dimensional (3D) exterior domains with nonslip or slip
boundary conditions. We prove that the strong solutions exists globally in time
provided that the gradient of the initial velocity is suitably small. Here the
initial density is allowed to contain vacuum states. Moreover, after developing
some new techniques and methods, the large-time behavior of the strong
solutions with exponential decay-in-time rates is also obtained.",2205.05925v1
2023-08-04,Explicit Local density bounds for Itô-processes with irregular drift,"We find explicit upper bounds for the density of marginals of continuous
diffusions where we assume that the diffusion coefficient is constant and the
drift is solely assumed to be progressively measurable and locally bounded. In
one dimension we extend our result to the case that the diffusion coefficient
is a locally Lipschitz-continuous function of the state. Our approach is based
on a comparison to a suitable doubly reflected Brownian motion whose density is
known in a series representation.",2308.02241v1
2021-05-19,Improved Exploring Starts by Kernel Density Estimation-Based State-Space Coverage Acceleration in Reinforcement Learning,"Reinforcement learning (RL) is currently a popular research topic in control
engineering and has the potential to make its way to industrial and commercial
applications. Corresponding RL controllers are trained in direct interaction
with the controlled system, rendering them data-driven and performance-oriented
solutions. The best practice of exploring starts (ES) is used by default to
support the learning process via randomly picked initial states. However, this
method might deliver strongly biased results if the system's dynamic and
constraints lead to unfavorable sample distributions in the state space (e.g.,
condensed sample accumulation in certain state-space areas). To overcome this
issue, a kernel density estimation-based state-space coverage acceleration
(DESSCA) is proposed, which improves the ES concept by prioritizing
infrequently visited states for a more balanced coverage of the state space
during training. Compared to neighbouring methods in the field of count-based
exploration, DESSCA can also be applied to continuous state spaces without the
need for artificial discretization of the states. Moreover, the algorithm
allows to define arbitrary reference state distributions such that the state
coverage can be shaped w.r.t. the application needs. Considered test scenarios
are mountain car, cartpole and electric motor control environments. Using DQN
and DDPG as exemplary RL algorithms, it can be shown that DESSCA is a simple
yet effective algorithmic extension to the established ES approach that enables
an increase in learning stability as well as the final control performance.",2105.08990v2
2023-07-06,Bose metal in exactly solvable model with infinite-range Hatsugai-Kohmoto interaction,"In a conventional boson system, the ground state can either be an insulator
or a superfluid (SF) due to the duality between particle number and phase. This
paper reveals that the long-sought Bose metal (BM) state can be realized in an
exactly solvable interacting bosonic model, i.e. the Bose-Hatsugai-Kohmoto
(BHK) model, which acts as the nontrivial extension of Bose-Hubbard (BH) model.
By tuning the parameters such as bandwidth $W$, chemical potential $\mu$, and
interaction strength $U$, a BM state without any symmetry-breaking can be
accessed for a generic $W/U$ ratio, while a Mott insulator (MI) with integer
boson density is observed at small $W/U$. The quantum phase transition between
the MI and BM states belongs to the universality class of the Lifshitz
transition, which is further confirmed by analyzing the momentum-distribution
function, the Drude weight, and the superfluid density. Additionally, our
investigation at finite temperature reveals similarities between the BM state
and the Fermi liquid, such as a linear-$T$ dependent heat capacity ($Cv\sim
\gamma T$) and a saturated charge susceptibility ($\chi_{c} \sim $ constant) as
$T$ approaches zero. Comparing the BM state with the SF state in the standard
BH model, we find that the key feature of the BM state is a compressible total
wavefunction accompanied by an incompressible zero-momentum component. Given
that the BM state prevails over the SF state at any finite $U$ in the BHK
model, our work suggests the possibility of realizing the BM state with on-site
repulsion interactions in momentum space.",2307.03051v3
2004-03-16,Graph-based simulation of quantum computation in the density matrix representation,"Quantum-mechanical phenomena are playing an increasing role in information
processing, as transistor sizes approach the nanometer level, and quantum
circuits and data encoding methods appear in the securest forms of
communication. Simulating such phenomena efficiently is exceedingly difficult
because of the vast size of the quantum state space involved. A major
complication is caused by errors (noise) due to unwanted interactions between
the quantum states and the environment. Consequently, simulating quantum
circuits and their associated errors using the density matrix representation is
potentially significant in many applications, but is well beyond the
computational abilities of most classical simulation techniques in both time
and memory resources. The size of a density matrix grows exponentially with the
number of qubits simulated, rendering array-based simulation techniques that
explicitly store the density matrix intractable. In this work, we propose a new
technique aimed at efficiently simulating quantum circuits that are subject to
errors. In particular, we describe new graph-based algorithms implemented in
the simulator QuIDDPro/D. While previously reported graph-based simulators
operate in terms of the state-vector representation, these new algorithms use
the density matrix representation. To gauge the improvements offered by
QuIDDPro/D, we compare its simulation performance with an optimized array-based
simulator called QCSim. Empirical results, generated by both simulators on a
set of quantum circuit benchmarks involving error correction, reversible logic,
communication, and quantum search, show that the graph-based approach far
outperforms the array-based approach.",0403114v2
2013-12-13,Differentiable but exact formulation of density-functional theory,"The universal density functional $F$ of density-functional theory is a
complicated and ill-behaved function of the density-in particular, $F$ is not
differentiable, making many formal manipulations more complicated. Whilst $F$
has been well characterized in terms of convex analysis as forming a conjugate
pair $(E,F)$ with the ground-state energy $E$ via the Hohenberg-Kohn and Lieb
variation principles, $F$ is nondifferentiable and subdifferentiable only on a
small (but dense) set of its domain. In this article, we apply a tool from
convex analysis, Moreau-Yosida regularization, to construct, for any
$\epsilon>0$, pairs of conjugate functionals $({}^\epsilon\!E,{}^\epsilon\!F)$
that converge to $(E,F)$ pointwise everywhere as $\epsilon\rightarrow 0^+$, and
such that ${}^\epsilon\!F$ is (Fr\'echet) differentiable. For technical
reasons, we limit our attention to molecular electronic systems in a finite but
large box. It is noteworthy that no information is lost in the Moreau-Yosida
regularization: the physical ground-state energy $E(v)$ is exactly recoverable
from the regularized ground-state energy ${}^\epsilon\!E(v)$ in a simple way.
All concepts and results pertaining to the original $(E,F)$ pair have direct
counterparts in results for $({}^\epsilon\! E, {}^\epsilon\!F)$. The
Moreau-Yosida regularization therefore allows for an exact, differentiable
formulation of density-functional theory. In particular, taking advantage of
the differentiability of ${}^\epsilon\!F$, a rigorous formulation of Kohn-Sham
theory is presented that does not suffer from the noninteracting
representability problem in standard Kohn-Sham theory.",1312.3734v2
2017-08-23,The equation of state for dense nucleonic matter from a metamodeling. I. Foundational aspects,"A metamodeling for the nucleonic equation of state (EOS), inspired from a
Taylor expansion around the saturation density of symmetric nuclear matter, is
proposed and parameterized in terms of the empirical parameters. The present
knowledge of nuclear empirical parameters is first reviewed in order to
estimate their average values and associated uncertainties, and thus defining
the parameter space of the metamodeling. They are divided into isoscalar and
isovector type, and ordered according to their power in the density expansion.
The goodness of the metamodeling is analyzed against the predictions of the
original models. In addition, since no correlation among the empirical
parameters is assumed a priori, all arbitrary density dependences can be
explored, which might not be accessible in existing functionals. Spurious
correlations due to the assumed functional form are also removed. This meta-EOS
allows direct relations between the uncertainties on the empirical parameters
and the density dependence of the nuclear equation of state and its
derivatives, and the mapping between the two can be done with standard Bayesian
techniques. A sensitivity analysis shows that the more influential empirical
parameters are the isovector parameters $L_{sym}$ and $K_{sym}$, and that
laboratory constraints at super-saturation densities are essential to reduce
the present uncertainties. The present metamodeling for the EOS for nuclear
matter is proposed for further applications in neutron stars and supernova
matter.",1708.06894v3
2022-02-04,Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers,"A novel parallel hybrid quantum-classical algorithm for the solution of the
quantum-chemical ground-state energy problem on gate-based quantum computers is
presented. This approach is based on the reduced density-matrix functional
theory (RDMFT) formulation of the electronic structure problem. For that
purpose, the density-matrix functional of the full system is decomposed into an
indirectly coupled sum of density-matrix functionals for all its subsystems
using the adaptive cluster approximation to RDMFT. The approximations involved
in the decomposition and the adaptive cluster approximation itself can be
systematically converged to the exact result. The solutions for the
density-matrix functionals of the effective subsystems involves a constrained
minimization over many-particle states that are approximated by parametrized
trial states on the quantum computer similarly to the variational quantum
eigensolver. The independence of the density-matrix functionals of the
effective subsystems introduces a new level of parallelization and allows for
the computational treatment of much larger molecules on a quantum computer with
a given qubit count. In addition, for the proposed algorithm techniques are
presented to reduce the qubit count, the number of quantum programs, as well as
its depth. The new approach is demonstrated for Hubbard-like systems on IBM
quantum computers based on superconducting transmon qubits.",2202.02417v2
2023-12-03,Structural transitions in interacting lattice systems,"We consider two-dimensional systems of point particles located on rectangular
lattices and interacting via pairwise potentials. The goal of this paper is to
investigate the phase transitions (and their nature) at fixed density for the
minimal energy of such systems. The 2D rectangle lattices we consider have an
elementary cell of sides $a$ and $b$, the aspect ratio is defined as
$\Delta=b/a$ and the inverse particle density $A = a b$; therefore, the
""symmetric'' state with $\Delta=1$ corresponds to the square lattice and the
""non-symmetric'' state to the rectangular lattice with $\Delta\ne 1$. For
certain types of the interaction potential, by changing continuously the
particle density, such lattice systems undertake at a specific value of the
(inverse) particle density $A^*$ a structural transition from the symmetric to
the non-symmetric state. The structural transition can be either of first order
($\Delta$ unstick from its symmetric value $\Delta=1$ discontinuously) or of
second order ($\Delta$ unstick from $\Delta=1$ continuously); the first and
second-order phase transitions are separated by the so-called tricritical
point. We develop a general theory on how to determine the exact values of the
transition densities and the location of the tricritical point. The general
theory is applied to the double Yukawa and Yukawa-Coulomb potentials.",2312.01395v1
2024-02-13,Finite density QCD equation of state: critical point and lattice-based $T'$-expansion,"We present a novel construction of the QCD equation of state (EoS) at finite
baryon density. Our work combines a recently proposed resummation scheme for
lattice QCD results with the universal critical behavior at the QCD critical
point. This allows us to obtain a family of equations of state in the range $0
\leq \mu_B \leq 700$ MeV and 25 MeV $\leq T \leq 800$ MeV, which match lattice
QCD results near $\mu_B=0$ while featuring a critical point in the 3D Ising
model universality class. The position of the critical point can be chosen
within the range accessible to beam-energy scan heavy-ion collision
experiments. The strength of the singularity and the shape of the critical
region are parameterized using a standard parameter set. We impose stability
and causality constraints and discuss the available ranges of critical point
parameter choices, finding that they extend beyond earlier parametric QCD EoS
proposals. We present thermodynamic observables, including baryon density,
pressure, entropy density, energy density, baryon susceptibility and speed of
sound, that cover a wide range in the QCD phase diagram relevant for
experimental exploration.",2402.08636v2
1996-03-14,Ensemble Density Functional Theory for Inhomogeneous Fractional Quantum Hall Systems,"The fractional quantum Hall effect (FQHE) occurs at certain magnetic field
strengths B*(n) in a two-dimensional electron gas of density n at strong
magnetic fields perpendicular to the plane of the electron gas. At these
magnetic fields strengths, the system is incompressible, i.e., there is a
finite cost in energy for creating charge density fluctuations in the bulk,
while the boundary of the electron gas has gapless modes of density waves. The
bulk energy gap arises because of the strong electron-electron interactions.
While there are very good models for infinite homogeneous systems and for the
gapless excitations of the boundary of the electron gas, computational methods
to accurately model finite, inhomogeneous systems with more then about ten
electrons have not been available until very recently. We will here review an
ensemble density functional approach to studying the ground state of large
inhomogeneous spin polarized FQHE systems.",9603100v1
2000-08-21,Application of the density dependent hadron field theory to neutron star matter,"The density dependent hadron field (DDRH) theory, previously applied to
isospin nuclei and hypernuclei is used to describe $\beta$-stable matter and
neutron stars under consideration of the complete baryon octet. The
meson-hyperon vertices are derived from Dirac-Brueckner calculations of nuclear
matter and extended to hyperons. We examine properties of density dependent
interactions derived from the Bonn A and from the Groningen NN potential as
well as phenomenological interactions. The consistent treatment of the density
dependence introduces rearrangement terms in the expression for the baryon
chemical potential. This leads to a more complex condition for the
$\beta$-equilibrium compared to standard relativistic mean field (RMF)
approaches. We find a strong dependence of the equation of state and the
particle distribution on the choice of the vertex density dependence. Results
for neutron star masses and radii are presented. We find a good agreement with
other models for the maximum mass. Radii are smaller compared to RMF models and
indicate a closer agreement with results of non-relativistic Brueckner
calculations.",0008038v1
2002-10-18,Density Dependence of Two-Body Interactions for Beyond Mean-Field Calculations,"This paper deals with the theoretical foundation of effective two-body forces
for the Generator Coordinate Method (GCM) and the projected mean-field method.
The first aim of this paper is to reduce into various local-densities the
in-medium content of a generalized $G$ matrix removing the hard core problem in
this extended context. Then, we consider the possible renormalization of
multi-body forces through a density-dependent two-body interaction in the
context of configuration mixing calculations. A density dependence of the form
$\rho^{\sigma}$, as used in Skyrme and Gogny forces, is successfully
interpreted as doing so when the mixed density is used. Finally, we propose a
simple extension of the Skyrme force dedicated to the calculation of matrix
elements between non-orthogonal product states, which are needed to evaluate
the correlated energy.",0210057v2
2007-01-24,Density reorganization in hot nuclei,"The density profile of a hot nuclear system produced in intermediate energy
heavy ion collisions is studied in a microcanonical formulation with a momentum
and density dependent finite range interaction. The caloric curve and the
density evolution with excitation are calculated for a number of systems for
the equilibrium mononuclear configuration; they compare favorably with the
recent experimental data. The studied density fluctuations are seen to build up
rapidly beyond an excitation energy of 8 MeV/u indicating the instability of
the system towards nuclear disassembly. Explicit introduction of deformation in
the expansion path of the heated nucleus, however, shows that the system might
fragment even earlier. We also explore the effects of the nuclear equation of
state and of the mass and isospin asymmetry on the nuclear equilibrium
configuration and the relevant experimental observables.",0701072v1
2012-11-13,Quarkonium at non-zero isospin density,"We calculate the energies of quarkonium bound states in the presence of a
medium of nonzero isospin density using lattice QCD. The medium, created using
a canonical (fixed isospin charge) approach, induces a reduction of the
quarkonium energies. As the isospin density increases, the energy shifts first
increase and then saturate. The saturation occurs at an isospin density close
to that where previously a qualitative change in the behaviour of the energy
density of the medium has been observed, which was conjectured to correspond to
a transition from a pion gas to a Bose-Einstein condensed phase. The reduction
of the quarkonium energies becomes more pronounced as the heavy-quark mass is
decreased, similar to the behaviour seen in two-colour QCD at non-zero quark
chemical potential. In the process of our analysis, the $\eta_b$-$\pi$ and
$\Upsilon$-$\pi$ scattering phase shifts are determined at low momentum. An
interpolation of the scattering lengths to the physical pion mass gives
$a_{\eta_b,\pi} = 0.0025(8)(6)$ fm and $a_{\Upsilon,\pi} = 0.0030(9)(7)$ fm.",1211.3156v3
2015-01-15,Energy in density gradient,"Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and
they naturally tend to relax into lower energy states by developing
instabilities or by diffusion. But the actual amount of energy in such
inhomogeneities has remained unknown. In the present work the amount of energy
stored in a density gradient is calculated for several specific density
profiles in a cylindric configuration. This is of practical importance for
drift wave instability in various plasmas, and in particular in its application
in models dealing with the heating of solar corona because the instability is
accompanied with stochastic heating, so the energy contained in inhomogeneity
is effectively transformed into heat. It is shown that even for a rather
moderate increase of the density at the axis in magnetic structures in the
corona by a factor 1.5 or 3, the amount of excess energy per unit volume stored
in such a density gradient becomes several orders of magnitude greater than the
amount of total energy losses per unit volume (per second) in quiet regions in
the corona. Consequently, within the life-time of a magnetic structure such
energy losses can easily be compensated by the stochastic drift wave heating.",1501.03730v1
2019-07-13,"Energy Density, Temperature and Entropy Dynamics in Perturbative Reheating","We discuss the perturbative decay of the energy density of a non standard
inflaton field $\rho_{\phi}$ and the corresponding creation of the energy
density of the relativistic fields $\rho_r$ at the end of inflation, in the
perfect fluid description, refining some concepts and providing some new
computations. In particular, the process is characterized by two fundamental
time scales. The first one, $t_\text{max}$, occurs when the energy density
$\rho_r$ reaches its largest value, slightly after the beginning of the
reheating phase. The second one, $t_\text{reh}$, is the time in which the
reheating is completely realized and the thermalization is attained. By
assuming a non-instantaneous reheating phase, we are able to derive the energy
densities and the temperatures of the produced relativistic bath at
$t_\text{max}$ and $t_\text{reh}$, as well as the value of the corresponding
horizon entropy $S_\text{hor}$, for an Equation-of-State (EoS) parameter $w\ne
0$.",1907.06084v2
2019-07-29,Ruling out the supersoft high-density symmetry energy from the discovery of PSR J0740+6620 with mass $2.14^{+0.10}_{-0.09}M_\odot$,"Using the very recently reported mass $2.14^{+0.10}_{-0.09}M_\odot$ of PSR
J0740+6620 together with the data of finite nuclei and the constraints on the
equation of state of symmetric nuclear matter at suprasaturation densities from
flow data in heavy-ion collisions, we show that the symmetry energy $E_{\rm
sym}(n)$ cannot be supersoft so that it becomes negative at suprasaturation
densities in neutron stars (NSs) and thus may make the NS have a pure neutron
matter core. This is in contrast to the fact that using the mass $2.01 \pm 0.04
M_\odot$ of PSR J0348+0432 as the NS maximum mass cannot rule out the supersoft
high-density $E_{\rm sym}(n)$. Furthermore, we find the stiffer high-density
$E_{\rm sym}(n)$ based on the existence of $2.14M_\odot$ NSs leads to a strong
constraint of $\Lambda_{1.4} \ge 348^{+88}_{-51}$ for the dimensionless tidal
deformability of the canonical $1.4M_\odot$ NS.",1907.12284v2
2021-10-19,Scission configuration in the self-consistent calculations with neck constraint,"The calculations of the potential energy surface are essential in the
theoretical description of the fission process. In the constrained
self-consistent approach, the smooth evolution of nuclear shape is described
from the ground state until a very elongated one with a narrow neck. In all
microscopic calculations, the rupture of the neck at scission is associated
with a substantial change of nuclear matter density distribution and rapid
energy decrease. In this paper, we show that there is no discontinuity of the
potential energy surface at scission when multi-constrained calculations are
applied with the neck constraint. An early rupture of the neck at lower
quadrupole and octupole moments is discussed as competitive with the
conventional fission path. We discuss the neck properties in the scission
configuration. We find that the neck radius in the asymmetric fission mode
cannot decrease below 2 fm, and the nuclear matter density cannot decrease
below the saturation density. In the compact fission mode, nuclear density may
go down to half of the saturation density before the rupture of the neck.",2110.10028v1
2021-10-26,Modelling of spatial infection spread through heterogeneous population: from lattice to PDE models,"We present a simple model for the spread of an infection that incorporates
spatial variability in population density. Starting from first principle
considerations, we explore how a novel PDE with state-dependent diffusion can
be obtained. This model exhibits higher infection rates in the areas of higher
population density, a feature that we argue to be consistent with
epidemiological observations. The model also exhibits an infection wave whose
speed varies with population density. In addition, we demonstrate the
possibility that an infection can ``jump'' (i.e., tunnel) across areas of low
population density towards the areas of high population density. We briefly
touch upon the data reported for coronavirus spread in the Canadian province of
Nova Scotia as a case example with a number of qualitatively similar features
as our model. Lastly, we propose a number of generalizations of the model
towards future studies.",2110.13956v1
2022-03-13,"Accurate non-empirical range-separated hybrid van der Waals density functional for complex molecular problems, solids, and surfaces","We introduce a new, general-purpose, range-separated hybrid van der Waals
density \ph{functional, termed vdW-DF-ahbr,} within the non-empirical vdW-DF
method [JPCM 32, 393001 (2020)]. It combines correlation from vdW-DF2 with a
screened Fock exchange that is fixed by \ph{a new model of exchange effects} in
the density-explicit vdW-DF2-b86r functional [PRB 89, 121103(R) (2014)]. The
new vdW-DF2-ahbr prevents spurious exchange binding and has a
small-density-gradient form set from many-body perturbation analysis. It is
accurate for \ph{bulk as well as layered materials} and it systematically and
significantly improves the performance of present vdW-DFs for molecular
problems. Importantly, vdW-DF2-ahbr also outperforms present-standard
(dispersion-corrected) range-separated hybrids on a broad collection of
noncovalent-interaction benchmark sets, while at the same time successfully
mitigating the density-driven errors that often affect the description of
molecular transition states and isomerization calculations. vdW-DF2-ahbr
furthermore improves on state of the art density functional theory approaches
by 1) correctly predicting both the substrate structure and the site preference
for CO adsorption on Pt(111), 2) outperforming existing non-empirical vdW-DFs
for the description of CO$_2$ adsorption in both a functionalized and in a
simple metal-organic framework, and 3) being highly accurate \ph{for the} set
of base-pair interactions in a model of DNA assembly.",2203.06682v2
2022-07-08,Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory,"Ground-state Kohn-Sham density functional theory provides, in principle, the
exact ground-state energy and electronic spin-densities of real interacting
electrons in a static external potential. In practice, the exact density
functional for the exchange-correlation (xc) energy must be approximated in a
computationally efficient way. About twenty mathematical properties of the
exact xc functional are known. In this work, we review and discuss these known
constraints on the xc energy and hole. By analyzing a sequence of increasingly
sophisticated density functional approximations (DFAs), we argue that: (1) the
satisfaction of more exact constraints and appropriate norms makes a functional
more predictive over the immense space of many-electron systems; (2) fitting to
bonded systems yields an interpolative DFA that may not extrapolate well to
systems unlike those in the fitting set. We discuss how the class of
well-described systems has grown along with constraint satisfaction, and the
possibilities for future functional development.",2207.03855v1
2023-05-15,Spectral-partitioned Kohn-Sham density functional theory,"We introduce a general, variational scheme applied to Kohn-Sham density
functional theory that allows for partitioning of the ground-state density
matrix into distinct spectral domains, each of which spanned by an independent
diagonal representation without requirement of mutual orthogonality. It is
shown that by generalizing the entropic contribution to the free energy to
allow for independent representations in each spectral domain, the free energy
becomes an upper bound to the exact one, attaining this limit as
representations approach Kohn-Sham eigenfunctions. A numerical procedure is
devised for effective calculation of the generalized entropy associated with
spectral partitioning of the density matrix. The result is a powerful framework
for Kohn-Sham calculations of systems whose occupied subspaces span multiple
energy regimes. As a case in point, we apply the proposed framework to warm-
and hot-dense matter described by finite-temperature density functional theory,
where at high energies the density matrix is represented by that of the
free-electron gas, while at low energies it is variationally optimized. We
derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic
forces, and macroscopic stresses within the projector-augmented wave (PAW) and
the norm-conserving pseudopotential methods. It is demonstrated that at high
temperatures, spectral partitioning facilitates accurate calculations at
dramatically reduced computational cost. Moreover, as temperature is increased,
fewer exact Kohn-Sham states are required for a given accuracy, leading to
further reductions in computational cost. Finally, it is shown that standard
multi-projector expansions of electronic orbitals within atomic spheres in the
PAW method lack sufficient completeness at high temperatures. Spectral
partitioning provides a systematic solution for this fundamental problem.",2305.08762v2
2019-04-18,A density functional method for general excited states in atoms,"This chapter presents the development of a density functional theory
(DFT)-based method for accurate, reliable treatment of various resonances in
atoms. Many of these are known to be notorious for their strong correlation,
proximity to more than one thresholds, degeneracy with more than one minima.
Therefore these pose unusual challenges to both theoreticians and
experimentalists. Our method uses a work-function-based exchange potential in
conjunction with the popular gradient-corrected Lee-Yang-Parr correlation
functional. The resulting Kohn-Sham equation, in the non-relativistic
framework, is numerically solved accurately and efficiently by means of a
generalized pseudospectral method through a non-uniform, optimal spatial
discretization. This has been applied to a variety of excited states, such as
low and high states; single, double, triple as well as multiple excitations;
valence and core excitations; autoionizing states; satellites; hollow and
doubly-hollow states; very high-lying Rydberg resonances; etc., of atoms and
ions, with remarkable success. A thorough and systematic comparison with
literature data reveals that, for all these systems, the exchange-only results
are practically of Hartree-Fock quality; while with inclusion of correlation,
this offers excellent agreement with available experimental data as well as
those obtained from other sophisticated theoretical methods. Properties such as
individual state energies, excitation energies, radial densities as well as
various expectation values are studied. This helps us in predicting many states
for the first time.",1904.08717v1
2005-07-14,Angularly localized Skyrmions,"Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and
angularly localized wavefunctions for them are found. By combining a few low
angular momentum states, one can construct a quantum state whose spatial
density is close to that of the classical Skyrmion, and has the same
symmetries. For the B=1 case we find the best localized wavefunction among
linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we
find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced
localization compared to the classical solution. For B=4, where the classical
Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by
combining the $j=0$ ground state with the lowest rotationally excited $j=4$
state. We use the rational map approximation to compare the classical and
quantum baryon densities in the B=2 and B=4 cases.",0507028v1
2009-01-22,Density-Wave and Antiferromagnetic States of Fermionic Atoms in Optical Lattices,"We study the two-band effects on ultracold fermionic atoms in optical
lattices by means of dynamical mean-field theory. We find that at half-filling
the atomic-density-wave (ADW) state emerges owing to the two-band effects in
the attractive interaction region, while the antiferromagnetic state appears in
the repulsive interaction region. As the orbital splitting is increased, the
quantum phase transitions from the ADW state to the superfluid state and from
the antiferromagnetic state to the metallic state occur in respective regions.
Systematically changing the orbital splitting and the interaction, we obtain
the phase diagram at half-filling. The results are discussed using the
effective boson model derived for the strong attractive interaction.",0901.3555v2
2022-03-30,Density Matrix Renormalization Group Algorithm For Mixed Quantum States,"Density Matrix Renormalization Group (DMRG) algorithm has been extremely
successful for computing the ground states of one-dimensional quantum many-body
systems. For problems concerned with mixed quantum states, however, it is less
successful in that either such an algorithm does not exist yet or that it may
return unphysical solutions. Here we propose a positive matrix product ansatz
for mixed quantum states which preserves positivity by construction. More
importantly, it allows to build a DMRG algorithm which, the same as the
standard DMRG for ground states, iteratively reduces the global optimization
problem to local ones of the same type, with the energy converging
monotonically in principle. This algorithm is applied for computing both the
equilibrium states and the non-equilibrium steady states, and its advantages
are numerically demonstrated.",2203.16350v2
1996-01-19,A Renormalization-Group approach to the Coulomb Gap,"The free energy of the Coulomb Gap problem is expanded as a set of Feynman
diagrams, using the standard diagrammatic methods of perturbation theory. The
gap in the one-particle density of states due to long-ranged interactions
corresponds to a renormalization of the two-point vertex function. By
collecting the leading order logarithmic corrections we have derived the
standard result for the density of states in the critical dimension, d=1. This
method, which is shown to be identical to the approach of Thouless, Anderson
and Palmer to spin glasses, allows us to derive the strong-disorder behaviour
of the density of states. The use of the renormalization group allows this
derivation to be extended to all disorders, and the use of an epsilon-expansion
allows the method to be extended to d=2 and d=3. We speculate that the
renormalization group equations can also be derived diagrammatically, allowing
a simple derivation of the crossover behaviour observed in the case of weak
disorder.",9601080v2
2006-02-10,Electron Spin Dynamics in a Quantum Dot due to Hyperfine Coupling with Nuclei in the Dot - An Exact Analysis,"The time-dependent Schrodinger equation of a many particle spin system
consisting of an electron in a quantum dot interacting with the spins of the
nuclei (N) in the dot due to hyperfine interaction is solved exactly for a
given arbitrary initial state. The electron spin dynamics is then expressed in
terms of the reduced density matrix of the composite system by computing the
marginal density matrix of the electron. This is accomplished by classifying
states of the system by the total spin of the coupled electron and nuclear
system that commutes with the system Hamiltonian. These states are used in
enumerating and finding the exact solution of the time-dependent Schrodinger
equation. In each sector of the total spin, the problem reduces to solving a
linear simultaneous set of equations that are solved by matrix inversion. Such
solutions enable one to make a reliable approximate scheme for purposes of
numerical estimation of the various physical quantities. A methematical and
physical discussion of this procedure with the density matrix approach to this
problem is given here. To elucidate the procedure and its advantages, special
cases of N=3,4 are given in some detail in an Appendix.",0602092v1
2018-12-02,Structure of hot strange quark stars: an NJL model approach at finite temperature,"In this paper, we investigated the thermodynamic properties of strange quark
matter using Nambu-Jona-Lasinio (NJL) model at finite temperatures where we
considered the dynamical mass as the effective interaction between quarks.
  By considering the pressure of strange quark matter (SQM) at finite
temperatures, we showed that the equation of state of this system gets stiffer
by increasing temperature. In addition, we investigated the energy conditions
and stability of the equation of state and showed that the equation of state of
SQM satisfy the conditions of stability. Finally, we computed the structure
properties of hot strange quark stars (SQS) including the gravitational mass,
radius, Schwarzschild radius, average density, compactness and gravitational
redshift. Our calculations showed that in this model, the maximum mass and
radius of SQS increase by increasing temperature. Furthermore it was shown that
the average density of SQS is greater than the normal nuclear density, and it
is an increasing function of temperature. We also discussed the temperature
dependence of the maximum gravitational mass calculated from different methods.",1812.02577v1
2021-05-10,Electronic Structure of the Solvated Benzene Radical Anion,"The benzene radical anion is a molecular ion pertinent to several organic
reactions, including the Birch reduction of benzene in liquid ammonia. The
species exhibits a dynamic Jahn-Teller effect due to its open-shell nature and
undergoes pseudorotation of its geometry. Here we characterize the complex
electronic structure of this condensed-phase system based on ab initio
molecular dynamics simulations and GW calculations of the benzene radical anion
solvated in liquid ammonia. Using detailed analysis of molecular and electronic
structure, we find that the spatial character of the excess electron of the
solvated radical anion follows the underlying Jahn-Teller distortions of the
molecular geometry. We decompose the electronic density of states to isolate
the contribution of the solute and to examine the response of the solvent to
its presence. Our findings show the correspondence between instantaneous
molecular structure and spin density, provide important insights into the
electronic stability of the species, revealing that it is indeed a bound state
in the condensed phase, and offer electronic densities of states that aid in
the interpretation of experimental photoelectron spectra.",2105.04543v2
2021-07-07,Densities of States and the CKN Bound,"The holographic principle implies that quantum field theory overcounts the
number of independent degrees of freedom in quantum gravity. An argument due to
Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom
well-described by QFT is even smaller than required by holographic bounds, and
CKN interpreted this result as indicative of a correlation between the UV and
IR cutoffs on QFT. Here we consider an alternative interpretation in which the
QFT degrees of freedom are depleted as a function of scale. We use a simple
recipe to estimate the impact of depleted densities of states on precision
observables, including the Lamb shift and lepton $g-2$. Although these
observables are not sensitive to the level of depletion motivated by
gravitational considerations, the phenomenological exercises also provide an
interesting test of quantum field theory that is independent of underlying
quantum gravity assumptions. A depleted density of states can also render the
QFT vacuum energy UV-insensitive, reconciling the success of QFT in describing
ordinary particle physics processes and its apparent failure in predicting the
cosmological constant.",2107.03530v1
2023-12-21,Effect of the equation of state for dilute neutron matter on the composition of the inner crust of neutron stars,"The composition of the inner crust of neutron stars is usually studied using
phenomenological interactions such as Skyrme energy-density functionals. But
most of these functionals do not agree well with ab-initio calculations of very
dilute neutron matter. In this work, we study the inner crust of neutron stars
in the model of phase coexistence of dense neutron-rich nuclear clusters and
dilute neutron gas, and we investigate how employing a realistic microscopic
equation of state to the neutron gas alters the composition. Our results
indicate that with a functional that reproduces the correct equation of state
of neutron matter at moderate densities, one can obtain a good description of
the crust even if the functional does not have the correct behavior at
extremely low density.",2312.13836v1
2015-06-27,Handover Count Based Velocity Estimation and Mobility State Detection in Dense HetNets,"In wireless cellular networks with densely deployed base stations, knowing
the velocities of mobile devices is a key to avoid call drops and improve the
quality of service to the user equipments (UEs). A simple and efficient way to
estimate a UE's velocity is by counting the number of handovers made by the UE
during a predefined time window. Indeed, handover-count based mobility state
detection has been standardized since Long Term Evolution (LTE) Release-8
specifications. The increasing density of small cells in wireless networks can
help in accurate estimation of velocity and mobility state of a UE. In this
paper, we model densely deployed small cells using stochastic geometry, and
then analyze the statistics of the number of handovers as a function of UE
velocity, small-cell density, and handover count measurement time window. Using
these statistics, we derive approximations to the Cramer-Rao lower bound (CRLB)
for the velocity estimate of a UE. Also, we determine a minimum variance
unbiased (MVU) velocity estimator whose variance tightly matches with the CRLB.
Using this velocity estimator, we formulate the problem of detecting the
mobility state of a UE as low, medium, or high-mobility, as in LTE
specifications. Subsequently, we derive the probability of correctly detecting
the mobility state of a UE. Finally, we evaluate the accuracy of the velocity
estimator under more realistic scenarios such as clustered deployment of small
cells, random way point (RWP) mobility model for UEs, and variable UE velocity.
Our analysis shows that the accuracy of velocity estimation and mobility state
detection increases with increasing small cell density and with increasing
handover count measurement time window.",1506.08248v3
2017-03-07,Higgs Modes in the Pair Density Wave Superconducting State,"The pair density wave (PDW) superconducting state has been proposed to
explain the layer- decoupling effect observed in the compound
La$_{2-x}$Ba$_x$CuO$_4$ at $x=1/8$ (Phys. Rev. Lett. 99, 127003). In this state
the superconducting order parameter is spatially modulated, in contrast with
the usual superconducting (SC) state where the order parameter is uniform. In
this work, we study the properties of the amplitude (Higgs) modes in a
unidirectional PDW state. To this end we consider a phenomenological model of
PDW type states coupled to a Fermi surface of fermionic quasiparticles. In
contrast to conventional superconductors that have a single Higgs mode,
unidirectional PDW superconductors have two Higgs modes. While in the PDW state
the Fermi surface largely remains gapless, we find that the damping of the PDW
Higgs modes into fermionic quasiparticles requires exceeding an energy
threshold. We show that this suppression of damping in the PDW state is due to
kinematics. As a result, only one of the two Higgs modes is significantly
damped. In addition, motivated by the experimental phase diagram, we discuss
the mixing of Higgs modes in the coexistence regime of the PDW and uniform SC
states. These results should be observable directly in a Raman spectroscopy, in
momentum resolved electron energy loss spectroscopy, and in resonant inelastic
X-ray scattering, thus providing evidence of the PDW states.",1703.02541v2
2022-06-10,Unique quantum impurity states driven by a vortex in topological superconductors,"The interplay of magnetic impurity and vortex in a topological superconductor
is of fundamental interest with major implications for implementing quantum
computation. There are multiple degrees of freedom interacting with the
impurity in the system, including the Majorana zero mode (MZM), the Caroli de
Gennes Matricon (CdGM) states, and the electron bulk states that form Cooper
pairs, which makes the impurity pinned vortex state elusive to date in
topological superconductors. Here, we present an accurate solution of the
problem, based on a generalized mapping scheme and the density-matrix
renormalization group (DMRG) method. We identify in-gap states that are
distinct from the established Yu-Shiba-Rusinov (YSR) states. The newly found
in-gap physics is driven by three prominent mechanisms: (i) the coupling of
impurity and bulk states leading to competition between Kondo screening and
Cooper pairing, resulting in a singlet-doublet quantum phase transition, (ii)
the coupling of impurity and CdGM states introducing an effective Zeeman
splitting to the doublet state, and (iii) the coupling of impurity and MZM
turning the singlet-doublet transition into a crossover. These mechanisms
cooperatively produce a unique spin-resolved local density of states. Despite
the MZM, a robust nearly zero-energy peak is generated, with comparable height
but opposite spin polarization as that of the MZM. These results signify novel
emergent physics and offer insights to elucidate intriguing experimental
phenomena.",2206.04862v1
2011-08-23,"Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces","The standard formulation of tunneling transport rests on an open-boundary
modeling. There, conserving approximations to nonequilibrium Green function or
quantum-statistical mechanics provide consistent but computational costly
approaches; alternatively, use of density-dependent ballistic-transport
calculations [e.g., Phys. Rev. B 52, 5335 (1995)], here denoted `DBT', provide
computationally efficient (approximate) atomistic characterizations of the
electron behavior but has until now lacked a formal justification. This paper
presents an exact, variational nonequilibrium thermodynamic theory for fully
interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT
calculations as a lowest order approximation to an exact nonequilibrium
thermodynamics density functional evaluation. The theory starts from the
complete electron nonequilibrium quantum statistical mechanics and I identify
the operator for the nonequilibrium Gibbs free energy. I demonstrate a minimal
property of a functional for the nonequilibrium thermodynamic grand potential
which thus uniquely identifies the solution as the exact nonequilibrium density
matrix. I also show that a uniqueness-of-density proof from a closely related
study [Phys. Rev. B 78, 165109 (2008)] makes it possible to provide a
single-particle formulation based on universal electron-density functionals. I
illustrate a formal evaluation of the thermodynamics grand potential value
which is closely related to the variation in scattering phase shifts and hence
to Friedel density oscillations. This paper also discusses the difference
between the here-presented exact thermodynamics forces and the often-used
electrostatic forces. Finally the paper documents an inherent adiabatic nature
of the thermodynamics forces and observes that these are suited for a
nonequilibrium implementation of the Born-Oppenheimer approximation.",1108.4536v3
2012-11-06,Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces,"We investigate the finite temperature expectation values of the charge and
current densities for a complex scalar field with nonzero chemical potential in
background of a flat spacetime with spatial topology $R^{p}\times (S^{1})^{q}$.
Along compact dimensions quasiperiodicity conditions with general phases are
imposed on the field. In addition, we assume the presence of a constant gauge
field which, due to the nontrivial topology of background space, leads to
Aharonov-Bohm-like effects on the expectation values. By using the
Abel-Plana-type summation formula and zeta function techniques, two different
representations are provided for both the current and charge densities. The
current density has nonzero components along the compact dimensions only and,
in the absence of a gauge field, it vanishes for special cases of twisted and
untwisted scalar fields. In the high-temperature limit, the current density and
the topological part in the charge density are linear functions of the
temperature. The Bose-Einstein condensation for a fixed value of the charge is
discussed. The expression for the chemical potential is given in terms of the
lengths of compact dimensions, temperature and gauge field. It is shown that
the parameters of the phase transition can be controlled by tuning the gauge
field. The separate contributions to the charge and current densities coming
from the Bose-Einstein condensate and from excited states are also
investigated.",1211.5174v1
2013-09-30,Synthesis of thin silicon dioxide layers with high E' center densities and investigation of the E' center spin relaxation dynamics for single spin readout applications,"Methods for the creation of thin amorphous silicon dioxide (aSiO2) layers on
crystalline silicon substrates with very high densities of silicon dangling
bonds (so called E' centers) have been explored and volume densities of [E']>
5x10^18 cm-3 throughout a 60nm thick film have been demonstrated by exposure of
a thermal oxide layer to a low pressure Argon radio frequency plasma. While the
generated high E' center densities can be annealed completely at 300C, they are
comparatively stable at room temperature with a half life of about one month.
Spin relaxation time measurements of these states between T = 5K and T = 70K
show that the phase relaxation time T2 does not strongly depend on temperature
and compared to SiO2 films of lower E' density, is significantly shortened. The
longitudinal relaxation time T1 ~195(5)us at room temperature is in agreement
with low-density SiO2. In contrast, T1 ~625(51)us at T = 5K is much shorter
than in films of lower E' density. These results are discussed in the context
of E' centers being used as probe spins for spin-selection rules based single
spin-readout.",1310.0094v1
2016-10-29,Density Tracking by Quadrature for Stochastic Differential Equations,"We develop and analyze a method, density tracking by quadrature (DTQ), to
compute the probability density function of the solution of a stochastic
differential equation. The derivation of the method begins with the
discretization in time of the stochastic differential equation, resulting in a
discrete-time Markov chain with continuous state space. At each time step, DTQ
applies quadrature to solve the Chapman-Kolmogorov equation for this Markov
chain. In this paper, we focus on a particular case of the DTQ method that
arises from applying the Euler-Maruyama method in time and the trapezoidal
quadrature rule in space. Our main result establishes that the density computed
by DTQ converges in $L^1$ to both the exact density of the Markov chain (with
exponential convergence rate), and to the exact density of the stochastic
differential equation (with first-order convergence rate). We establish a
Chernoff bound that implies convergence of a domain-truncated version of DTQ.
We carry out numerical tests to show that the empirical performance of DTQ
matches theoretical results, and also to demonstrate that DTQ can compute
densities several times faster than a Fokker-Planck solver, for the same level
of error.",1610.09572v4
2023-06-12,A simple all-inorganic hole-only device structure for monitoring the trap densities in perovskite solar cells,"One of the most critical challenges in soaring the performance of perovskite
solar cells is decreasing the density of trap states in the light-absorbing
perovskite layer. These traps cause an increase in the recombination of charge
carriers and decrease the efficiency of devices. One of the methods to study
the trap density is space charge limited current (SCLC) analysis. For this
purpose, some structures are needed with the ability to transport only
electrons or holes. The trap density can be calculated by investigating the
current-voltage diagram and finding the voltage corresponding to the slope
change point. One of the challenges in these structures is using organic
polymers like Spiro-OMeTAD, PEDOT: PSS, and PTAA as hole transport layers. They
have problems like high acidity, lack of stability against moisture, low charge
mobility, low conductivity, and high cost. In this work, a hole-only device
structure is explained, made based on inorganic materials, which possesses high
stability, a simple preparation method, and reasonable cost compared to
conventional hole-only device structures. This structure is built by coating a
nanostructured NiOx layer, perovskite, CIS, and Au on the ITO substrate. To
investigate the performance of this structure, various perovskite layers were
made at different experimental conditions, and their trap density was obtained
by the proposed hole-only device structure. The analysis of the photovoltaic
characteristics of cells revealed a clear correlation between the perovskite
layer's trap density and the cells' performance. Our results show the
introduced structure is a simple and stable structure that can be utilized in
studying the trap density in perovskite layers to make more efficient cells.",2306.07136v1
2023-11-18,On the Interpretation of XSPEC Abundances and Emission Measures,"The purpose of this work is to describe the assumptions built into the X-ray
spectrum fitting software XSPEC for the calculation of element abundances and
emission measure of a plasma and to describe the effects when those assumptions
are not accurate. The ratio of electron density to hydrogen density in XSPEC is
fixed at a constant. The correct ratio can be calculated from the ionization
states of the elements. We show the constant value used in XSPEC is valid to
within 3.5% for a solar abundance plasma. For a plasma that deviates from solar
abundance, such as hydrogen-poor or heavy element rich plasmas as found in the
ejecta of supernova remnants, this ratio can smaller by factors of 0.1 to
0.001. The hydrogen emission measure, defined by integral of electron density
times hydrogen density over plasma volume, is derived from the norm in XSPEC,
but one needs to include the hydrogen abundance factor. For other elements, the
emission measures are the XSPEC values multiplied by the element abundance
factors. Using the correct electron-to-hydrogen ratio and emission measures, we
show the correct electron density is smaller by the square root of the correct
electron density ratio divided by the XSPEC value. Element densities and total
masses (for given distance and volume) are larger by the abundance factors
divided by the above square root. Because hydrogen-poor plasmas occur in the
ejecta of Type Ia supernova remnants, previously estimated element masses from
X-ray spectra are likely significantly underestimated.",2311.11181v3
2024-02-27,Bound-state confinement after trap-expansion dynamics in integrable systems,"Integrable systems possess stable families of quasiparticles, which are
composite objects (bound states) of elementary excitations. Motivated by recent
quantum computer experiments, we investigate bound-state transport in the
spin-$1/2$ anisotropic Heisenberg chain ($XXZ$ chain). Specifically, we
consider the sudden vacuum expansion of a finite region $A$ prepared in a
non-equilibrium state. In the hydrodynamic regime, if interactions are strong
enough, bound states remain confined in the initial region. Bound-state
confinement persists until the density of unbound excitations remains finite in
the bulk of $A$. Since region $A$ is finite, at asymptotically long times bound
states are ""liberated"" after the ""evaporation"" of all the unbound excitations.
Fingerprints of confinement are visible in the space-time profiles of local
spin-projection operators. To be specific, here we focus on the expansion of
the $p$-N\'eel states, which are obtained by repetition of a unit cell with $p$
up spins followed by $p$ down spins. Upon increasing $p$, the bound-state
content is enhanced. In the limit $p\to\infty$ one obtains the domain-wall
initial state. We show that for $p<4$, only bound states with $n>p$ are
confined at large chain anisotropy. For $p\gtrsim 4$, also bound states with
$n=p$ are confined, consistent with the absence of transport in the limit
$p\to\infty$. The scenario of bound-state confinement leads to a hierarchy of
timescales at which bound states of different sizes are liberated, which is
also reflected in the dynamics of the von Neumann entropy.",2402.17623v1
2009-08-17,Entanglement in Valence-Bond-Solid States,"This article reviews the quantum entanglement in Valence-Bond-Solid (VBS)
states defined on a lattice or a graph. The subject is presented in a
self-contained and pedagogical way. The VBS state was first introduced in the
celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki
(abbreviation AKLT is widely used). It became essential in condensed matter
physics and quantum information (measurement-based quantum computation). Many
publications have been devoted to the subject. Recently entanglement was
studied in the VBS state. In this review we start with the definition of a
general AKLT spin chain and the construction of VBS ground state. In order to
study entanglement, a block subsystem is introduced and described by the
density matrix. Density matrices of 1-dimensional models are diagonalized and
the entanglement entropies (the von Neumann entropy and Renyi entropy) are
calculated. In the large block limit, the entropies also approach finite
limits. Study of the spectrum of the density matrix led to the discovery that
the density matrix is proportional to a projector.",0908.2345v3
2007-08-24,"Ground and excited-state fermions in a 1D double-well, exact and time-dependent density-functional solutions","Two of the most popular quantum mechanical models of interacting fermions are
compared to each other and to potentially exact solutions for a pair of
contact-interacting fermions trapped in a 1D double-well potential, a model of
atoms in a quasi-1D optical lattice or electrons of a Hydrogen molecule in a
strong magnetic field. An exact few-body Hamiltonian is solved numerically in
momentum space yielding a highly-correlated eigenspectrum. Additionally,
approximate ground-state energies are obtained using both density functional
theory (DFT) functional and 2-site Hubbard models. A 1D adiabatic LDA kernel is
constructed for use in time-dependent density functional theory (TDDFT), and
the resulting excited-state spectrum is compared to the exact and Hubbard
results. DFT is shown to give accurate results for wells with small separations
but fails to describe localization of opposite spin fermions to different
sites. A locally cognizant (LC) density functional based on an effective local
fermion number would provide a solution to this problem, and an approximate
treatment presented here compares favorably with the exact and Hubbard results.
The TDDFT excited-state spectrum is accurate in the small parameter regime with
non-adiabatic effects accounting for any deviations. As expected, the
ground-state Hubbard model outperforms DFT at large separations but breaks down
at intermediate separations due to improper scaling to the united-atom limit.
At strong coupling, both Hubbard and TDDFT methods fail to capture the
appropriate energetics.",0708.3265v3
2017-06-05,Quantum Kinetic Theory of the Chiral Anomaly,"We present a general quantum kinetic theory of low-field magnetotransport in
weakly disordered crystals that accounts fully for the interplay between
electric-field induced interband coherence, Bloch-state scattering, and an
external magnetic field. The quantum kinetic equation we derive for the
Bloch-state density matrix naturally incorporates the momentum-space Berry
phase effects whose influence on Bloch-state wavepacket dynamics is normally
incorporated into transport theory in an ad hoc manner. The Berry phase
correction to the momentum-space density of states in the presence of an
external magnetic field implied by semiclassical wavepacket dynamics is
captured by our theory as an intrinsic density-matrix response to a magnetic
field. We propose a simple and general procedure for expanding the linear
response of the Bloch-state density matrix to an electric field in powers of
magnetic field. As an illustration, we apply our theory to magnetotransport in
Weyl semimetals. We show that the chiral anomaly (positive magnetoconductivity
quadratic in magnetic field) that appears when separate Fermi surface pockets
surround distinct Weyl points survives only when intervalley scattering is very
weak compared to intravalley scattering.",1706.01200v3
2023-01-14,Emergent Electronic Kagome Lattice in Correlated Charge-Density-Wave State of 1T-TaS$_2$,"Quantum materials with tunable correlated and/or topological electronic
states, such as the electronic Kagome lattice, provide an ideal platform to
study the exotic quantum properties. However, the real-space investigations on
the correlated electronic Kagome lattice have been rarely reported. Herein, we
report on the electronic Kagome lattice emerging in the correlated
charge-density-wave (CDW) state of 1T-TaS$_2$ at ~200 K via
variable-temperature scanning tunneling microscopy (VT-STM). This emergent
Kagome lattice can be considered a fractional electron-filling superstructure
with reduced translational and rotational symmetries, confirmed by STM
measurements and density functional theory simulations. The characteristic band
structure and density of states of this electronic Kagome lattice are further
explored based on theoretical calculations. Our results demonstrate a
self-organized electronic Kagome lattice from the correlated CDW state via the
effective tuning parameter of temperature and provide a platform to directly
explore the interplay of correlated electrons and topological physics.",2301.05885v1
2006-11-08,1+1 Dimensional Hydrodynamics for High-energy Heavy-ion Collisions,"A 1+1 dimensional hydrodynamical model in the light-cone coordinates is used
to describe central heavy-ion collisions at ultrarelativistic bombarding
energies. Deviations from Bjorken's scaling are taken into account by choosing
finite-size profiles for the initial energy density. The sensitivity of fluid
dynamical evolution to the equation of state and the parameters of initial
state is investigated. Experimental constraints on the total energy of produced
particles are used to reduce the number of model parameters. Spectra of
secondary particles are calculated assuming that the transition from the
hydrodynamical stage to the collisionless expansion of matter occurs at a
certain freeze-out temperature. An important role of resonances in the
formation of observed hadronic spectra is demonstrated. The calculated rapidity
distributions of pions, kaons and antiprotons in central Au+Au collisions at
the c.m. energy 200 GeV per NN pair are compared with experimental data of the
BRAHMS Collaboration. Parameters of the initial state are reconstructed for
different choices of the equation of state. The best fit of these data is
obtained for a soft equation of state and Gaussian-like initial profiles of the
energy density, intermediate between the Landau and Bjorken limits.",0611099v1
2018-01-23,Parametrized Equation of State for QCD from 3D Ising Model,"The only first principle knowledge of the QCD equation of state at finite
baryonic density is given from Lattice QCD as a Taylor expansion around $\mu_B
= 0$. The coefficients of such an expansion are currently available up to order
${\cal O}(\mu_B^6)$. The expected critical behavior of QCD is in the same
static universality class as the 3D Ising model. By means of a suitable
parametrization for the scaling equation of state of 3D Ising and a
parametrized map to connect to QCD, we present an equation of state matching
first principle Lattice QCD calculations, which spans the values of baryonic
densities explored in the BES-II program, and includes the correct scaling
behavior in the proximity of the critical point.
  This EoS can serve as an important ingredient for the fluid dynamical
simulations of heavy ion collisions at BES energies needed as a basis for the
calculation of observables. Future comparisons between such calculations and
BES-II data can constrain the parameters in the EoS -- including the parameters
that describe the location of the critical point.
  This contribution reports on work done within the Fluctuations/Equation of
State working group of the BEST Collaboration.",1801.07801v1
2019-10-06,Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model,"We have studied nonequilibrium dynamics of the one-dimensional Hubbard model
using the generalized hydrodynamic theory. We mainly investigated the
spatio-temporal profile of charge density, energy density and their currents
using the partitioning protocol; the initial state consists of two
semi-infinite different thermal equilibrium states joined at the origin. In
this protocol, there appears around the origin a transient region where
currents flow. We examined how density and current profiles depend on initial
conditions and have found a clogged region where charge current is zero but
nonvanishing energy current flows. This region appears when one of the initial
states has half-filled electron density. We have proved analytically the
existence of the clogged region in the infinite temperature case of the
half-filled initial state. The existence is confirmed also for finite
temperatures by numerical calculations. A similar analytical proof is also
given for a clogged region of spin current when magnetic field is applied to
one and only one of the two initial states. A universal proportionality of
charge and spin currents is also proved for a special region, for general
initial conditions of electron density and magnetic field. Except for the
clogged region, charge and energy densities are in good proportion to each
other, and their ratio depends on the initial conditions. This proportionality
in nonequilibrium dynamics is reminiscent of Wiedemann-Franz law in thermal
equilibrium. The long-time stationary values of charge and energy currents were
also studied with varying initial conditions. We have compared the results with
the values of non-interacting systems and discussed the effects of electron
correlations. We have found that the temperature dependence of the ratio of
these stationary currents is strongly suppressed by electron correlations and
even reversed.",1910.02427v2
2023-10-05,Global density equations for a population of actively switching particles,"There are many processes in cell biology that can be modelled in terms of an
actively switching particle. The continuous degrees of freedom evolve according
to a hybrid stochastic differential equation (hSDE) whose drift term depends on
a discrete internal or environmental state that switches according to a
continuous time Markov chain. In this paper we derive global density equations
for a population of non-interacting actively switching particles, either
independently switching or subject to a common randomly switching environment.
In the case of a random environment, we show that the global particle density
evolves according to a hybrid stochastic partial differential equation (hSPDE).
Averaging with respect to the Gaussian noise processes yields a hybrid partial
differential equation (hPDE) for the one-particle density. We use the
corresponding functional Chapman-Kolmogorov equation to derive moment equations
for the one-particle density and show how a randomly switching environment
induces statistical correlations. We also discuss the effects of particle
interactions, which generate moment closure problems at both the hSPDE and hPDE
levels. The former can be handled by taking a mean field limit, but the
resulting hPDE is now a nonlinear functional of the one-particle density. We
then develop the analogous constructions for independently switching particles.
We introduce a discrete set of global densities that are indexed by the
single-particle internal states. We derive an SPDE for the densities by taking
expectations with respect to the switching process, and then use a slow/fast
analysis to reduce the SPDE to a scalar stochastic Fokker-Planck equation in
the fast-switching limit. We end by deriving path integrals for the global
densities in the absence of interactions and relate this to recent studies of
Brownian gases and run-and-tumble particles.",2310.03418v2
1994-10-19,Searching for the Quark-Gluon Plasma,"The claims for production of high energy densities and possible new states of
matter in collisions of nuclei by George F. Bertsch (Science, {\bf 265} (1994)
480-481) are examined and compared with simple explanations of the data which
have appeared in the literature.",9410328v1
2007-06-27,Kondo quantum dot coupled to ferromagnetic leads: Numerical renormalization group study,"We systematically study the influence of ferromagnetic leads on the Kondo
resonance in a quantum dot tuned to the local moment regime. We employ Wilson's
numerical renormalization group method, extended to handle leads with a spin
asymmetric density of states, to identify the effects of (i) a finite spin
polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in
the bands (governed by the band edges) and (iii) an arbitrary shape of the
leads density of states. For a generic lead density of states the quantum dot
favors being occupied by a particular spin-species due to exchange interaction
with ferromagnetic leads leading to a suppression and splitting of the Kondo
resonance. The application of a magnetic field can compensate this asymmetry
restoring the Kondo effect. We study both the gate-voltage dependence (for a
fixed band structure in the leads) and the spin polarization dependence (for
fixed gate voltage) of this compensation field for various types of bands.
Interestingly, we find that the full recovery of the Kondo resonance of a
quantum dot in presence of leads with an energy dependent density of states is
not only possible by an appropriately tuned external magnetic field but also
via an appropriately tuned gate voltage. For flat bands simple formulas for the
splitting of the local level as a function of the spin polarization and gate
voltage are given.",0706.3997v1
2018-02-18,Spontaneous emission from radiative chiral nematic liquid crystals at the photonic band gap edge: an investigation into the role of the density of photon states near resonance,"In this article, we investigate the spontaneous emission properties of
radiating molecules embedded in a chiral nematic liquid crystal, under the
assumption that the electronic transition frequency is close to the photonic
edge mode of the structure, i.e. at resonance. We take into account the
transition broadening and the decay of electromagnetic field modes supported by
the so-called `mirror-less' cavity. We employ the Jaynes-Cummings Hamiltonian
to describe the electron interaction with the electromagnetic field, focusing
on the mode with the diffracting polarization in the chiral nematic layer. As
known in these structures, the density of photon states, calculated via the
Wigner method, has distinct peaks on either side of the photonic band gap,
which manifests itself as a considerable modification of the emission spectrum.
We demonstrate that, near resonance, there are notable differences between the
behavior of the density of states and the spontaneous emission profile of these
structures. In addition, we examine in some detail the case of the logarithmic
peak exhibited in the density of states in 2D photonic structures and obtain
analytic relations for the Lamb shift and the broadening of the atomic
transition in the emission spectrum. The dynamical behavior of the atom-field
system is described by a system of two first order differential equations,
solved using the Green's function method and the Fourier transform. The
emission spectra are then calculated and compared with experimental data.",1802.06317v1
2020-08-30,The density of states and local eigenvalue statistics for random band matrices of fixed width,"We prove that the local eigenvalue statistics for $d=1$ random band matrices
with fixed bandwidth and, for example, Gaussian entries, is given by a Poisson
point process and we identify the intensity of the process. The proof relies on
an extension of the localization bounds of Schenker \cite{schenker} and the
Wegner and Minami estimates. These two estimates are proved using averaging
over the diagonal disorder. The new component is a proof of the uniform
convergence and the smoothness of the density of states function. The limit
function, known to be the semicircle law with a band-width dependent error
\cite{bmp,dps,dl,mpk}, is identified as the intensity of the limiting Poisson
point process. The proof of these results for the density of states relies on a
new result that simplifies and extends some of the ideas used by Dolai,
Krishna, and Mallick \cite{dkm}. These authors proved regularity properties of
the density of states for random Schr\""odinger operators (lattice and
continuum) in the localization regime. The proof presented here applies to the
random Schr\""odinger operators on a class of infinite graphs treated by in
\cite{dkm} and extends the results of \cite{dkm} to probability measures with
unbounded support. The method also applies to fixed bandwidth RBM for $d=2,3$
provided certain localization bounds are known.",2008.13167v1
2016-10-18,Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians,"We derive families of optimal and near-optimal probe states for quantum
estimation of the coupling constants of a general two-mode number-conserving
bosonic Hamiltonian describing one-body and two-body dynamics. We find that the
optimal states for estimating the dephasing of the modes, the self-interaction
strength, and the contact interaction strength are related to the NOON states,
whereas the optimal states for estimation of the intermode single particle
tunneling amplitude are superpositions of antipodal SU(2) coherent states. For
estimation of the amplitude of pair tunneling and the amplitude of
density-dependent single particle tunneling processes, respectively, we
introduce classes of variational superposition probe states that provide near
perfect saturation of the corresponding quantum Cram\'{e}r-Rao bounds. We show
that the ground state of the pair tunneling term in the Hamiltonian has a high
fidelity with the optimal states for estimation of a single particle tunneling
amplitude, suggesting that high-performance probes for tunneling amplitude
estimation may be produced by tuning the two-mode system through a quantum
phase transition.",1610.05807v1
2022-04-21,Beyond the density operator and Tr(ρA): Exploiting the higher-order statistics of random-coefficient pure states for quantum information processing,"Two types of states are widely used in quantum mechanics, namely
(deterministic-coefficient) pure states and statistical mixtures. A density
operator can be associated with each of them. We here address a third type of
states, that we previously introduced in a more restricted framework. These
states generalize pure ones by replacing each of their deterministic ket
coefficients by a random variable. We therefore call them Random-Coefficient
Pure States, or RCPS. We analyze their properties and their relationships with
both types of usual states. We show that RCPS contain much richer information
than the density operator and mean of observables that we associate with them.
This occurs because the latter operator only exploits the second-order
statistics of the random state coefficients, whereas their higher-order
statistics contain additional information. That information can be accessed in
practice with the multiple-preparation procedure that we propose for RCPS, by
using second-order and higher-order statistics of associated random
probabilities of measurement outcomes. Exploiting these higher-order statistics
opens the way to a very general approach for performing advanced quantum
information processing tasks. We illustrate the relevance of this approach with
a generic example, dealing with the estimation of parameters of a quantum
process and thus related to quantum process tomography. This parameter
estimation is performed in the non-blind (i.e. supervised) or blind (i.e.
unsupervised) mode. We show that this problem cannot be solved by using only
the density operator \rho of an RCPS and the associated mean value Tr(\rho A)
of the operator A that corresponds to the considered physical quantity. We
succeed in solving this problem by exploiting a fourth-order statistical
parameter of state coefficients, in addition to second-order statistics.
Numerical tests validate this result.",2204.10031v1
2002-01-18,Density of states in d-wave superconductors disordered by extended impurities,"The low-energy quasiparticle states of a disordered d-wave superconductor are
investigated theoretically. A class of such states, formed via tunneling
between the Andreev bound states that are localized around extended impurities
(and result from scattering between pair-potential lobes that differ in sign)
is identified. Its (divergent) contribution to the total density of states is
determined by taking advantage of connections with certain one-dimensional
random tight-binding models. The states under discussion should be
distinguished from those associated with nodes in the pair potential.",0201339v2
2010-07-13,Doping evolution of superconducting gaps and electronic densities of states in Ba(Fe1-xCox)2As2 iron pnictides,"An extensive calorimetric study of the normal- and superconducting-state
properties of Ba(Fe1-xCox)2As2 is presented for 0 < x < 0.2. The normal-state
Sommerfeld coefficient increases (decreases) with Co doping for x < 0.06 (x >
0.06), which illustrates the strong competition between magnetism and
superconductivity to monopolize the Fermi surface in the underdoped region and
the filling of the hole bands for overdoped Ba(Fe1-xCox)2As2. All
superconducting samples exhibit a residual electronic density of states of
unknown origin in the zero-temperature limit, which is minimal at optimal
doping but increases to the normal-state value in the strongly under- and
over-doped regions. The remaining specific heat in the superconducting state is
well described using a two-band model with isotropic s-wave superconducting
gaps.",1007.2218v1
2013-11-28,Inhomegeneous cosmological models and fine-tuning of the initial state,"Inhomogeneous cosmological models are often reported to suffer from a
fine-tuning problem because of the observer's location. We study if this is a
generic feature in the Lema\^{i}tre-Tolman (LT) models, by investigating if
there are models with freedom in the initial state. In these cases, the present
fine-tuned location would be evolved from a non-fine-tuned initial state and
thus vanishing the problem. In this paper, we show that this is not a generic
problem and we give the condition when the LT models do not have fine-tuned
initial state. The physical meaning of this condition, however, requires more
investigation. We investigate if this condition can be found from a special
case: homogeneous models with matter, dark, and curvature density as
parameters. We found that with any reasonable density values, these models do
not satisfy this condition and thus do not have freedom in the initial state.
We interpret this to be linked with the fine-tuning problem of the initial
state of the homogeneous models, when the early time inflation is not included
to them. We discuss of the condition in the context of non-homogeneous models.",1311.7290v2
2013-12-09,Non-equilibrium theory of tunneling into localized state in superconductor,"A single static magnetic impurity in a fully-gapped superconductor leads to
formation of an intragap quasiparticle bound state. At temperatures much below
the superconducting transition, the energy relaxation and spin dephasing of the
state are expected to be exponentially suppressed. The presence of such a state
can be detected in electron tunneling experiments as a pair of conductance
peaks at positive and negative biases. Here we show, that for an arbitrarily
weak tunneling strength, the peaks have to be symmetric with respect to the
applied bias. This is in contrast to the standard result that the tunneling
conductance is proportional to the local (in general particle-hole asymmetric)
density of states. The asymmetry can be recovered is one allows for either a
finite density of impurity states, or that impurities are coupled to another,
non-superconducting, equilibrium bath.",1312.2602v1
2016-04-11,Topological phase transition and quantum spin Hall edge states of antimony few layers,"While two-dimensional topological insulators (2D TI) initiated the field of
topological materials, only very few materials were discovered to date and the
direct access to their quantum spin Hall edge states has been challenging due
to material issues. Here, we introduce a new 2D TI material, Sb few layer
films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are
investigated by scanning tunneling microscopy. The maps of local density of
states clearly identify robust edge electronic states over the thickness of
three bilayers in clear contrast to thinner islands. This indicates the
topological edge states emerged through a 2D topological phase transition
predicted between three and four bilayer films in recent theory. The
non-trivial phase transition and edge states are confirmed for epitaxial films
by extensive density-functional-theory calculations. This work provides an
important material platform to exploit miscroscopic aspects of the quantum spin
Hall phase and its quantum phase transition.",1604.02940v1
2017-06-26,Correlated electronic states at domain walls of a Mott-charge-density-wave insulator 1T-TaS2,"Domain walls in interacting electronic systems can have distinct localized
states, which often govern physical properties and may lead to unprecedented
functionalities and novel devices. However, electronic states within domain
walls themselves have not been clearly identified and understood for strongly
correlated electron systems. Here, we resolve the electronic states localized
on domain walls in a Mott-charge-density-wave(CDW) insulator 1T-TaS2 using
scanning tunneling spectroscopy. We establish that the domain wall state
decomposes into two nonconducting states located at the center of domain walls
and edges of domains. Theoretical calculations reveal their atomistic origin as
the local reconstruction of domain walls under the strong influence of electron
correlation. Our results introduce a concept for the domain wall electronic
property, the wall's own internal degrees of freedom, which is potentially
related to the controllability of domain wall electronic properties.",1706.08607v1
2017-11-03,Subgap in the surface bound states spectrum of Superfluid $^3$He-B with Rough Surface,"Subgap structure in the surface bound states spectrum of Superfluid $^3$He-B
with rough surface is discussed. The subgap is formed by the level repulsion
between the surface bound state and the continuum states in the course of
multiple scattering by the surface roughness. We show that the level repulsion
is originated from the nature of the wave function of the surface bound state
that is now recognized as Majorana Fermion. We study the superfluid $^3$He-B
with a rough surface and under magnetic field perpendicular to the surface
using the quasi-classical Green function together with random S-matrix model.
We calculate the self-consistent order parameters, the spin polarization
density and the surface density of states. It is shown that the subgap is found
also under the magnetic field perpendicular to the surface. Magnetic field
dependence of the transverse acoustic impedance is also discussed.",1711.01056v1
2019-12-04,Enhanced Edelstein effect and interdimensional effects in an electron gas with Rashba spin-orbit coupling interface,"We examine the bound-state and free-state contributions to the density of
states in a three-dimensional electron gas with a two-dimensional interface
with Rashba spin-orbit coupling. Confinement of electrons to the interface is
achieved through the inclusion of an attractive potential in the interface.
Motivation for our research comes from interest in heterostructure materials
that exhibit the Edelstein and inverse Edelstein effects on surfaces or
interfaces due to large Rashba spin-orbit coupling. By modifying the
Hamiltonian of a three-dimensional free electron gas to include an interface
with Rashba spin-orbit coupling and an attractive potential, we are able to
calculate the bound-state and free-state wavefunctions and corresponding
density of states analytically. We find that one of the spin-split energy bands
in the interface has an upper bound, resulting in an enhancement of the
Edelstein and inverse Edelstein effect.",1912.01804v1
2021-12-06,Lattice-Driven Chiral Charge Density Wave State in 1T-TaS$_{2}$,"We use scanning tunneling microscopy to study the domain structure of the
nearly-commensurate charge density wave (NC-CDW) state of 1T-TaS$_2$. In our
sub-angstrom characterization of the state, we find a continual evolution of
the CDW lattice from domain wall to domain center, instead of a fixed CDW
arrangement within a domain. Further, we uncover an intradomain chirality
characterizing the NC-CDW state. Unlike the orbital-driven chirality previously
observed in related transition metal dichalcogenides, the chiral nature of the
NC-CDW state in 1T-TaS$_2$ appears driven by a strong coupling of the NC-CDW
state to the lattice.",2112.03367v1
1995-10-14,Ab initio molecular dynamics using density based energy functionals: application to ground state geometries of some small clusters,"The ground state geometries of some small clusters have been obtained via ab
initio molecular dynamical simulations by employing density based energy
functionals. The approximate kinetic energy functionals that have been employed
are the standard Thomas-Fermi $(T_{TF})$ along with the Weizsacker correction
$T_W$ and a combination $F(N_e)T_{TF} + T_W$. It is shown that the functional
involving $F(N_e)$ gives superior charge densities and bondlengths over the
standard functional. Apart from dimers and trimers of Na, Mg, Al, Li, Si,
equilibrium geometries for $Li_nAl, n=1,8$ and $Al_{13}$ clusters have also
been reported. For all the clusters investigated, the method yields the ground
state geometries with the correct symmetries with bondlengths within 5\% when
compared with the corresponding results obtained via full orbital based
Kohn-Sham method. The method is fast and a promising one to study the ground
state geometries of large clusters.",9510083v2
2006-03-02,Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses,"We investigate the spectral and localization properties of unmagnetized
Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0.
We use numerical transfer-matrix methods combined with finite-size scaling to
calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with
Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we
find that all states are localized, with the localization length diverging as
$\omega^{-1}$, as energy $\omega \to 0$. Logarithmic corrections to density of
states behave in accordance with theoretical predictions. In $d=3$ the
density-of-states dependence on energy is the same as for spin waves in pure
antiferromagnets, again in agreement with theoretical predictions, though the
corresponding amplitudes differ.",0603043v1
2007-02-01,Traffic jams induced by rare switching events in two-lane transport,"We investigate a model for driven exclusion processes where internal states
are assigned to the particles. The latter account for diverse situations,
ranging from spin states in spintronics to parallel lanes in intracellular or
vehicular traffic. Introducing a coupling between the internal states by
allowing particles to switch from one to another induces an intriguing
polarization phenomenon. In a mesoscopic scaling, a rich stationary regime for
the density profiles is discovered, with localized domain walls in the density
profile of one of the internal states being feasible. We derive the shape of
the density profiles as well as resulting phase diagrams analytically by a
mean-field approximation and a continuum limit. Continuous as well as
discontinuous lines of phase transition emerge, their intersections induce
multicritical behavior.",0702022v2
2007-06-28,Exact ground state density functional theory for impurity models coupled to external reservoirs and transport calculations,"A method is presented, which employs the density matrix renormalization group
technique in order to construct exact ground state exchange correlation
functionals for models of correlated electron systems coupled to external
reservoirs. The technique is applied to the M-site resonant level model. We
calculate its exact Kubo-conductance, which is available within DMRG, and
compare to the single-particle conductance obtained from Kohn-Sham energies and
orbitals of the exact ground state density functional theory (DFT). It is found
that the position of transport resonances is reproduced essentially exactly,
while deviations in the level broadening can be less than 1% and do not exceed
10%. Our findings lend strong support to a recently held point of view, namely
that approximations in the ground state functionals used in DFT based transport
calculations can lead to drastic errors in transport calculations while
exchange correlation contributions to the induced effective potential tend to
be less significant.",0706.4253v1
2012-02-28,On Disturbance State-Space Models and the Particle Marginal Metropolis-Hastings Sampler,"We investigate nonlinear state-space models without a closed-form transition
density, and propose reformulating such models over their latent noise
variables rather than their latent state variables. In doing so the tractable
noise density emerges in place of the intractable transition density. For
importance sampling methods such as the auxiliary particle filter, this enables
importance weights to be computed where they could not be otherwise. As case
studies we take two multivariate marine biogeochemical models and perform state
and parameter estimation using the particle marginal Metropolis-Hastings
sampler. For the particle filter within this sampler, we compare several
proposal strategies over noise variables, all based on lookaheads with the
unscented Kalman filter. These strategies are compared using conventional means
for assessing Metropolis-Hastings efficiency, as well as with a novel metric
called the conditional acceptance rate for assessing the consequences of using
an estimated, and not exact, likelihood. Results indicate the utility of
reformulating the model over noise variables, particularly for fast-mixing
process models.",1202.6159v3
2013-02-21,Quantum discord for two-qubit CS states: Analytical solution,"We found an universal local unitary (orthogonal) transformation which
transforms any centrosymmetric (CS) density matrix \rho_{CS} into the X density
matrix \rho_X: H\otimes H\rho_{CS}H\otimes H=\rho_X, where H is the Hadamard
transformation. Because quantum discord is invariant under the local unitary
transformations, this remarkable property allows to get the discord of general
two-qubit CS states in the analytical form using the corresponding well-known
formulas for the X states. Examples of systems with CS density matrices
provided from the recent literature, including XXZ spin model with the
Dzyaloshinsky-Moriya interaction, a gas of spin-carrying particles in closed
nanopore, and a family of pseudopure states.",1302.5239v3
2013-11-05,Universal equation of state and pseudogap in the two-dimensional Fermi gas,"We determine the thermodynamic properties and the spectral function for a
homogeneous two-dimensional Fermi gas in the normal state using the
Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of
state deviates strongly from that of the ideal Fermi gas even for moderate
interactions, and our calculations suggest that temperature has a pronounced
effect on the pressure in the crossover from weak to strong coupling,
consistent with recent experiments. We also compute the superfluid transition
temperature for a finite system in the crossover region. There is a pronounced
pseudogap regime above the transition temperature: the spectral function shows
a Bogoliubov-like dispersion with back-bending, and the density of states is
significantly suppressed near the chemical potential. The contact density at
low temperatures increases with interaction and compares well with both
experiment and zero-temperature Monte Carlo results.",1311.1000v2
2014-11-12,Charge density waves in graphite; towards the magnetic ultra-quantum limit,"Graphite is a model system for the study of three-dimensional electrons and
holes in the magnetic quantum limit, in which the charges are confined to the
lowest Landau levels. We report magneto-transport measurements in pulsed
magnetic fields up to 60 T, which resolve the collapse of two density wave
states in two, electron and hole, Landau levels at 52.3 and 54.2 T
respectively. We report evidence for a commensurate density wave at 47.1 T in
the electron Landau level. The theoretical modelling of these results predicts
that the ultra-quantum limit is entered above 73.5 T. This state is an
insulator, and we discuss its correspondence to the ""metallic"" state reported
earlier. We propose that this (interaction-induced) insulating phase supports
surface states that carry no charge or spin within the planes, but does however
support charge transport out of plane.",1411.3323v3
2017-04-04,"Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments and parallel distribution","We present developments in the calculation of reduced density matrices (RDMs)
in the full configuration interaction quantum Monte Carlo (FCIQMC) method. An
efficient scheme is described to allow storage of RDMs across distributed
memory, thereby allowing their calculation and storage in large basis sets. We
demonstrate the calculation of RDMs for general states by using the
recently-introduced excited-state FCIQMC approach [J. Chem. Phys. 143, 134117
(2015)] and further introduce calculation of transition density matrices (TDMs)
in the method. These approaches are combined to calculate excited-state dipole
and transition dipole moments for heteronuclear diatomic molecules, including
LiH, BH and MgO, and initiator error is investigated in these quantities.",1704.00864v2
2017-07-17,A steady-state magneto-optical trap with 100 fold improved phase-space density,"We demonstrate a continuously loaded $^{88}\mathrm{Sr}$ magneto-optical trap
(MOT) with a steady-state phase-space density of $1.3(2) \times 10^{-3}$. This
is two orders of magnitude higher than reported in previous steady-state MOTs.
Our approach is to flow atoms through a series of spatially separated laser
cooling stages before capturing them in a MOT operated on the 7.4-kHz linewidth
Sr intercombination line using a hybrid slower+MOT configuration. We also
demonstrate producing a Bose-Einstein condensate at the MOT location, despite
the presence of laser cooling light on resonance with the 30-MHz linewidth
transition used to initially slow atoms in a separate chamber. Our steady-state
high phase-space density MOT is an excellent starting point for a continuous
atom laser and dead-time free atom interferometers or clocks.",1707.05370v3
2021-04-21,Balanced-imbalanced transitions in indirect reciprocity dynamics on networks,"Here we investigate the dynamics of indirect reciprocity on networks, a type
of social dynamics in which the attitude of individuals, either cooperative or
antagonistic, toward other individuals changes over time by their actions and
mutual monitoring. We observe an absorbing state phase transition as we change
the network's link or edge density. When the edge density is either small or
large enough, opinions quickly reach an absorbing state, from which opinions
never change anymore once reached. In contrast, if the edge density is in the
middle range the absorbing state is not reached and the state keeps changing
thus being active. The result shows a novel effect of social networks on
spontaneous group formation.",2104.10568v1
2021-11-30,Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles,"We applied renormalized singles (RS) in the multireference density functional
theory (DFT) to calculate accurate energies of ground and excited states. The
multireference DFT approach determines the total energy of the $N$-electron
system as the sum of the ($N-2$)-electron energy from a density functional
approximation (DFA) and the two-electron addition energies from the
particle-particle Tamm-Dancoff approximation (ppTDA), naturally including
multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian
capturing all singles contributions in calculating two-electron addition
energies, and its total energy is optimized with the optimized effective
potential method. It significantly improves the original ppTDA@DFA. For ground
states, ppTDA@RS-DFA properly describes dissociation curves tested and the
double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides
accurate excitation energies and largely eliminates the DFA dependence.
ppTDA@RS-DFA thus provides an efficient multireference approach to systems with
static correlation.",2111.15654v3
1997-02-11,Near-Infrared Spectroscopy of Molecular Filaments in the Reflection Nebula NGC 7023,"We present near-infrared spectroscopy of fluorescent molecular hydrogen (H_2)
emission from molecular filaments in the reflection nebula NGC 7023. We derive
the relative column densities of H_2 rotational-vibrational states from the
measured line emission and compare these results with several model
photodissociation regions covering a range of densities, incident UV-fields,
and excitation mechanisms. Our best-fit models for one filament suggest, but do
not require, either a combination of different densities, suggesting clumps of
10^6 cm^{-3} in a 10^4 - 10^5 cm^{-3} filament, or a combination of fluorescent
excitation and thermally-excited gas, perhaps due to a shock from a bipolar
outflow. We derive densities and UV fields for these molecular filaments that
are in agreement with previous determinations.",9702091v1
2001-11-15,Millions of Single Cloud Weak MgII Systems,"We report on a population of absorption systems selected by the presence of
very weak Mg II doublets. A sub-population of these systems are iron enriched
and have near solar metallicities. This would indicated advanced stages (i.e.
few Gyr) of in situ star formation within the absorbing structures. From
photoionization modeling, we infer low ionization fractions of f(HI/H)~0.01,
and gas densities of ~0.1 cm^-3. Since the maximum HI column densities are
\~10^17 cm^-2, the inferred cloud sizes are ~10 pc. From their redshift number
densities, this implies that their co-moving spatial density outnumbers normal
bright galaxies by a factor of a few million.",0111315v1
1997-12-03,Quantum Corrections to the Energy Density of a Homogeneous Bose Gas,"Quantum corrections to the properties of a homogeneous interacting Bose gas
at zero temperature can be calculated as a low-density expansion in powers of
$\sqrt{\rho a^3}$, where $\rho$ is the number density and $a$ is the S-wave
scattering length. We calculate the ground state energy density to second order
in $\sqrt{\rho a^3}$. The coefficient of the $\rho a^3$ correction has a
logarithmic term that was calculated in 1959. We present the first calculation
of the constant under the logarithm. The constant depends not only on $a$, but
also on an extra parameter that describes the low energy $3\to 3$ scattering of
the bosons. In the case of alkali atoms, we argue that the second order quantum
correction is dominated by the logarithmic term, where the argument of the
logarithm is $\rho a \ell_V^2$, and $\ell_V$ is the length scale set by the van
der Waals potential.",9712041v2
2001-12-20,Theory of Magnetic Field Induced Spin Density Wave in High Temperature Superconductors,"The induction of spin density wave (SDW) and charge density wave (CDW)
orderings in the mixed state of high $T_c$ superconductors (HTS) is
investigated by using the self-consistent Bogoliubov-de Gennes equations based
upon an effective model Hamiltonian with competing SDW and d-wave
superconductivity interactions. For optimized doping sample, the modulation of
the induced SDW and its associated CDW is determined by the vortex lattice and
their patterns obey the four-fold symmetry. By deceasing doping level, both SDW
and CDW show quasi-one dimensional like behavior, and the CDW has a period just
half that of the SDW along one direction. From the calculation of the local
density of states (LDOS), we found that the majority of the quasi-particles
inside the vortex core are localized. All these results are consistent with
several recent experiments on HTS.",0112369v2
2005-04-20,Thermodynamics of the two-dimensional Falicov-Kimball model: a classical Monte Carlo study,"The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo
method. In the case of concentrations of both itinerant and localized particles
equal to 0.5 we determine temperature dependence of specific heat, charge
density wave susceptibility and density-density correlation function. In the
weak interaction regime we find a first order transition to the ordered state
and anomalous temperature dependence of the correlation function. We construct
the phase diagram of half-filled FK model. Also, the role of
next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we
discuss the density of states and the spectral functions for the mobile
particles in weak and strong interaction regime.",0504533v2
2006-09-14,Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas,"The Luther-Emery liquid is a state of matter that is predicted to occur in
one-dimensional systems of interacting fermions and is characterized by a
gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a
realization of the Luther-Emery phase in a trapped cold-atom gas. We study by
means of the density-matrix renormalization-group technique a two-component
atomic Fermi gas with attractive interactions subject to parabolic trapping
inside an optical lattice. We demonstrate how this system exhibits compound
phases characterized by the coexistence of spin pairing and atomic-density
waves. A smooth crossover occurs with increasing magnitude of the atom-atom
attraction to a state in which tightly bound spin-singlet dimers occupy the
center of the trap. The existence of atomic-density waves could be detected in
the elastic contribution to the light-scattering diffraction pattern.",0609346v1
2006-09-27,Optimized Effective Potential Method in Current-Spin Density Functional Theory,"Current-spin density functional theory (CSDFT) provides a framework to
describe interacting many-electron systems in a magnetic field which couples to
both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density
functional theory, approximations to the exchange-correlation energy based on
the model of the uniform electron gas face problems in practical applications.
In this work, explicitly orbital-dependent functionals are used and a
generalization of the Optimized Effective Potential (OEP) method to the CSDFT
framework is presented. A simplifying approximation to the resulting integral
equations for the exchange-correlation potentials is suggested. A detailed
analysis of these equations is carried out for the case of open-shell atoms and
numerical results are given using the exact-exchange energy functional. For
zero external magnetic field, a small systematic lowering of the total energy
for current-carrying states is observed due to the inclusion of the current in
the Kohn-Sham scheme. For states without current, CSDFT results coincide with
those of spin density functional theory.",0609696v1
2003-09-30,Numerical study of the equation of state for two flavor QCD at finite density,"We discuss the equation of state for 2 flavor QCD at non-zero temperature and
density. Derivatives of $\ln Z$ with respect to quark chemical potential
$\mu_q$ up to fourth order are calculated, enabling estimates of the pressure,
quark number density and associated susceptibilities as functions of $\mu_q$
via a Taylor series expansion. It is found that the fluctuations in the quark
number density increase in the vicinity of the phase transition temperature and
the susceptibilities start to develop a pronounced peak as $\mu_q$ is
increased. This suggests the presence of a critical endpoint in the $(T,
\mu_q)$ plane.",0309188v2
2004-07-09,Dense baryonic matter in strong coupling lattice gauge theory,"We investigate the strong coupling limit of lattice QCD in the Hamiltonian
formulation for systems with non-zero baryon density. In leading order the
Hamiltonian looks like an antiferromagnet that is invariant under global
U(N_f)xU(N_f) and local SU(N_c). Physically it describes meson dynamics with a
fixed background of baryon density. We study this Hamiltonian with several
baryon number distributions, and concentrate on the global symmetries of the
ground state and on the properties of low lying excitations. In particular, for
uniform non-zero baryon density we write the partition function as a path
integral that is tractable in the limit of large N_c. We find that the ground
state spontaneously breaks chiral symmetry as well as discrete lattice
rotations in a way that depends on N_f and the density. The low energy
excitations include type I and type II Goldstone bosons. The energies of the
latter are of order 1/N_c, and are quadratic in momentum. Bosons of either type
can develop anisotropic dispersion relations.",0407018v1
2001-01-03,Aspects of Color Superconductivity,"I discuss some aspects of recent developments in color superconductivity in
high density quark matter. I calculate the Cooper pair gap and the critical
points at high density, where magnetic gluons are not screened. The ground
state of high density QCD with three light flavors is shown to be a
color-flavor locking state, which can be mapped into the low-density hadronic
phase. The meson mass at the CFL superconductor is also calculated. The CFL
color superconductor is bosonized, where the Fermi sea is identified as a
$Q$-matter and the gapped quarks as topological excitations, called
superqualitons, of mesons. Finally, as an application of color
supercoductivity, I discuss the neutrino interactions in the CFL color
superconductor.",0101025v1
2004-12-22,Ground State Energy of the Low Density Fermi Gas,"Recent developments in the physics of low density trapped gases make it
worthwhile to verify old, well known results that, while plausible, were based
on perturbation theory and assumptions about pseudopotentials. We use and
extend recently developed techniques to give a rigorous derivation of the
asymptotic formula for the ground state energy of a dilute gas of $N$ fermions
interacting with a short-range, positive potential of scattering length $a$.
For spin 1/2 fermions, this is $E \sim E^0 + (\hbar^2/2m) 2 \pi N \rho a$,
where $E^0$ is the energy of the non-interacting system and $\rho$ is the
density. A similar formula holds in 2D, with $\rho a$ replaced by $\rho
/|\ln(\rho a^2)|$. Obviously this 2D energy is not the expectation value of a
density-independent pseudopotential.",0412080v1
2007-03-19,Unitary Fermi Gas in a Harmonic Trap,"We present an {\it ab initio} calculation of small numbers of trapped,
strongly interacting fermions using the Green's Function Monte Carlo method
(GFMC). The ground state energy, density profile and pairing gap are calculated
for particle numbers $N = 2 \sim 22$ using the parameter-free ""unitary""
interaction. Trial wave functions are taken of the form of correlated pairs in
a harmonic oscillator basis. We find that the lowest energies are obtained with
a minimum explicit pair correlation beyond that needed to exploit the
degeneracy of oscillator states. We find that energies can be well fitted by
the expression $a_{TF} E_{TF} + \Delta {\rm mod}(N,2)$ where $E_{TF}$ is the
Thomas-Fermi energy of a noninteracting gas in the trap and $\Delta$ is a
pairing gap. There is no evidence of a shell correction energy in the
systematics, but the density distributions show pronounced shell effects. We
find the value $\Delta= 0.7\pm 0.2\omega$ for the pairing gap. This is smaller
than the value found for the uniform gas at a density corresponding to the
central density of the trapped gas.",0703190v1
2007-06-12,Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides,"A generalized Fermi-Bose mapping method is used to determine the exact ground
states of several models of mixtures of strongly interacting ultracold gases in
tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D
Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D
spin-aligned Fermi gas with infinitely strong zero-range attractions). We
detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and
boson-fermion (BF) interactions. Exact results are given for density profiles
in a harmonic trap, single-particle density matrices, momentum distributions,
and density-density correlations. Since the ground state is highly degenerate,
we analyze the splitting of the ground manifold for large but finite BB and BF
repulsions.",0706.1797v2
2007-11-19,Strongly paired fermions: Cold atoms and neutron matter,"Experiments with cold Fermi atoms can be tuned to probe strongly interacting
fluids that are very similar to the low-density neutron matter found in the
crusts of neutron stars. In contrast to traditional superfluids and
superconductors, matter in this regime is very strongly paired, with gaps of
the order of the Fermi energy. We compute the T=0 equation of state and pairing
gap for cold atoms and low-density neutron matter as a function of the Fermi
momentum times the scattering length. Results of quantum Monte Carlo
calculations show that the equations of state are very similar. The neutron
matter pairing gap at low densities is found to be very large but, except at
the smallest densities, significantly suppressed relative to cold atoms because
of the finite effective range in the neutron-neutron interaction.",0711.3006v2
2008-03-24,Excitonic condensation of massless fermions in graphene bilayers,"Graphene, a single sheet of graphite with honeycomb lattice structure, has
massless carriers with tunable density and polarity. We investigate the ground
state phase diagram of two graphene sheets (embedded in a dielectric) separated
by distance $d$ where the top layer has electrons and the bottom layer has
holes, using mean-field theory. We find that a uniform excitonic condensate
occurs over a large range of carrier densities and is weakly dependent on the
relative orientation of the two sheets. We obtain the excitonic gap,
quasiparticle energy and the density of states. We show that both, the
condensate phase stiffness and the mass of the excitons, with massless
particles as constituents, vary as the square-root of the carrier density, and
predict that the condensate will not undergo Wigner crystallization.",0803.3451v2
2008-04-10,Eigen power-flow-density vortices of magnetostatic modes in thin ferrite disks,"In confined magnetically ordered structures one can observe vortices of
magnetization and electromagnetic power flow vortices. There are topologically
distinct and robust states. In this paper we show that in a normally magnetized
quasi-2D ferrite disk there exist eigen power-flow-density vortices of
magnetic-dipolar-mode oscillations. Because of such circular power flows, the
oscillating modes are characterized by stable magnetostatic energy states and
discrete angular moments of the wave fields. We show that the
power-flow-density vortices of magnetostatic modes can be excited by
electromagnetic fields of a microwave cavity. There is a clear correspondence
between the power-flow-density vortex structures in a ferrite disk derived from
an analytical solution of the magnetostatic-wave spectral problem and obtained
by the numerical-simulation electromagnetic program.",0804.1666v1
2008-05-15,A possible mechanism of concurring diagonal and off-diagonal long-range order for soft interactions,"This paper is a contribution to the theory of coherent crystals. We present
arguments claiming that negative minima in the Fourier transform of a soft pair
interaction may give rise to the coexistence of diagonal and off-diagonal
long-range order at high densities, and that this coexistence may be detectable
due to a periodicity seen on the off-diagonal part of the one-body reduced
density matrix, without breaking translation invariance. As an illustration, we
study the ground state of a homogenous system of bosons in continuous space,
from the interaction retaining only the Fourier modes $v(\k)$ belonging to a
single nonzero wave number $|\k|=q$. The result is a mean-field model. We prove
that for $v(\k)>0$ the ground state is asymptotically fully Bose-condensed,
while for $v(\k)<0$ at densities exceeding a multiple of $\hbar^2
q^2/2m|v(\k)|$ it exhibits both Bose-Einstein condensation and diagonal
long-range order, and the latter can be seen on both the one- and the two-body
density matrix.",0805.2339v2
2009-10-09,Fermionisation dynamics of a strongly interacting 1D Bose gas after an interaction quench,"We study the dynamics of a one-dimensional Bose gas after a sudden change of
the interaction strength from zero to a finite value using the numerical
time-evolving block decimation (TEBD) algorithm. It is shown that despite the
integrability of the system, local quantities such as the two-particle
correlation $g^{(2)}(x,x)$ attain steady state values in a short characteristic
time inversely proportional to the Tonks parameter $\gamma$ and the square of
the density. The asymptotic values are very close to those of a finite
temperature grand canonical ensemble with a local temperature corresponding to
initial energy and density. Non-local density-density correlations on the other
hand approach a steady state on a much larger time scale determined by the
finite propagation velocity of oscillatory correlation waves.",0910.1749v4
2009-10-15,Ground-state degeneracies leave recognizable topological scars in the one-particle density,"In Kohn-Sham density functional theory (KS-DFT) a fictitious system of
non-interacting particles is constructed having the same ground-state (GS)
density as the physical system of interest. A fundamental open question in DFT
concerns the ability of an exact KS calculation to spot and characterize the GS
degeneracies in the physical system. In this article we provide theoretical
evidence suggesting that the GS density, as a function of position on a 2D
manifold of parameters affecting the external potential, is ""topologically
scarred"" in a distinct way by degeneracies. These scars are sufficiently
detailed to enable determination of the positions of degeneracies and even the
associated Berry phases. We conclude that an exact KS calculation can spot and
characterize the degeneracies of the physical system.",0910.2947v8
2010-10-26,Helstrom's Theory on Quantum Binary Decision Revisited,"For a binary system specified by the density operators r0 and r1 and by the
prior probabilities q0 and q1, Helstrom's theory permits the evaluation of the
optimal measurement operators and of the corresponding maximum correct
detection probability. The theory is based on the eigendecomposition (EID) of
the operator, given by the difference of the weighted density operators, namely
D = q1r1-q0r0. In general, this EID is obtained explicitly only with pure
states, whereas with mixed states it must be carried out numerically. In this
letter we show that the same evaluation can be performed on the basis of a
modified version of the Gram matrix. The advantage is due to the fact that the
outer products of density operators are replaced by inner product, with a
considerable dimensionality reduction. At the limit, in quantum optical
communications the density operators have infinite dimensions, whereas the
inner products are simply scalar quantities. The Gram matrix approach permits
the explicit (not numerical) evaluation of a binary system performance in cases
not previously developed.",1010.5388v1
2011-10-11,Sensitivity of nuclear stopping towards density dependent symmetry energy,"The effect of density dependent symmetry energy on nuclear-stopping is
studied using isospin-dependent quantum molecular dynamics model(IQMD). We have
used the reduced isospin-dependent cross-section with soft(S) equation of state
for the systems having different isostopic content, to explore the various
aspects of nuclear stopping. The aim is to pin down the nature of the nuclear
stopping with density dependent symmetry energy. Nuclear stopping is found to
be sensitive towards the various forms of the density dependent symmetry
energy. The nuclear stopping tends to decrease for the stiffer equation of
state (EOS), i.e. larger values of gamma.",1110.2290v3
2013-11-11,Fermionized photons in the ground state of one-dimensional coupled cavities,"The Density Matrix Renormalization Group algorithm is used to characterize
the ground states of one-dimensional coupled cavities in the regime of low
photon densities. Numerical results for photon and spin excitation densities,
one- and two-body correlation functions, superfluid and condensate fractions,
as well as the entanglement entropy and localizable entanglement are obtained
for the Jaynes-Cummings-Hubbard (JCH) model, and are compared with those for
the Bose-Hubbard (BH) model where applicable. The results indicate that a
Tonks-Girardeau phase, in which the photons are strongly fermionized, appears
between the Mott-insulating and superfluid phases as a function of the
inter-cavity coupling. In fact, the superfluid density is found to be zero in a
wide region outside the Mott-insulator phase boundary. The presence of two
different species of excitation (spin and photon) in the JCH model gives rise
to properties with no analog in the BH model, such as the (quasi)condensation
of spin excitations and the spontaneous generation of entanglement between the
atoms confined to each cavity.",1311.2348v1
2014-01-20,Blind deconvolution of density-matrix renormalization-group spectra,"We present a numerical method for calculating piecewise smooth spectral
functions of correlated quantum systems in the thermodynamic limit from the
spectra of finite systems computed using the dynamical or correction-vector
density-matrix renormalization group method. The key idea is to consider this
problem as a blind deconvolution with an unknown kernel which causes both a
broadening and finite-size corrections of the spectrum. In practice, the method
reduces to a least-square optimization under non-linear constraints which
enforce the positivity and piecewise smoothness of spectral functions. The
method is demonstrated on the single-particle density of states of
one-dimensional paramagnetic Mott insulators represented by the half-filled
Hubbard model on an open chain. Our results confirm that the density of states
has a step-like shape but no square-root singularity at the spectrum onset.",1401.4918v2
2015-06-23,2+1 flavors QCD equation of state at zero temperature within Dyson-Schwinger equations,"Within the framework of Dyson-Schwinger equations (DSEs), we discuss the
equation of state (EOS) and quark number densities of 2+1 flavors, that is to
say, $u$, $d$, and $s$ quarks. The chemical equilibrium and electric charge
neutrality conditions are used to constrain the chemical potential of different
quarks. The EOS in the cases of 2 flavors and 2+1 flavors are discussed, and
the quark number densities, the pressure, and energy density per baryon are
also studied. The results show that there is a critical chemical potential for
each flavor of quark, at which the quark number density turns to nonzero from
0; and furthermore, the system with 2+1 flavors of quarks is more stable than
that with 2 flavors in the system. These discussion may provide some useful
information to some research fields, such as the studies related to the QCD
phase transitions or compact stars.",1506.06846v1
2015-07-09,Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings,"We analyze the stability of excitonic ground states in the two-band Hubbard
model with additional electron-phonon and Hund's rule couplings using a
combination of mean-field and variational cluster approaches. We show that both
the interband Coulomb interaction and the electron-phonon interaction will
cooperatively stabilize a charge density wave (CDW) state which typifies an
""excitonic"" CDW if predominantly triggered by the effective interorbital
electron-hole attraction or a ""phononic"" CDW if mostly caused by the coupling
to the lattice degrees of freedom. By contrast, the Hund's rule coupling
promotes an excitonic spin density wave. We determine the transition between
excitonic charge and spin density waves and comment on a fixation of the phase
of the excitonic order parameter that would prevent the formation of a
superfluid condensate of excitons. The implications for exciton condensation in
several material classes with strongly correlated electrons are discussed.",1507.02494v2
2015-08-19,Dynamics and instantaneous normal modes in a liquid with density anomalies,"We investigate the relation between the dynamical features of a supercooled
liquid and those of its potential energy landscape, focusing on a model liquid
with density anomalies. We consider, at fixed temperature, pairs of state
points with different density but the same diffusion constant, and find that
surprisingly they have identical dynamical features at all length and time
scales. This is shown by the collapse of their mean square displacements and of
their self--intermediate scattering functions at different wavevectors. We then
investigate how the features of the energy landscape change with density, and
establish that state points with equal diffusion constant have different
landscapes. In particular, we find a correlation between the fraction of
instantaneous normal modes connecting different energy minima and the diffusion
constant, but unlike in other systems these two quantities are not in
one--to--one correspondence with each other, showing that additional landscape
features must be relevant in determining the diffusion constant.",1508.04517v1
2015-11-05,Nonequilibrium response of an electron mediated charge-density-wave-ordered material to a large dc electric field,"Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical
mean-field theory to exactly solve for the nonlinear response of an
electron-mediated charge-density-wave-ordered material. We examine both the dc
current and the order parameter of the conduction electrons as the ordered
system is driven by the electric field. Although the formalism we develop
applies to all models, for concreteness, we examine the charge-density-wave
phase of the Falicov-Kimball model, which displays a number of anomalous
behaviors including the appearance of subgap density of states as the
temperature increases. These subgap states should have a significant impact on
transport properties, particularly the nonlinear response of the system to a
large dc electric field.",1511.01595v1
2017-05-07,Quantum capacitance of double-layer graphene,"We study the ground-state properties of a double layer graphene system with
the Coulomb interlayer electron-electron interaction modeled within the random
phase approximation. We first obtain an expression of the quantum capacitance
of a two layer system. In addition, we calculate the many-body
exchange-correlation energy and quantum capacitance of the hybrid double layer
graphene system at zero-temperature. We show an enhancement of the majority
density layer thermodynamic density-of-states owing to an increasing interlayer
interaction between two layers near the Dirac point. The quantum capacitance
near the neutrality point behaves like square root of the total density,
$\alpha \sqrt{n}$, where the coefficient $\alpha$ decreases by increasing the
charge density imbalance between two layers. Furthermore, we show that the
quantum capacitance changes linearly by the gate voltage. Our results can be
verified by current experiments.",1705.02630v2
2017-05-25,Construction of the steady state density matrix and quasilocal charges for the spin-1/2 XXZ chain with boundary magnetic fields,"We construct the nonequilibrium steady state (NESS) density operator of the
spin-1/2 XXZ chain with non-diagonal boundary magnetic fields coupled to
boundary dissipators. The Markovian boundary dis- sipation is found with which
the NESS density operator is expressed in terms of the product of the Lax
operators by relating the dissipation parameters to the boundary parameters of
the spin chain. The NESS density operator can be expressed in terms of a
non-Hermitian transfer operator (NHTO) which forms a commuting family of
quasilocal charges. The optimization of the Mazur bound for the high
temperature Drude weight is discussed by using the quasilocal charges and the
conventional local charges constructed through the Bethe ansatz.",1705.09105v1
2018-11-05,Signatures of pair-density wave order in phase-sensitive measurements of La$_{2-x}$Ba$_x$CuO$_4$-Nb Josephson junctions and SQUIDs,"The interplay of charge order, spin order, and superconductivity in
La$_{2-x}$Ba$_x$CuO$_4$ creates a complex physical system that hosts several
interesting phases, such as two-dimensional superconductivity within the
CuO$_2$ planes and the ordered pair-density wave state in which charge ordering
is intertwined with superconductivity. Using Josephson interferometry
techniques, we measure the current-phase relation of junctions and SQUIDs
incorporating this material and observe a significant sin($2\phi$)-component
indicative of closely-spaced alternations of the sign of the Josephson coupling
predicted by the pair-density wave model. We find that the ratio of the
sin(2$\phi$)-component to the conventional sin($\phi$)-component to be largest
near x=1/8 doping, where the pair-density wave state is believed to be the
strongest, and that it increases with increasing temperature as the Josephson
coupling in the junction weakens.",1811.02048v1
2016-11-11,Functional Fit Approach (FFA) for Density of States method: SU(3) spin system and SU(3) lattice gauge theory with static color sources,"We apply a recently developed variant of the Density of States (DoS) method,
the so-called Functional Fit Approach (FFA) to two different models: the SU(3)
spin model and SU(3) lattice gauge theory with static color sources. Both
models can be derived from QCD and inherit the complex action problem at finite
density. We discuss the implementation of DoS FFA in the two models and compute
observables related to the particle density. For the SU(3) spin model we show
that the results are in good agreement with the results from a Monte Carlo
simulation in the dual formulation, which is free of the complex action
problem. For the case of SU(3) lattice gauge theory with static color sources
we present first results for the particle number as a function of the coupling
for different values of the chemical potential.",1611.03719v2
2017-07-21,Many-body localization of spinless fermions with attractive interactions in one dimension,"We study the finite-energy density phase diagram of spinless fermions with
attractive interactions in one dimension in the presence of uncorrelated
diagonal disorder. Unlike the case of repulsive interactions, a delocalized
Luttinger-liquid phase persists at weak disorder in the ground state, which is
a well-known result. We revisit the ground-state phase diagram and show that
the recently introduced occupation-spectrum discontinuity computed from the
eigenspectrum of one-particle density matrices is noticeably smaller in the
Luttinger liquid compared to the localized regions. Moreover, we use the
functional renormalization scheme to study the finite-size dependence of the
conductance, which resolves the existence of the Luttinger liquid as well and
is computationally cheap. Our main results concern the finite-energy density
case. Using exact diagonalization and by computing various established measures
of the many-body localization-delocalization transition, we argue that the
zero-temperature Luttinger liquid smoothly evolves into a finite-energy density
ergodic phase without any intermediate phase transition.",1707.06759v3
2017-10-23,"Fermi liquid, clustering, and structure factor in dilute warm nuclear matter","Properties of nuclear systems at subsaturation densities can be obtained from
different approaches. We demonstrate the use of the density autocorrelation
function which is related to the isothermal compressibility and, after
integration, to the equation of state. This way we connect the Landau Fermi
liquid theory well elaborated in nuclear physics with the approaches to dilute
nuclear matter describing cluster formation. A quantum statistical approach is
presented, based on the cluster decomposition of the polarization function. The
fundamental quantity to be calculated is the dynamic structure factor.
Comparing with the Landau Fermi liquid theory which is reproduced in lowest
approximation, the account of bound state formation and continuum correlations
gives the correct low-density result as described by the second virial
coefficient and by the mass action law (nuclear statistical equilibrium). Going
to higher densities, the inclusion of medium effects is more involved compared
with other quantum statistical approaches, but the relation to the Landau Fermi
liquid theory gives a promising approach to describe not only thermodynamic but
also collective excitations and non-equilibrium properties of nuclear systems
in a wide region of the phase diagram.",1710.08251v1
2018-09-10,Density decay and growth of correlations in the Game of Life,"We study the Game of Life as a statistical system on an $L\times L$ square
lattice with periodic boundary conditions. Starting from a random initial
configuration of density $\rho_{\rm in}=0.3$ we investigate the relaxation of
the density as well as the growth with time of spatial correlations. The
asymptotic density relaxation is exponential with a characteristic time
$\tau_L$ whose system size dependence follows a power law $\tau_L\propto L^z$
with $z=1.66\pm 0.05$ before saturating at large system sizes to a constant
$\tau_\infty$. The correlation growth is characterized by a time dependent
correlation length $\xi_t$ that follows a power law $\xi_t\propto
t^{1/z^\prime}$ with $z^\prime$ close to $z$ before saturating at large times
to a constant $\xi_\infty$. We discuss the difficulty of determining the
correlation length $\xi_\infty$ in the final ""quiescent"" state of the system.
The decay time $t_{\rm q}$ towards the quiescent state is a random variable, we
present simulational evidence as well as a heuristic argument indicating that
for large $L$ its distribution peaks at a value $t_{\rm q}^*(L) \simeq
2\tau_\infty\log L$.",1809.03266v2
2018-09-20,Holographic QCD in the Veneziano limit and neutron stars,"We use the holographic V-QCD models to analyse the physics of dense QCD and
neutron stars. Accommodating lattice results for thermodynamics of QCD enables
us to make generic predictions for the Equation of State (EoS) of the quark
matter phase in the cold and dense regime. We demonstrate that the resulting
pressure in V-QCD matches well with a family of neutron-star-matter EoSs that
interpolate between state-of-the-art theoretical results for low and high
density QCD. After implementing the astrophysical constraints, i.e., the
largest known neutron star mass and the recent LIGO/Virgo results for the tidal
deformability, we analyse the phase transition between the baryonic and quark
matter phases. We find that the baryon density $n_B$ at the transition is at
least 2.9 times the nuclear saturation density $n_s$. The transition is of
strongly first order at low and intermediate densities, i.e., for $n_B/n_s
\lesssim 7.5$.",1809.07770v3
2021-05-10,Supersymmetry and multicriticality in a ladder of constrained fermions,"Supersymmetric lattice models of constrained fermions are known to feature
exotic phenomena such as superfrustration, with an extensive degeneracy of
ground states, the nature of which is however generally unknown. Here we
address this issue by considering a superfrustrated model, which we deform from
the supersymetric point. By numerically studying its two-parameter phase
diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric
point features period-4 and period-5 density waves which are connected by a
floating phase (incommensurate Luttinger liquid) with smoothly varying density.
The supersymmetric point emerges as a multicritical point between these three
phases. Inside the period-4 phase we report a valence-bond solid type ground
state that persists up to the supersymmetric point. Our numerical data for
transitions out of density-wave phases are consistent with the
Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a
period-3 phase with a boundary determined by a competition between single and
two-particle instabilities accompanied by a doubling of the wavevector of the
density profiles along a line in the phase diagram.",2105.04359v3
2023-03-03,Bayesian uncertainty quantification of perturbative QCD input to the neutron-star equation of state,"The equation of state of neutron-star cores can be constrained by requiring a
consistent connection to the perturbative Quantum Chromodynamics (QCD)
calculations at high densities. The constraining power of the QCD input depends
on uncertainties from missing higher-order terms, the choice of the unphysical
renormalization scale, and the reference density where QCD calculations are
performed. Within a Bayesian approach, we discuss the convergence of the
perturbative QCD series, quantify its uncertainties at high densities, and
present a framework to systematically propagate the uncertainties down to
neutron-star densities. We find that the effect of the QCD input on the
neutron-star inference is insensitive to the various unphysical choices made in
the uncertainty estimation.",2303.02175v2
2023-10-13,Bounds on the Equation of State from QCD Inequalities and Lattice QCD,"We derive robust bounds on the equation of state (EoS) at finite baryon
chemical potential using QCD inequalities and input from recent lattice-QCD
calculations of thermodynamic properties of matter at nonzero isospin chemical
potential. We use lattice data to deduce an upper bound on the baryon density
of the symmetric nuclear matter at a given baryon chemical potential and a
lower bound on the pressure as a function of the energy density. We also use
constraints from perturbative calculations of the QCD EoS at high density
derived in earlier work and causality to delineate robust bounds on the EoS of
isospin symmetric matter at densities relevant to heavy-ion collisions.",2310.09427v1
2023-12-12,Emergent Gauge Symmetry in Active Brownian Matter,"We investigate a two-dimensional system of interacting Active Brownian
Particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we
built up the generating functional for correlation functions. We study in
detail the hydrodynamic regime with a constant density stationary state. Our
findings reveal that, within a small density fluctuations regime, an emergent
$U(1)$ gauge symmetry arises, originated from the conservation of fluid
vorticity. Consequently, the interaction between the orientational order
parameter and density fluctuations can be cast into a gauge theory, where the
concept of ``electric charge density"" aligns with the local vorticity of the
original fluid. We study in detail the case of a microscopic local two-body
interaction. We show that, upon integrating out the gauge fields, the
stationary states of the rotational degrees of freedom satisfy a non-local
Frank free energy for a nematic fluid. We give explicit expressions for the
splay and bend elastic constants as a function of the P\'eclet number (${\rm
Pe}$) and the diffusion interaction constant ($k_d$).",2312.07283v2
2024-01-04,Intrinsic insulating transport characteristics in low-carrier density EuCd2As2 films,"Searching for an ideal magnetic Weyl semimetal hosting only a single pair of
Weyl points has been a focal point for systematic clarification of its unique
magnetotransport derived from the interplay between topology and magnetization.
Among the candidates, triangular-lattice antiferromagnet EuCd$_2$As$_2$ has
been attracting special attention due to the prediction of the ideal Weyl
semimetal phase in the ferromagnetic state, however, transport properties of
low-carrier density samples have remained elusive. Here we report molecular
beam epitaxy growth of EuCd$_2$As$_2$ films, achieving low-hole density in the
range of $10^{15}$-$10^{16}$ cm$^{-3}$ at low temperature. Transport
measurements of such low-carrier density films reveal an insulating behavior
with an activation gap of about 200 meV, which persists even in the
field-induced ferromagnetic state. Our work provides an important experimental
clue that EuCd$_2$As$_2$ is intrinsically insulating, contrary to the previous
prediction.",2401.02026v1
2014-02-01,The Relativistic Inverse Stellar Structure Problem,"The observable macroscopic properties of relativistic stars (whose equations
of state are known) can be predicted by solving the stellar structure equations
that follow from Einstein's equation. For neutron stars, however, our knowledge
of the equation of state is poor, so the direct stellar structure problem can
not be solved without modeling the highest density part of the equation of
state in some way. This talk will describe recent work on developing a model
independent approach to determining the high-density neutron-star equation of
state by solving an inverse stellar structure problem. This method uses the
fact that Einstein's equation provides a deterministic relationship between the
equation of state and the macroscopic observables of the stars which are
composed of that material. This talk illustrates how this method will be able
to determine the high-density part of the neutron-star equation of state with
few percent accuracy when high quality measurements of the masses and radii of
just two or three neutron stars become available. This talk will also show that
this method can be used with measurements of other macroscopic observables,
like the masses and tidal deformabilities, which can (in principle) be measured
by gravitational wave observations of binary neutron-star mergers.",1402.0035v1
2004-02-13,Density dependencies of interaction strengths and their influence on nuclear matter and neutron star in relativistic mean field theory,"The density dependencies of various effective interaction strengths in the
relativistic mean field are studied and carefully compared for nuclear matter
and neutron stars. The influences of different density dependencies are
presented and discussed on mean field potentials, saturation properties for
nuclear matter, equations of state, maximum masses and corresponding radii for
neutron stars. Though the interaction strengths and the potentials given by
various interactions are quite different in nuclear matter, the differences of
saturation properties are subtle, except for NL2 and TM2, which are mainly used
for light nuclei, while the properties by various interactions for pure neutron
matter are quite different. To get an equation of state for neutron matter
without any ambiguity, it is necessary to constrain the effective interactions
either by microscopic many-body calculations for the neutron matter data or the
data of nuclei with extreme isospin. For neutron stars, the interaction with
large interaction strengths give strong potentials and large
Oppenheimer-Volkoff (OV) mass limits. The density-dependent interactions DD-ME1
and TW-99 favor a large neutron population due to their weak $\rho$-meson field
at high densities. The OV mass limits calculated from different equations of
state are 2.02 $\sim$ 2.81$ M_\odot$, and the corresponding radii are 10.78
$\sim$ 13.27 km. After the inclusion of the hyperons, the corresponding values
become 1.52 $\sim$ 2.06 $M_\odot$ and 10.24 $\sim$ 11.38 km.",0402045v1
2019-09-30,"Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for 1D delta-function potential","In contrast with the 3D result, the Beth-Uhlenbeck (BU) formula in 1D
contains an extra -1/2 term. The origin of this -1/2 term is explained using a
spectral density approach. To be explicit, a delta-function potential is used
to show that the correction term arises from a pole of the density of states at
zero energy. The spectral density method shows that this term is actually an
artifact of the non-normalizability of the scattering states and an infrared
cutoff regularization scheme has to be used to get the correct result in 1D.
The formal derivation of the BU formula would miss this term since it ignores
the effects of the boundary terms. While the result is shown for the
delta-function potential, the method and result are valid for more general
potentials. Additionally, the 1D Levinson's theorem can be extracted from the
spectral density method using the asymptotic form of general potentials. The
importance of the result lies in the fact that all these correction terms in 1D
have a universal source: a pole at zero energy. Similar calculations using
quantum field theoretical approaches (without explicit infrared cutoff
regularization schemes) also show the same subtleties with the correction term
originating from the zero energy scattering states (appendix A).",1910.00052v1
2020-04-27,Transition to a supersolid phase in a two-dimensional dilute gas of electron-hole pairs,"Using coherent-state formalism (the Keldysh formalism), the article describes
a transition from a homogeneous superfluid state to a supersolid state in a
two-dimensional dilute gas of electron-hole pairs with spatially separated
components. Such a transition is heralded by the appearance of a roton-type
minimum in the collective excitation spectrum, which touches the abscissa axis
as the distance between the layers or the pair density increases. This signals
the instability of the system with respect to the appearance of a spatial
modulation of the pair density. It has been found that a first-order transition
to a hexagonal supersolid phase takes place a little earlier. A theory without
phenomenological constants has been developed for an arbitrary relation between
the effective masses of an electron and a hole. A phase diagram for the system
has been plotted in the variables ""the chemical potential of pairs - the
distance between the layers"". It has been shown that there is a jump in the
average density of the condensate during the phase transition. It has been
established that with an increase in the chemical potential, the inhomogeneous
phase breaks up into high-density regions surrounded by lines at which the
density becomes zero, with these lines forming a continuous network.",2004.12930v1
2004-12-20,Full characterization of a three-photon GHZ state using quantum state tomography,"We have performed the first experimental tomographic reconstruction of a
three-photon polarization state. Quantum state tomography is a powerful tool
for fully describing the density matrix of a quantum system. We measured 64
three-photon polarization correlations and used a ""maximum-likelihood""
reconstruction method to reconstruct the GHZ state. The entanglement class has
been characterized using an entanglement witness operator and the maximum
predicted values for the Mermin inequality was extracted.",0412151v1
2016-11-19,Spatially-indirect Exciton Condensate Phases in Double Bilayer Graphene,"We present a theory of spatially indirect exciton condensate states in
systems composed of a pair of electrically isolated Bernal graphene bilayers.
The ground state phase diagram in a two-dimensional
displacement-field/inter-bilayer-bias space includes layer-polarized
semiconductors, spin-density-wave states, exciton condensates, and states with
mixed excitonic and spin order. We find that two different condensate states,
distinguished by a chirality index, are stable under different electrical
control conditions.",1611.06410v1
2001-02-19,Spin Polarized Ground State for Interacting Electrons in Two Dimensions,"We study numerically the ground state magnetization for clusters of
interacting electrons in two dimensions in the regime where the single particle
wavefunctions are localized by disorder. It is found that the Coulomb
interaction leads to a spontaneous ground state magnetization. For a constant
electronic density, the total spin increases linearly with the number of
particles, suggesting a ferromagnetic ground state in the thermodynamic limit.
The magnetization is suppressed when the single particle states become
delocalized.",0102326v1
2004-01-23,Ground state phases of the Half-Filled One-Dimensional Extended Hubbard Model,"Using quantum Monte Carlo simulations, results of a strong-coupling
expansion, and Luttinger liquid theory, we determine quantitatively the ground
state phase diagram of the one-dimensional extended Hubbard model with on-site
and nearest-neighbor repulsions U and V. We show that spin frustration
stabilizes a bond-ordered (dimerized) state for U appr. V/2 up to U/t appr. 9,
where t is the nearest-neighbor hopping. The transition from the dimerized
state to the staggered charge-density-wave state for large V/U is continuous
for U up to appr. 5.5 and first-order for higher U.",0401472v1
1997-12-21,More on Mixed Boundary Conditions and D-branes Bound States,"In this article, applying different types of boundary conditions; Dirichlet,
Neumann, or Mixed, on open strings we realize various new brane bound states in
string theory. Calculating their interactions with other D-branes, we find
their charge densities and their tension. A novel feature of $(p-2,p)$ brane
bound state is its ""non-commutative"" nature which is manifestly seen both in
the open strings mode expansions and in their scattering off a $D_p$-brane.
Moreover we study three or more object bound states in string theory language.
Finally we give a M-theoretic picture of these bound states.",9712199v1
1996-12-23,Displaced and Squeezed Number States,"After beginning with a short historical review of the concept of displaced
(coherent) and squeezed states, we discuss previous (often forgotten) work on
displaced and squeezed number states. Next, we obtain the most general
displaced and squeezed number states. We do this in both the functional and
operator (Fock) formalisms, thereby demonstrating the necessary equivalence. We
then obtain the time-dependent expectation values, uncertainties,
wave-functions, and probability densities. In conclusion, there is a discussion
on the possibility of experimentally observing these states.",9612050v1
1999-12-17,Quantum Teleportation with Entangled States given by Beam Splittings,"Quantum teleportation is rigorously discussed with coherent entang led states
given by beam splittings. The mathematical scheme of beam splitti ng has been
used to study quantum communication and quantum stochastic. We d iscuss the
teleportation process by means of coherent states in this scheme for the
following two cases: (1) Delete the vacuum part from coherent states, whose
compensation provides us a perfect teleportation from Alice to Bob. (2) Use
fully realistic (physical) coherent states, which give s a non-perfect
teleportation but shows that it is exact when the average en ergy (density) of
the coherent vectors goes to infinity.",9912083v1
2000-11-22,On the LOCC Classification of Bipartite Density Matrices,"We provide a unifying framework for exact, probabilistic, and approximate
conversions by local operations and classical communication (LOCC) between
bipartite states. This framework allows us to formulate necessary and
sufficient conditions for LOCC conversions from pure states to mixed states and
it provides necessary conditions for LOCC conversions between mixed states. The
central idea is the introduction of convex sets for exact, probabilistic, and
approximate conversions, which are closed under LOCC operations and which are
largely characterized by simple properties of pure states.",0011095v1
2007-05-14,Recovery of Hidden Interference in Mott Insulators,"Particle statistics plays a crucial role in a strongly interacting quantum
many-body system. Here, we study the Hubbard model for distinguishable
particles at unit filling. Starting from the superfluid-like state in the
strong tunneling limit and gradually reducing the tunneling so that the on-site
repulsive interaction dominates, the state ends up in a symmetric superposition
of Mott insulator states. This result can be experimentally confirmed by the
recovery of interference patterns in the density correlation functions. We also
show that this state is a maximally entangled state, in contrast to the
standard picture.",0705.2023v1
2009-01-21,Monogamy and entanglement in tripartite quantum states,"We present an interesting monogamy equation for $(2 \otimes 2 \otimes
n)$-dimensional pure states, by which a quantity is found to characterize the
tripartite entanglement with the GHZ type and W typeentanglements as a whole.
In particular, we, for the first time, reveals that for any quantum state of a
pair of qubits, the difference between the two remarkable entanglement
measures, concurrence and negativity, characterizes the W type entanglement of
tripartite pure states with the two-qubit state as reduced density.",0901.3274v1
2009-02-25,Minimally entangled typical quantum states at finite temperature,"We introduce a class of states, called minimally entangled typical thermal
states (METTS), designed to resemble a typical state of a quantum system at
finite temperature with a bias towards classical (minimally entangled)
properties. These states reveal in an intuitive way properties such as
short-range order which may be hidden in correlation functions. An algorithm is
presented which, when used with the density matrix renormalization group
(DMRG), is faster by a factor of $10^3 - 10^{10}$ than previous heat-bath
approaches for thermally averaged quantities.",0902.4475v2
2009-11-10,An $η$-condensate of fermionic atom pairs via adiabatic state preparation,"We discuss how an $\eta$-condensate, corresponding to an exact excited
eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an
optical lattice. Using time-dependent density matrix renormalisation group
methods, we analyse a state preparation scheme beginning from a band insulator
state in an optical superlattice. This state can act as an important test case,
both for adiabatic preparation methods and the implementation of the many-body
Hamiltonian, and measurements on the final state can be used to help detect
associated errors.",0911.2005v1
2010-04-03,Witnessing quantum discord in 2 x N systems,"Bipartite states with vanishing quantum discord are necessarily separable and
hence positive partial transpose (PPT). We show that 2 x N states satisfy
additional property: the positivity of their partial transposition is
recognized with respect to the canonical factorization of the original density
operator. We call such states SPPT (for strong PPT). Therefore, we provide a
natural witness for a quantum discord: if a 2 x N state is not SPPT it must
contain nonclassical correlations measured by quantum discord. It is an analog
of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be
entangled.",1004.0434v1
2010-11-01,Bound state of a hole and a triplet spin in the $t_1$-$t_2$-$J_1$-$J_2$ model,"We show that a hole and a triplet spin form a bound state in a nearly
half-filled band of the one- and two-dimensional $t_1$-$t_2$-$J_1$-$J_2$
models. Numerical calculation indicates that the bound state is a spatially
small object and moves as a composite particle with spin 1 and charge $+e$ in
the spin-gapped background. Two bound states repulsively interact with each
other in a short distance and move independently as long as they keep their
distance. If a finite density of bound states behave as bosons, the system
undergoes the Bose-Einstein condensation which means a superconductivity with
charge $+e$.",1011.0255v1
2011-06-01,The Fulde-Ferrell-Larkin-Ovchinnikov states for the d-wave superconductor in the two-dimensional orthorhombic lattice,"The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of a two-dimensional (2D)
orthorhombic lattice superconductor is studied based on the
Bogoliubov-de-Gennes equations. It is illustrated that the 2D FFLO state is
suppressed and only one-dimensional (1D) stripe state is stable. The stripe
changes its orientation with the increasing Zeeman field. There exists a
crossover region where the gap structure has some local 2D features. These
results are significantly different from those of the tetragonal lattice
system. The local density of states is also studied which can be checked and
compared with experiments in future.",1106.0115v1
2011-12-09,Quantum Entanglement and Detection of Topological Order in Numerics,"""Topological ordered"" phases such as gapped quantum spin-liquids and
fractional quantum Hall states possess ground state degeneracy on a torus. We
show that the topological nature of this degeneracy has interesting
consequences for the entanglement structure of the degenerate ground states.
This leads to a simple method for detecting topological order, which is
ready-made for numerical schemes such as density matrix renormalization group.
The method is valid for phases that do or do not possess edge states alike. We
demonstrate it by calculating the entanglement spectrum and the topological
entanglement entropy for a chiral spin-liquid state on a 18 site system.",1112.2215v1
2015-09-03,Dynamic Entanglement Evolution of Two-qubit XYZ Spin Chain in Markovian Environment,"We propose a new approach called Ket-Bra Entangled State (KBES) Method for
converting master equation into Schr\""{o}dinger-like equation. With this
method, we investigate decoherence process and entanglement dynamics induced by
a $2$-qubit spin chain that each qubit coupled with reservoir. The spin chain
is an anisotropy $XYZ$ Heisenberg model in the external magnetic field $B$, the
corresponding master equation is solved concisely by KBES method; Furthermore,
the effects of anisotropy, temperature, external field and initial state on
concurrence dynamics is analyzed in detail for the case that initial state is
Extended Wenger-Like(EWL) state. Finally we research the coherence and
concurrence of the final state (namely the density operator for time tend to
infinite)",1509.01001v1
2019-11-01,Generalized overlap quantum state tomography,"We propose and experimentally demonstrate a quantum state tomography protocol
that generalizes the Wallentowitz-Vogel-Banaszek-W\'odkiewicz point-by-point
Wigner function reconstruction. The full density operator of an arbitrary
quantum state is efficiently reconstructed in the Fock basis, using
semidefinite programming, after interference with a small set of calibrated
coherent states. This new protocol is resource- and computationally efficient,
is robust against noise, does not rely on approximate state displacements, and
ensures the physicality of results.",1911.00173v2
2017-11-21,An algorithm to explore entanglement in small systems,"A quantum state's entanglement across a bipartite cut can be quantified with
entanglement entropy or, more generally, Schmidt norms. Using only Schmidt
decompositions, we present a simple iterative algorithm to maximize Schmidt
norms. Depending on the choice of norm, the optimizing states maximize or
minimize entanglement, possibly across several bipartite cuts at the same time
and possibly only among states in a specified subspace.
  Recognizing that convergence but not success is certain, we use the algorithm
to explore topics ranging from fermionic reduced density matrices and varieties
of pure quantum states to absolutely maximally entangled states and minimal
output entropy of channels.",1711.07943v3
2022-09-28,Quantum Hall states in higher Landau levels,"The unitary correspondence between Quantum Hall states in higher Landau
levels and states in the lowest Landau level is discussed together with the
resulting transformation formulas for particle densities and interaction
potentials. This correspondence leads in particular to a representation of
states in arbitrary Landau levels in terms of holomorphic functions. Some
important special Quantum Hall states in higher Landau levels are also briefly
discussed.",2209.14203v1
2023-07-21,All holographic systems have scar states,"Scar states are special finite-energy density, but non-thermal states of
chaotic Hamiltonians. We argue that all holographic quantum field theories,
including $\mathcal{N}=4$ super Yang--Mills, have scar states. Their presence
is tied to the existence of non-topological, horizonless soliton solutions in
gravity: oscillons and a novel family of excited boson stars. We demonstrate
that these solutions have periodic oscillations in the correlation functions
and posses low-entanglement entropy as expected for scar states. Also we find
that they can be very easily prepared with Euclidean path integral.",2307.11348v1
2004-04-02,Uncorrelated Estimates of Dark Energy Evolution,"Type Ia supernova data have recently become strong enough to enable, for the
first time, constraints on the time variation of the dark energy density and
its equation of state. Most analyses, however, are using simple two or
three-parameter descriptions of the dark energy evolution, since it is well
known that allowing more degrees of freedom introduces serious degeneracies.
Here we present a method to produce uncorrelated and nearly model-independent
band power estimates of the equation of state of dark energy and its density as
a function of redshift. We apply the method to recently compiled supernova
data. Our results are consistent with the cosmological constant scenario, in
agreement with other analyses that use traditional parameterizations, though we
find marginal (2-sigma) evidence for w(z) < -1 at z < 0.2. In addition to easy
interpretation, uncorrelated, localized band powers allow intuitive and
powerful testing of the constancy of either the energy density or equation of
state. While we have used relatively coarse redshift binning suitable for the
current set of about 150 supernovae, this approach should reach its full
potential in the future, when applied to thousands of supernovae found from
ground and space, combined with complementary information from other
cosmological probes.",0404062v1
2003-11-17,A Possible Mechanism for Generating a Small Positive Cosmological Constant,"We argue that in the context of string theory a large number N of connected
degenerate vacua that mix will lead to a ground state with much lower energy,
essentially because of the standard level repulsion of quantum theory for the
wavefunction of the Universe. We imagine a history where initial quantum
fluctuations give an energy density $\sim m_{susy}^2m_{Pl}^2$, but the universe
quickly cascades to an energy density $\sim m_{susy}^2m_{Pl}^2/N$. Then at
various phase transitions there are large contributions to the energy density
and rearrangement of levels, followed again by a rapid cascade to the ground
state or near it. If this mechanism is correct, the ground state of the theory
describing our world would be a superposition of a large number of connected
string vacua,with shared superselection sets of properties such as three
families etc. The observed value of the cosmological constant in terms of the
Planck mass, the scale of supersymmetry breaking and the number of connected
string vacua.",0311152v1
2004-05-03,Spectral Analysis of Percolation Hamiltonians,"We study the family of Hamiltonians which corresponds to the adjacency
operators on a percolation graph. We characterise the set of energies which are
almost surely eigenvalues with finitely supported eigenfunctions. This set of
energies is a dense subset of the algebraic integers. The integrated density of
states has discontinuities precisely at this set of energies. We show that the
convergence of the integrated densities of states of finite box Hamiltonians to
the one on the whole space holds even at the points of discontinuity. For this
we use an equicontinuity-from-the-right argument. The same statements hold for
the restriction of the Hamiltonian to the infinite cluster. In this case we
prove that the integrated density of states can be constructed using local data
only. Finally we study some mixed Anderson-Quantum percolation models and
establish results in the spirit of Wegner, and Delyon and Souillard.",0405006v3
2009-08-26,Two-dimensional Anderson-Hubbard model in DMFT+Sigma approximation,"Density of states, dynamic (optical) conductivity and phase diagram of
paramagnetic two-dimensional Anderson-Hubbard model with strong correlations
and disorder are analyzed within the generalized dynamical mean-field theory
(DMFT+Sigma approximation). Strong correlations are accounted by DMFT, while
disorder is taken into account via the appropriate generalization of the
self-consistent theory of localization. We consider the two-dimensional system
with the rectangular ""bare"" density of states (DOS). The DMFT effective single
impurity problem is solved by numerical renormalization group (NRG). Phases of
""correlated metal"", Mott insulator and correlated Anderson insulator are
identified from the evolution of density of states, optical conductivity and
localization length, demonstrating both Mott-Hubbard and Anderson
metal-insulator transitions in two-dimensional systems of the finite size,
allowing us to construct the complete zero-temperature phase diagram of
paramagnetic Anderson-Hubbard model. Localization length in our approximation
is practically independent of the strength of Hubbard correlations. However,
the divergence of localization length in finite size two-dimensional system at
small disorder signifies the existence of an effective Anderson transition.",0908.3747v2
2011-03-13,Vibrational Behavior of Metal Nanowires under Tensile Stress,"We have investigated the vibrational density of states (VDOS) of a thin Cu
nanowire with $<100>$ axial orientation and considered the effect of axial
strain. The VDOS are calculated using a real space Green's function approach
with the force constant matrices extracted from interaction potential based on
the embedded atom method. Results for the vibrational density of states of a
strain-free nanowire show quite distinctive characteristics compared to that of
a bulk atom, the most striking feature of which is the existence of high
frequency modes above the top of the bulk spectrum. We further predict that the
low frequency characteristics of the VDOS reveal the quasi-1 dimensional (Q1D)
behavior only when the wire is extremely thin. Through decomposition of VDOS
into local atoms we also exhibit that while the anomalous increase in low
frequency density of states is mainly due to the corner atoms, the enhancement
in high frequency modes is primarily moderated by core atoms. We, additionally,
find that while the high frequency band above the top of the bulk phonon shifts
to higher frequencies, the characteristics at low frequencies remains almost
the same upon stretching the nanowire along the axial direction.",1103.2521v1
2011-06-28,Theoretical analysis of the density of states of graphene at high magnetic field using Haldane pseudopotentials,"We study the density of states in graphene at high magnetic field, when the
physics is dominated by strong correlations between electrons. In particular we
use the method of Haldane pseudopotentials to focus on almost empty or almost
filled Landau levels. We find that, besides the usual Landau level peaks,
additional peaks (""sashes"") appear in the spectrum. The energies of these peaks
are determined by the strength of Haldane's pseudopotentials, but as opposed to
the usual two-dimensional gas, when there is a one-to-one correspondence
between a Haldane pseudopotential and a peak in the spectrum, the energy of
each peak is determined in general by a combination of more than one
pseudopotential values. An eventual measure of these peak in the density of
states spectrum of graphene would allow one to determine the value of the
pseudopotentials in graphene, and thus test the strength of the interactions in
this system.",1106.5748v1
2017-01-30,P-wave superfluidity of atomic lattice fermions,"We discuss the emergence of p-wave superfluidity of identical atomic fermions
in a two-dimensional optical lattice. The optical lattice potential manifests
itself in an interplay between an increase in the density of states on the
Fermi surface and the modification of the fermion-fermion interaction
(scattering) amplitude. The density of states is enhanced due to an increase of
the effective mass of atoms. In deep lattices the scattering amplitude is
strongly reduced compared to free space due to a small overlap of wavefunctions
of fermion sitting in the neighboring lattice sites, which suppresses the
p-wave superfluidity. However, for moderate lattice depths the enhancement of
the density of states can compensate the decrease of the scattering amplitude.
Moreover, the lattice setup significantly reduces inelastic collisional losses,
which allows one to get closer to a p-wave Feshbach resonance. This opens
possibilities to obtain the topological $p_x+ip_y$ superfluid phase, especially
in the recently proposed subwavelength lattices. We demonstrate this for the
two-dimensional version of the Kronig-Penney model allowing a transparent
physical analysis.",1701.08520v4
2008-07-23,"Vortices in rotating optical lattices: commensurability, hysteresis, and proximity to the Mott State","Quantized vortices stunningly illustrate the coherent nature of a superfluid
Bose condensate of alkali atoms. Introducing an optical lattice depletes this
coherence. Consequently, novel vortex physics may emerge in an experiment on a
harmonically trapped gas in the presence of a rotating optical lattice. The
most dramatic effects would occur in proximity to the Mott state, an
interaction dominated insulator with a fixed integer number of particles per
site. We model such a rotating gas, showing that the lattice-induced spatial
profile of the superfluid density drives a gross rearrangement of vortices. For
example, instead of the uniform vortex lattices commonly seen in experiments,
we find parameters for which the vortices all sit at a fixed distance from the
center of the trap, forming a ring. Similarly, they can coalesce at the center,
forming a giant vortex. We find that the properties of this system are
hysteretic, even far from the Mott state. We explain this hysteresis in terms
of vortex pinning, commensurability between vortex density and pinning site
density, and energy barriers against changing the number of vortices. Finally,
we model time-of-flight expansion, demonstrating the experimental observability
of our predictions.",0807.3609v1
2017-07-24,Classifications of Twin Star Solutions for a Constant Speed of Sound Parameterized Equation of State,"We explore the possible mass radius relation of compact stars for the
equation of states with a first order phase transition. The low density matter
is described by a nuclear matter equation of state resulting from fits to
nuclear properties. A constant speed of sound parametrization is used to
describe the high density matter phase with the speed of sound $c_s^2=1$.
  A classification scheme of four distinct categories including twin star
solutions, i. e. solutions with the same mass but differing radii, is found
which are compatible with the $M \ge 2M_\odot$ pulsar mass constraint.
  We show the dependence of the mass and radius differences on the transition
parameters and delineate that higher twin star masses are more likely to be
accompanied by large radius differences. These massive twin stars are generated
by high values of the discontinuity in the energy density and the lowest
possible values of the transition pressure that still result in masses of $M
\geq 2M_\odot$ at the maximum of the hadronic branch.",1707.07524v1
2017-09-04,Spin-polarized ballistic conduction through correlated Au-NiMnSb-Au heterostructures,"We examine the ballistic conduction through Au-NiMnSb-Au heterostructures
consisting of up to four units of NiMnSb in the scattering region. We
investigate the dependence of the transmission function computed within the
local spin density approximation (LSDA) of the density functional theory (DFT)
on the number of half-metallic units in the scattering region. For a single
NiMnSb unit the transmission function displays a spin polarization of around 50
% in a window of 1 eV centered around the Fermi level. By increasing the number
of layers an almost complete spin polarization of the transmission is obtained
in the same energy window. Supplementing the DFT-LSDA calculations with local
electronic interactions, of Hubbard-type on the Mn sites, leads to a
hybridization between the interface and many-body states. The significant
reduction of the spin polarization seen in the density of states is not
apparent in the spin-polarization of the conduction electron transmission,
which suggests the localized nature of the hybridized interface and many-body
induced states.",1709.00983v1
2021-04-08,Density-tuned isotherms and dynamic change at phase transition in a gate-controlled superconducting system,"Two-dimensional electron gases in SrTiO3-based heterostructures provide a
platform to study the real-time evolution of the macroscopic state with a
variation of the carrier density, and the impact of structural properties on
the emergence of the superconducting state. We have explored the isothermal
evolution of the electron gas in AlOx/SrTiO3 by measuring the variation of
resistance with continuous gate-voltage-controlled tuning of its carrier
density. It is seen that condensation of the ordered phase leads to
non-monotonic isotherms within the superconducting dome. The timescale for
dynamic change following changes in gate voltage is measured across the phase
transition. It is found to be tens of seconds near the onset of
superconductivity, significantly larger compared to the normal state. Such a
large timescale governing the kinetics of the phase transition presumably
arises from the strong impact of structural defects and distortions of the
substrate on the development of superconducting islands.",2104.03633v2
2014-12-15,Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates,"We analyze the interplay between charge-density-wave (CDW) and
pair-density-wave (PDW) orders within the spin-fermion model for the cuprates.
We specifically consider CDW order with transferred momenta $(\pm Q,0)$/$(0,\pm
Q)$, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. We show that both
emerge in the spin-fermion model near the onset of antiferromagnetism. We
further argue that the two orders are nearly degenerate due to an approximate
SU(2) particle-hole symmetry of the model. The ${\rm SU}(2)$ symmetry becomes
exact if one neglects the curvature of the Fermi surface in hot regions, in
which case ${\rm U}(1)$ CDW and PDW order parameters become components of an
SO(4)-symmetric PDW/CDW ""super-vector"". We develop a Ginzburg-Landau theory for
PDW/CDW order parameters and find two possible ground states: a ""stripe"" state,
and a ""checkerboard"" state. We show that the ${\rm SO}(4)$ symmetry between CDW
and PDW is broken by two effects. One is the inclusion of Fermi surface
curvature, which selects a PDW order immediately below the instability
temperature. Another is the overlap between different hot regions, which favors
CDW order at low temperatures. For the stripe state, we show that the
competition between the two effects gives rise to a first-order transition from
PDW to CDW inside the ordered state. We also argue that beyond mean-field
theory, the onset temperature for CDW order is additionally enhanced due to
feedback from a preemptive breaking of ${\mathbb Z}_2$ time-reversal symmetry.
We discuss the ground state properties of a pure PDW state and a pure CDW
state, and show that the PDW checkerboard state yields a vortex-anti-vortex
lattice. For the checkerboard state, we considered a situation when both CDW
and PDW orders are present at low $T$ and show that the presence of both
condensates induces a long sought chiral $s+id_{xy}$ superconductivity.",1412.4798v2
2010-05-26,Two-dimensional surface charge transport in topological insulators,"We construct a theory of charge transport by the surface states of
topological insulators in three dimensions. The focus is on the experimentally
relevant case when the electron doping is such that the Fermi energy
$\epsilon_F$ and transport scattering time $\tau$ satisfy $\epsilon_F
\tau/\hbar \gg 1$, but sufficiently low that $\epsilon_F$ lies below the bottom
of the conduction band. Our theory is based on the spin density matrix and
takes the quantum Liouville equation as its starting point. The scattering term
is determined accurately to linear order in the impurity density. We consider
scattering by charged impurities and short-range scatterers such as surface
roughness. We calculate also the polarization function in topological
insulators, emphasizing the differences from graphene. We find that the main
contribution to the conductivity is $\propto n_i^{-1}$, where $n_i$ is the
impurity density, and will have different carrier density dependencies for
different forms of scattering. Two different contributions to this conductivity
are traced to the scalar and spin-dependent terms in the Hamiltonian and their
relative weight depends on the doping density. Our results contain all
contributions to the conductivity to orders zero and one in the impurity
density. We discuss also a way to determine the dominant scattering angles by
studying the ratio of the transport relaxation time to the Bloch lifetime as a
function of the Wigner-Seitz radius $r_s$. We also discuss the effect on the
surface states of adding metallic contacts.",1005.4931v3
2018-08-08,FLUX: Progressive State Estimation Based on Zakai-type Distributed Ordinary Differential Equations,"We propose a homotopy continuation method called FLUX for approximating
complicated probability density functions. It is based on progressive
processing for smoothly morphing a given density into the desired one.
Distributed ordinary differential equations (DODEs) with an artificial time
$\gamma \in [0,1]$ are derived for describing the evolution from the initial
density to the desired final density. For a finite-dimensional parametrization,
the DODEs are converted to a system of ordinary differential equations (SODEs),
which are solved for $\gamma \in [0,1]$ and return the desired result for
$\gamma=1$. This includes parametric representations such as Gaussians or
Gaussian mixtures and nonparametric setups such as sample sets. In the latter
case, we obtain a particle flow between the two densities along the artificial
time.
  FLUX is applied to state estimation in stochastic nonlinear dynamic systems
by gradual inclusion of measurement information. The proposed approximation
method (1) is fast, (2) can be applied to arbitrary nonlinear systems and is
not limited to additive noise, (3) allows for target densities that are only
known at certain points, (4) does not require optimization, (5) does not
require the solution of partial differential equations, and (6) works with
standard procedures for solving SODEs. This manuscript is limited to the
one-dimensional case and a fixed number of parameters during the progression.
Future extensions will include consideration of higher dimensions and on the
fly adaption of the number of parameters.",1808.02825v1
2015-12-27,The Stability of the Vacuum Polarization Surrounding a Charged Particle,"The internal stability of the electron has been debated for a century at both
the classical and the quantum level. Recently, a local force density balance
was established for the 1s electron in the H atom, based on the energy-momentum
tensor of the classical Dirac field. This methodology is now extended to
quantum fields by considering the force densities acting on the vacuum
polarization induced by a point charge. Such a model is applicable to any
charged particle at large distances, since the only vestige of its internal
structure is the electric Coulomb field together with the vacuum polarization
induced by it. While the polarization charge density is attracted to the point
charge, it is kept from collapsing by repulsive forces due to confinement and
degeneracy. It is shown analytically that the corresponding force densities are
balanced for every filled shell of mj states at a given angular momentum j. The
force densities are then summed over all single-electron states in the Dirac
sea and renormalized by subtracting singular terms. In leading order of alpha,
the force densities remain balanced. This result establishes a local force
balance for a prototypical manybody system.",1512.08257v3
2017-07-01,Intrinsic translational symmetry breaking in a doped Mott insulator,"A central issue of Mott physics, with symmetries being fully retained in the
spin background, concerns the charge excitation. In a two-leg spin ladder with
spin gap, an injected hole can exhibit either a Bloch wave or a density wave by
tuning the ladder anisotropy through a `quantum critical point' (QCP). The
nature of such a QCP has been a subject of recent studies by density matrix
renormalization group (DMRG). In this paper, we reexamine the ground state of
the one doped hole, and show that a two-component structure is present in the
density wave regime in contrast to the single component in the Bloch wave
regime. In the former, the density wave itself is still contributed by a
standing-wave-like component characterized by a quasiparticle spectral weight
$Z$ in a finite-size system. But there is an additional charge incoherent
component emerging, which intrinsically breaks the translational symmetry
associated with the density wave. The partial momentum is carried away by
neutral spin excitations. Such an incoherent part does not manifest in the
single-particle spectral function, directly probed by the angle-resolved
photoemission spectroscopy (ARPES) measurement, however it is demonstrated in
the momentum distribution function. The Landau's one-to-one correspondence
hypothesis for a Fermi liquid breaks down here. The microscopic origin of this
density wave state as an intrinsic manifestation of the doped Mott physics will
be also discussed.",1707.00068v2
2019-06-03,The polytropic state of the intracluster medium in the X-COP cluster sample,"In this work, we investigate the relation between the radially-resolved
thermodynamic quantities of the intracluster medium in the X-COP cluster
sample, aiming to assess the stratification properties of the ICM. We model the
relations between radius, gas temperature, density and pressure using a
combination of power-laws, also evaluating the intrinsic scatter in these
relations. We show that the gas pressure is remarkably well correlated to the
density, with very small scatter. Also, the temperature correlates with gas
density with similar scatter. The slopes of these relations have values that
show a clear transition from the inner cluster regions to the outskirts. This
transition occurs at the radius $r_t = 0.19(\pm0.04)R_{500}$ and electron
density $n_t = (1.91\pm0.21)\cdot10^{-3} cm^{-3} E^2 (z)$. We find that above
0.2 $R_{500}$ the radial thermodynamic profiles are accurately reproduced by a
well defined and physically motivated framework, where the dark matter follows
the NFW potential and the gas is represented by a polytropic equation of state.
By modeling the gas temperature dependence upon both the gas density and
radius, we propose a new method to reconstruct the hydrostatic mass profile
based only on the quite inexpensive measurement of the gas density profile.",1906.00977v2
2013-06-24,On column density thresholds and the star formation rate,"We present the results of a numerical study designed to address the question
of whether there is a column density threshold for star formation within
molecular clouds. We have simulated a large number of different clouds, with
volume and column densities spanning a wide range of different values, using a
state-of-the-art model for the coupled chemical, thermal and dynamical
evolution of the gas. We show that star formation is only possible in regions
where the mean (area-averaged) column density exceeds $10^{21} \: {\rm
cm^{-2}}$. Within the clouds, we also show that there is a good correlation
between the mass of gas above a K-band extinction $A_{\rm K} = 0.8$ and the
star formation rate (SFR), in agreement with recent observational work.
Previously, this relationship has been explained in terms of a correlation
between the SFR and the mass in dense gas. However, we find that this
correlation is weaker and more time-dependent than that between the SFR and the
column density. In support of previous studies, we argue that dust shielding is
the key process: the true correlation is one between the SFR and the mass in
cold, well-shielded gas, and the latter correlates better with the column
density than the volume density.",1306.5714v3
2015-03-16,Light-front representation of chiral dynamics in peripheral transverse densities,"The nucleon's electromagnetic form factors are expressed in terms of the
transverse densities of charge and magnetization at fixed light-front time. At
peripheral transverse distances $b = O(M_\pi^{-1})$ the densities are governed
by chiral dynamics and can be calculated model-independently using chiral
effective field theory (EFT). We represent the leading-order chiral EFT results
for the peripheral transverse densities as overlap integrals of chiral
light-front wave functions, describing the transition of the initial nucleon to
soft pion-nucleon intermediate states and back. The new representation (a)
explains the parametric order of the peripheral transverse densities; (b)
establishes an inequality between the spin-independent and -dependent
densities; (c) exposes the role of pion orbital angular momentum in chiral
dynamics; (d) reveals a large left-right asymmetry of the current in a
transversely polarized nucleon and suggests a simple interpretation. The
light-front representation enables a first-quantized, quantum-mechanical view
of chiral dynamics that is fully relativistic and exactly equivalent to the
second-quantized, field-theoretical formulation. It relates the charge and
magnetization densities measured in low-energy elastic scattering to the
generalized parton distributions probed in peripheral high-energy scattering
processes. The method can be applied to nucleon form factors of other
operators, e.g. the energy-momentum tensor.",1503.04839v1
2018-09-24,Simulations of radiative turbulent mixing layers,"Radiative turbulent mixing layers should be ubiquitous in multi-phase gas
with shear flow. They are a potentially attractive explanation for the high
ions such as OVI seen in high velocity clouds and the circumgalactic medium
(CGM) of galaxies. We perform 3D MHD simulations with non-equilibrium (NEI) and
photoionization modeling, with an eye towards testing simple analytic models.
Even purely hydrodynamic collisional ionization equilibrium (CIE) calculations
have column densities much lower than observations. Characteristic inflow and
turbulent velocities are much less than the shear velocity, and the layer width
$h \propto t_\mathrm{cool}^{1/2}$ rather than $h \propto t_\mathrm{cool}$.
Column densities are not independent of density or metallicity as analytic
scalings predict, and show surprisingly weak dependence on shear velocity and
density contrast. Radiative cooling, rather than Kelvin-Helmholtz instability,
appears paramount in determining the saturated state. Low pressure due to fast
cooling both seeds turbulence and sets the entrainment rate of hot gas, whose
enthalpy flux, along with turbulent dissipation, energizes the layer.
Regardless of initial geometry, magnetic fields are amplified and stabilize the
mixing layer via magnetic tension, producing almost laminar flow and depressing
column densities. NEI effects can boost column densities by factors of a few.
Suppression of cooling by NEI or photoionization can in principle also increase
OVI column densities, but in practice is unimportant for CGM conditions. To
explain observations, sightlines must pierce hundreds or thousands of mixing
layers, which may be plausible if the CGM exists as a `fog' of tiny cloudlets.",1809.09101v2
2019-12-19,The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons,"We investigate the combined effects of boundaries and topology on the vacuum
expectation values (VEVs) of the charge and current densities for a massive 2D
fermionic field confined on a conical ring threaded by a magnetic flux.
Different types of boundary conditions on the ring edges are considered for
fields realizing two inequivalent irreducible representations of the Clifford
algebra. The related bound states and zero energy fermionic modes are
discussed. The edge contributions to the VEVs of the charge and azimuthal
current densities are explicitly extracted and their behavior in various
asymptotic limits is considered. On the ring edges the azimuthal current
density is equal to the charge density or has an opposite sign. We show that
the absolute values of the charge and current densities increase with
increasing planar angle deficit. Depending on the boundary conditions, the VEVs
are continuous or discontinuous at half-integer values of the ratio of the
effective magnetic flux to the flux quantum. The discontinuity is related to
the presence of the zero energy mode. By combining the results for the fields
realizing the irreducible representations of the Clifford algebra, the charge
and current densities are studied in parity and time-reversal symmetric
fermionic models. If the boundary conditions and the phases in quasiperiodicity
conditions for separate fields are the same the total charge density vanishes.
Applications are given to graphitic cones with edges (conical ribbons).",1912.09143v1
2020-05-21,Insights into one-body density matrices using deep learning,"The one-body reduced density matrix (1-RDM) of a many-body system at zero
temperature gives direct access to many observables, such as the charge
density, kinetic energy and occupation numbers. It would be desirable to
express it as a simple functional of the density or of other local observables,
but to date satisfactory approximations have not yet been found. Deep learning
is the state-of the art approach to perform high dimensional regressions and
classification tasks, and is becoming widely used in the condensed matter
community to develop increasingly accurate density functionals. Autoencoders
are deep learning models that perform efficient dimensionality reduction,
allowing the distillation of data to its fundamental features needed to
represent it. By training autoencoders on a large data-set of 1-RDMs from
exactly solvable real-space model systems, and performing principal component
analysis, the machine learns to what extent the data can be compressed and
hence how it is constrained. We gain insight into these machine learned
constraints and employ them to inform approximations to the 1-RDM as a
functional of the charge density. We exploit known physical properties of the
1-RDM in the simplest possible cases to perform feature engineering, where we
inform the structure of the models from known mathematical relations, allowing
us to integrate existing understanding into the machine learning methods. By
comparing various deep learning approaches we gain insight into what physical
features of the density matrix are most amenable to machine learning, utilising
both known and learned characteristics.",2005.10672v1
2020-08-28,Deconvoluting Kernel Density Estimation and Regression for Locally Differentially Private Data,"Local differential privacy has become the gold-standard of privacy literature
for gathering or releasing sensitive individual data points in a
privacy-preserving manner. However, locally differential data can twist the
probability density of the data because of the additive noise used to ensure
privacy. In fact, the density of privacy-preserving data (no matter how many
samples we gather) is always flatter in comparison with the density function of
the original data points due to convolution with privacy-preserving noise
density function. The effect is especially more pronounced when using
slow-decaying privacy-preserving noises, such as the Laplace noise. This can
result in under/over-estimation of the heavy-hitters. This is an important
challenge facing social scientists due to the use of differential privacy in
the 2020 Census in the United States. In this paper, we develop density
estimation methods using smoothing kernels. We use the framework of
deconvoluting kernel density estimators to remove the effect of
privacy-preserving noise. This approach also allows us to adapt the results
from non-parameteric regression with errors-in-variables to develop regression
models based on locally differentially private data. We demonstrate the
performance of the developed methods on financial and demographic datasets.",2008.12466v2
2008-12-17,Topological Methods for Exploring Low-density States in Biomolecular Folding Pathways,"Characterization of transient intermediate or transition states is crucial
for the description of biomolecular folding pathways, which is however
difficult in both experiments and computer simulations. Such transient states
are typically of low population in simulation samples. Even for simple systems
such as RNA hairpins, recently there are mounting debates over the existence of
multiple intermediate states. In this paper, we develop a computational
approach to explore the relatively low populated transition or intermediate
states in biomolecular folding pathways, based on a topological data analysis
tool, Mapper, with simulation data from large-scale distributed computing. The
method is inspired by the classical Morse theory in mathematics which
characterizes the topology of high dimensional shapes via some functional level
sets. In this paper we exploit a conditional density filter which enables us to
focus on the structures on pathways, followed by clustering analysis on its
level sets, which helps separate low populated intermediates from high
populated uninteresting structures. A successful application of this method is
given on a motivating example, a RNA hairpin with GCAA tetraloop, where we are
able to provide structural evidence from computer simulations on the multiple
intermediate states and exhibit different pictures about unfolding and
refolding pathways. The method is effective in dealing with high degree of
heterogeneity in distribution, capturing structural features in multiple
pathways, and being less sensitive to the distance metric than nonlinear
dimensionality reduction or geometric embedding methods. It provides us a
systematic tool to explore the low density intermediate states in complex
biomolecular folding systems.",0812.3426v1
2003-12-19,"Reduced density matrices, their spectral resolutions, and the Kimball-Overhauser approach","Recently, it has been shown, that the pair density of the homogeneous
electron gas can be parametrized in terms of 2-body wave functions (geminals),
which are scattering solutions of an effective 2-body Schr\""odinger equation.
For the corresponding scattering phase shifts, new sum rules are reported in
this paper. These sum rules describe not only the normalization of the pair
density (similar to the Friedel sum rule of solid state theory), but also the
contraction of the 2-body reduced density matrix. This allows one to calculate
also the momentum distribution, provided that the geminals are known from an
appropriate screening of the Coulomb repulsion. An analysis is presented
leading from the definitions and (contraction and spectral) properties of
reduced density matrices to the Kimball-Overhauser approach and its
generalizations. Thereby cumulants are used. Their size-extensivity is related
to the thermodynamic limit.",0312518v1
2005-08-01,Quantum Hall states of atomic Bose gases: density profiles in single-layer and multi-layer geometries,"We describe the density profiles of confined atomic Bose gases in the
high-rotation limit, in single-layer and multi-layer geometries. We show that,
in a local density approximation, the density in a single layer shows a
landscape of quantized steps due to the formation of incompressible liquids,
which are analogous to fractional quantum Hall liquids for a two-dimensional
electron gas in a strong magnetic field. In a multi-layered set-up we find
different phases, depending on the strength of the inter-layer tunneling t. We
discuss the situation where a vortex lattice in the three-dimensional
condensate (at large tunneling) undergoes quantum melting at a critical
tunneling $t_{c_1}$. For tunneling well below $t_{c_1}$ one expects weakly
coupled or isolated layers, each exhibiting a landscape of quantum Hall
liquids. After expansion, this gives a radial density distribution with
characteristic features (cusps) that provide experimental signatures of the
quantum Hall liquids.",0508031v1
2006-11-02,A New Phase at Finite Quark Density from AdS/CFT,"We explore phases of N=2 super Yang-Mills theory at finite quark density by
introducing quark chemical potential in a D3-D7 setup. We formulate the
thermodynamics of brane embeddings and find that we need to renormalize the
finite chemical potential due to the divergence of the thermodynamic potentials
and we find that the density versus chemical potential equation of state has
rich structure. This yields two distinct first order phase transitions in a
small window of quark density. In order words, there is a new first order phase
transition in the region of deconfined quarks. In this new phase, the chemical
potential is a decreasing function of the density. We suggest that this might
be relevant to the difference in sQGP--wQGP phases of QCD.",0611021v1
2004-11-30,Nuclear density functional constrained by low-energy QCD,"We have developed a relativistic point-coupling model of nuclear many-body
dynamics constrained by the low-energy sector of QCD. The effective Lagrangian
is characterized by density-dependent coupling strengths determined by chiral
one- and two-pion exchange (with single and double delta isobar excitations)
and by large isoscalar background fields that arise through changes of the
quark condensate and the quark density at finite baryon density. The model has
been tested in the analysis of nuclear ground-state properties along different
isotope chains of medium and heavy nuclei. The agreement with experimental data
is comparable with purely phenomenological predictions. The built-in QCD
constraints and the explicit treatment of pion exchange restrict the freedom in
adjusting parameters and functional forms of density-dependent couplings. It is
shown that chiral pionic fluctuations play an important role for nuclear
binding and saturation mechanism, whereas background fields of about equal
magnitude and opposite sign generate the effective spin-orbit potential in
nuclei.",0411122v1
2006-04-12,Two-body correlation functions in nuclear matter with $np$ condensate,"The density, spin and isospin correlation functions in nuclear matter with a
neutron-proton ($np$) condensate are calculated to study the possible
signatures of the BEC-BCS crossover in the low-density region. It is shown that
the criterion of the crossover (Phys. Rev. Lett. {\bf 95}, 090402 (2005)),
consisting in the change of the sign of the density correlation function at low
momentum transfer, fails to describe correctly the density-driven BEC-BCS
transition at finite isospin asymmetry or finite temperature. As an unambiguous
signature of the BEC-BCS transition, there can be used the presence (BCS
regime) or absence (BEC regime) of the singularity in the momentum distribution
of the quasiparticle density of states.",0604028v1
2007-10-18,Transport and percolation in a low-density high-mobility two-dimensional hole system,"We present a study of the temperature and density dependence of the
resistivity of an extremely high quality two-dimensional hole system grown on
the (100) surface of GaAs. For high densities in the metallic regime ($p\agt 4
\times 10^{9}$ cm$^{-2}$), the nonmonotonic temperature dependence ($\sim
50-300$ mK) of the resistivity is consistent with temperature dependent
screening of residual impurities. At a fixed temperature of $T$= 50 mK, the
conductivity vs. density data indicates an inhomogeneity driven
percolation-type transition to an insulating state at a critical density of
$3.8\times 10^9$ cm$^{-2}$.",0710.3542v1
2007-11-14,Possible evidence for an inverted temperature-density relation in the intergalactic medium from the flux distribution of the Lyman-alpha forest,"We compare the improved measurement of the Lya forest flux probability
distribution at 1.7<z<3.2 presented by Kim et al. (2007) to a large set of
hydrodynamical simulations of the Lya forest with different cosmological
parameters and thermal histories. The simulations are in good agreement with
the observational data if the temperature-density relation for the low density
intergalactic medium (IGM), T=T_0 Delta^{gamma-1}, is either close to
isothermal or inverted (gamma<1). Our results suggest that the voids in the IGM
may be significantly hotter and the thermal state of the low density IGM may be
substantially more complex than is usually assumed at these redshifts. We
discuss radiative transfer effects which alter the spectral shape of ionising
radiation during the epoch of HeII reionisation as a possible physical
mechanism for achieving an inverted temperature-density relation at z~3.",0711.2064v2
2010-07-12,The phases of deuterium at extreme densities,"We consider deuterium compressed to higher than atomic, but lower than
nuclear densities. At such densities deuterium is a superconducting quantum
liquid. Generically, two superconducting phases compete, a ""ferromagnetic"" and
a ""nematic"" one. We provide a power counting argument suggesting that the
dominant interactions in the deuteron liquid are perturbative (but screened)
Coulomb interactions. At very high densities the ground state is determined by
very small nuclear interaction effects that probably favor the ferromagnetic
phase. At lower densities the symmetry of the theory is effectively enhanced to
SU(3), and the quantum liquid enters a novel phase, neither ferromagnetic nor
nematic. Our results can serve as a starting point for investigations of the
phase dynamics of deuteron liquids, as well as exploration of the stability and
dynamics of the rich variety of topological objects that may occur in phases of
the deuteron quantum liquid, which range from Alice strings to spin skyrmions
to Z_2 vortices.",1007.1972v2
2013-04-24,Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: Phase diagram and clustering,"We report an accurate Monte Carlo calculation of the phase diagram and
clustering properties of the restricted primitive model with non-additive
hard-sphere diameters. At high density the positively non-additive fluid shows
more clustering than the additive model and the negatively non-additive fluid
shows less clustering than the additive model, at low density the reverse
scenario appears. A negative nonadditivity tends to favor the formation of
neutrally charged clusters starting from the dipole. A positive nonadditivity
favors the pairing of like ions at high density. The critical point of the
gas-liquid phase transition moves at higher temperatures and higher densities
for a negative nonadditivity and at lower temperatures and lower densities for
a positive nonadditivity. The law of corresponding states does not seem to hold
strictly. Our results can be used to interpret recent experimental works on
room temperature ionic liquids.",1304.6757v2
2015-06-29,Relativistic Bondi-Hoyle-Lyttleton Accretion onto a Rotating Black-Hole: Density Gradients,"In this work, we present, for the first time, a numerical study of the
Bondi-Hoyle accretion with density gradients in the fully relativistic regime.
In this context, we consider accretion onto a Kerr Black Hole (BH) of a
supersonic ideal gas, which has density gradients perpendicular to the relative
motion. The set of parameters of interest in this study are the Mach number, M,
the spin of the BH, a, and the density-gradient parameter of the gas, {\rho} .
We show that, unlike in the Newtonian case, all the studied cases, especially
those with density gradient, approach a stationary flow pattern. To illustrate
that the system reaches steady state we calculate the mass and angular momentum
accretion rates on a spherical surface located almost at the event horizon. In
the particular case of M = 1, {\rho} = 0.5 and BH spin a = 0.5, we observe a
disk-like configuration surrounding the BH. Finally, we present the gas
morphology and some of its properties.",1506.08713v1
2016-03-15,Origin of static and dynamic steps in exact Kohn-Sham potentials,"Knowledge of exact properties of the exchange-correlation (xc) functional is
important for improving the approximations made within density functional
theory. Features such as steps in the exact xc potential are known to be
necessary for yielding accurate densities, yet little is understood regarding
their shape, magnitude and location. We use systems of a few electrons, where
the exact electron density is known, to demonstrate general properties of
steps. We find that steps occur at points in the electron density where there
is a change in the `local effective ionization energy' of the electrons. We
provide practical arguments, based on the electron density, for determining the
position, shape and height of steps for ground-state systems, and extend the
concepts to time-dependent systems. These arguments are intended to inform the
development of approximate functionals, such as the mixed localization
potential (MLP), which already demonstrate their capability to produce steps in
the Kohn-Sham potential.",1603.04816v2
2019-11-13,New DoS approaches to finite density lattice QCD,"We present two new suggestions for density of states (DoS) approaches to
finite density lattice QCD. Both proposals are based on the recently developed
and successfully tested DoS FFA technique, which is a DoS approach for bosonic
systems with a complex action problem. The two different implementations of DoS
FFA we suggest for QCD make use of different representations of finite density
lattice QCD in terms of suitable pseudo-fermion path integrals. The first
proposal is based on a pseudo-fermion representation of the grand canonical QCD
partition sum, while the second is a formulation for the canonical ensemble. We
work out the details of the two proposals and discuss the results of
exploratory 2-d test studies for free fermions at finite density, where exact
reference data allow one to verify the final results and intermediate steps.",1911.05320v2
2016-11-08,Time-dependent potential through an Ansatz for the Kohn-Sham orbitals,"Given the time-evolution of an electron charge density, the local potential
in Kohn-Sham time-dependent density functional theory (KS-TDDFT) can be modeled
as a sum of instantaneous and dynamic contributions by assuming a certain form
of the time-dependent Kohn-Sham (TD-KS) orbitals. The instantaneous part is
obtained numerically using methods from ground-state density functional theory
(DFT) and the dynamic part is expressed in terms of a velocity potential that
depends on the electron current density. The suggested form of the TD-KS
orbitals satisfies several known constraints (orthonormality,
N-representability, J-representability), and the domain of validity is shown to
depend on the evolution of the instantaneous quantities. Through this
decomposition, we can relate time-dependent and ground -state
V-representability. The resulting potentials are shown numerically to
approximate the exact time-dependent Kohn-Sham potentials for a set of 3
non-singlet two-particle systems (a Kohn-mode, a Coulomb explosion, and a
double quantum well) where the exact solutions and reference densities are
known or obtained through configuration interaction (CI) approaches.",1611.02636v1
2018-09-13,Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor,"Charge density waves are a common occurrence in all families of high critical
temperature superconducting cuprates. Although consistently observed in the
underdoped region of the phase diagram and at relatively low temperatures, it
is still unclear to what extent they influence the unusual properties of these
systems. Using resonant x-ray scattering we carefully determined the
temperature dependence of charge density modulations in
(Y,Nd)Ba$_2$Cu$_3$O$_{7-{\delta}}$ for three doping levels. We discovered
short-range dynamical charge density fluctuations besides the previously known
quasi-critical charge density waves. They persist up to well above the
pseudogap temperature T*, are characterized by energies of few meV and pervade
a large area of the phase diagram, so that they can play a key role in shaping
the peculiar normal-state properties of cuprates.",1809.04949v1
2020-05-04,Reduction of SO in $^{34}$Si: weak binding or density-depletion effect ?,"The reduction of the neutron spin-orbit splitting $2p_{3/2} - 2p_{1/2}$
between the $^{41}$Ca and $^{35}$Si isotones is a unique feature throughout the
chart of nuclides, as the spin-orbit splitting usually increases with $A$.
Moreover, its way of decrease, gradual between $^{41}$Ca and $^{35}$Si or
abrupt between $^{37}$S and $^{35}$Si, as well as its origin, caused by the
weak binding energy of the $p$ states or by the sudden central proton density
depletion in $^{35}$Si, are subject of debate. The results reported here using
the self-consistent Covariant Energy Density Functional calculations with the
DD-ME2 parametrization rather point to an abrupt, local decrease in $^{35}$Si,
and to the large dominance of the central density depletion effect. It is
concluded that weak binding, central density depletion as well as correlations
must be taken into account to fully evaluate the amplitude and causes of this
spin-orbit reduction.",2005.03087v2
2020-05-13,Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems,"Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a
time-\textit{independent} extension of density-functional theory (DFT) which
allows to compute excited-state energies via the derivatives of the ensemble
energy with respect to the ensemble weights. Contrary to the time-dependent
version of DFT (TD-DFT), double excitations can be easily computed within
GOK-DFT. However, to take full advantage of this formalism, one must have
access to a \textit{weight-dependent} exchange-correlation functional in order
to model the infamous ensemble derivative contribution to the excitation
energies. In the present article, we discuss the construction of first-rung
(i.e., local) weight-dependent exchange-correlation density-functional
approximations for two-electron atomic and molecular systems (He and H$_2$)
specifically designed for the computation of double excitations within GOK-DFT.
In the spirit of optimally-tuned range-separated hybrid functionals, a two-step
system-dependent procedure is proposed to obtain accurate energies associated
with double excitations.",2005.06159v2
2021-05-17,Incompressibility and Symmetry Energy of Neutron Star,"We trace a systematic and consistent method to precisely numerate the
magnitude range for various structural and isospin compositional properties of
the neutron star. Incompressibility, symmetry energy, slope parameter and
curvature of a neutron star are investigated using the relativistic energy
density functional within the framework of coherent density fluctuation model.
The analytical expression for the energy density functional of the neutron star
matter is motivated from the Br$\ddot{u}$ckner functional and acquired by the
polynomial fitting of the saturation curves for three different relativistic
mean-field parameter sets (NL3, G3 and IU-FSU). The modified functional is
folded with the neutron star's density-dependent weight function to calculate
the numerical values for incompressibility and symmetry energy using the
coherent density fluctuation model. NL3 parameter set, being the stiffest
equation of state, endue us with a higher magnitude of all the properties
compared to the other two parameter sets.",2105.07721v3
2023-03-02,The structure of the density-potential mapping. Part II: Including magnetic fields,"The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly
considered the conceptual basis for a full characterization of an electronic
system in its ground state by just the one-body particle density. In this
Part~II of a series of two articles, we aim at clarifying the status of this
theorem within different extensions of DFT including magnetic fields. We will
in particular discuss current-density-functional theory (CDFT) and review the
different formulations known in the literature, including the conventional
paramagnetic CDFT and some non-standard alternatives. For the former, it is
known that the Hohenberg-Kohn theorem is no longer valid due to
counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework
closest to standard DFT and, just like in standard DFT, non-differentiability
of the density functional can be mitigated through Moreau-Yosida
regularization. Interesting insights can be drawn from both
Maxwell-Schr\""odinger DFT and quantum-electrodynamical DFT, which are also
discussed here.",2303.01357v2
2023-05-26,Hybrid Energy Based Model in the Feature Space for Out-of-Distribution Detection,"Out-of-distribution (OOD) detection is a critical requirement for the
deployment of deep neural networks. This paper introduces the HEAT model, a new
post-hoc OOD detection method estimating the density of in-distribution (ID)
samples using hybrid energy-based models (EBM) in the feature space of a
pre-trained backbone. HEAT complements prior density estimators of the ID
density, e.g. parametric models like the Gaussian Mixture Model (GMM), to
provide an accurate yet robust density estimation. A second contribution is to
leverage the EBM framework to provide a unified density estimation and to
compose several energy terms. Extensive experiments demonstrate the
significance of the two contributions. HEAT sets new state-of-the-art OOD
detection results on the CIFAR-10 / CIFAR-100 benchmark as well as on the
large-scale Imagenet benchmark. The code is available at:
https://github.com/MarcLafon/heatood.",2305.16966v3
2023-07-27,Towards quantitative precision in ultracold atoms with functional renormalisation,"We compute the equation of state, the gap as well as the density fluctuations
of a two-component superfluid Fermi gas over the whole range of BEC-BCS
crossover at vanishing temperature within the functional renormalisation group
approach. With an improved understanding of the relation between density and
chemical potential, already a rather simple truncation yields a very good
quantitative agreement with experimental data and theoretical results, in
particular in the unitarity limit and on the BEC side. The current approach
utilises higher order density fluctuations as a fundamental building block for
the computation of the density as a function of the chemical potential. This
circumvents the fine-tuning problem of the density-related fundamental
parameters on the microscopic level that has been observed in previous
approaches. The quantitative reliability of the functional renormalisation
group approach already within simple approximations opens the path towards
precision results in more elaborate truncations.",2307.14787v1
2002-05-20,Density dependence of the s-wave repulsion in pionic atoms,"Several mechanisms of density dependence of the s-wave repulsion in pionic
atoms, beyond the conventional model, are tested by parameter fits to a large
(106 points) set of data from $^{16}$O to $^{238}$U, including `deeply bound'
states in $^{205}$Pb. Special attention is paid to the proper choice of nuclear
density distributions. A density-dependent isovector scattering amplitude
suggested recently by Weise to result from a density dependence of the pion
decay constant is introduced and found to account for most of the so-called
anomalous repulsion. The presence of such an effect might indicate partial
chiral symmetry restoration in dense matter. The anomalous repulsion is fully
accounted for when an additional relativistic impulse approximation term is
included in the potential.",0205054v2
2002-10-16,Isospin dependence of the critical quark-deconfinement densities,"We explore the dependence of the critical density, separating hadronic matter
from a mixed phase of quarks and hadrons, on the ratio $Z/A$. We use both the
MIT bag model and the Color Dielectric Model to describe the quark dynamics,
while for the hadronic phase we employ various relativistic equations of state.
We find that, if the parameters of quark models are fixed so that the existence
of quark stars is allowed, then the critical density drops dramatically in the
range $Z/A \sim $ 0.3--0.4. Moreover, for $Z/A \sim $ 0.3 the critical density
is only slightly larger than the saturation density of symmetric
nuclear-matter. This opens the possibility to verify the Witten-Bodmer
hypothesis on absolute stability of quark matter using ground-based experiments
in which neutron-rich nuclei are tested.",0210052v1
2011-03-03,Collapse and fragmentation of Gaussian barotropic protostellar clouds,"We examine the problem of the collapse and fragmentation of molecular clouds
with a Gaussian density distribution with high resolution, double precision
numerical simulations using the GADGET-2 code. To describe the thermodynamic
properties of the cloud during the collapse -to mimic the rise of temperature
predicted by radiative transfer- we use a barotropic equation of state that
introduces a critical density to separate the isothermal and adiabatic regimes.
We discuss the effects of this critical density in the formation of multiple
systems. We confirm the tendency found for Plummer and Gaussian models that if
the collapse changes from isothermal to adiabatic at earlier times that occurs
for the models with a lower critical density, the collapse is slowed down, and
this enhances the fragments' change to survive. However, this effect happens up
to a threshold density below which single systems tend to form. On the other
hand, by setting a bigger initial perturbation amplitude, the collapse is
faster and in some cases a final single object is formed.",1103.0752v1
2011-03-15,Gravitational Fragmentation of Expanding Shells. I. Linear Analysis,"We perform a linear perturbation analysis of expanding shells driven by
expansions of HII regions. The ambient gas is assumed to be uniform. As an
unperturbed state, we develop a semi-analytic method for deriving the time
evolution of the density profile across the thickness. It is found that the
time evolution of the density profile can be divided into three evolutionary
phases, deceleration-dominated, intermediate, and self-gravity-dominated
phases. The density peak moves relatively from the shock front to the contact
discontinuity as the shell expands. We perform a linear analysis taking into
account the asymmetric density profile obtained by the semi-analytic method,
and imposing the boundary conditions for the shock front and the contact
discontinuity while the evolutionary effect of the shell is neglected. It is
found that the growth rate is enhanced compared with the previous studies based
on the thin-shell approximation. This is due to the boundary effect of the
contact discontinuity and asymmetric density profile that were not taken into
account in previous works.",1103.2909v3
2013-11-08,An Introduction to Microscopic Theories for Inhomogeneous Liquids: Getting Started with Density Functional Theory,"Classical density functional theory (DFT) is a statistical mechanical theory
for calculating the density profiles of the molecules in a liquid. It is widely
used, for example. to calculate the density distribution of the molecules in
the vicinity of a confining wall, the interfacial tension, the wetting
behaviour and many other properties of nonuniform liquids. DFT can however be
somewhat daunting to students entering the field, because of the many
connections to other areas of liquid-state science that are required and used
to develop the theories. Here we give an introduction to some of the key ideas,
based on a lattice-gas (Ising) model fluid. This builds on knowledge covered in
most undergraduate statistical mechanics and thermodynamics courses and so
students can quickly get to the stage of calculating density profiles, etc for
themselves. We derive a simple DFT for the lattice-gas and present some typical
results that can readily be calculated using the theory.",1311.1964v1
2015-06-10,Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of 2D Density-Dependent Navier-Stokes Equations with Vacuum,"We are concerned with the Cauchy problem of the two-dimensional (2D)
nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field
density. It is proved that if the initial density decays not too slow at
infinity, the 2D Cauchy problem of the density-dependent Navier-Stokes
equations on the whole space $\mathbb{R}^2$ admits a unique global strong
solution. Note that the initial data can be arbitrarily large and the initial
density can contain vacuum states and even have compact support. Furthermore,
we also obtain the large time decay rates of the spatial gradients of the
velocity and the pressure which are the same as those of the homogeneous case.",1506.03143v1
2021-03-03,Review of approximations for the exchange-correlation energy in density-functional theory,"In this chapter, we provide a review of ground-state Kohn-Sham
density-functional theory of electronic systems and some of its extensions, we
present exact expressions and constraints for the exchange and correlation
density functionals, and we discuss the main families of approximations for the
exchange-correlation energy: semilocal approximations, single-determinant
hybrid approximations, multideterminant hybrid approximations,
dispersion-corrected approximations, as well as orbital-dependent
exchange-correlation density functionals. The chapter aims at providing both a
consistent bird's-eye view of the field and a detailed description of some of
the most used approximations. It is intended to be readable by
chemists/physicists and applied mathematicians.",2103.02645v2
2021-03-25,Negative energy enhancement in layered holographic conformal field theories,"Using a holographic model, we study quantum field theories with a layer of
one CFT surrounded by another CFT, on either a periodic or an infinite
direction. We study the vacuum energy density in each CFT as a function of the
central charges, the thickness of the layer(s), and the properties of the
interfaces between the CFTs. The dual spacetimes in the holographic model
include two regions separated by a dynamical interface with some tension. For
two or more spatial dimensions, we find that a layer of CFT with more degrees
of freedom than the surrounding one can have an anomalously large negative
vacuum energy density for certain types of interfaces. The negative energy
density (or null-energy density in the direction perpendicular to the
interface) becomes arbitrarily large for fixed layer width when the tension of
the bulk interface approaches a lower critical value. We argue that in cases
where we have large negative energy density, we also have an anomalously high
transition temperature to the high-temperature thermal state.",2103.14046v2
2005-04-11,A transition in the spectrum of the topological sector of $φ_2^4$ theory at strong coupling,"We investigate the strong coupling region of the topological sector of the
two-dimensional $\phi^4$ theory. Using discrete light cone quantization (DLCQ),
we extract the masses of the lowest few excitations and observe level
crossings. To understand this phenomena, we evaluate the expectation value of
the integral of the normal ordered $\phi^2$ operator and we extract the number
density of constituents in these states. A coherent state variational
calculation confirms that the number density for low-lying states above the
transition coupling is dominantly that of a kink-antikink-kink state. The
Fourier transform of the form factor of the lowest excitation is extracted
which reveals a structure close to a kink-antikink-kink profile. Thus, we
demonstrate that the structure of the lowest excitations becomes that of a
kink-antikink-kink configuration at moderately strong coupling. We extract the
critical coupling for the transition of the lowest state from that of a kink to
a kink-antikink-kink. We interpret the transition as evidence for the onset of
kink condensation which is believed to be the physical mechanism for the
symmetry restoring phase transition in two-dimensional $\phi^4$ theory.",0504094v1
2017-02-07,Critical exponents and amplitudes of analytical equation of state,"The paper analyzes a general case of an equation of state, which is an
analytical function at the critical point of the liquid-vapor first order phase
transition of pure substance. It is shown that the equality to zero of the
first- and second-order partial derivatives of pressure with respect to volume
(density) at the critical point is the consequence of the thermodynamic
conditions of phase equilibrium. We obtained the relations of critical
exponents and amplitudes with parameters of the analytical equation of state.
It is shown that the substance with the analytical equation of state can have
critical exponents of lattice gas which is equivalent to the two dimensional
Ising model. It is shown that the analytical equation of state can take into
account the density fluctuations.",1702.02226v1
1995-05-11,THE ANOMALOUS DIFFUSION IN HIGH MAGNETIC FIELD AND THE QUASIPARTICLE DENSITY OF STATES,"We consider a disordered two-dimensional electronic system in the limit of
high magnetic field at the metal-insulator transition. Density of states close
to the Fermi level acquires a divergent correction to the lowest order in
electron-electron interaction and shows a new power-law dependence on the
energy, with the power given by the anomalous diffusion exponent $\eta$. This
should be observable in the tunneling experiment with double-well GaAs
heterostructure of the mobility $\propto 10^{4}V/s$ at temperatures of $\propto
10 mK$ and voltages of $\propto 1 \mu V$.",9505047v1
1995-06-06,Quantitative Description of $V_2O_3$ by the Hubbard Model in Infinite Dimensions,"We show that the analytic single-particle density of states and the optical
conductivity for the half-filled Hubbard model on the Bethe lattice in infinite
dimensions describe quantitatively the behavior of the gap and the kinetic
energy ratio of the correlated insulator $V_2O_3$. The form of the optical
conductivity shows $\omega^{3/2}$ rising and is quite similar to the
experimental data, and the density of states shows $\omega^{1/2}$ behavior near
the band edges.",9506022v1
1996-06-12,Temperature and Pressure Effects on the Resistivity of the Manganese Oxides,"The temperature and pressure effects on the resistivity of the manganese
oxides are studied analytically via the Kondo lattice model with a strong
Hund's coupling. We obtain analytically the single-particle density of states
on the Bethe lattice in the large connectivity limit using the analytical
variant of the dynamic Lanczos method. From the density of states for the doped
system, we obtain resistivity and show resistivity drop when temperature
crosses the magnetic transition point. We also demonstrate the effect of
pressure both below and above the transition temperature.",9606079v1
1997-02-12,Mean Green's function of the Anderson model at weak disorder with an infra-red cut-off,"We develop a polymer expansion with large/small field conditions for the mean
resolvent of a weakly disordered system. Then we show that we can apply our
result to a two-dimensional model, for energies outside the unperturbed
spectrum or in the free spectrum provided the potential has an infra-red
cut-off. This leads to an asymptotic expansion for the density of states. We
believe this is an important first step towards a rigourous analysis of the
density of states in the free spectrum of a random Schr\""odinger operator at
weak disorder.",9702111v1
1998-01-12,Bloch electrons in a Jahn-Teller crystal and an orbital-density-wave state due to the Berry phase,"The effect of the Berry phase is included explicitly in the wavefunction
describing conduction electrons in a crystal composed of periodically arrayed
Jahn-Teller centers that have conically intersecting potential energy surfaces.
The Berry phase can make a drastic change in the band structure, leading
generally to the formation of an orbital-density-wave state. We discuss
implications of our theory and possible relations to the orbital ordering
observed in the manganese perovskites.",9801093v1
1998-11-24,Local Density of States in Superconductor-Ferromagnetic Hybrid Systems,"In this Letter we discuss various properties of the local density of states
(DOS) for a superconductor-ferromagnet hybrid system. The DOS is modified at
small energies on both sides of the interface. Due to the interplay of
superconductivity and ferromagnetism, the local DOS depends on the spin
direction. The spin polarization effects extend over a long distance from the
interface both in the superconductor and in the ferromagnet. If the ferromagnet
is of finite lenght, the DOS shows a (spin dependent) gap.",9811334v1
1999-05-21,Theory of Unconventional Spin Density Wave: A Possible Mechanism of the Micromagnetism in U-based Heavy Fermion Compounds,"We propose a novel spin density wave (SDW) state as a possible mechanism of
the anomalous antiferromagnetism, so-called the micromagnetism, in URu_2Si_2
below 17.5[K]. In this new SDW, the electron-hole pair amplitude changes its
sign in the momentum space as in the case of the unconventional
superconductivity. It is shown that this state can be realized in an extended
Hubbard model within the mean field theory. We also examine some characteristic
properties of this SDW to compare with the experimental results. All these
properties well explain the unsolved problem of the micromagnetism.",9905316v1
2000-01-30,Strong compensation of the quantum fluctuation corrections in clean superconductor,"The theory of fluctuation conductivity for an arbitrary impurity
concentration including ultra-clean limit is developed. It is demonstrated that
the formal divergency of the fluctuation density of states contribution
obtained previously for the clean case is removed by the correct treatment of
the non-local ballistic electron scattering. We show that in the ultra-clean
limit ($T\tau \gg \sqrt{\frac{T_c}{T-T_c}}$) the density-of-states quantum
corrections are canceled by the Maki-Thompson term and only quasi-classical
paraconductivity remains.",0001433v1
2000-07-27,"Pairing, Stripes, Lattice Distortions and Superconductivity in Cuprate Oxides","We propose a model for a spatially modulated collective state of
superconducting cuprates in which the electronic properties vary locally in
space. In this model the regions of higher hole density (called stripes) are
described as Luttinger liquids and the regions of lower density
(antiferromagnetic ladders) as an interacting bosonic gas of d$_{x^2-y^2}$ hole
pairs. We show that the transition to the superconducting state is topological
and driven by decay processes among these elementary excitations in the
presence of vibrations.",0007434v1
2000-08-01,Plasticity and memory effects in the vortex solid phase of twinned YBa2Cu3O7 single crystals,"We report on marked memory effects in the vortex system of twinned YBa2Cu3O7
single crystals observed in ac susceptibility measurements. We show that the
vortex system can be trapped in different metastable states with variable
degree of order arising in response to different system histories. The pressure
exerted by the oscillating ac field assists the vortex system in ordering,
locally reducing the critical current density in the penetrated outer zone of
the sample. The robustness of the ordered and disordered states together with
the spatial profile of the critical current density lead to the observed memory
effects.",0008001v1
2000-09-13,Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder,"We review recent work on the random hopping problem in a
quasi-one-dimensional geometry of N coupled chains (quantum wire with
off-diagonal disorder). Both density of states and conductance show a
remarkable dependence on the parity of N. The theory is compared to numerical
simulations.",0009198v1
2001-07-19,Fluctuations Indicate Strong Interlayer Coupling in Cuprate Superconductors,"From study of the Kosterlitz-Thouless-Berezinskii (KTB) transition in the
superfluid density, n_s(T), of ultrathin c-axis oriented
YBa_{2}Cu_{3}O_{7-\delta} (YBCO) films, we find that interlayer coupling is
unexpectedly strong. The KTB transition occurs at a high temperature, as if the
films were isotropic rather than quasi-two-dimensional. This result agrees with
a comparison of the superfluid density of YBCO with Bi_{2}Sr_{2}CaCu_{2}O_{8}
and with numerical simulations of Josephson junction arrays, and challenges the
thermal phase fluctuation interpretation of critical behavior near T_c in YBCO.",0107406v1
2001-10-09,Evidence for three dimensional superconductivity in the cuprates oxides,"We review the empirical scenario emerging from the measured doping dependence
of the transition temperature and the anisotropy parameter $% \gamma $ $=\xi
_{ab}/\xi_{c}$, defined as the ratio of the correlation lengths parallel and
perpendicular to the ab-planes. It suggests that two dimensional models cannot
explain the occurrence of superconductivity in the cuprates. This conclusion is
confirmed and extended in terms of a novel scaling relation. It involves the
transition temperature, the aerial superfluid density in the ground state,
$\gamma $ and the dynamic critical exponent of the quantum superconductor to
insulator transition. The important implication there is that a non vanishing
superfluid density in the ground state of the cuprates is unalterably linked to
an anisotropic but 3D condensation mechanism.",0110173v1
2002-01-31,Exact Density of States for finite Gaussian Random Matrix Ensembles via Supersymmetry,"We calculate the exact density of states (DOS) for the three classical and
two non-classical Random Matrix Ensembles for finite matrix size N using
supersymmetric integrals. The 1/N-Expansion yields already in lowest order good
approximations to the exact result even for small values of N~5. We conjecture
a connection between the N-dependence of the oscillating part of the DOS and
the short-distance behavior of the two-level correlation function.",0201585v1
2002-03-27,Uniform spin susceptibility tensor and quasiparticle density of states in organic quasi-one-dimensional superconductors,"We perform calculations relating the order parameter symmetry of organic
quasi-one-dimensional superconductors to the bulk quasiparticle density of
states and the bulk uniform spin susceptibility tensor at finite temperatures.
Current experimental results suggest that some organic quasi-one-dimensional
superconductors may exhibit triplet pairing symmetry. The purpose of our
analysis is to attempt to narrow down the number of possibilities for the
symmetry of the order parameter based on the experimental evidence.",0203570v1
2002-09-15,Schroedinger equation for current carrying states,"Schr\""odinger equation with given, {\it a priori} known current is
formulated. A non-zero current density is maintained in the quantum system via
a subsidiary condition imposed by vector, local Lagrange multiplier.
Constrained minimization of the total energy on the manifold of an arbitrary
current density topology results into a non-linear self-consistent
Schr\""odinger equation. The applications to electronic transport in
two-terminal molecular devices are developed and new macroscopic definition of
a molecular current-voltage characteristic is proposed. The Landauer formula
for the conductance of an ideal one-dimensional lead is obtained within the
approach. The method is examined by modeling of current carrying states of
one-dimensional harmonic oscillator.",0209347v1
2003-02-07,Density of states in a superconductor carrying a supercurrent,"We have measured the tunneling density of states (DOS) in a superconductor
carrying a supercurrent or exposed to an external magnetic field. The pair
correlations are weakened by the supercurrent, leading to a modification of the
DOS and to a reduction of the gap. As predicted by the theory of
superconductivity in diffusive metals, we find that this effect is similar to
that of an external magnetic field.",0302153v1
2003-06-09,Stripes and superconductivity in one-dimensional self-consistent model,"We show that many observable properties of high temperature superconductors
can be obtained in the frameworks of one-dimensional self-consistent model with
included superconducting correlations. Analytical solutions for spin, charge
and superconductivity order parameters are found.
  The ground state of the model at low hole doping is a spin-charge solitonic
superstructure. Increasing of doping leads to the phase transition to
superconducting phase. There is a region of doping where superconductivity,
spin density wave and charged stripe structure coexist.
  The charge density modulation presents in the vicinity of vortices (kinks in
the 1D model) in the superconducting state.",0306211v2
2003-07-23,Density of states and magnetoconductance of disordered Au point contacts,"We report the first low temperature magnetotransport measurements on
electrochemically fabricated atomic scale gold nanojunctions. As $T \to 0$, the
junctions exhibit nonperturbatively large zero bias anomalies (ZBAs) in their
differential conductance. We consider several explanations and find that the
ZBAs are consistent with a reduced local density of states (LDOS) in the
disordered metal. We suggest that this is a result of Coulomb interactions in a
granular metal with moderate intergrain coupling. Magnetoconductance of atomic
scale junctions also differs significantly from that of less geometrically
constrained devices, and supports this explanation.",0307576v1
2004-09-09,Wide energy-window view on the density of states and hole mobility of poly(p-phenylene vinylene),"Using an electrochemically gated transistor, we achieved controlled and
reversible doping of poly(p-phenylene vinylene) in a large concentration range.
Our data open a wide energy-window view on the density of states (DOS) and
show, for the first time, that the core of the DOS function is Gaussian, while
the low-energy tail has a more complex structure. The hole mobility increases
by more than four orders of magnitude when the electrochemical potential is
scanned through the DOS.",0409218v1
2004-12-20,Geometrical structure effect on localization length of carbon nanotubes,"The localization length and density of states of carbon nanotubes are
evaluated within the tight-binding approximation. By comparison with the
corresponding results for the square lattice tubes, it is found that the
hexagonal structure affects strongly the behaviors of the density of states and
localization lengths of carbon nanotubes.",0412525v2
2005-01-26,Vibrations and diverging length scales near the unjamming transition,"We numerically study the vibrations of jammed packings of particles
interacting with finite-range, repulsive potentials at zero temperature. As the
packing fraction $\phi$ is lowered towards the onset of unjamming at
$\phi_{c}$, the density of vibrational states approaches a non-zero value in
the limit of zero frequency. For $\phi>\phi_{c}$, there is a crossover
frequency, $\omega^{*}$ below which the density of states drops towards zero.
This crossover frequency obeys power-law scaling with $\phi-\phi_{c}$.
Characteristic length scales, determined from the dominant wavevector
contributing to the eigenmode at $\omega^{*}$, diverge as power-laws at the
unjamming transition.",0501616v1
2005-11-23,Photon density of states for deformed surfaces,"A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries
and a rather general class of boundary conditions is introduced. We derive the
boundary induced change of the density of states in terms of the free Green's
function from which we obtain both perturbative and non-perturbative results
for the Casimir interaction between deformed surfaces. As an example, we
compute the lateral electrodynamic Casimir force between two corrugated
surfaces over a wide parameter range. Universal behavior, fixed only by the
largest wavelength component of the surface shape, is identified at large
surface separations. This complements known short distance expansions which are
also reproduced.",0511588v1
2006-07-05,Semiclassical theory in Andreev billiards: beyond the diagonal approximation,"Recently semiclassical approximations have been successfully applied to study
the effect of a superconducting lead on the density of states and conductance
in ballistic billiards. However, the summation over classical trajectories
involved in such theories was carried out using the intuitive picture of
Andreev reflection rather than the semiclassical reasoning. We propose a method
to calculate the semiclassical sums which allows us to go beyond the diagonal
approximation in these problems. In particular, we address the question of
whether the off-diagonal corrections could explain the gap in the density of
states of a chaotic Andreev billiard.",0607128v1
2006-09-22,The geometrically-averaged density of states as a measure of localization,"Motivated by current interest in disordered systems of interacting electrons,
the effectiveness of the geometrically averaged density of states,
$\rho_g(\omega)$, as an order parameter for the Anderson transition is
examined. In the context of finite-size systems we examine complications which
arise from finite energy resolution. Furthermore we demonstrate that even in
infinite systems a decline in $\rho_g(\omega)$ with increasing disorder
strength is not uniquely associated with localization.",0609590v2
2007-02-01,Zero-bias anomaly in the tunneling density of states of graphene,"In the vicinity of the Fermi energy, the band structure of graphene is well
described by a Dirac equation. Impurities will generally induce both a scalar
potential as well as a (fictitious) gauge field acting on the Dirac fermions.
We show that the angular dependence of the zero-bias anomaly in the spatially
resolved tunneling density of states (TDOS) around a particular impurity allows
one to distinguish between these two contributions. Our predictions can be
tested in scanning-tunneling-microscopy measurements on graphene.",0702019v1
2007-02-09,Tunneling into a Fractional Quantum Hall System and the Infrared Catastrophe,"We calculate the tunneling density of states of a two-dimensional interacting
electron gas in a quantizing magnetic field. We show that the observed
pseudogap in the density of states can be understood as the result of an
infrared catastrophe in a noninteracting electron model. This catastrophe stems
from the response of an electronic system to the potential produced by the
abruptly added charge during a tunneling event. Our formalism can be applied at
any filling factor without the use of Chern-Simons or composite fermion theory.",0702238v1
2006-08-21,Lattice QCD Calculation for the Physical Equation of State,"In this report we consider the numerical simulations at finite temperature
using lattice QCD data for the computation of the thermodynamical quantities
including the pressure, energy density and the entropy density. These physical
quantities can be related to the equation of state for quarks and gluons. We
shall apply the lattice data to the evaluation of the specific structure of the
gluon and quark condensates at finite temperature in relation to the
deconfinement and chiral phase transitions. Finally we mention the quantum
nature of the phases at lower temperatures.",0608234v1
1994-05-13,Are p-Branes Asymptotically Black Holes?,"An attempt is made to compare the asymptotic state density of twisted
$p$-branes and the related state density of mass level $M$ of a $D$-dimensional
neutral black hole. To this aim, the explicit form of the twisted $p$-brane
total level degeneracy is calculated. The prefactor of the degeneracy, in
contrast to the leading behaviour, is found to depend on the winding number of
the $p$-brane.",9405090v1
2002-12-19,Integrated density of states for random metrics on manifolds,"We study ergodic random Schr""odinger operators on a covering manifold, where
the randomness enters both via the potential and the metric. We prove
measurability of the random operators, almost sure constancy of their spectral
properties, the existence of a selfaveraging integrated density of states and a
\v{S}ubin type trace formula.",0212058v1
2004-08-06,On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials,"The present paper is devoted to the study of spectral properties of random
Schroedinger operators. Using a finite section method for Toeplitz matrices, we
prove a Wegner estimate for some alloy type models where the single site
potential is allowed to change sign. The results apply to the corresponding
discrete model, too. In certain disorder regimes we are able to prove the
Lipschitz continuity of the integrated density of states and/or localization
near spectral edges.",0408013v3
1998-11-27,Equation of state for finite nuclei and liquid-gas phase transition,"We construct the equation of state (EOS) of finite nuclei including surface
and Coulomb effects in a Thomas-Fermi framework using a finite range, momentum
and density dependent two-body interaction. We identify critical temperatures
for nuclei below which the EOS so constructed shows clear signals for
liquid-gas phase transition in these finite systems. Comparison with the EOS of
infinite nuclear matter shows that the critical density and temperature of the
phase transition in nuclei are influenced by the mentioned finite size effects.",9811097v1
2003-01-21,The Equation of State for Cold and Dense Strongly Interacting Matter,"We discuss recent results for the equation of state for cold and dense
strongly interacting matter. We consider the extreme cases of very high
densities, where weak-coupling approaches may in principle give reasonable
results, and very low densities, where we use the framework of heavy-baryon
chiral perturbation theory. We also speculate on the nature of the chiral
transition and present possible astrophysical implications.",0301062v2
1995-06-06,All local quantum states are mixtures of direct products,"According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797
(1994)], {\it nonideal} measurements, rather than ideal ones, may be more
sensitive to reveal nonlocal correlations between distant parts of composite
quantum systems. The outcome statistics of joint nonideal measurements on local
states should by definition admit local hidden variable models. We prove that
the density operator of a local composite system must be convex mixture of the
subsystems' density operators. This result depends essentially on a plausible
consistency condition restricting the class of admissible local hidden variable
models.",9506004v1
1997-03-16,Least-squares inversion for density-matrix reconstruction,"We propose a method for reconstruction of the density matrix from measurable
time-dependent (probability) distributions of physical quantities. The
applicability of the method based on least-squares inversion is - compared with
other methods - very universal. It can be used to reconstruct quantum states of
various systems, such as harmonic and and anharmonic oscillators including
molecular vibrations in vibronic transitions and damped motion. It also enables
one to take into account various specific features of experiments, such as
limited sets of data and data smearing owing to limited resolution. To
illustrate the method, we consider a Morse oscillator and give a comparison
with other state-reconstruction methods suggested recently.",9703026v1
1999-12-28,Complete Separability and Fourier representations of n-qubit states,"Necessary conditions for separability are most easily expressed in the
computational basis, while sufficient conditions are most conveniently
expressed in the spin basis. We use the Hadamard matrix to define the
relationship between these two bases and to emphasize its interpretation as a
Fourier transform. We then prove a general sufficient condition for complete
separability in terms of the spin coefficients and give necessary and
sufficient conditions for the complete separability of a class of generalized
Werner densities. As a further application of the theory, we give necessary and
sufficient conditions for full separability for a particular set of $n$-qubit
states whose densities all satisfy the Peres condition.",9912116v1
2000-05-16,The Entanglement of Formation for Isotropic States,"We give an explicit expression for the entanglement of formation for
isotropic density matrices in arbitrary dimensions in terms of the convex hull
of a simple function. For two qutrit isotropic states we determine the convex
hull and we have strong evidence for its exact form for arbitrary dimension.
Unlike for two qubits, the entanglement of formation for two qutrits or more is
found to be a nonanalytic function of the maximally entangled fraction in the
regime where the density matrix is entangled.",0005062v1
2007-01-13,Average Fidelity in n-Qubit systems,"This letter generalizes the expression for the average fidelity of single
qubits, as found by Bowdrey et al., to the case of n qubits. We use a simple
algebraic approach with basis elements for the density-matrix expansion
expressed as Kronecker products of n Pauli spin matrices. An explicit
integration over initial states is avoided by invoking the invariance of the
state average under unitary transformations of the initial density matrix. The
results have applications to measurements of quantum information, for example
in ion-trap and NMR experiments.",0701084v2
1996-09-18,Density of States and NMR Relaxation Rate in Anisotropic Superconductivity with Intersecting Line Nodes,"We show that the density of states in an anisotropic superconductor with
intersecting line nodes in the gap function is proportional to $E log (\alpha
\Delta_0 /E)$ for $|E| << \Delta_0$, where $\Delta_0$ is the maximum value of
the gap function and $\alpha$ is constant, while it is proportional to $E$ if
the line nodes do not intersect. As a result, a logarithmic correction appears
in the temperature dependence of the NMR relaxation rate and the specific heat,
which can be observed experimentally. By comparing with those for the heavy
fermion superconductors, we can obtain information about the symmetry of the
gap function.",9609003v1
2007-08-16,A generation-based particle-hole density-matrix renormalization group study of interacting quantum dots,"The particle-hole version of the density-matrix renormalization-group method
(PH-DMRG) is utilized to calculate the ground-state energy of an interacting
two-dimensional quantum dot. We show that a modification of the method, termed
generation-based PH-DMRG, leads to significant improvement of the results, and
discuss its feasibility for the treatment of large systems. As another
application we calculate the addition spectrum.",0708.2237v1
2007-09-05,The geometrically-averaged density of states calculated from the local Green's function as a measure of localization,"With the goal of measuring localization in disordered interacting systems, we
examine the finite-size scaling of the geometrically-averaged density of states
calculated from the local Green's function with finite energy resolution. Our
results show that, unlike in a simple energy binning procedure, there is no
limit in which the finite energy resolution is irrelevant.",0709.0713v1
2007-11-11,Controllable density of states in molecular devices: the magnetic effect on cyclic molecules,"Through the analysis of density of states (DOS), we study two different kinds
of cyclic molecules, a sodium atomic circle and a Polycyclic Aromatic
Hydrocarbons (PAH) molecule respectively under an external magnetic field. The
results of calculation show that original DOS peaks split into two and the
positions of peaks can be modulated periodically by controlling the magnetic
field. We attribute this phenomenon to the interaction between the molecular
orbital magnetic momentum and the magnetic field. Generally, this effect is
obscure for a usual structure but obvious for the cyclic molecules.",0711.1647v1
2007-11-29,On the question of ferromagnetism in alkali metal thin films,"Electronic and magnetic structure of $(100)$ films of K and Cs are calculated
within the plane-wave projector augmented wave (PAW) formalism of the density
functional theory (DFT) using both local spin density approximation (LSDA) and
the PW91 generalized gradient approximation (GGA). Only a 6 layer Cs film is
found to have a ferromagnetic (FM) state which is degenerate with a
paramagnetic (PM) state within the accuracy of these calculations. This is at
variance with the results obtained from a finite thickness uniform jellium
model (UJM). Implications of these results for the experiments on transition
metal doped alkali metal thin films and bulk hosts are discussed.",0711.4744v1
2007-12-06,Rigorous description of exchange-correlation energy of many-electron systems,"With the eigenfunctional theory, we study a general interacting electron
system, and give a rigorous expression of its ground state energy which is
composed of two parts, one part is contributed by the non-interacting
electrons, and another one is represented by the correlation functions that are
controlled by the electron correlation. Moreover, according to the rigorous
expression of the ground state energy, an effective method beyond the local
density approximation of the density functional theory is proposed.",0712.0865v1
2008-03-24,Electronic structure of negatively curved graphene,"We study the electronic structure of graphene in the presence of either
sevenfolds or eightfolds by using a gauge field-theory model. The graphene
sheet with topological defects is considered as a negative cone surface with
infinite Gaussian curvature at the center. The density of electronic states is
calculated for a single seven- and eightfold as well as for a pair of
sevenfolds with different morphology. The density of states at the Fermi energy
is found to be zero in all cases except two sevenfolds with translational
factor $M\neq 0$.",0803.3387v1
2008-05-26,Quasiparticle properties of graphene in the presence of disorder,"We calculate the quasiparticle properties of chiral two-dimensional Dirac
electrons in graphene within the Landau Fermi Liquid scheme based on $GW$
approximation in the presence of disorder. Disorder effects due to charged
impurity scattering plays a crucial role in density dependence of quasiparticle
quantities. Mode-coupling approach to scattering rate and self-energy in $GW$
approximation for quasiparticle renormalized Fermi velocity and
spin-antisymmetric Landau Fermi parameter incorporating the many-body
interactions and the disorder effects show reduction of these quantities by
5-15 percent at available experimental charge carrier density region.",0805.3890v1
2008-09-17,Phonon Density of States in Nd(O$_{1-x}$F$_{x}$)FeAs,"We report measurements of the phonon density-of-states in iron oxypnictide
superconductors by inelastic x-ray scattering. A good agreement with ab-initio
calculations that do not take into account strong electronic correlations is
found, and an unpredicted softening of phonon branches under F doping of these
compounds is observed. Raman scattering experiments lead us to conclude that
this softening is not related to zone center phonons, and consequently imply an
important softening of the relevant phonon branches at finite momentum transfer
Q.",0809.2898v1
2009-02-18,"Structural, Magnetic, and Electronic Properties of the Monometallofullerene Gd@C_82 : Theory","The structural, electronic, and magnetic properties of Gd@C_82 endohedral
metallofullerene have been studied by employing on-site correlation corrected,
scalar-relativistic and full-relativistic density functional theory within the
local density and generalized gradient approximations. The experimentally
observed reduction of the magnetic moment of Gd@C_82 with respect to that of a
free Gd^+3 ion can be explained by a tiny hybridization between unoccupied
Gd-4f states and carbon-pi states, resulting in a generic antiferromagnetic
coupling of the Gd-4f spin with the remaining unpaired spin in the hybridized
molecular orbital.",0902.3218v1
2009-06-29,General condition of the Mott transition expressed with the density of state,"We have investigated a contribution of the density of state (DOS) to the Mott
metal-insulator transition (MIT). The MIT condition is given by the DOS, which
usually requires the complicated fundamental equations. To simplify the
process, we have derived a general solution of the MIT condition by an integral
contains the DOS in the framework of coherent potential approximation. The
formula is concise and presents the direct relationship between the MIT
condition and the DOS. It is able to calculate the contribution quantitatively
and to compare various DOSs analytically.",0906.5244v1
2010-01-17,Phase Structure and Transport Properties of Dense Quark Matter,"We provide a summary of our current knowledge of the phase structure of very
dense quark matter. We concentrate on the question how the ground state at
asymptotically high density -- color-flavor-locked (CFL) matter -- is modified
as the density is lowered. We discuss the nature of the quasi-particle
excitations, and present work on the transport properties of dense QCD matter.",1001.2917v1
2010-02-24,The maximum and minimum mass of protoneutron stars in the Brueckner theory,"We study the structure of protoneutron stars within the finite-temperature
Brueckner-Bethe-Goldstone theoretical approach, paying particular attention to
how it is joined to a low-density nuclear equation of state (EOS). We find a
slight sensitivity of the minimum value of the protoneutron star mass on the
low-density equation of state, whereas the maximum mass is hardly affected.",1002.4497v2
2010-06-17,Phase coexistence in congested states of pedestrian dynamics,"Experimental results for congested pedestrian traffic are presented. For data
analysis we apply a method providing measurements on an individual scale. The
resulting velocity-density relation shows a coexistence of moving and stopping
states revealing the complex structure of pedestrian fundamental diagrams and
supporting new insights into the characteristics of pedestrian congestions.
Furthermore we introduce a model similar to event driven approaches. The
velocity-density relation as well as the phase separation is reproduced.
Variation of the parameter distribution indicates that the diversity of
pedestrians is crucial for phase separation.",1006.3546v1
2010-08-04,Density-functional studies of spin-orbit splitting in graphene on metals,"Spin-orbit splitting in graphene on Ni, Au, or Ag (111) substrates was
examined on the basis of density-functional theory. Graphene grown on the three
metals was found to have Rashba splitting of a few or several tens of meV. The
strong splitting obtained on Au or Ag substrates was mainly ascribed to
effective hybridization of graphene $p_{z}$ state with Au or Ag $d_{z^{2}}$
states, rather than charge transfer as previously proposed. Our work provides
theoretical understandings of the metal-induced Rashba effect in graphene.",1008.0696v1
2011-03-16,Second-order calculation of the local density of states above a nanostructured surface,"We have numerically implemented a perturbation series for the scattered
electromagnetic fields above rough surfaces, due to Greffet, allowing us to
evaluate the local density of states to second order in the surface profile
function. We present typical results for thermal near fields of surfaces with
regular nanostructures, investigating the relative magnitude of the
contributions appearing in successive orders. The method is then employed for
estimating the resolution limit of an idealized Near-Field Scanning Thermal
Microscope (NSThM).",1103.3221v1
2011-08-31,Underlining some limitations of the statistical formalism in quantum mechanics,"We show that two chosen ensembles of spin states, which are differently
prepared but are described by the same density matrix in quantum mechanics, do
not fully share the same measurable characteristics. One characteristic on
which they differ is shown to be the variance of the spin along a given
direction. We conclude that the statistical description of an ensemble of
states as given by its density matrix, although sufficient in many cases,
should be considered incomplete, as it does not fully describe the measurable
characteristics of the ensemble. A discussion a posteriori on the problem is
provided.",1108.6249v1
2011-10-31,On Grover's Search Algorithm from a Quantum Information Geometry Viewpoint,"We present an information geometric characterization of Grover's quantum
search algorithm. First, we quantify the notion of quantum distinguishability
between parametric density operators by means of the Wigner-Yanase quantum
information metric. We then show that the quantum searching problem can be
recast in an information geometric framework where Grover's dynamics is
characterized by a geodesic on the manifold of the parametric density operators
of pure quantum states constructed from the continuous approximation of the
parametric quantum output state in Grover's algorithm. We also discuss possible
deviations from Grover's algorithm within this quantum information geometric
setting.",1110.6713v1
2012-02-15,Radiative and non-radiative local density of states on disordered plasmonic films,"We present numerical calculations of the Local Density of Optical States
(LDOS) in the near field of disordered plasmonic films. The calculations are
based on an integral volume method, that takes into account polarization and
retardation effects, and allows us to discriminate radiative and non-radiative
contributions to the LDOS. At short distance, the LDOS is dominated by
non-radiative channels, showing that changes in the spontaneous dynamics of
dipole emitters are driven by non-radiative coupling to plasmon modes. Maps of
radiative and non-radiative LDOS exhibit strong fluctuations, but with
substantially different spatial distributions.",1202.3360v2
2012-09-07,Density of states and extent of wave function: two crucial factors for small polaron hopping conductivity in 1D,"We introduce a theoretical model to scrutinize the conductivity of small
polarons in one-dimensional disordered systems, focusing on two crucial --as
will be demonstrated-- factors: the density of states and the spatial extent of
the electronic wave function. The investigation is performed for any
temperature up to 300 K and under electric field of arbitrary strength up to
the polaron dissociation limit. To accomplish this task we combine analytical
work with numerical calculations.",1209.1582v2
2013-03-19,Tunnel conductance spectroscopy via harmonic generation in a hybrid capacitor device,"We address the measurement of density of states within and beyond the
superconducting gap in tunnel-coupled finite-size nanostructures using a
capacitive method. Third-harmonic generation is used to yield the full
differential conductance spectrum without destruction of the low dimensionality
otherwise induced by intimate ohmic coupling to an electrode. The method is
particularly relevant to attempts to discern the presence of the fragile
Majorana quasiparticle at the end of spin-orbit-coupled nanowires in
appropriate magnetic field conditions by their signature mid-gap density of
states.",1303.4719v4
2013-04-09,PIMC Simulations of Metal Hydrogen: Phase Transition and Equation of State,"The article is devoted to numerical studies of atomic (metal) hydrogen with
Path Integral Monte Carlo (PIMC) technique. The research is focused on the
range of temperatures and densities where quantum statistics effects are
crucial for electrons and negligible for protons. In this range the equations
of state are obtained as a dependence of internal energy and pressure on
temperature and density. These dependences allow to detect and describe the
phase transition between solid and liquid phases.",1304.2548v1
2013-05-15,Quantized space-time and its influences on some physical problems,"Based on the idea of quantized space-time of Snyder, we derive new
generalized uncertainty principle and new modified density of states.
Accordingly we discuss the influences of the modified density of states on some
physical quantities and laws. In addition we analyzed the exact solution of the
harmonic oscillator in Snyder's quantized space-time.",1305.3363v1
2013-05-25,Note on multidimensional Breeden-Litzenberger representation for state price densities,"In this note, we consider European options of type $h(X^1_T, X^2_T,\ldots,
X^n_T)$ depending on several underlying assets. We give a multidimensional
version of the result of Breeden and Litzenberger \cite{Breeden} on the
relation between derivatives of the call price and the risk-neutral density of
the underlying asset. The pricing measure is assumed to be absolutely
continuous with respect to the Lebesgue measure on the state space.",1305.5963v2
2014-01-10,Nonequilibrium thermal entanglement for simple qubit systems,"The dynamics of simple qubit systems in a chain configuration coupled at both
ends to separate bosonic baths at different temperatures is studied. An exact
analytical solution of the master equation in the Born-Markov approximation for
the reduced density matrix of the qubit system is constructed. The unique
non-equilibrium stationary state for the long time behavior of the reduced
density matrix in obtained. Dynamical and steady state properties of the
concurrence between the first and the last spin are studied.",1401.2306v1
2014-07-31,Electronic structure of non-centrosymmetric superconductors Re24(Nb;Ti)5 by ab initio calculations,"Electronic structures of superconducting Re24Nb5 and Re24Ti5 have been
calculated employing the full-potential local-orbital method within the density
functional theory. The investigations were focused on the influence of the
antisymmetric spin-orbit coupling on band structures and Fermi surfaces of
these non-centrosymmetric systems. The predicted here density of states at the
Fermi level for Re24Ti5 is abnormally low with respect to that deduced from
previous heat capacity measurements. This discrepancy suggests an intermediate
coupled superconducting state in Re24Ti5. The differences between electronic
properties of both compounds could explain more robust superconductivity in the
Nb-based material.",1407.8416v1
2014-09-10,Local Nonequilibrium Configurational Entropy in Quasi-one-dimensional Heat Conduction,"In a quasi-one-dimensional system the particles remain ordered from left to
right allowing the association of a volume element to the particle which on
average resides there. Thus the properties of that single particle can give the
local densities in the volume element. With reservoirs of different
temperatures connected to each end of the system a steady heat current with an
anomalous thermal conductivity results. A local configurational entropy density
is calculated from two-particle correlation functions which varies locally
within the nonequilibrium steady state. This local configurational entropy is
proposed as the configurational component of the local entropy of the
nonequilibrium steady state.",1409.3259v1
2015-03-17,Topological phase in a $d_{x^2-y^2}+(p+ip)$ superconductor in presence of spin-density-wave,"We consider a mean-field Hamiltonian for a $d_{x^2-y^2}+(p+ip)$
superconductor(SC) in presence of spin-density-wave(SDW) order. This is due to
the fact that the non-commutativity of any two orders produces the third one.
The energy spectrum of such a Hamiltonian is shown to be gapped and it yields a
topological phase in addition to the conventional one. A phase diagram
characterizing different topological phases is construted. The Chern numbers
and hence the nature of the topological phases are determined. The edge state
spectrum and the possibility of whether the vortex state harbouring the zero
modes are discussed.",1503.04969v1
2015-08-20,Neutron star structure from QCD,"In this review article, we argue that our current understanding of the
thermodynamic properties of cold QCD matter, originating from first principles
calculations at high and low densities, can be used to efficiently constrain
the macroscopic properties of neutron stars. In particular, we demonstrate that
combining state-of-the-art results from Chiral Effective Theory and
perturbative QCD with the current bounds on neutron star masses, the Equation
of State of neutron star matter can be obtained to an accuracy better than 30%
at all densities.",1508.05019v1
2018-02-22,Quantum entropy and polarization measurements of the two-photon system,"We consider the bipartite state of a two-photon polarization system and
obtain the exact analytical expression for the von Neumann entropy in the
particular case of a 5-parameter polarization density matrix. We investigate
and graphically illustrate the dependence of the entropy on these five
parameters, in particular, the existence of exotic, transition from exotic to
non-exotic, and non-exotic states, where the quantum conditional entropy is
negative, both positive and negative, and positive, respectively. We study the
""cooling"" or ""heating"" effect that follows from the reduced density of photon 2
when a measurement is performed on photon 1.",1802.08276v1
2018-04-23,The Density Operators of Qubit Systems in the Multiparticle Spacetime Algebra,"We provide a method to write down the density operator for any pure state of
multi-qubit systems in the multiparticle spacetime algebra (MSTA) introduced by
Doran, Gull, and Lasenby. Using the MSTA formulation, we analyze several
aspects of quantum mechanics in a geometrical way including the Bell inequality
and the dynamics of two coupled qubits. Lastly, we provide a natural way to
construct the local unitary invariants in the MSTA. Using these invariants, we
analyze the space of the two-qubit and three-qubit pure states with local and
non-local degrees of freedom separated.",1804.08375v1
2018-06-27,Dynamical Control of Order in a Cavity-BEC System,"We demonstrate dynamical control of the superradiant transition of cavity-BEC
system via periodic driving of the pump laser. We show that the dominant
density wave order of the superradiant state can be suppressed, and that the
subdominant competing order of Bose-Einstein condensation emerges in the steady
state. Furthermore, we show that additional, non-equilibrium density wave
orders, which do not exist in equilibrium, can be stabilized dynamically.
Finally, for strong driving, chaotic dynamics emerges.",1806.10573v2
2020-07-14,Quasi Modes and Density of States (DOS) of 1D Photonics Crystal,"1-Dimensional (1D) photonics crystals with and without defects have been
numerically studied using efficient Transfer Matrix Method (TMM). Detailed
numerical recipe of the TMM has been laid out. Dispersion relation is verified
for the periodic Photonics Band Gap (PBG) structure. When there are defects,
the transmission spectrum can be decomposed into one or more quasi modes with
excellent agreement. The Density of States (DOS) is obtained from the phase
derivative of the transmission spectrum. Green's function is also obtained
showing much sharper mode characteristics when the excitation source is
localized at the peaks of the quasi modes.",2007.07818v1
2013-08-05,Critical state solution and AC loss computation of polygonally arranged thin superconducting tapes,"The current density and field distributions in polygonally arranged thin
superconducting tapes carrying AC current are derived under the assumption of
the critical state model. Starting from the generic Biot-Savart law for a
general polygonal geometry, we derive a suitable integral equation for the
calculation of the current density and magnetic field in each tape. The model
works for any transport current below $I_c$, which makes it attractive for
studying cases of practical interest, particularly the dependence of AC losses
on parameters such as the number of tapes, their distance from the center, and
their separation.",1308.0915v2
2016-11-03,Green Function Approach for Calculation of the Local Density of States in the Graphitic Nanocone,"Graphene and other nanostructures belong to the center of interest of today's
physics research. The local density of states of the graphitic nanocone
influenced by the spin-orbit interaction was calculated. Numerical calculations
and the Green function approach were used to solve this problem. It was proven
in the second case that the second order pproximation is not sufficient for
this purpose.",1611.00935v1
2011-11-02,Symmetry restoration for odd-mass nuclei with a Skyrme energy density functional,"In these proceedings, we report first results for particle-number and
angular-momentum projection of self-consistently blocked triaxial
one-quasiparticle HFB states for the description of odd-A nuclei in the context
of regularized multi-reference energy density functionals, using the entire
model space of occupied single-particle states. The SIII parameterization of
the Skyrme energy functional and a volume-type pairing interaction are used.",1111.0451v1
2015-12-22,Odd-frequency Superconductivity in Driven Systems,"We show that Berezinskii's classification of the symmetries of Cooper pair
amplitudes holds for driven systems even in the absence of translation
invariance. We then consider a model Hamiltonian for a superconductor coupled
to an external driving potential and, treating the driving potential as a
perturbation, we investigate the corrections to the anomalous Green's function,
density of states, and spectral function. We find that in the presence of an
external drive the anomalous Green's function develops terms that are odd in
frequency and that the same mechanism responsible for these odd-frequency terms
generates additional features in the density of states and spectral function.",1512.07031v2
2021-01-06,Real-Space Green's functions for Warm Dense Matter,"Accurate modeling of the electronic structure of warm dense matter is a
challenging problem whose solution would allow a better understanding of
material properties like equation of state, opacity, and conductivity, with
resulting applications from astrophysics to fusion energy research. Here we
explore the real-space Green's function method as a technique for solving the
Kohn-Sham density functional theory equations under warm dense matter
conditions. We find the method to be tractable and accurate throughout the
density and temperature range of interest, in contrast to other approaches.
Good agreement on equation of state is found when comparing to other methods,
where they are thought to be accurate.",2101.02088v1
2021-12-17,A Mechanism to Attract Electrons,"In a startling discovery it has been recently found that certain density of
states (DOS) can become negative in mesoscopic systems wherein electrons can
travel back in time. We give a brief introduction to the hierarchy of density
of states in mesoscopic systems as we want to point out some robust phenomenon
that can be experimentally observed with our present day technologies. They can
have direct consequences on thermodynamic effects and also can provide indirect
evidence of time travel. Essentially certain members of the hierarchy of DOS
become negative in these regimes and that can attract other electrons.",2112.09390v3
2021-12-22,Density of states for gravitational waves,"We present ongoing investigations of the first-order confinement transition
of a composite dark matter model, to predict the resulting spectrum of
gravitational waves. To avoid long autocorrelations at the first-order
transition, we employ the Logarithmic Linear Relaxation (LLR) density of states
algorithm. After testing our calculations by reproducing existing results for
compact U(1) lattice gauge theory, we focus on the pure-gauge SU(4) theory
related to the Stealth Dark Matter model.",2112.11868v1
2021-12-11,Dynamics of group formation,"We consider a specific dynamical system of groups formation. It is based
simultaneously on a gradient competition between groups and a strong
accumulation inside groups. Such a dynamical system demonstrates interesting
behavior of densities of emerging groups of $1$, $2$, $3$, ... elements in a
steady-state depending on the densities of one-elements groups in a randomly
chosen initial state.",2112.12733v2
2022-03-09,Smoothness of integrated density of states and level statistics of the Anderson model when single site distribution is convolution with the Cauchy distribution,"In this work we consider the Anderson model on $\ell^2(\mathbb{Z}^d)$ when
the single site distribution (SSD) is given by $\mu_1 * \mu_2$, where $\mu_1$
is the Cauchy distribution and $\mu_2$ is any probability measure. For this
model we prove that the integrated density of states (IDS) is infinitely
differentiable irrespective of the disorder strength. Also, we investigate the
local eigenvalue statistics of this model in $d\ge 2$, without any assumption
on the localization property.",2203.04569v1
2022-06-06,Comprehensive simulation of heavy-ion collisions at non-zero baryon chemical potential,"We present results of hydrodynamic modelling of Au-Au collisions from
$\sqrt{s_{NN}}$ = 7.7 to 200 GeV. Our simulations have three novel components.
Firstly, we use a Linear EXtrapolation of Ultrarelativistic nucleon-nucleon
Scattering to nucleus-nucleus collisions (LEXUS) inspired Monte-Carlo initial
state model. Secondly, we use a crossover equation of state at finite baryon
densities without a critical point. Finally, we use departure functions derived
from the quasiparticle theory of transport coefficients for hadronic matter at
non-zero baryon densities.",2206.02655v2
2023-03-20,Electron Wave Spin in Excited States,"The wave spin of an electron can be fully characterized by the current
density calculated from the exact four-spinor solution of the Dirac equation.
In the excited states of the electron in a magnetic field-free quantum well,
the current density has a multiple vortex topology. The interaction of the
current with a magnetic potential produces a finer structure of anomalous
Zeeman splitting. When the magnetic potential is comparable to the size of the
individual vortices, fractional or zero spin effects can be observed.",2303.10855v1
2021-10-29,Turning Traffic Monitoring Cameras into Intelligent Sensors for Traffic Density Estimation,"Accurate traffic state information plays a pivotal role in the Intelligent
Transportation Systems (ITS), and it is an essential input to various smart
mobility applications such as signal coordination and traffic flow prediction.
The current practice to obtain the traffic state information is through
specialized sensors such as loop detectors and speed cameras. In most
metropolitan areas, traffic monitoring cameras have been installed to monitor
the traffic conditions on arterial roads and expressways, and the collected
videos or images are mainly used for visual inspection by traffic engineers.
Unfortunately, the data collected from traffic monitoring cameras are affected
by the 4L characteristics: Low frame rate, Low resolution, Lack of annotated
data, and Located in complex road environments. Therefore, despite the great
potentials of the traffic monitoring cameras, the 4L characteristics hinder
them from providing useful traffic state information (e.g., speed, flow,
density). This paper focuses on the traffic density estimation problem as it is
widely applicable to various traffic surveillance systems. To the best of our
knowledge, there is a lack of the holistic framework for addressing the 4L
characteristics and extracting the traffic density information from traffic
monitoring camera data. In view of this, this paper proposes a framework for
estimating traffic density using uncalibrated traffic monitoring cameras with
4L characteristics. The proposed framework consists of two major components:
camera calibration and vehicle detection. The camera calibration method
estimates the actual length between pixels in the images and videos, and the
vehicle counts are extracted from the deep-learning-based vehicle detection
method. Combining the two components, high-granular traffic density can be
estimated. To validate the proposed framework, two case studies were conducted
in Hong Kong and Sacramento. The results show that the Mean Absolute Error
(MAE) in camera calibration is less than 0.2 meters out of 6 meters, and the
accuracy of vehicle detection under various conditions is approximately 90%.
Overall, the MAE for the estimated density is 9.04 veh/km/lane in Hong Kong and
1.30 veh/km/lane in Sacramento. The research outcomes can be used to calibrate
the speed-density fundamental diagrams, and the proposed framework can provide
accurate and real-time traffic information without installing additional
sensors.",2111.00941v1
2007-10-22,The quantum entanglement contained in density matrices,"We point out that density matrices can only be used to describe quantum
states, so the entanglement contained in a density matrix is just quantum
entanglement. This means a bipartite state described by a density matrix
contains quantum entanglement, unless the density matrix has the form
$\rho_{AB}=\rho_A\otimes \rho_B$.",0710.4061v3
2018-10-12,Ab initio based equation of state of dense water for planetary and exoplanetary modeling,"As a first step toward a multi-phase equation of state for dense water, we
develop a temperature-dependent equation of state for dense water covering the
liquid and plasma regimes and extending to the super-ionic and gas regimes.
This equation of state covers the complete range of conditions encountered in
planetary modeling.
  We use first principles quantum molecular dynamics simulations and its
Thomas-Fermi extension to reach the highest pressures encountered in giant
planets several times the size of Jupiter. Using these results, as well as the
data available at lower pressures, we obtain a parametrization of the Helmholtz
free energy adjusted over this extended temperature and pressure domain. The
parametrization ignores the entropy and density jumps at phase boundaries but
we show that it is sufficiently accurate to model interior properties of most
planets and exoplanets.
  We produce an equation of state given in analytical form that is readily
usable in planetary modeling codes and dynamical simulations (a fortran
implementation can be found at http://www.ioffe.ru/astro/H2O/). The EOS
produced is valid for the entire density range relevant to planetary modeling,
for densities where quantum effects for the ions can be neglected, and for
temperatures below 50,000K. We use this equation of state to calculate the
mass-radius relationship of exoplanets up to 5,000M_Earth, explore temperature
effects in ocean and wet Earth-like planets, and quantify the influence of the
water EOS for the core on the gravitational moments of Jupiter.",1810.05658v2
2017-11-29,Generic pure quantum states as steady states of quasi-local dissipative dynamics,"We investigate whether a generic multipartite pure state can be the unique
asymptotic steady state of locality-constrained purely dissipative Markovian
dynamics. In the simplest tripartite setting, we show that the problem is
equivalent to characterizing the solution space of a set of linear equations
and establish that the set of pure states obeying the above property has either
measure zero or measure one, solely depending on the subsystems' dimension. A
complete analytical characterization is given when the central subsystem is a
qubit. In the N-partite case, we provide conditions on the subsystems' size and
the nature of the locality constraint, under which random pure states cannot be
quasi-locally stabilized generically. Beside allowing for the possibility to
approximately stabilize entangled pure states that cannot be exact steady
states in settings where stabilizability is generic, our results offer insights
into the extent to which random pure states may arise as unique ground states
of frustration free parent Hamiltonians. We further argue that, to high
probability, pure quantum states sampled from a t-design enjoy the same
stabilizability properties of Haar-random ones as long as suitable dimension
constraints are obeyed and t is sufficiently large. Lastly, we demonstrate a
connection between the tasks of quasi-local state stabilization and unique
state reconstruction from local tomographic information, and provide a
constructive procedure for determining a generic N-partite pure state based
only on knowledge of the support of any two of the reduced density matrices of
about half the parties, improving over existing results.",1711.11142v1
2003-04-15,Estimating purity in terms of correlation functions,"We prove a rigorous inequality estimating the purity of a reduced density
matrix of a composite quantum system in terms of cross-correlation of the same
state and an arbitrary product state. Various immediate applications of our
result are proposed, in particular concerning Gaussian wave-packet propagation
under classically regular dynamics.",0304103v1
2017-10-03,Note on Localized Objects as Constrained States of Holographic Variables,"We argue that localized excitations in Minkowski space must be thought of as
constrained states of holographic degrees of freedom. The Minkowski ""vacuum"" is
in fact a density matrix of infinite entropy. The argument assumes that
Minkowski space can be viewed as a limit of a space-time with non-vanishing
cosmological constant, either positive or negative.",1710.01211v1
2001-08-27,Reconstructing the equation of state for cold nuclear matter from the relationship of any two properties of neutron stars,"A direct method is developed to reconstruct the equation of state for
high-density nuclear matter from the relationship between any two properties of
neutron stars, such as masses, radii, moments of inertia, baryonic masses,
binding energies, gravitational redshifts, and their combinations.",0108410v1
2001-09-26,High Angular Momentum Core States and Impurity Effects in the Mixed State of d-Wave Superconductors,"The local quasiparticle spectra around the vortex core of a d-wave
superconductor in the mixed state is studied by solving the lattice
Bogoliubov-de Gennes equations self-consistently. It is shown that in addition
to the zero-energy states, there also exist core states of high angular
momentum. A nonmagnetic unitary impurity sitting at the core center is
nondestructive to these core states and the zero-energy resonant state induced
by itself is still visible in the local quasiparticle spectrum. The calculated
imaging shows a fourfold ``star'' shape of the local density of states whose
orientation is energy dependent. It is also found that, although the
zero-energy states are extended, the core states of finite energy level could
be localized.",0109503v1
2003-04-19,Phase diagram of a surface superconductor in parallel magnetic field,"Detailed theory of phase diagram of clean 2D surface superconductor in a
parallel magnetic field is presented. Regular spin-orbital interaction of the
Rashba type is known to produce inhomogeneous superconductive state similar to
the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state with $\Delta({\bf r})\propto
\cos({\bf Qr})$ at high magnetic fields, with $Q \sim g\mu_B h/v_F$. We
consider the case of relatively strong Rashba interaction and show that at low
temperatures $T\leq 0.4 T_{c0}$ the LOFF-type state is separated from the usual
homogeneous state by the first-order phase transition line. At higher
temperatures new ""helical"" state with $\Delta({\bf r}) \propto \exp(i{\bf Qr})$
intervene between uniform BCS state and LOFF-like state. One component of
superfluid density tensor $n_s$ vanishes on the second-order transition line
between BCS state and helical state. Nonmagnetic impurities suppresses both
inhomogeneous states, and eliminate them completely at $T_{c0}\tau \leq 0.11$.",0304445v2
2015-06-22,Two-band superconductivity of bulk and surface states in Ag thin films on Nb,"We use epitaxial strain to shift the energy of the two-dimensional Ag(111)
surface states of Ag islands on Nb(110) substrates, allowing to spatially tune
the bottom of the surface-state band $E_{\rm SS}$ through the Fermi level
$E_{\rm F}$. Bulk and surface-state contributions to the Ag(111) local density
of states (LDOS) can be separated with scanning tunneling spectroscopy. For
thick islands ($\approx$\, 20 nm), the Ag surface states are decoupled from the
Ag bulk states via orthogonality, and the superconductive gap induced by
proximity to Nb is due to bulk states only. However, for thin islands (3-4 nm),
surface-state electrons develop superconducting correlations as identified by a
complete energy gap in the LDOS when $E_{\rm F}$ is smaller than but close to
$E_{\rm F}$. The induced superconductivity in this case is of two-band nature
and appears to occur when the surface-state wave function reaches down to the
Ag/Nb interface.",1506.06524v3
2016-02-09,Topological magnon bound-states in periodically modulated Heisenberg XXZ chains,"Strongly interacting topological states in multi-particle quantum systems
pose great challenges to both theory and experiment. Recently, bound states of
elementary spin waves (magnons) in quantum magnets have been experimentally
observed in quantum Heisenberg chains comprising ultracold Bose atoms in
optical lattices. Here, we explore a strongly interacting topological state
called topological magnon bound-state in the quantum Heisenberg chain under
cotranslational symmetry. We find that the cotranslational symmetry is the key
to the definition of a topological invariant for multi-particle quantum states,
which enables us to characterize the topological features of multi-magnon
excitations. We calculate energy spectra, density distributions, correlations
and Chern numbers of the two-magnon bound-states and show the existence of
topological protected edge bound-states. Our study not only opens a new
prospect to pursue topological magnon bound-states, but also gives insights
into the characterization and understanding of strongly interacting topological
states.",1602.03217v2
2023-05-10,N-Representability Violations in Truncated Equation-of-Motion Coupled-Cluster Methods,"One-electron reduced density matrices (1RDMs) from equation-of-motion (EOM)
coupled-cluster with single and double excitations (CCSD) calculations are
analyzed to assess their N-representability ({\em i.e.}, whether they are
derivable from an physical N-electron state). We identify EOM-CCSD stationary
states whose 1RDMs violate either ensemble-state N-representability conditions
or pure-state conditions known as generalized Pauli constraints (GPCs). As
such, these 1RDMs do not correspond to any physical N-electron state.
Unphysical states are also encountered in the course of time-dependent EOM-CC
simulations; when an external field drives transitions between a pair of
stationary states with pure-state N-representable 1RDMs, the 1RDM of the
time-dependent state can violate ensemble-state conditions. These observations
point to potential challenges in interpreting the results of time-dependent
EOM-CCSD simulations.",2305.06457v3
2024-02-20,Radiation back-reaction during dark-matter freeze-out via metastable bound states,"The formation and decay of metastable bound states can deplete significantly
the density of multi-TeV thermal-relic dark matter. The effect depends on the
interplay of bound-state formation, ionisation, transition and decay processes.
Existing calculations take into account bound-state ionisation and excitations
due to the radiation of the thermal bath. However, the dynamics of Hydrogen
recombination suggests that the resonant radiation produced in bound-state
formation or de-excitations may backreact, ionising or exciting the bound
states thus impeding recombination. In this paper we examine this effect in the
context of dark-matter freeze-out. To this end, we employ the generalised Saha
equilibrium equation for metastable bound states, and discuss its salient
features. We show that, in sharp contrast to Hydrogen recombination, the
radiation produced during dark matter freeze-out is more likely to thermalise
or redshift, rather than ionise or excite the metastable bound states. This
holds not only for the low-energy (resonant) radiation produced in bound-state
formation and transition processes, but also for the high-energy radiation
produced in dark-matter annihilations and bound-state decays. While our
computations are carried out in a minimal dark $U(1)$ model, our conclusions
only strengthen in more complex models.",2402.13069v1
2018-07-09,Cavity-induced emergent topological spin textures in a Bose Einstein condensate,"The coupled nonlinear dynamics of ultracold quantum matter and
electromagnetic field modes in an optical resonator exhibits a wealth of
intriguing collective phenomena. Here we study a $\Lambda$-type,
three-component Bose-Einstein condensate coupled to four dynamical running-wave
modes of a ring cavity, where only two of the modes are externally pumped.
However, the unpumped modes play a crucial role in the dynamics of the system
due to coherent back-scattering of photons. On a mean- field level we identify
three fundamentally different steady-state phases with distinct characteristics
in the density and spatial spin textures: a combined density and spin wave, a
continuous spin spiral with a homogeneous density, and a spin spiral with a
modulated density. The spin-spiral states, which are topological, are
intimately related to cavity-induced spin-orbit coupling emerging beyond a
critical pump power. The topologically trivial density-wave--spin-wave state
has the characteristics of a supersolid with two broken continuous symmetries.
The transitions between different phases are either simultaneously topological
and first order, or second order. The proposed setup allows the simulation of
intriguing many-body quantum phenomena by solely tuning the pump amplitudes and
frequencies, with the cavity output fields serving as a built-in nondestructive
observation tool.",1807.03316v1
2023-08-10,Filtering Dynamical Systems Using Observations of Statistics,"We consider the problem of filtering dynamical systems, possibly stochastic,
using observations of statistics. Thus, the computational task is to estimate a
time-evolving density $\rho(v, t)$ given noisy observations of the true density
$\rho^\dagger$; this contrasts with the standard filtering problem based on
observations of the state $v$. The task is naturally formulated as an
infinite-dimensional filtering problem in the space of densities $\rho$.
However, for the purposes of tractability, we seek algorithms in state space;
specifically, we introduce a mean-field state-space model, and using
interacting particle system approximations to this model, we propose an
ensemble method. We refer to the resulting methodology as the ensemble
Fokker-Planck filter (EnFPF).
  Under certain restrictive assumptions, we show that the EnFPF approximates
the Kalman-Bucy filter for the Fokker-Planck equation, which is the exact
solution to the infinite-dimensional filtering problem. Furthermore, our
numerical experiments show that the methodology is useful beyond this
restrictive setting. Specifically, the experiments show that the EnFPF is able
to correct ensemble statistics, to accelerate convergence to the invariant
density for autonomous systems, and to accelerate convergence to time-dependent
invariant densities for non-autonomous systems. We discuss possible
applications of the EnFPF to climate ensembles and to turbulence modeling.",2308.05484v3
1999-11-05,ORFEUS II echelle spectra: deuterium and molecular hydrogen in the ISM towards BD +39 3226,"In ORFEUS II spectra of the sdO star BD +39 3226 interstellar hydrogen and
deuterium is detected. From Ly alpha profile fitting and a curve of growth
analysis of the Lyman series of H I and D I we derive the column densities
N(H)=1.20(+0.28/-0.22)*10^20 cm^(-2) and N(D)=1.45(+0.50/-0.38)*10^(15)
cm^(-2). From the analysis of metal absorption lines in ORFEUS and IUE spectra
we obtain column densities for 11 elements. In addition, we examine absorption
lines of H_2 for rotational excitation states up to J=7. We find an H_2
ortho-to-para ratio of 2.5, the fractional abundance of molecular hydrogen has
a low value of log f=-4.08 for a total amount of N(H_2)=4.8(+2.0/-1.6)*10^15
cm^(-2). The column densities of the excitation states reveal a moderate
Boltzmann excitation temperature of 130 K and an equivalent excitation
temperature for the excited upper states due to UV pumping of <1800 K.",9911097v1
2002-10-18,A logarithmic contribution to the density of states of rectangular Andreev billiards,"We demonstrate that the exact quantum mechanical calculations are in good
agreement with the semiclassical predictions for rectangular Andreev billiards
and therefore for a large number of open channels it is sufficient to
investigate the Bohr-Sommerfeld approximation of the density of states. We
present exact calculations of the classical path length distribution $P(s)$
which is a non-differentiable function of $s$, but whose integral is a smooth
function with logarithmically dependent asymptotic behavior. Consequently, the
density of states of rectangular Andreev billiards has two contributions on the
scale of the Thouless energy: one which is well-known and it is proportional to
the energy, and the other which shows a logarithmic energy dependence. It is
shown that the prefactors of both contributions depend on the geometry of the
billiards but they have universal limiting values when the width of the
superconductor tends to zero.",0210412v2
2004-03-01,Spin-orbit-induced correlations of the local density of states in two-dimensional electron gas,"We study the local density of states (LDOS) of two-dimensional electrons in
the presence of spin-orbit (SO) coupling. Although SO coupling has no effect on
the average density of states, it manifests itself in the correlations of the
LDOS. Namely, the correlation function acquires two satellites centered at
energy difference equal to the SO splitting, $2\omega_{SO}$, of the electron
Fermi surface. For a smooth disorder the satellites are well separated from the
main peak. Weak Zeeman splitting $\omega_{Z} \ll \omega_{SO}$ in a parallel
magnetic field causes an anomaly in the shape of the satellites. We consider
the effect of SO-induced satellites in the LDOS correlations on the shape of
the correlation function of resonant-tunneling conductances at different
source-drain biases, which can be measured experimentally. This shape is
strongly sensitive to the relation between $\omega_{SO}$ and $\omega_{Z}$.",0403057v1
2009-04-26,Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: I. Spectral properties,"The screening effect due to a scanning tunneling microscope tip which is
placed in the vicinity of an interacting quantum wire is considered. With the
help of a bosonization procedure, we are able to determine non perturbatively
the Green's functions of the quantum wire in the presence of both electrostatic
screening by the tip and Coulomb interactions in the wire. In our approach we
justify that the working Hamiltonian of the whole system is quadratic when
$K_c>1/2$ and can be solved by integration over the degrees of freedom of the
tip. Once the Green's functions are known, we calculate the spectral
properties. We show that the spectral function, as well as the tunnel density
of states, is affected by the screening and that the local density of states
strongly deviates from its unscreened value when the tip gets close to the
wire. Moreover, we observe that the spatial extension of the deviation of the
local density of states is related to both the Coulomb interactions parameter
and the screening strength.",0904.4019v2
2011-10-21,Magnetic properties of spin diluted iron pnictides from muSR and NMR in LaFe1-xRuxAsO,"The effect of isoelectronic substitutions on the microscopic properties of
LaFe1-xRuxAsO, for 0< x< 0.8, has been investigated by means of muSR and 139La
NMR. It was found that Ru substitution causes a progressive reduction of the
N\`eel temperature (T_N) and of the magnetic order parameter without leading to
the onset of superconductivity. The temperature dependence of 139La nuclear
spin-lattice relaxation rate 1/T_1 can be suitably described within a two-band
model. One band giving rise to the spin density wave ground-state, while the
other one is characterized by weakly correlated electrons. Fe for Ru
substitution yields to a progressive decrease of the density of states at the
Fermi level close to the one derived from band structure calculations. The
reduction of T_N with doping follows the predictions of the J_1-J_2 model on a
square lattice, which appears to be an effective framework to describe the
magnetic properties of the spin density wave ground-state.",1110.4812v1
2012-06-11,Exact analysis on the singularity of the joint density of states and its relationship to the quasiparticle interference,"Singularities of the joint density of states (JDOS) and Fourier-transformed
local density of states (FT-LDOS) correspond to the hot spots in quasiparticle
interference patterns. In this paper the singularity of JDOS is analyzed
exactly, with three types of singularities being classified. In particular, the
third type of singularities are found exactly to be envelopes of the contours
of constant energy. Remarkably, we show that JDOS and FT-LDOS have the same
singular points. Approaching to the singular points, both quantities diverge
complementarily in an inverse-square-root manner if the joint curvature is
nonzero. The relative magnitude of divergence is governed by the joint
curvature as well as the product of the quasiparticle velocities. If the joint
curvature of certain singularity is zero, the divergence has a higher order
than -1/2.",1206.2195v1
2012-10-12,Constraining the High-Density Behavior of Nuclear Symmetry Energy with the Tidal Polarizability of Neutron Stars,"Using a set of model equations of state satisfying the latest constraints
from both terrestrial nuclear experiments and astrophysical observations as
well as state-of-the-art nuclear many-body calculations of the pure neutron
matter equation of state, the tidal polarizability of canonical neutron stars
in coalescing binaries is found to be a very sensitive probe of the
high-density behavior of nuclear symmetry energy which is among the most
uncertain properties of dense neutron-rich nucleonic matter. Moreover, it
changes less than $\pm 10%$ by varying various properties of symmetric nuclear
matter and symmetry energy around the saturation density within their
respective ranges of remaining uncertainty.",1210.3402v1
2014-01-13,Mapping the radiative and the apparent non-radiative local density of states in the near field of a metallic nanoantenna,"We present a novel method to extract the various contributions to the
photonic local density of states from near-field fluorescence maps. The
approach is based on the simultaneous mapping of the fluorescence intensity and
decay rate, and on the rigorous application of the reciprocity theorem. It
allows us to separate the contributions of the radiative and the apparent
non-radiative local density of states to the change in the decay rate. The
apparent non-radiative contribution accounts for losses due to radiation out of
the detection solid angle and to absorption in the environment. Data analysis
relies on a new analytical calculation, and does not require the use of
numerical simulations. One of the most relevant applications of the method is
the characterization of nanostructures aimed at maximizing the number of
photons emitted in the detection solid angle, which is a crucial issue in
modern nanophotonics.",1401.2858v2
2015-06-23,A generalised Gauss circle problem and integrated density of states,"Counting lattice points inside a ball of large radius in Euclidean space is a
classical problem in analytic number theory, dating back to Gauss. We propose a
variation on this problem: studying the asymptotics of the measure of an
integer lattice of affine planes inside a ball. The first term is the volume of
the ball; we study the size of the remainder term. While the classical problem
is equivalent to counting eigenvalues of the Laplace operator on the torus, our
variation corresponds to the integrated density of states of the Laplace
operator on the product of a torus with Euclidean space. The asymptotics we
obtain are then used to compute the density of states of the magnetic
Schroedinger operator.",1506.07115v3
2016-04-18,Majorana spectroscopy of 3D Kitaev spin-liquids,"We analyse the dynamical response of a range of 3D Kitaev quantum
spin-liquids, using lattice models chosen to explore the different possible
low-energy spectra for gapless Majorana fermions, with either Fermi surfaces,
nodal lines or Weyl points. We find that the behaviour of the dynamical
structure factor is distinct in all three cases, reflecting the quasiparticle
density of states in two fundamentally different ways. First, the low-energy
response is either straightforwardly related to the power with which the
low-energy density of states vanishes; or for a non-vanishing density of
states, to the phase shifts encountered in the corresponding X-ray edge
problem, whose phenomenology we extend to the case of Majorana fermions.
Second, at higher energies, there is a rich fine-structure, determined by
microscopic features of the Majorana spectrum. Our theoretical results test the
usefulness of inelastic neutron scattering as a probe of these quantum spin
liquids: we find that although spin flips fractionalise, the main features of
the dynamical spin response nevertheless admit straightforward interpretations
in terms of Majorana and flux loop excitations.",1604.05199v2
2016-10-09,Metal hydrogen critical temperature at the pressure 500 GPa,"\'Eliashberg theory, being generalized to the case of the electron-phonon
(EP) systems with the not constant density of electronic states, as well as to
the frequency behavior of the renormalization of both the electron mass and the
chemical potential, is used to study the normal properties and of the metal
hydrogen phase under pressure of P = 500 GPa. The phonon contribution to the
anomalous electron Green's function (GF) is considered. The pairing is
considered within the overall width of the electron band, and not only in a
narrow layer at the Fermi surface. The frequency dependence of the electron
mass renormalization ReZ , the density of electronic states , the spectral
function of the electron-phonon interaction, obtained by calculation are used
to calculate the electronic abnormal GF. The \'Eliashberg generalized equations
with the variable density of electronic states are resolved. The dependence of
both the real and the imaginary parts of the order parameter on the frequency
in the phase is obtained. The value for the metal hydrogen phase at the
pressure P = 500 GPa has been defined.",1610.02688v1
2017-02-02,Atomic population kinetics in the context of XUV/X-ray free electron laser generating warm dense matter and strongly coupled plasmas,"In the present paper we propose the use of desnity matrix formalism for the
calculation of the atomic spectroscopic properties of autoionizing states in
dense plasmas, i.e. warm dense matter and strongly coupled plasmas. This is
motivated by the importance of taking into account the effect of the electric
microfield generated by the plasma charge constituents in the calculation of
the atomic populations of autoionizing states. For autoionizing states,
electron densities justifying the statistical approach exceed solid density
bringing serious doubts to the statistical approach even in dense plasmas. This
leads also to the change of the spectral line shapes in the frame of the
standard methods. We discuss the importance of the present analysis in view of
the radiation emission originating from dense plasmas created by the
interaction of the X-ray Free Electron Lasers (XFEL) with solid density matter.",1702.00680v1
2018-07-15,Chaplygin Gas models without Chaplygin Gas EoS,"The equation of state of Chaplygin Gas is one of the simplest ways to
illustrate dark energy effects during the late time. Indeed, while one uses the
equation of state of Chaplygin Gas, the continuity equation gives specific
energy density which satisfies both deceleration (matter dominated) and
acceleration (dark energy epoch). In other words, for the earlier universe, the
energy density of whole energy-matter component behaves as matter era (baryonic
and dark matter) and treats such as dark energy in the standard model of
cosmology Lambda-CDM when a goes to infinity. Here, by using the general form
of F(R) gravity while the pressure of matter is non-zero, we show that even for
Einstein gravity (GR), one obtains a viable cosmological model with the same
energy density of Chaplygin Gas while Chaplygin Gas EoS is not used. Further,
we investigate cosmic evolution through two other different forms of F(R)
gravity and show general behavior of Hubble parameter, cosmological scale
factor and equation of state throughout cosmic time.",1807.07411v1
2018-12-24,Signatures of spin-triplet Cooper pairing in the density of states of spin-textured superconductor-ferromagnet bilayers,"The existence of spin-triplet superconductivity in non-collinear magnetic
heterostructures with superconductors is by now well established. This
observation lays the foundation of superconducting spintronics with the aim to
create a low-power consuming devices in order to replace the conventional
electronics limited by heating. From a fundamental point of view the
investigation of the structure and properties of spin-triplet Cooper pairs
continues. Recently, spectroscopic evidence has shown to offer more detailed
insights in the structure of triplet Cooper pairs than the supercurrent. Hence,
we study here the structure of spin-triplet Cooper pairs through the density of
states in bilayers of a textured magnetic insulator in proximity to a
superconductor. Using quasiclassical Green function methods, we study the local
density of states, both spin-resolved and spin-independent. We show that the
equal-spin and mixed-spin triplet Cooper pairs leads to different spectroscopic
signatures, which can be further enhanced by spin-polarized spectroscopy. Our
results show the huge potential spin-polarized tunneling methods offer in
characterizing unconventional superconductivity in heterostructures.",1812.09937v1
2020-07-30,Marcus-Hush-Chidsey Kinetics at Electrode-Electrolyte Interfaces,"Electrochemical kinetics at electrode-electrolyte interfaces limit
performance of devices including fuel cells and batteries. While the importance
of moving beyond Butler-Volmer kinetics and incorporating the effect of
electronic density of states of the electrode have been recognized, a unified
framework that incorporates these aspects directly into electrochemical
performance models is still lacking. In this work, we explicitly account for
the DFT-calculated density of states numerically in calculating electrochemical
reaction rates for a variety of electrode-electrolyte interfaces. We first show
the utility of this for two cases related to Li metal electrodeposition and
stripping on a Li surface and a Cu surface (anode-free configuration). The
deviation in reaction rates is minor for cases with flat densities of states
such as Li, but is significant for Cu due to nondispersive d-bands creating
large variation. Finally, we consider a semiconducting case of a
solid-electrolyte interphase (SEI) consisting of LiF and Li$_2$CO$_3$ and note
the importance of the Fermi level at the interface, pinned by the redox
reaction occuring there. We identify the asymmetry in reaction rates as a
function of discharge/charge naturally within this approach. The analysis code
used in this work is available open-source on Github.",2007.15756v1
2020-05-29,Neutron star equation of state and tidal deformability with nuclear energy density functionals,"Neutron star is the ultimate testing place for the physics of dense nuclear
matter. Before the detection of gravitational waves from the merger of binary
neutron stars, various nuclear equations of state have been used to estimate
the macroscopic properties of neutron stars, such as masses and radii, based on
the electromagnetic observations. However, recent observations on the tidal
deformability of neutron star from the gravitational waves GW170817 opened a
new era of multi-messenger astronomy and astrophysics, and many theoretical
works have been extended to estimate the tidal deformability of neutron stars.
In this article, we review our recent works on the application of nuclear
energy density functionals to the properties of neutron stars including tidal
deformability. We found that many nuclear energy density functionals, including
new KIDS (Korea: IBS-Daegu-Sungkyunkwan) model, satisfy both constraints from
current electromagnetic and gravitational wave observations. We discuss future
possibilities of constraining nuclear matter equation of state from
ground-based experiments and multi-messenger observations.",2005.14443v1
2021-12-10,Determination of the symmetry energy from the neutron star equation of state,"We analyze the uncertainties introduced in the determination of the neutron
star matter proton fraction, in a range of densities close to the saturation
density, if the cold $\beta$-equilibrium neutron star matter equation of state
(EoS) is known. In particular, we discuss the effect of neglecting the muon
contribution and of considering that the energy density of nuclear matter is
well described by taking only terms until second order in the proton-neutron
asymmetry. It is shown that two types of uncertainties may be associated with
the extraction of the symmetry energy from the $\beta$-equilibrium equation of
state: an overestimation if terms above the parabolic approximation on the
asymmetry parameter are neglected, or an underestimation if the muon
contribution is not considered. The effect of the uncertainty on the symmetric
nuclear matter EoS on the determination of the proton fraction is discussed. It
could be shown that the neutron star mass-radius curve is sensitive to the
parabolic approximation on the asymmetry parameter.",2112.05551v2
2010-10-21,Best-fit quasi-equilibrium ensembles: a general approach to statistical closure of underresolved Hamiltonian dynamics,"A new method of deriving reduced models of Hamiltonian dynamical systems is
developed using techniques from optimization and statistical estimation. Given
a set of resolved variables that define a model reduction, the
quasi-equilibrium ensembles associated with the resolved variables are employed
as a family of trial probability densities on phase space. The residual that
results from submitting these trial densities to the Liouville equation is
quantified by an ensemble-averaged cost function related to the information
loss rate of the reduction. From an initial nonequilibrium state, the
statistical state of the system at any later time is estimated by minimizing
the time integral of the cost function over paths of trial densities.
Statistical closure of the underresolved dynamics is obtained at the level of
the value function, which equals the optimal cost of reduction with respect to
the resolved variables, and the evolution of the estimated statistical state is
deduced from the Hamilton-Jacobi equation satisfied by the value function. In
the near-equilibrium regime, or under a local quadratic approximation in the
far-from-equilibrium regime, this best-fit closure is governed by a
differential equation for the estimated state vector coupled to a Riccati
differential equation for the Hessian matrix of the value function. Since
memory effects are not explicitly included in the trial densities, a single
adjustable parameter is introduced into the cost function to capture a
time-scale ratio between resolved and unresolved motions. Apart from this
parameter, the closed equations for the resolved variables are completely
determined by the underlying deterministic dynamics.",1010.4362v1
2017-03-08,Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams,"A generalized approach to Wang-Landau simulations, macroscopically
constrained Wang-Landau, is proposed to simulate the density of states of a
system with multiple macroscopic order parameters. The method breaks a
multidimensional random-walk process in phase space into many separate,
one-dimensional random-walk processes in well-defined subspaces. Each of these
random walks is constrained to a different set of values of the macroscopic
order parameters. When the multi-variable density of states is obtained for one
set of values of field-like model parameters, the density of states for any
other values of these parameters can be obtained by a simple transformation of
the total system energy. All thermodynamic quantities of the system can then be
rapidly calculated at any point in the phase diagram. We demonstrate how to use
the multi-variable density of states to draw the phase diagram, as well as
order-parameter probability distributions at specific phase points, for a model
spin-crossover material: an antiferromagnetic Ising model with ferromagnetic
long-range interactions. The field-like parameters in this model are an
effective magnetic field and the strength of the long-range interaction.",1703.03019v2
2014-03-04,Power and efficiency analysis of a realistic resonant tunneling diode thermoelectric,"Low-dimensional systems with sharp features in the density of states have
been proposed as a means to improving the efficiency of thermoelectric devices.
Quantum dot systems, which offer the sharpest density of states achievable,
however, suffer from low power outputs while bulk (3-D) thermoelectrics, while
displaying high power outputs, offer very low efficiencies. Here, we analyze
the use of a resonant tunneling diode structure that combines the best of both
aspects, that is, density of states distortion with a finite bandwidth due to
confinement that aids the efficiency and a large number of current carrying
transverse modes that enhances the total power output. We show that this device
can achieve a high power output ($\sim 0.3$ MW$/m^2$) at efficiencies of $\sim
40\%$ of the Carnot efficiency due to the contribution from these transverse
momentum states at a finite bandwidth of $kT/2$. We then provide a detailed
analysis of the physics of charge and heat transport with insights on parasitic
currents that reduce the efficiency. Finally, a comparison between the resonant
tunneling diode and a quantum dot device with comparable bandwidth reveals that
a similar performance requires ultra-dense areal quantum dot densities of $\sim
10^{12}/cm^2$.",1403.0694v2
2022-07-14,Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime,"Using the Jacobian matrix, we obtain theoretical expression of rigidity and
the density of states of two-dimensional amorphous solids consisting of
frictional grains in the linear response to an infinitesimal strain, in which
we ignore the dynamical friction caused by the slip processes of contact
points. The theoretical rigidity agrees with that obtained by molecular
dynamics simulations. We confirm that the rigidity is smoothly connected to the
value in the frictionless limit. For the density of states, we find that there
are two modes in the density of states for sufficiently small $k_{T}/k_{N}$,
which is the ratio of the tangential to normal stiffness. Rotational modes
exist at low frequencies or small eigenvalues, whereas translational modes
exist at high frequencies or large eigenvalues. The location of the rotational
band shifts to the high-frequency region with an increase in $k_{T}/k_{N}$ and
becomes indistinguishable from the translational band for large $k_{T}/k_{N}$.
The rigidity determined by the translational modes agrees with that obtained by
the molecular dynamics simulations, whereas the contribution of the rotational
modes is almost zero for small $k_{T}/k_{N}$.",2207.06632v4
2005-08-17,Meson Supercurrent State in High Density QCD,"We study the effect of a non-zero strange quark mass on the
color-flavor-locked (CFL) phase of high density quark matter. We have
previously shown that for a strange quark mass $m_s\sim m_u^{1/3}\Delta^{2/3}$
the CFL state becomes unstable toward the formation of a neutral kaon
condensate. Recently, several authors discovered that for $m_s\sim (2\Delta
p_F)^{1/2}$ the CFL state contains gapless fermions, and that the gapless modes
lead to an instability in current-current correlation functions. Using an
effective theory of the CFL state we demonstrate that this instability is
resolved by the formation of an inhomogeneous meson condensate, analogous to
Migdal's p-wave pion condensate. This state has a non-zero meson current which
is canceled by a backflow of gapless fermions.",0508190v2
2007-09-26,Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions,"We have obtained the exact ground state wave functions of the
Anderson-Hubbard model for different electron fillings on a 4x4 lattice with
periodic boundary conditions - for 1/2 filling such ground states have roughly
166 million states. When compared to the uncorrelated ground states (Hubbard
interaction set to zero) we have found strong evidence of the very effective
screening of the charge homogeneities due to the Hubbard interaction. We have
successfully modelled these local charge densities using a non-interacting
model with a static screening of the impurity potentials. In addition, we have
compared such wave functions to self-consistent real-space unrestricted
Hartree-Fock solutions and have found that these approximate ground state wave
functions are remarkably successful at reproducing the local charge densities,
and may indicate the role of dipolar backflow in producing a novel metallic
state in two dimensions.",0709.4212v2
2009-01-09,Tunneling conductance and local density of states in time-reversal symmetry breaking superconductors under the influence of an external magnetic field,"We consider different effects that arise when time-reversal symmetry breaking
superconductors are subjected to an external magnetic field, thus rendering the
superconductor to be in the mixed state. We focus in particular on two
time-reversal symmetry breaking order parameters which are believed to be
realized in actual materials: $p+\i p'$-wave and $d+\i s$- or $d+\i d'$-wave.
The first order parameter is relevant for Sr$_2$RuO$_4$, while the latter order
parameters have been suggested to exist near surfaces in some of the high-$T_c$
cuprates. We investigate the interplay between surface states and vortex states
in the presence of an external magnetic field and their influence on both the
tunneling conductance and the local density of states. Our findings may be
helpful to experimentally identify the symmetry of unconventional time-reversal
symmetry breaking superconducting states.",0901.1222v1
2009-06-05,Pseudogap in a thin film of a conventional superconductor,"A superconducting state is characterized by the gap in the electronic density
of states which vanishes at the superconducting transition temperature Tc. It
was discovered that in high temperature superconductors a noticeable depression
in the density of states still remains even at temperatures above Tc; this
feature being called pseudogap. Here we show that a pseudogap exists in a
conventional superconductor: ultrathin titanium nitride films over a wide range
of temperatures above Tc. Our study reveals that this pseudogap state is
induced by superconducting fluctuations and favored by two-dimensionality and
by the proximity to the transition to the insulating state. A general character
of the observed phenomenon provides a powerful tool to discriminate between
fluctuations as the origin of the pseudogap state, and other contributions in
the layered high temperature superconductor compounds.",0906.1193v2
2010-11-12,Irradiated bilayer graphene,"We describe the gated bilayer graphene system when it is subjected to intense
terahertz frequency electromagnetic radiation. We examine the electron band
structure and density of states via exact diagonalization methods within
Floquet theory. We find that dynamical states are induced which lead to
modification of the band structure. We first examine the situation where there
is no external magnetic field. In the unbiased case, dynamical gaps appear in
the spectrum which manifest as dips in the density of states. For finite
interlayer bias (where a static gap is present in the band structure of
unirradiated bilayer graphene), dynamical states may be induced in the static
gap. These states can show a high degree of valley polarization. When the
system is placed in a strong magnetic field, the radiation induces coupling
between the Landau levels which allows dynamical levels to exist. For strong
fields, this means the Landau levels are smeared to form a near-continuum of
states.",1011.3043v1
2011-02-23,Analytical approach for treating unitary quantum systems with initial mixed states,"The mixed states are important in quantum optics since they frequently appear
in the decoherence problems. When one of the components of the system is
prepared in the mixed state and the evolution operator of this system is not
available, one cannot deduce the density matrix. We present analytical approach
to accurately solve this problem. The approach can be applied on the condition
that the Schr\""odinger's equation of the system is solvable with any arbitrary
initial state. In deriving the solution we exploit the fact that any mixed
state can be expressed in terms of a phase state. The approach is illustrated
by deriving the density matrix of a single-mode heat environment interacting
asymmetrically with two qubits. Our results are in good agreement with the
available results in the literature. This approach opens new perspectives for
treating complicated systems and may impact other applications in the quantum
theory.",1102.4685v1
2011-09-28,Sub-gap in the Edge States of 2-D Chiral Superconductor with Rough Surface,"We discuss the rough surface effects on a two-dimensional chiral $k_x+ik_y$
superconductor. The atomic scale roughness at the surface is considered using
the random $S$ matrix model. The roughness effects on the self-consistent order
parameter, the surface mass current and the surface density of states are
studied using the quasi-classical theory. We find that the surface mass current
is suppressed by the surface roughness. The surface density of states shows a
quite similar behavior to that of superfluid ${}^3$He B phase. When the surface
is specular, the surface Andreev bound states form a band which fills the bulk
energy gap $\Delta_{\rm bulk}$. When the surface becomes diffusive, there
occurs a sharp upper edge of the surface bound states band and there opens a
sub-gap between the edge and the bulk energy gap. We show that this sub-gap is
induced by the repulsion between the surface bound states and the propagating
Bogoliubov quasi-particles through the second order process of roughness.",1109.6068v1
2014-07-03,The electronic structure of Co-substituted $\textrm{Fe}\textrm{Se}$ superconductor probed by soft X-ray spectroscopy and density functional theory,"We study the crystalline and electronic properties of the
$\textrm{Fe}_{1-x}\textrm{Co}_x\textrm{Se}$ system ($x=0$, 0.25, 0.5, 0.75, and
1.0) using X-ray diffraction, X-ray spectroscopy and density functional theory.
We show that the introduction of Co $3d$ states in FeSe relaxes the bond
strengths and induces a structural transition from tetragonal to hexagonal
whose crossover takes place at $x\approx0.38$. This structural transition in
turn modifies the magnetic order which can be related to the spin state. Using
resonant inelastic X-ray spectroscopy we estimate the spin state of the system;
FeSe is found to be in a high spin state (S=2), but Fe is reduced to a low spin
state upon Co substitution of $x \le 0.25$, well below the structural
transition. Finally, we show evidence that FeSe is a moderately correlated
system but the introduction of Co into the host lattice weakens the correlation
strength for $x\ge0.25$. These novel findings are important to unravel the
mechanisms responsible for the superconducting state in iron-chalcogenide
superconductors.",1407.0746v1
2020-01-13,"The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing","In this paper, we present a method to solve the quantum marginal problem for
symmetric $d$-level systems. The method is built upon an efficient
semi-definite program that determines the compatibility conditions of an
$m$-body reduced density with a global $n$-body density matrix supported on the
symmetric space. We illustrate the applicability of the method in central
quantum information problems with several exemplary case studies. Namely, (i) a
fast variational ansatz to optimize local Hamiltonians over symmetric states,
(ii) a method to optimize symmetric, few-body Bell operators over symmetric
states and (iii) a set of sufficient conditions to determine which symmetric
states cannot be self-tested from few-body observables. As a by-product of our
findings, we also provide a generic, analytical correspondence between
arbitrary superpositions of $n$-qubit Dicke states and
translationally-invariant diagonal matrix product states of bond dimension $n$.",2001.04440v1
2021-08-01,Large-scale spatio-temporal patterns in a ring of non-locally coupled oscillators with a repulsive coupling,"Non-locally coupled oscillators with a phase lag exhibit various non-trivial
spatio-temporal patterns such as the chimera states and the multi-twisted
states. We numerically study large-scale spatio-temporal patterns in a ring of
oscillators with a repulsive coupling with a phase delay parameter $\alpha$. We
find that the multi-chimera state disappears when $\alpha$ exceeds a critical
value. Analyzing the density of incoherent regions, we show that the transition
is analogous to that of directed percolation with two absorbing states, but
their critical behaviors are different. The multi-chimera state reappears when
$\alpha$ is further increased, exhibiting non-trivial spatio-temporal patterns
with a plateau in the density of incoherent regions. A transition from the
multi-chimera to multi-twisted states follows at a larger value of $\alpha$,
resulting in five collective phases in total.",2108.00427v1
2023-09-08,Electrical Control of Two-Dimensional Electron-Hole Fluids in the Quantum Hall Regime,"We study the influence of quantizing perpendicular magnetic fields on the
ground state of a bilayer with electron and hole fluids separated by an opaque
tunnel barrier. In the absence of a field, the ground state at low carrier
densities is a condensate of s-wave excitons that has spontaneous interlayer
phase coherence. We find that a series of phase transitions emerge at strong
perpendicular fields between condensed states and incompressible incoherent
states with full electron and hole Landau levels. When the electron and hole
densities are unequal, condensation can occur in higher angular momentum
electron-hole pair states and, at weak fields, break rotational symmetry. We
explain how this physics is expressed in dual-gate phase diagrams, and predict
transport and capacitively-probed thermodynamic signatures that distinguish
different states.",2309.04600v2
2006-04-05,Connection between accretion disk and superluminal radio jets and the role of radio plateau state in GRS 1915+105,"We investigate the association between the accretion disk during radio
plateau state and the following superluminal relativistic radio jets with peak
intensity varies from 200 mJy to 1000 mJy observed over a period of five years
and present the evidences of direct accretion disc-jet connection in
microquasar GRS 1915+105. We have analysed RXTE PCA/HEXTE X-ray data and have
found that the accretion rate, $\dot{m}_{accr}$, as inferred from the X-ray
flux, is very high during the radio plateaux. We suggest that the accretion
disk during the radio plateaux always associated with radiation-driven wind
which is manifested in the form of enhanced absorption column density for X-ray
and the depleted IR emission. We find that the wind density increases with the
accretion disk luminosity during the radio plateaux. The wind density is
similar to the density of the warm absorber proposed in extragalactic AGNs and
Quasars. We suggest a simple model for the origin of superluminal relativistic
jets. Finally, We discuss the implications of this work for galactic
microquasars and the extragalactic AGNs and Quasars.",0604096v1
1995-04-07,Density functional calculations for 4He droplets,"A novel density functional, which accounts correctly for the equation of
state, the static response function and the phonon-roton dispersion in bulk
liquid helium, is used to predict static and dynamic properties of helium
droplets. The static density profile is found to exhibit significant
oscillations, which are accompanied by deviations of the evaporation energy
from a liquid drop behaviour in the case of small droplets. The connection
between such oscillations and the structure of the static response function in
the liquid is explicitly discussed. The energy and the wave function of excited
states are then calculated in the framework of time dependent density
functional theory. The new functional, which contains backflow-like effects, is
expected to yield quantitatively correct predictions for the excitation
spectrum also in the roton wave-length range.",9504026v1
2000-07-19,From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature,"We investigate the density, current, and spin response functions above the
critical temperature for a system of three-dimensional fermions interacting via
an attractive short-range potential. In the strong-coupling (bosonic) limit of
this interaction, we identify the dominant diagrammatic contributions for a
``dilute'' system of composite bosons which form as bound-fermion pairs, and
compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and
density-of-states) terms occurring in the theory of superconducting
fluctuations above the critical temperature for a clean system in the
weak-coupling limit. We show that, at the zeroth order in the diluteness
parameter for the composite bosons, the Aslamazov-Larkin term still represents
formally the dominant contribution to the density and current response
functions, while the Maki-Thompson and density-of-states terms are strongly
suppressed. Corrections to the Aslamazov-Larkin term are then considered at the
next order in the diluteness parameter for the composite bosons. The spin
response function is also examined, and it is found to be exponentially
suppressed in the bosonic limit only when appropriate sets of diagrams are
considered simultaneously.",0007305v2
2001-08-23,The Dilute Bose-Einstein Condensate with Large Scattering Length,"We study a dilute Bose gas of atoms whose scattering length a is large
compared to the range of their interaction. We calculate the energy density of
the homogeneous Bose-Einstein condensate to second order in the low-density
expansion, expressing it in terms of a and a second parameter Lambda_* that
determines the low-energy observables in the 3-body sector. The second-order
correction to the energy density has a small imaginary part that reflects the
instability due to 3-body recombination. In the case of a trapped Bose-Einstein
condensate with large negative scattering length, we calculate the coefficient
of the 3-body mean-field term in the energy density in terms of a and Lambda_*.
It can be very large if there is an Efimov state near threshold.",0108380v2
2003-05-27,Unrestricted Hartree-Fock for Quantum Dots,"We present detailed results of Unrestricted Hartree-Fock (UHF) calculations
for up to eight electrons in a parabolic quantum dot. The UHF energies are
shown to provide rather accurate estimates of the ground-state energy in the
entire range of parameters from high densities with shell model characteristics
to low densities with Wigner molecule features. To elucidate the significance
of breaking the rotational symmetry, we compare Restricted Hartree-Fock (RHF)
and UHF. While UHF symmetry breaking admits lower ground-state energies,
misconceptions in the interpretation of UHF densities are pointed out. An
analysis of the orbital energies shows that for very strong interaction the UHF
Hamiltonian is equivalent to a tight-binding Hamiltonian. This explains why the
UHF energies become nearly spin independent in this regime while the RHF
energies do not. The UHF densities display an even-odd effect which is related
to the angular momentum of the Wigner molecule. In a weak transversal magnetic
field this even-odd effect disappears.",0305623v1
2005-10-31,An orbital-free self-consistent field approach for molecular clusters and liquids,"We present an ``orbital'' free density functional theory for computing the
quantum ground state of atomic clusters and liquids. Our approach combines the
Bohm hydrodynamical description of quantum mechanics with an information
theoretical approach to determine an optimal quantum density function in terms
of density approximates to a statistical sample. The ideas of Bayesian
statistical analysis and an expectation-maximization procedure are combined to
develop approximations to the quantum density and thus find the approximate
quantum force. The quantum force is then combined with a Lennard-Jones force to
simulate clusters of Argon atoms and to obtain the ground state configurations
and energies.
  As demonstration of the utility and flexibility of the approach, we compute
the lowest energy structures for small rare-glass clusters. Extensions to many
atom systems is straightforward.",0510826v1
2006-07-17,Density fingerprint of giant vortices in Fermi gases near a Feshbach resonance,"The structure of multiply quantized or giant vortex states in atomic Fermi
gases across a Feshbach resonance is studied within the context of
self-consistent Bogoliubov-de Gennes theory. The particle density profile of
vortices with $\kappa>1$ flux quanta is calculated. Owing to $\kappa$ discrete
branches of vortex core bound states, inside the core the density oscillates as
a function of the distance from the vortex line and displays a non-monotoic
dependence on the interaction strengths, in marked contrast to the singly
quantized case, in which the density depletes monotonically. This feature,
never reported so far, can make a direct visualization of the giant vortices in
atomic Fermi gases.",0607405v3
2004-08-31,Numerical study of the equation of state for two flavor QCD at non-zero baryon density,"We discuss the equation of state (EoS) for two flavor QCD at non-zero
temperature and density. Derivatives of $\ln Z$ with respect to quark chemical
potential $\mu_q$ are calculated up to sixth order. From this Taylor series,
the pressure, quark number density and associated susceptibilities are
estimated as functions of temperature and $\mu_q$. It is found that the
fluctuations in the quark number density increase in the vicinity of the phase
transition temperature and the susceptibilities start to develop a pronounced
peak as $\mu_q$ is increased. This suggests the presence of a critical endpoint
in the $(\mu_q, T)$ plane. Moreover, we comment on the hadron resonance gas
model, which explains well our simulation results below $T_c$.",0408046v1
2001-11-29,Lattice Study of the High Density State of SU(2)-QCD,"We investigate high density state of SU(2) QCD by using Lattice QCD
simulation with Wilson fermions. The ratio of fermion determinants is evaluated
at each step of the Metropol is link update by Woodbury formula. At
$\beta=0.7$, and $\kappa = 0.150$, we calculate the baryon number density, the
Polyakov lines, and the energy density of gluon sector with chemical potential
$\mu$=0 to 0.8 on the $4^{3} \times 12$ lattice. Behavior of the meson
propagators and diquark propagators with finite chemical potential are also
investigated.",0111082v1
2009-03-24,Random close packing of polydisperse hard spheres,"We study jammed configurations of hard spheres as a function of compression
speed using an event-driven molecular dynamics algorithm. We find that during
the compression, the pressure follows closely the metastable liquid branch
until the system gets arrested into a glass state as the relaxation time
exceeds the compression speed. Further compression yields a jammed
configuration that can be regarded as the infinite pressure configuration of
that glass state. Consequently, we find that the density of jammed packings
varies from 0.638 to 0.658 for polydisperse hard spheres and from 0.635 to
0.645 for pure hard spheres upon decreasing the compression rate. This
demonstrates that the density at which the systems falls out of equilibrium
determines the density at which the system jams at infinite pressure. In
addition, we give accurate data for the jamming density as a function of
compression rate and size polydispersity.",0903.4075v1
2010-09-15,Local density of states and Friedel oscillation in graphene,"We investigate the local density of states and Friedel oscillation in
graphene around a well localized impurity in Born approximation. In our
analytical calculations Green's function technique has been used taking into
account both the localized atomic wavefunctions in a tight-binding scheme and
the corresponding symmetries of the lattice. As a result we obtained long
wavelength oscillations in the density of electrons with long range behavior
proportional to the inverse square of the distance from the impurity. These
leading oscillations are out of phase on nearby lattice sites (in fact for an
extended defect they cancel each other within one unit cell), therefore a probe
with resolution worse than a few unit cells will experience only the next to
leading inverse cube decay of density oscillations even for a short range
scatterer.",1009.2905v1
2011-02-08,The Role of Exact Conditions in TDDFT,"This chapter is devoted to exact conditions in time-dependent density
functional theory. Many conditions have been derived for the exact ground-state
density functional, and several have played crucial roles in the construction
of popular approximations. We believe that the reliability of the most
fundamental approximation of any density functional theory, the local density
approximation (LDA), is due to the exact conditions that it satisfies. Improved
approximations should satisfy at least those conditions that LDA satisfies,
plus others. (Which others is part of the art of functional approximation). In
the time-dependent case, as we shall see, the adiabatic LDA (ALDA) plays the
same role as LDA in the ground-state case, as it satisfies many exact
conditions. But we do not have a generally applicable improvement beyond ALDA
that includes nonlocality in time. For TDDFT, we have a surfeit of exact
conditions, but that only makes finding those that are useful to impose an even
more demanding task.",1102.1706v2
2011-02-17,Theory of flux cutting and flux transport at the critical current of a type-II superconducting cylindrical wire,"I introduce a critical-state theory incorporating both flux cutting and flux
transport to calculate the magnetic-field and current-density distributions
inside a type-II superconducting cylinder at its critical current in a
longitudinal applied magnetic field. The theory is an extension of the elliptic
critical-state model introduced by Romero-Salazar and Perez-Rodriguez. The
vortex dynamics depend in detail upon two nonlinear effective resistivities for
flux cutting (\rho_\parallel) and flux flow (\rho_\perp), and their ratio r =
\rho_\parallel/\rho_\perp. When r < 1, the low relative efficiency of flux
cutting in reducing the magnitude of the internal magnetic-flux density leads
to a paramagnetic longitudinal magnetic moment. As a model for understanding
the experimentally observed interrelationship between the critical currents for
flux cutting and depinning, I calculate the forces on a helical vortex arc
stretched between two pinning centers when the vortex is subjected to a current
density of arbitrary angle \phi. Simultaneous initiation of flux cutting and
flux transport occurs at the critical current density J_c(\phi) that makes the
vortex arc unstable.",1102.3678v1
2011-07-28,"Two-neutron correlations in microscopic wave functions of He-6, He-8 and C-12","Two-neutron densities obtained from microscopic wave functions of $^6$He and
$^8$He are investigated to reveal di-neutron correlations. In particular, the
comparison of the two-neutron density with the product of one-neutron densities
is useful for a quantitative discussion of di-neutron correlations. The
calculations show that the S=0 spatial two-neutron correlation increases at the
surface of $^6$He$(0^+_1)$ and $^8$He$(0^+_2)$. The enhancement is remarkable
in the $^6$He$(0^+_1)$ ground state but not as prominent in the $^8$He$(0^+_1)$
ground state. Configuration mixing of many Slater determinants is essential to
describe the di-neutron correlations. Two-neutron densities in $^{12}$C wave
functions with $\alpha$-cluster structures are also studied.",1107.5616v1
2012-12-21,Density outbursts in a food web model with closed nutrient cycle,"A spatial three level food web model with a closed nutrient cycle is
presented and analyzed via Monte Carlo simulations. The time evolution of the
model reveals two asymptotic states: an absorbing one with all species being
extinct, and a coexisting one, in which concentrations of all species are
non-zero. There are two possible ways for the system to reach the absorbing
state. In some cases the densities increase very quickly at the beginning of a
simulation and then decline slowly and almost monotonically. In others, well
pronounced peaks in the $R$, $C$ and $D$ densities appear regularly before the
extinction. Those peaks correspond to density outbursts (waves) traveling
through the system. We investigate the mechanisms leading to the waves. In
particular, we show that the percolation of the detritus (i. e. the
accumulation of nutrients) is necessary for the emergence of the waves.
Moreover, our results corroborate the hypothesis that top-level predators play
an essential role in maintaining the stability of a food web (top-down
control).",1212.5538v1
2013-02-12,Quantum correlations which imply causation,"In ordinary, non-relativistic, quantum physics, time enters only as a
parameter and not as an observable: a state of a physical system is specified
at a given time and then evolved according to the prescribed dynamics. While
the state can, and usually does, extend across all space, it is only defined at
one instant of time, in conflict with special relativity where space and time
are treated on an equal footing. Here we ask what would happen if we defined
the notion of the quantum density matrix for multiple spatial and temporal
measurements. We introduce the concept of a pseudo-density matrix which treats
space and time indiscriminately. This matrix in general fails to be positive
for timelike separated measurements, motivating us to define a measure of
causality that discriminates between spacelike and timelike correlations.
Important properties of this measure, such as monotonicity under local
operations, are proved. Two qubit NMR experiments are presented that illustrate
how a temporal pseudo-density matrix approaches a genuinely allowed density
matrix as the amount of decoherence is increased between two consecutive
measurements.",1302.2731v1
2014-04-28,The density of states approach to dense quantum systems,"We develop a first-principle generalised density of state method for studying
numerically quantum field theories with a complex action. As a proof of
concept, we show that with our approach we can solve numerically the strong
sign problem of the $Z_3$ spin model at finite density. Our results are
confirmed by standard simulations of the theory dual to the considered model,
which is free from a sign problem. Our method opens new perspectives on ab
initio simulations of cold dense quantum systems, and in particular of
Yang-Mills theories with matter at finite densities, for which Monte Carlo
based importance sampling are unable to produce sufficiently accurate results.",1404.7187v1
2014-07-05,Orbital density wave order and electronic correlation driven insulating 1T-TaS2 monolayer,"We present the orbital resolved electronic properties of structurally
distorted 1T-TaS2 monolayers. After optimizing the crystal structures, we
obtain the lattice parameters and atomic positions in the star-of-David
structure, and show the low-temperature band structures of distorted bulk are
consistent with recent angle resolved photoemission spectroscopy (ARPES) data.
We further clearly demonstrate that $5d$ electrons of Ta form ordered
orbital-density-wave (ODW) state with dominant $5d_{3{z}^2-{r}^2}$ character in
central Ta, driving the one-dimensional metallic state in paramagnetic bulk and
half-filled insulator in monolayer. Meanwhile, the star-of-David distortion in
monolayers favors charge density wave and the flat band stabilizes
ferromagnetic density wave of Ta spins with the same wavevector of ODW 4/13
b_1+1/13 b2. We propose that $1$T-TaS$_{2}$ monolayer may pave a new way to
study the exciton physics, exciton-polaron coupling, and potential applications
for its exciton luminescence.",1407.1407v1
2014-11-06,Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice,"We investigate the harmonic-trap control of size and shape of Mott regions in
the Fermi Hubbard model on a square optical lattice. The use of Lanczos
diagonalization on clusters with twisted boundary conditions, followed by an
average over 50-80 samples, drastically reduce finite-size effects in some
ground state properties; calculations in the grand canonical ensemble together
with a local-density approximation (LDA) allow us to simulate the radial
density distribution. We have found that as the trap closes, the atomic cloud
goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of
Mott atoms reaches a maximum at the core-ring transition. A `phase diagram' in
terms of an effective density and the on-site repulsion is proposed, as a guide
to maximize the Mott coverage. We also predict that the usual experimentally
accessible quantities, the global compressibility and the average double
occupancy (rather, its density derivative) display detectable signatures of the
core-ring transition. Some spin correlation functions are also calculated, and
predict the existence N\'eel ordering within Mott cores and rings.",1411.1706v1
2015-05-14,Double-slit interference with charged particles. Density matrices and decoherence from time-dependent quantum Monte Carlo,"In this paper we apply the time-dependent quantum Monte Carlo (TDQMC) method
to explore a midified single- and double-slit diffraction of matter waves. By
using a simplified model of two electrons prepared in the ground state of an
atom (molecule) and then suddenly released we are able to calculate the
diffraction patterns in one spatial dimension in close correspondence with the
numerically exact results. Through the Coulomb repulsion the one electron
serves as an environment for the other thus introducing decoherence in the
quantum state which is easily quantified. It is demonstrated that the set of
single particle wave functions yield by TDQMC can be used to directly construct
density matrix for that particle without tracing out the other particles from
the density matrix of the whole system. In this way it is possible to build
explicitly time-dependent density matrices for different components of a
complex quantum system straight within the TDQMC algorithm which may widen our
understanding of quantum dynamics in many-body systems.",1505.03746v2
2016-06-26,Resonant inelastic scattering spectra at the Ir $L$-edge in Na$_2$IrO$_3$,"We analyze resonant x-ray scattering (RIXS) spectra in Na$_2$IrO$_3$ on the
basis of the itinerant electron picture. Employing a multi-orbital
tight-binding model on a honeycomb lattice, we find that the zigzag magnetic
order is the most stable with sizable energy gap in the one-electron band
within the Hartree-Fock approximation. We derive the RIXS spectra, which are
connected to the generalized density-density correlation function. We calculate
the spectra as a function of excitation energy $\omega$, within the random
phase approximation. The spectra consist of the peaks with $\omega$ $<20$ meV,
and of the peaks with $0.4<\omega<0.8$ eV. The former peaks are composed of
four bound states in the density-density correlation function, and may be
identified as the magnetic excitations, while the latter peaks are composed of
sixteen bound states below the energy continuum of individual electron-hole
pair excitations, and may be identified as the excitonic excitations. The
calculated spectra agree qualitatively with the recent RIXS experiment.",1606.08006v1
2018-06-18,Emergent superconductivity upon disordering a charge density wave ground state,"We explore the interplay of a charge density wave (CDW) order and s-wave
superconductivity (sSC) in a disordered system. Recent experiments on
1T-TiSe_2, where the pristine sample has a commensurate CDW order and the
superconductivity appears upon copper intercalation, motivates our study.
Starting with an extended Hubbard model, with parameters which yield a CDW
ground state within Hartree-Fock-Bogoliubov formalism in pure systems, we show
that the addition of disorder quickly wipes out the global charge order by
disrupting periodic modulation of density at some (low) strength of disorder.
Along with this, the subdominant superconducting order emerges in regions that
spatially anti-correlates with islands of strong local CDW order. The
short-range density modulations, however, continue to persist and show
discernible effects up to a larger disorder strength. The local CDW puddles
reduce in size with increasing disorder and they finally lose their relevance
in effecting the properties of the system. Our results have strong implications
for the experimental phase diagram of transition metal dichalcogenides.",1806.06568v1
2019-05-08,Finite response time in stripe formation by bacteria with density-suppressed motility,"Genetically engineered bacteria to increase the tumbling frequency of the
run-and-tumble motion for the higher local bacterial density form visible
stripe pattern composed of successive high and low density regions on an agar
plate. We propose a model that includes a simplified regulatory dynamics of the
tumbling frequency in individual cells to clarify the role of finite response
time. We show that the time-delay due to the response dynamics results in the
instability in a homogeneous steady state allowing a pattern formation. For
further understanding, we propose a simplified two-state model that allows us
to describe the response time dependence of the instability analytically. We
show that the instability occurs at long wave length as long as the response
time is comparable with the tumbling timescale and the non-linearity of the
response function to the change of the density is high enough. The minimum
system size to see the instability grows with the response time $\tau$,
proportional to $\sqrt{\tau}$ in the large delay limit.",1905.02933v2
2017-04-10,"Energy-transport systems for optical lattices: derivation, analysis, simulation","Energy-transport equations for the transport of fermions in optical lattices
are formally derived from a Boltzmann transport equation with a periodic
lattice potential in the diffusive limit. The limit model possesses a formal
gradient-flow structure like in the case of the energy-transport equations for
semiconductors. At the zeroth-order high temperature limit, the
energy-transport equations reduce to the whole-space logarithmic diffusion
equation which has some unphysical properties. Therefore, the first-order
expansion is derived and analyzed. The existence of weak solutions to the
time-discretized system for the particle and energy densities with periodic
boundary conditions is proved. The difficulties are the nonstandard degeneracy
and the quadratic gradient term. The main tool of the proof is a result on the
strong convergence of the gradients of the approximate solutions. Numerical
simulations in one space dimension show that the particle density converges to
a constant steady state if the initial energy density is sufficiently large,
otherwise the particle density converges to a nonconstant steady state.",1704.02845v1
2017-04-22,The finite density scaling laws of condensation phase transition in zero range processes on scale-free networks,"The dynamics of zero-range processes on complex networks is expected to be
influenced by the topological structure of underlying networks. A real space
complete condensation phase transition in the stationary state may occur. We
have studied the finite density effects of the condensation transition in both
the stationary and dynamical zero-range process on scale-free networks. By
means of grand canonical ensemble method, we predict analytically the scaling
laws of the average occupation number with respect to the finite density for
the steady state. We further explore the relaxation dynamics of the
condensation phase transition. By applying the hierarchical evolution and
scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte
Carlo simulations are performed and the predicted density scaling laws are
nicely validated.",1704.06750v4
2020-09-29,Novel feature of doubly bubble nuclei in 50$\leq$Z(N)$\leq$82 region along with magicity and weakly bound structure,"In this work, we identify a unique and novel feature of central density
depletion in both proton and neutron named as doubly bubble nuclei in
50$\leq$Z(N)$\leq$82 region. The major role of 2d-3s single-particle (s.p.)
states in the existence of halo and bubble nuclei is probed. The occupancy in
s.p. state 3s$_{1/2}$ leads to the extended neutron density distribution or
halo while the unoccupancy results in the central density depletion. By
employing the Relativistic Mean-Field (RMF) approach along with NL3* parameter,
the separation energies, single-particle energies, pairing energies, proton,
and neutron density profiles along with deformations of even-even nuclei are
investigated. Our results are in concise with few other theories and available
experimental data. Emergence on new shell closure and the magicity of
conventional shell closures are explored systematically in this yet unknown
region.",2009.13835v2
2014-05-06,Revealing single-trap condensate fragmentation by measuring density-density correlations after time of flight,"We consider ultracold bosonic atoms in a single trap in the Thomas-Fermi
regime, forming many-body states corresponding to stable macroscopically
fragmented two-mode condensates. It is demonstrated that upon free expansion of
the gas, the spatial dependence of the density-density correlations at late
times provides a unique signature of fragmentation. This hallmark of fragmented
condensate many-body states in a single trap is due to the fact that time of
flight modifies the correlation signal such that two opposite %with respect to
points in the expanding cloud become uncorrelated, in distinction to a
nonfragmented Bose-Einstein condensate, where they remain correlated.",1405.1344v2
2017-06-03,Kinetic Energy Density Functionals by Axiomatic Approach,"An axiomatic approach is herein used to determine the physically acceptable
forms for general $D$-dimensional kinetic energy density functionals (KEDF).
The resulted expansion captures most of the known forms of one-point KEDFs. By
statistically training the KEDF forms on a model problem of non-interacting
kinetic energy in 1D (6 terms only), the mean relative accuracy for 1000
randomly generated potentials is found to be better than the standard KEDF by
several orders of magnitudes. The accuracy improves with the number of occupied
states and was found to be better than $10^{-4}$ for a system with four
occupied states. Furthermore, we show that free fitting of the coefficients
associated with known KEDFs approaches the exactly analytic values. The
presented approach can open a new route to search for physically acceptable
kinetic energy density functionals and provide an essential step towards more
accurate large-scale orbital free density functional theory calculations.",1706.01957v1
2018-01-06,Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena,"We benchmark the ground state energies and the density profiles of atomic
repulsive Fermi gases in optical lattices computed via Density Functional
Theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations.
The main focus is on a half-filled one-dimensional optical lattices, for which
the DMC simulations performed within the fixed-node approach provide unbiased
results. This allows us to demonstrate that the local spin-density
approximation (LSDA) to the exchange-correlation functional of DFT is very
accurate in the weak and intermediate interactions regime, and also to
underline its limitations close to the strongly-interacting Tonks-Girardeau
limit and in very deep optical lattices. We also consider a three dimensional
optical lattice at quarter filling, showing also in this case the high accuracy
of the LSDA in the moderate interaction regime. The one-dimensional data
provided in this study may represent a useful benchmark to further develop DFT
methods beyond the LSDA and they will hopefully motivate experimental studies
to accurately measure the equation of state of Fermi gases in
higher-dimensional geometries.",1801.02095v2
2019-03-07,Pairing effects on neutron matter equation of state and symmetry energy at subsaturation densities,"Within the framework of BCS theory and Skyrme-Hartree-Fock model, we employ
various microscopic pairing gaps and effective pairing interactions to study
pairing effects on the equation of state (EOS) of neutron matter and the
symmetry energy at subsaturation densities. We find pairing effects may have
considerable contributions to the EOS of neutron matter at very low densities
($\lesssim 0.02~\rm{fm}^{-3}$), while only have a small impact on the symmetry
energy at subsatruation densities. In addition, the reliability of the
parabolic approximation for the isospin asymmetry dependence of nuclear matter
EOS with pairing correlations included is also discussed.",1903.03057v2
2019-03-27,Unitary circuits of finite depth and infinite width from quantum channels,"We introduce an approach to compute reduced density matrices for local
quantum unitary circuits of finite depth and infinite width. Suppose the
time-evolved state under the circuit is a matrix-product state with bond
dimension $D$; then the reduced density matrix of a half-infinite system has
the same spectrum as an appropriate $D\times D$ matrix acting on an ancilla
space. We show that reduced density matrices at different spatial cuts are
related by quantum channels acting on the ancilla space. This quantum channel
approach allows for efficient numerical evaluation of the entanglement spectrum
and R\'enyi entropies and their spatial fluctuations at finite times in an
infinite system. We benchmark our numerical method on random unitary circuits,
where many analytic results are available, and also show how our approach
analytically recovers the behaviour of the kicked Ising model at the self-dual
point. We study various properties of the spectra of the reduced density
matrices and their spatial fluctuations in both the random and
translation-invariant cases.",1903.11611v1
2019-07-04,Global dynamics and spatio-temporal patterns of predator-prey systems with density-dependent motion,"In this paper, we investigate the global boundedness, asymptotic stability
and pattern formation of predator-prey systems with density-dependent preytaxis
in a two-dimensional bounded domain with Neumann boundary conditions, where the
coefficients of motility (diffusion) and mobility (preytaxis) of the predator
are correlated through a prey density dependent motility function. We establish
the existence of classical solutions with uniform-in time bound and the global
stability of the spatially homogeneous prey-only steady states and coexistence
steady states under certain conditions on parameters by constructing Lyapunov
functionals. With numerical simulations, we further demonstrate that spatially
homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns
and chaotic spatio-temporal patterns are all possible for the parameters
outside the stability regime. We also find from numerical simulations that the
temporal dynamics between linearized system and nonlinear systems are quite
different, and the prey density-dependent motility function can trigger the
pattern formation.",1907.02312v1
2020-02-10,Complex density of continuum states in resonant quantum tunneling,"We introduce a complex-extended continuum level density and apply it to
one-dimensional scattering problems involving tunneling through finite-range
potentials. We show that the real part of the density is proportional to a real
""time shift"" of the transmitted particle, while the imaginary part reflects the
imaginary time of an instanton-like tunneling trajectory. We confirm these
assumptions for several potentials using the complex scaling method. In
particular, we show that stationary points of the potentials give rise to
specific singularities of both real and imaginary densities which represent
close analogues of excited-state quantum phase transitions in bound systems.",2002.03874v2
2020-05-05,The Sign of Three: Spin/Charge Density Waves at the Boundaries of Transition Metal Dichalcogenides,"One-dimensional grain boundaries of two-dimensional semiconducting {\MX} (M=
Mo,W; X=S,Se) transition metal di-chalcogenides are typically metallic at room
temperature. The metallicity has its origin in the lattice polarization, which
for these lattices with $D_{3h}$ symmetry is a topological invariant, and leads
to one-dimenional boundary states inside the band gap. For boundaries
perpendicular to the polarization direction, these states are necessarily 1/3
occupied by electrons or holes, making them susceptible to a metal-insulator
transition that triples the translation period. Using density-functional-theory
calculations we demonstrate the emergence of combined one-dimensional spin
density/charge density waves of that period at the boundary, opening up a small
band gap of $\sim 0.1$ eV. This unique electronic structure allows for soliton
excitations at the boundary that carry a fractional charge of $\pm 1/3\ e$.",2005.02519v1
2020-06-08,A density of states approach to the hexagonal Hubbard model at finite density,"We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes
the Wang-Landau algorithm to quantum systems with continuous degrees of
freedom, to the fermionic Hubbard model with repulsive interactions on the
honeycomb lattice. We compute the generalized density of states of the average
Hubbard field and divise two reconstruction schemes to extract physical
observables from this result. By computing the particle density as a function
of chemical potential we assess the utility of LLR in dealing with the sign
problem of this model, which arises away from half filling. We show that the
relative advantage over brute-force reweighting grows as the interaction
strength is increased and discuss possible future improvements.",2006.04607v2
2021-04-04,Hybrid stars can be self-bound,"Based on the properties of uniform nuclear matter at the nuclear saturation
density and basic thermodynamic relations, we first re-study the composition of
matter on the surface of normal neutron stars and hybrid stars. It is found
that the hybrid stars are composed of uniform hadronic matter on the surface
rather than heavy nuclei. Then we use the Walceka model and the self-consistent
NJL model to describe the equation of state of low-density hadrons and quark
matter at high densities respectively, and the P--interpolation method is
employed to connect the equation of state at the extreme densities to study
hybrid stars. As a result, we find that the obtained hybrid star mass-radius
relation and tidal deformability meet the latest astronomical data. More
importantly, we find that the hybrid stars we obtained can be self-bound rather
than gravitationally bound, which is completely different from previous related
studies.",2104.01519v2
2021-05-21,Few-to-many vortex states of density-angular-momentum coupled Bose-Einstein condensates,"Motivated by recent experiments, we theoretically study a gas of atomic
bosons confined in an elliptical harmonic trap; forming a quasi-two-dimensional
atomic Bose-Einstein condensate subject to a density-dependent gauge potential
which realises an effective density-angular-momentum coupling. We present exact
Thomas-Fermi solutions which allows us to identify the stable regimes of the
full parameter space of the model. Accompanying numerical simulations reveal
the effect of the interplay of the rigid body and density-angular-momentum
coupling for the elliptically confined condensate. By varying the strength of
the gauge potential and trap anisotropy we explore how the superfluid state
emerges in different experimentally accessible geometries, while for large
rotation strengths dense vortex lattices and concentric vortex ring
arrangements are obtained.",2105.10328v2
2021-08-05,Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density,"We investigate the behavior of self-propelled particles in infinite space
dimensions by comparing two powerful approaches in many-body dynamics: the
Fokker-Planck equation and dynamical mean-field theory. The dynamics of the
particles at low densities and infinite persistence time is solved in the
steady-state with both methods, thereby proving the consistency of the two
approaches in a paradigmatic out-of-equilibrium system. We obtain the analytic
expression for the pair distribution function and the effective self-propulsion
to first order in the density, confirming the results obtained in a previous
paper and extending them to the case of a non-monotonous interaction potential.
Furthermore, we obtain the transient behavior of active hard spheres when
relaxing from equilibrium to the nonequilibrium steady-state. Our results show
how collective dynamics is affected by interactions to first order in the
density, and point out future directions for further analytical and numerical
solutions of this problem.",2108.02407v2
2021-11-25,Finite-density-induced motility and turbulence of chimera solitons,"We consider a one-dimensional oscillatory medium with a coupling through a
diffusive linear field. In the limit of fast diffusion this setup reduces to
the classical Kuramoto-Battogtokh model. We demonstrate that for a finite
diffusion stable chimera solitons, namely localized synchronous domain in an
infinite asynchronous environment, are possible. The solitons are stable also
for finite density of oscillators, but in this case they sway with a nearly
constant speed. This finite-density-induced motility disappears in the
continuum limit, as the velocity of the solitons is inverse proportional to the
density. A long-wave instability of the homogeneous asynchronous state causes
soliton turbulence, which appears as a sequence of soliton mergings and
creations. As the instability of the asynchronous state becomes stronger, this
turbulence develops into a spatio-temporal intermittency.",2111.13177v1
2022-12-05,Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions,"We propose a general approach to analyse diagonal ordering patterns in
bosonic lattice models with algebraically decaying density-density interactions
on arbitrary lattices. The key idea is a systematic search for the
energetically best order on all unit cells of the lattice up to a given extent.
Using resummed couplings we evaluate the energy of the ordering patterns in the
thermodynamic limit using finite unit cells. We apply the proposed approach to
the atomic limit of the extended Bose-Hubbard model on the triangular lattice
at fillings $f=1/2$ and $f=1$. We investigate the ground-state properties of
the antiferromagnetic long-range Ising model on the triangular lattice and
determine a six-fold degenerate plain-stripe phase to be the ground state for
finite decay exponents. We also probe the classical limit of the
Fendley-Sengupta-Sachdev model describing Rydberg atom arrays. We focus on
arrangements where the atoms are placed on the sites or links of the Kagome
lattice. \changed{Our method provides a general framework to treat cristalline
structures resulting from long-range interactions.",2212.02091v2
2023-09-19,Maximum Entropy Density Control of Discrete-Time Linear Systems with Quadratic Cost,"This paper addresses the problem of steering the distribution of the state of
a discrete-time linear system to a given target distribution while minimizing
an entropy-regularized cost functional. This problem is called a maximum
entropy (MaxEnt) density control problem. Specifically, the running cost is
given by quadratic forms of the state and the control input, and the initial
and final distributions are Gaussian. We first reveal that our problem boils
down to solving two Riccati difference equations coupled through their boundary
values. Based on them, we give the closed-form expression of the unique optimal
policy. Next, we show that the optimal policy for the density control of the
time-reversed system can be obtained simultaneously with the forward-time
optimal policy. Finally, by considering the limit where the entropy
regularization vanishes, we derive the optimal policy for the unregularized
density control problem.",2309.10662v1
2000-11-07,Multiparticle entanglement and its experimental detection,"We discuss several aspects of multiparticle mixed state entanglement and its
experimental detection. First we consider entanglement between two particles
which is robust against disposals of other particles. To completely detect
these kinds of entanglement, full knowledge of the multiparticle density matrix
(or of all reduced density matrixes) is required. Then we review the relation
of the separability properties of l-partite splittings of a state $\rho$ to its
multipartite entanglement properties. We show that it suffices to determine the
diagonal matrix elements of $\rho$ in a certain basis in order to detect
multiparticle entanglement properties of $\rho$. We apply these observations to
analyze two recent experiments, where multiparticle entangled states of 3 (4)
particles were produced. Finally, we focus on bound entangled states
(non-separable, non-distillable states) and show that they can be activated by
joint actions of the parties. We also provide several examples which show the
activation of bound entanglement with bound entanglement.",0011025v1
2011-12-03,Spectroscopy of composite solid-state spin environments for improved metrology with spin ensembles,"For precision coherent measurements with ensembles of quantum spins the
relevant Figure-of-Merit (FOM) is the product of polarized spin density and
coherence lifetime, which is generally limited by the dynamics of the spin
environment. Here, we apply a coherent spectroscopic technique to characterize
the dynamics of the composite solid-state spin environment of Nitrogen-Vacancy
(NV) centers in room temperature diamond. For samples of very different NV
densities and impurity spin concentrations, we show that NV FOM values can be
almost an order of magnitude larger than previously achieved in other
room-temperature solid-state spin systems, and within an order of magnitude of
the state-of-the-art atomic system. We also identify a new mechanism for
suppression of electronic spin bath dynamics in the presence of a nuclear spin
bath of sufficient concentration. This suppression could inform efforts to
further increase the FOM for solid-state spin ensemble metrology and collective
quantum information processing.",1112.0667v2
1998-10-15,Matter wave interference using two-level atoms and resonant optical fields,"A theory of matter wave interference is developed in which resonant optical
fields interact with two-level atoms. When recoil effects are included, spatial
modulation of the atomic density can occur for times that are greater than or
comparable with the inverse recoil frequency. In this regime, the atoms exhibit
matter-wave interference. Two specific atom field geometries are considered. In
the first, atoms characterized by a homogeneous velocity distribution are
subjected to a single radiation pulse. The pulse excites the atoms which then
decay back to the lower state. The spatial modulation of the total atomic
density is calculated as a function of $t$, where $t$ is the time following the
pulse. In contrast to the normal Talbot effect, the spatially modulated density
is not a periodic function of $ t,$ owing to spontaneous emission; however,
after a sufficiently long time, the contribution from spontaneous processes no
longer plays a role and the Talbot periodicity is restored. In the second
atom-field geometry, there are two pulses separated by an interval $T$. The
atomic velocity distribution in this case is assumed to be inhomogeneously
broadened. In contrast to the normal Talbot-Lau effect, the spatially modulated
density is not a periodic function of $T$, owing to spontaneous emission;
however, for sufficiently long time, the contribution from spontaneous
processes no longer plays a role and the Talbot periodicity is restored. The
structure of the spatially modulated density is studied, and is found to mirror
the atomic density following the first pulse. The spatially modulated atomic
density serves as an indirect probe of the distribution of spontaneously
emitted radiation.",9810028v1
2013-11-18,Competition Between Kondo Screening and Magnetism at the LaAlO$_3$/SrTiO$_3$ Interface,"We present a theory of magnetic and magneto-transport phenomena at
LaAlO$_3$/SrTiO$_3$ interfaces, which as a central ingredient includes coupling
between the conduction bands and local magnetic moments originating from charge
traps at the interface. Tuning the itinerant electron density in the model
drives transitions between a heavy Fermi liquid phase with screened moments and
various magnetic states. The dependence of the magnetic phenomena on the
electron density or gate voltage stems from competing magnetic interactions
between the local moments and the different conduction bands. At low densities
only the lowest conduction band, composed of the $d_{xy}$ orbitals of Ti, is
occupied. Its antiferromagnetic interaction with the local moments leads to
screening of the moments at a Kondo scale that increases with density. However,
above a critical density, measured in experiments to be $n_c\approx 1.7\times
10^{13} cm^{-2}$, the $d_{xz}$ and $d_{yz}$ bands begin to populate. Their
ferromagnetic interaction with the local moments competes with the
antiferromagnetic interaction of the $d_{xy}$ band leading to eventual
reduction of the Kondo scale with density. We explain the distinct magneto
transport regimes seen in experiments as manifestations of the magnetic phase
diagram computed from the model. We present new data showing a relation between
the anomalous Hall effect and the resistivity in the system. The data strongly
suggests that the concentration of local magnetic moments affecting the
transport in the system is much lower than the carrier density, in accord with
the theoretical model.",1311.4541v2
2021-11-18,Perceiving and Modeling Density is All You Need for Image Dehazing,"In the real world, the degradation of images taken under haze can be quite
complex, where the spatial distribution of haze is varied from image to image.
Recent methods adopt deep neural networks to recover clean scenes from hazy
images directly. However, due to the paradox caused by the variation of real
captured haze and the fixed degradation parameters of the current networks, the
generalization ability of recent dehazing methods on real-world hazy images is
not ideal.To address the problem of modeling real-world haze degradation, we
propose to solve this problem by perceiving and modeling density for uneven
haze distribution. We propose a novel Separable Hybrid Attention (SHA) module
to encode haze density by capturing features in the orthogonal directions to
achieve this goal. Moreover, a density map is proposed to model the uneven
distribution of the haze explicitly. The density map generates positional
encoding in a semi-supervised way. Such a haze density perceiving and modeling
capture the unevenly distributed degeneration at the feature level effectively.
Through a suitable combination of SHA and density map, we design a novel
dehazing network architecture, which achieves a good complexity-performance
trade-off. The extensive experiments on two large-scale datasets demonstrate
that our method surpasses all state-of-the-art approaches by a large margin
both quantitatively and qualitatively, boosting the best published PSNR metric
from 28.53 dB to 33.49 dB on the Haze4k test dataset and from 37.17 dB to 38.41
dB on the SOTS indoor test dataset.",2111.09733v1
2001-06-28,Phase separation frustrated by the long range Coulomb interaction II: Applications,"The theory of first order density-driven phase transitions with frustration
due to the long range Coulomb (LRC) interaction develop on paper I of this
series is applied to the following physical systems: i) the low density
electron gas ii) electronic phase separation in the low density three
dimensional $t-J$ model iii) in the manganites near the charge ordered phase.
We work in the approximation that the density within each phase is uniform and
we assume that the system separates in spherical drops of one phase hosted by
the other phase with the distance between drops and the drop radius much larger
than the interparticle distance. For i) we study a well known apparent
instability related to a negative compressibility at low densities. We show
that this does not lead to macroscopic drop formation as one could expect
naively and the system is stable from this point of view. For ii) we find that
the LRC interaction significantly modifies the phase diagram favoring uniform
phases and mixed states of antiferromagnetic (AF) regions surrounded by
metallic regions over AF regions surrounded by empty space. For iii) we show
that the dependence of local densities of the phases on the overall density
found in paper I gives a non-monotonous behavior of the Curie temperature on
doping in agreement with experiments.",0106608v1
2018-03-09,Sequential Outlier Detection based on Incremental Decision Trees,"We introduce an online outlier detection algorithm to detect outliers in a
sequentially observed data stream. For this purpose, we use a two-stage
filtering and hedging approach. In the first stage, we construct a multi-modal
probability density function to model the normal samples. In the second stage,
given a new observation, we label it as an anomaly if the value of
aforementioned density function is below a specified threshold at the newly
observed point. In order to construct our multi-modal density function, we use
an incremental decision tree to construct a set of subspaces of the observation
space. We train a single component density function of the exponential family
using the observations, which fall inside each subspace represented on the
tree. These single component density functions are then adaptively combined to
produce our multi-modal density function, which is shown to achieve the
performance of the best convex combination of the density functions defined on
the subspaces. As we observe more samples, our tree grows and produces more
subspaces. As a result, our modeling power increases in time, while mitigating
overfitting issues. In order to choose our threshold level to label the
observations, we use an adaptive thresholding scheme. We show that our adaptive
threshold level achieves the performance of the optimal pre-fixed threshold
level, which knows the observation labels in hindsight. Our algorithm provides
significant performance improvements over the state of the art in our wide set
of experiments involving both synthetic as well as real data.",1803.03674v1
2017-06-05,On the effect of Lyman alpha trapping during the initial collapse of massive black hole seeds,"One viable seeding mechanism for supermassive black holes is the direct
gaseous collapse route in pre-galactic dark matter halos, producing objects on
the order of $10^4 - 10^6$ solar masses. These events occur when the gas is
prevented from cooling below $10^4$ K that requires a metal-free and relatively
H$_2$-free medium. The initial collapse cools through atomic hydrogen
transitions, but the gas becomes optically thick to the cooling radiation at
high densities. We explore the effects ofLyman-$\alpha$ trapping in such a
collapsing system with a suite of Monte Carlo radiation transport calculations
in uniform density and isotropic cases that are based from a cosmological
simulation. Our method includes both non-coherent scattering and two-photon
line cooling. We find that Lyman-$\alpha$ radiation is marginally trapped in
the parsec-scale gravitationally unstable central cloud, allowing the
temperature to increase to 50,000 K at a number density of $3 \times 10^4$
cm$^{-3}$ and increasing the Jeans mass by a factor of five. The effective
equation of state changes from isothermal at low densities to have an adiabatic
index of 4/3 around the temperature maximum and then slowly retreats back to
isothermal at higher densities. Our results suggest that Lyman-$\alpha$
trapping delays the initial collapse by raising the Jeans mass. Afterward the
high density core cools back to $10^4$ K that is surrounded by a warm envelope
whose inward pressure may alter the fragmentation scales at high densities.",1706.01467v2
2024-01-19,Robust Multi-Modal Density Estimation,"Development of multi-modal, probabilistic prediction models has lead to a
need for comprehensive evaluation metrics. While several metrics can
characterize the accuracy of machine-learned models (e.g., negative
log-likelihood, Jensen-Shannon divergence), these metrics typically operate on
probability densities. Applying them to purely sample-based prediction models
thus requires that the underlying density function is estimated. However,
common methods such as kernel density estimation (KDE) have been demonstrated
to lack robustness, while more complex methods have not been evaluated in
multi-modal estimation problems. In this paper, we present ROME (RObust
Multi-modal density Estimator), a non-parametric approach for density
estimation which addresses the challenge of estimating multi-modal, non-normal,
and highly correlated distributions. ROME utilizes clustering to segment a
multi-modal set of samples into multiple uni-modal ones and then combines
simple KDE estimates obtained for individual clusters in a single multi-modal
estimate. We compared our approach to state-of-the-art methods for density
estimation as well as ablations of ROME, showing that it not only outperforms
established methods but is also more robust to a variety of distributions. Our
results demonstrate that ROME can overcome the issues of over-fitting and
over-smoothing exhibited by other estimators, promising a more robust
evaluation of probabilistic machine learning models.",2401.10566v1
2016-11-11,Exploring the Thermal State of the Low-Density Intergalactic Medium at z=3 with an Ultra-High Signal-to-Noise QSO Spectrum,"At low densities the standard ionisation history of the intergalactic medium
(IGM) predicts a decreasing temperature of the IGM with decreasing density once
hydrogen (and helium) reionisation is complete. Heating the high-redshift,
low-density IGM above the temperature expected from photo-heating is difficult,
and previous claims of high/rising temperatures in low density regions of the
Universe based on the probability density function (PDF) of the opacity in
Lyman-$\alpha$ forest data at $2<z<4$ have been met with considerable
scepticism, particularly since they appear to be in tension with other
constraints on the temperature-density relation (TDR). We utilize here an
ultra-high signal-to-noise spectrum of the QSO HE0940-1050 and a novel
technique to study the low opacity part of the PDF. We show that there is
indeed evidence (at 90% confidence level) that a significant volume fraction of
the under-dense regions at $z \sim 3$ has temperatures as high or higher than
those at densities comparable to the mean and above. We further demonstrate
that this conclusion is nevertheless consistent with measurements of a slope of
the TDR in over-dense regions that imply a decreasing temperature with
decreasing density, as expected if photo-heating of ionised hydrogen is the
dominant heating process. We briefly discuss implications of our findings for
the need to invoke either spatial temperature fluctuations, as expected during
helium reionization, or additional processes that heat a significant volume
fraction of the low-density IGM.",1611.03805v1
2019-03-02,Stretched or noded orbital densities and self-interaction correction in density functional theory,"Semi-local approximations to the density functional for the
exchange-correlation energy of a many-electron system necessarily fail for
lobed one-electron densities, including not only the familiar stretched
densities but also the less familiar but closely-related noded ones. The
Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local
approximation makes that approximation exact for all one-electron ground- or
excited-state densities and accurate for stretched bonds. When the minimization
of the PZ total energy is made over real localized orbitals, the orbital
densities can be noded, leading to energy errors in many-electron systems.
Minimization over complex localized orbitals yields nodeless orbital densities,
which reduce but typically do not eliminate the SIC errors of atomization
energies. Other errors of PZ SIC remain, attributable to the loss of the exact
constraints and appropriate norms that the semi-local approximations satisfy,
and suggesting the need for a generalized SIC. These conclusions are supported
by calculations for one-electron densities, and for many-electron molecules.
While PZ SIC raises and improves the energy barriers of standard generalized
gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens
the atomization energies of molecules. Thus PZ SIC raises the energy more as
the nodality of the valence localized orbitals increases from atoms to
molecules to transition states. PZ SIC is applied here in particular to the
SCAN meta-GGA, for which the correlation part is already self-interaction-free.
That property makes SCAN a natural first candidate for a generalized SIC.",1903.00611v2
2013-05-10,Superhorizon entanglement entropy from particle decay in inflation,"In inflationary cosmology all particle states decay as a consequence of the
lack of kinematic thresholds. The decay of an initial single particle state
yields an \emph{entangled quantum state of the product particles}. We
generalize and extend a manifestly unitary field theoretical method to obtain
the time evolution of the quantum state. We consider the decay of a light
scalar field with mass $M\ll H$ with a cubic coupling in de Sitter space-time.
Radiative corrections feature an infrared enhancement manifest as poles in
$\Delta=M^2/3H^2$ and we obtain the quantum state in an expansion in $\Delta$.
To leading order in $\Delta$ the pure state density matrix describing the decay
of a particle with sub-horizon wavevector is dominated by the emission of
superhorizon quanta, describing \emph{entanglement between superhorizon and
subhorizon fluctuations and correlations across the horizon}. Tracing over the
superhorizon degrees of freedom yields a mixed state density matrix from which
we obtain the entanglement entropy. Asymptotically this entropy grows with the
\emph{physical} volume as a consequence of more modes of the decay products
crossing the Hubble radius. A generalization to localized wave packets is
provided. The cascade decay of single particle states into many particle states
is discussed. We conjecture on \emph{possible} impact of these results on
non-gaussianity and on the ``low multipole anomalies'' of the CMB.",1305.2441v2
2021-11-04,Quantum dark solitons in the 1D Bose gas: From single to double dark-solitons,"We study quantum double dark-solitons by constructing corresponding quantum
states in the Lieb-Liniger model for the one-dimensional Bose gas. Here we
expect that the Gross-Pitaevskii (GP) equation should play a central role in
the long distance mean-field behavior of the 1D Bose gas. We first introduce
novel quantum states of a single dark soliton with a nonzero winding number. We
show them by exactly evaluating not only the density profile but also the
profiles of the square amplitude and phase of the matrix element of the field
operator between the $N$-particle and $(N-1)$-particle states. For elliptic
double dark-solitons, the density and phase profiles of the corresponding
states almost perfectly agree with those of the classical solutions,
respectively, in the weak coupling regime. We then show that the scheme of the
mean-field product state is quite effective for the quantum states of double
dark solitons. Assigning the ideal Gaussian weights to a sum of the excited
states with two particle-hole excitations we obtain double dark-solitons of
distinct narrow notches with different depths. We suggest that the mean-field
product state should be well approximated by the ideal Gaussian weighted sum of
the low excited states with a pair of particle-hole excitations. The results of
double dark-solitons should be fundamental and useful for constructing quantum
multiple dark-solitons.",2111.02686v1
2008-10-25,Light nuclei quasiparticle energy shift in hot and dense nuclear matter,"Nuclei in dense matter are influenced by the medium. In the cluster mean
field approximation, an effective Schr\""odinger equation for the $A$-particle
cluster is obtained accounting for the effects of the correlated medium such as
self-energy, Pauli blocking and Bose enhancement. Similar to the single-baryon
states (free neutrons and protons), the light elements ($2 \le A \le 4$,
internal quantum state $\nu$) are treated as quasiparticles with energies
$E_{A,\nu}(\vec P; T, n_n,n_p)$. These energies depend on the center of mass
momentum $\vec P$, as well as temperature $T$ and the total densities $n_n,n_p$
of neutrons and protons, respectively. No $\beta$ equilibrium is considered so
that $n_n, n_p$ (or the corresponding chemical potentials $\mu_n, \mu_p$) are
fixed independently.
  For the single nucleon quasiparticle energy shift, different approximate
expressions such as Skyrme or relativistic mean field approaches are well
known. Treating the $A$-particle problem in appropriate approximations, results
for the cluster quasiparticle shifts are given. Properties of dense nuclear
matter at moderate temperatures in the subsaturation density region considered
here are influenced by the composition. This in turn is determined by the
cluster quasiparticle energies, in particular the formation of clusters at low
densities when the temperature decreases, and their dissolution due to Pauli
blocking as the density increases. Our finite-temperature Green function
approach covers different limiting cases: The low-density region where the
model of nuclear statistical equilibrium and virial expansions can be applied,
and the saturation density region where a mean field approach is possible.",0810.4645v1
2019-03-04,Quantum Joule Expansion of One-Dimensional Systems,"We investigate the Joule expansion of nonintegrable quantum systems that
contain bosons or spinless fermions in one-dimensional lattices. A barrier
initially confines the particles to be in half of the system in a thermal state
described by the canonical ensemble and is removed at time $t = 0$. We
investigate the properties of the time-evolved density matrix, the diagonal
ensemble density matrix and the corresponding canonical ensemble density matrix
with an effective temperature determined by the total energy conservation using
exact diagonalization. The weights for the diagonal ensemble and the canonical
ensemble match well for high initial temperatures that correspond to negative
effective final temperatures after the expansion. At long times after the
barrier is removed, the time-evolved R\'enyi entropy of subsystems bigger than
half can equilibrate to the thermal entropy with exponentially small
fluctuations. The time-evolved reduced density matrix at long times can be
approximated by a thermal density matrix for small subsystems. Few-body
observables, like the momentum distribution function, can be approximated by a
thermal expectation of the canonical ensemble with strongly suppressed
fluctuations. The negative effective temperatures for finite systems go to
nonnegative temperatures in the thermodynamic limit for bosons, but is a true
thermodynamic effect for fermions, which is confirmed by finite temperature
density matrix renormalization group calculations. We propose the Joule
expansion as a way to dynamically create negative temperature states for
fermion systems with repulsive interactions.",1903.01414v3
2022-08-15,A Semi-analytical Method of Calculating Nuclear Collision Trajectory in the QCD Phase Diagram,"The finite nuclear thickness affects the energy density $\epsilon(t)$ and
conserved-charge densities such as the net-baryon density $n_B(t)$ produced in
heavy ion collisions. While the effect is small at high collision energies
where the Bjorken energy density formula for the initial state is valid, the
effect is large at low collision energies, where the nuclear crossing time is
not small compared to the parton formation time. The temperature $T(t)$ and
chemical potentials $\mu(t)$ of the dense matter can be extracted from the
densities for a given equation of state (EOS). Therefore, including the nuclear
thickness is essential for the determination of the $T$-$\mu_B$ trajectory in
the QCD phase diagram for relativistic nuclear collisions at low to moderate
energies such as the RHIC-BES energies. In this proceeding, we will first
discuss our semi-analytical method that includes the nuclear thickness effect
and its results on the densities $\epsilon(t), n_B(t), n_Q(t)$, and $n_S(t)$.
Then, we will show the extracted $T(t), \mu_B(t), \mu_Q(t)$, and $\mu_S(t)$ for
a quark-gluon plasma using the ideal gas EOS with quantum or Boltzmann
statistics. Finally, we will show the results on the $T$-$\mu_B$ trajectories
in relation to the possible location of the QCD critical end point. This
semi-analytical model provides a convenient tool for exploring the trajectories
of nuclear collisions in the QCD phase diagram.",2208.07203v1
2016-03-11,Instability of three-band Tomonaga-Luttinger liquid: renormalization group analysis and possible application to K2Cr3As3,"Motivated by recently discovered quasi-one-dimensional superconductor
K$_{2}$Cr$_{3}$As$_{3}$ with $D_{3h}$ lattice symmetry, we study
one-dimensional three-orbital Hubbard model with generic electron repulsive
interaction described by intra-orbital repulsion $U$, inter-orbital repulsion,
and Hund's coupling $J$. As extracted from density functional theory
calculation, two of the three atomic orbitals are degenerate ($E^{\prime}$
states) and the third one is non-degenerate ($A^{\prime}_1$), and the system is
presumed to be at an incommensurate filling. With the help of bosonization, we
have usual three-band Tomonaga-Luttinger liquid for the normal state. Possible
charge density wave (CDW), spin density wave (SDW) and superconducting (SC)
instabilities are analyzed by renormalization group. The ground state depends
on the ratio $J/U$ and is sensitive to the degeneracy of $E^{\prime}$ bands. At
$0<J<U/3$, spin-singlet SC state is favored, while spin-triplet
superconductivity will be favored in the region $U/3<J<U/2$. The SDW state has
the lowest energy only in the unphysical parameter region $J>U/2$. When the
two-fold degeneracy of $E^{\prime}$ bands is lifted, SDW instability has the
tendency to dominate over the spin-singlet SC state at $0<J<U/3$, while the
order parameter of the spin-triplet SC state will be modulated by a phase
factor $2\Delta k_F x$ at $U/3<J<U/2$. Possible experimental consequences and
applications to K$_{2}$Cr$_{3}$As$_{3}$ are discussed.",1603.03651v3
2005-05-03,On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids,"The energy route to the equation of state of hard-sphere fluids is
ill-defined since the internal energy is just that of an ideal gas and thus it
is independent of density. It is shown that this ambiguity can be avoided by
considering a square-shoulder interaction and taking the limit of vanishing
shoulder width. The resulting hard-sphere equation of state coincides exactly
with the one obtained through the virial route. Therefore, the energy and
virial routes to the equation of state of hard-sphere fluids can be considered
as equivalent.",0505067v1
1999-03-09,State determination in continuous measurement,"The possibility of determining the state of a quantum system after a
continuous measurement of position is discussed in the framework of quantum
trajectory theory. Initial lack of knowledge of the system and external noises
are accounted for by considering the evolution of conditioned density matrices
under a stochastic master equation. It is shown that after a finite time the
state of the system is a pure state and can be inferred from the measurement
record alone. The relation to emerging possibilities for the continuous
experimental observation of single quanta, as for example in cavity quantum
electrodynamics, is discussed.",9903030v1
2012-09-14,The Quantum State of Inflationary Perturbations,"This article reviews the properties of the quantum state of inflationary
perturbations. After a brief description of the inflationary background, the
wavefunction of the Mukhanov-Sasaki variable is calculated and shown to be that
of a strongly squeezed state. The corresponding Wigner function and density
matrix, which are convenient tools to characterize the properties of a quantum
state, are also evaluated. Finally, the issue of definite outcomes for
inflation is discussed.",1209.3092v1
2016-07-22,The Symmetry of Current of the Coherent State From the View of O(3) sigma-model,"In this paper, we apply the reduced density trajectory, phi-mapping
topological current theory and Ginzberg-Landau model to study the current of
the coherent state. We give the new expression of the current of the coherent
state. Based on this expression, the symmetry of the coherence is studied. We
find that the current of the coherent state corresponds to the supercurrent of
two-condensate system. The partial wave functions of the coherence carry new
charges and their interaction is mediated by new U(1) gauge potential.",1607.06548v1
2011-01-10,One plus two-body random matrix ensembles with parity: Density of states and parity ratios,"One plus two-body embedded Gaussian orthogonal ensemble of random matrices
with parity [EGOE(1+2)-$\pi$] generated by a random two-body interaction
(modeled by GOE in two particle spaces) in the presence of a mean-field, for
spinless identical fermion systems, is defined, generalizing the two-body
ensemble with parity analyzed by Papenbrock and Weidenm\""{u}ller [Phys. Rev. C
{\bf 78}, 054305 (2008)], in terms of two mixing parameters and a gap between
the positive $(\pi=+)$ and negative $(\pi=-)$ parity single particle (sp)
states. Numerical calculations are used to demonstrate, using realistic values
of the mixing parameters appropriate for some nuclei, that the EGOE(1+2)-$\pi$
ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue
densities (i.e. state densities). The random matrix model also generates many
features in parity ratios of state densities that are similar to those
predicted by a method based on the Fermi-gas model for nuclei. We have also
obtained, by applying the formulation due to Chang et al [Ann. Phys. (N.Y.)
{\bf 66}, 137 (1971)], a simple formula for the spectral variances defined over
fixed-$(m_1,m_2)$ spaces, where $m_1$ is the number of fermions in the +ve
parity sp states and $m_2$ is the number of fermions in the -ve parity sp
states. Similarly, using the binary correlation approximation, in the dilute
limit, we have derived expressions for the lowest two shape parameters. The
smoothed densities generated by the sum of fixed-$(m_1,m_2)$ Gaussians with
lowest two shape corrections describe the numerical results in many situations.
The model also generates preponderance of +ve parity ground states for small
values of the mixing parameters and this is a feature seen in nuclear shell
model results.",1101.1711v2
2007-03-19,Collisional excitation of OH(6049 MHz) masers in supernova remnant - molecular cloud interactions,"OH (1720 MHz) masers serve as indicators of SNR - molecular cloud interaction
sites. These masers are collisionally excited in warm (50-100K) shocked gas
with densities of order 1e5 cm^-3 when the OH column density is in the range
1e16-1e17 cm^-2. Here I present excitation calculations which show that when
the OH column density exceeds 1e17 cm^-2 at similar densities and temperatures,
the inversion of the 1720 MHz line switches off and instead the 6049 MHz
transition in the first excited rotational state of OH becomes inverted. This
line may serve as a complementary signal of warm, shocked gas when the OH
column density is large.",0703508v2
2002-03-28,Single-particle density matrix and superfluidity in the two-dimensional Bose Coulomb fluid,"A study by W. R. Magro and D. M. Ceperley [Phys. Rev. Lett. {\bf 73}, 826
(1994)] has shown that the ground state of the two-dimensional fluid of charged
bosons with logarithmic interactions is not Bose-condensed, but exhibits
algebraic off-diagonal order in the single-particle density matrix $\rho(r)$.
We use a hydrodynamic Hamiltonian expressed in terms of density and phase
operators, in combination with an $f$-sum rule on the superfluid fraction, to
reproduce these results and to extend the evaluation of the density matrix to
finite temperature $T$. This approach allows us to treat the liquid as a
superfluid in the absence of a condensate. We find that (i) the off-diagonal
order arises from the correlations between phase fluctuations; and (ii) the
exponent in the power-law decay of $\rho(r)$ is determined by the superfluid
density $n_s(T)$. We also find that the plasmon gap in the single-particle
energy spectrum at long wavelengths decreases with increasing $T$ and closes at
the critical temperature for the onset of superfluidity.",0203594v1
2003-01-22,First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach,"A coagulation-decoagulation model is introduced on a chain of length L with
open boundary. The model consists of one species of particles which diffuse,
coagulate and decoagulate preferentially in the leftward direction. They are
also injected and extracted from the left boundary with different rates. We
will show that on a specific plane in the space of parameters, the steady state
weights can be calculated exactly using a matrix product method. The model
exhibits a first-order phase transition between a low-density and a
high-density phase. The density profile of the particles in each phase is
obtained both analytically and using the Monte Carlo Simulation. The two-point
density-density correlation function in each phase has also been calculated. By
applying the Yang-Lee theory we can predict the same phase diagram for the
model. This model is further evidence for the applicability of the Yang-Lee
theory in the non-equilibrium statistical mechanics context.",0301407v2
2006-03-30,Unconventional Density Waves in Organic Conductors and in Superconductors,"Unconventional density waves (UDW) are one of the ground states in metallic
crystalline solids and have been speculated already in 1968. However, more
focused studies on UDW started only recently, perhaps after the identification
of the low temperature phase in alpha-(BEDT-TTF)_2KHg(SCN)_4 as unconventional
charge density wave (UCDW) in 2002. More recently, the metallic phase of
Bechgaard salts (TMTSF)_2X with X=PF_6 and ReO_4 under both pressure and
magnetic field appears to be unconventional spin density wave (USDW). The
pseudogap regime of high T_c superconductors LSCO, YBCO, Bi2212 and the one in
CeCoIn_5 belong to d-wave density waves (d-DW).
  In these identifications, the angular dependent magnetoresistance and the
giant Nernst effect have played the crucial role. These are the simplest
manifestations of the Landau quantization of quasiparticle energy in UDW in the
presence of magnetic field (the Nersesyan effect). Also we speculate that UDW
will be most likely found in alpha$-(BEDT-TTF)_2I_3, alpha-(BEDT-TTF)_2I_2Br,
kappa-(BEDT-TTF)_2Cu(NCS)_2, kappa-(BEDT-TTF)_2Cu(CN)_2Br,
lambda-(BEDT)_2GaCl_4 and in many other organic compounds.",0603806v1
1995-03-09,Deconfinement transition in a one-dimensional model at finite temperature,"We present a model for quark matter with a density dependent quark-quark
(confining) potential, which allows to describe a deconfinement phase
transition as the system evolves from a low density assembly of bound
structures to a high density free Fermi gas of quarks. A proper account of the
many-body correlations induced by the medium is crucial in order to disentangle
this behaviour, which does not uniquely stem from the the naive density
dependence of the interaction. We focus here on the effects of finite
(non-zero) temperatures on the dynamical behaviour of the system. In particular
we investigate the ground state energy per particle and the pair correlation
function, from which one can extract the relevant information about the quarks
being confined or not; the temperature dependence of the transition density is
also derived.",9503281v1
1994-12-07,Relativistic Density Dependent Hartree-Fock Approach for Finite Nuclei,"The self-energy of the Dirac Brueckner-Hartree-Fock calculation in nuclear
matter is parametrized by introducing density-dependent coupling constants of
isoscalar mesons in the relativistic Hartree-Fock (RHF) approach where
isoscalar meson $\sigma$ , $\omega$ and isovector meson $\pi$, $\rho$
contributions are included. The RHF calculations with density dependent
coupling constants obtained in this way not only reproduce the nuclear matter
saturation properties , but also provide the self-energy with an appropriate
density dependence. The relativistic density dependent Hartree-Fock (RDHF)
approach contains the features of the relativistic G matrix and in the meantime
simplifies the calculation. The ground state properties of spherical nuclei
calculated in the RDHF are in good agreement with the experimental data. The
contribution of isovector mesons $\pi$ and $\rho$ , especially the contribution
of the tensor coupling of $\rho$ meson , are discussed in this paper.",9412010v1
2005-08-03,"Connection between the ""Strutinsky level density"" and the semiclassical level density (published version)","We establish an analytical link between the level density obtained by means
of the Strutinsky averaging method, and the semiclassical level density. This
link occurs only in the so-called ""asymptotic limit"". It turns out that the
Strutinsky method amounts to an approximation to the semiclassical method. This
approximation contains an unavoidable remainder which constitutes an intrinsic
noise in comparison to the semiclassical method. Thus, the ""old"" problem of the
dependency of the Strutinsky procedure on the two free smoothing parameters of
the averaging is intimately connected to this noise. On the other hand, we
demonstrate that the noise of the method is small in the average density of
states and in the average energy, whereas it might be non-negligible in the
shell correction itself. In order to improve this method, we give a ""rule""
which consists simply of minimizing the relative error made on the average
energy.",0508010v2
2001-08-30,Collectivity in the optical response of small metal clusters,"The question whether the linear absorption spectra of metal clusters can be
interpreted as density oscillations (collective ``plasmons'') or can only be
understood as transitions between distinct molecular states is still a matter
of debate for clusters with only a few electrons. We calculate the
photoabsorption spectra of Na2 and Na5+ comparing two different methods:
quantum fluid-dynamics and time-dependent density functional theory. The
changes in the electronic structure associated with particular excitations are
visualized in ``snapshots'' via transition densities. Our analysis shows that
even for the smallest clusters, the observed excitations can be interpreted as
intuitively understandable density oscillations. For Na5+, the importance of
self-interaction corrections to the adiabatic local density approximation is
demonstrated.",0108071v1
2006-04-26,Non-universality of commonly used correlation-energy density functionals,"The correlation energies of the helium isoelectronic sequence and of Hooke's
atom isoelectronic sequence have been evaluated using an assortment of local,
gradient and meta-gradient density functionals. The results are compared with
the exact correlation energies, showing that while several of the more recent
density functionals reproduce the exact correlation energies of the helium
isoelectronic sequence rather closely, none is satisfactory for Hooke's atom
isoelectronic sequence. It is argued that the uniformly acceptable results for
the helium sequence can be explained through simple scaling arguments that do
not hold for Hooke's atom sequence, so that the latter system provides a more
sensitive testing ground for approximate density functionals. This state of
affairs calls for further effort towards formulating correlation-energy density
functionals that would be truly universal at least for spherically-symmetric
two-fermion systems.",0604206v1
2007-09-07,Surprises in the suddenly-expanded infinite well,"I study the time-evolution of a particle prepared in the ground state of an
infinite well after the latter is suddenly expanded. It turns out that the
probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour:
for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is
constant on finite intervals for $x$. Elements of theoretical explanation are
given by analyzing the singular component of the second derivative
$\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some
specific times, which easily allow to show that, at these times, the density
organizes itself into regular patterns provided the size of the box in large
enough; more, above some critical time-dependent size, the density patterns are
independent of the expansion parameter. It is seen how the density at these
times simply results from a construction game with definite rules acting on the
pieces of the initial density.",0709.1101v1
2007-10-31,On the phase diagram of QCD at finite isospin density,"Using a canonical formalism, we determine the equation of state and the phase
diagram of eight-flavour QCD, as a function of temperature and isospin density.
Two mechanisms are at work: Bose condensation of pions at high density, and
deconfinement at high temperature. We study their interplay and find that on
our small and coarse lattice the first order deconfinement transition appears
to end at a critical point at finite density. We investigate the strength of
the overlap and of the sign problems and discuss implications for the baryonic
density case.",0711.0023v1
2008-08-07,Cosmological constant in a quantum fluid model,"Possible analogies between vacuum state and quantum fluid provide a model to
study vacuum energy density induced by thermal corrections, space-time
curvature, boundary conditions and quantum back-reaction. We find that vacuum
energy density in this quantum fluid model is not naturally of the order of the
matter energy density. We show how higher-order corrections in quantum
back-reaction can also contribute to vacuum energy density, and how the
cosmological expansion is a manifestation of an universe out of mechanical
equilibrium. This last fact implies that simple thermodynamic arguments are not
enough to explain the cosmological constant problem due to the calculation of
the associated vacuum energy density requires first the knowing of the
underlying microscopic physics of vacuum.",0808.1047v2
2009-10-30,Evidence for a Self-Bound Liquid State and the Commensurate-Incommensurate Coexistence in 2D $^3$He on Graphite,"We made heat-capacity measurements of two dimensional (2D) $^3$He adsorbed on
graphite preplated with monolayer $^4$He in a wide temperature range (0.1 $\leq
T \leq$ 80 mK) at densities higher than that for the 4/7 phase (= 6.8
nm$^{-2}$). In the density range of 6.8 $\leq \rho \leq$ 8.1 nm$^{-2}$, the 4/7
phase is stable against additional $^3$He atoms up to 20% and they are promoted
into the third layer. We found evidence that such promoted atoms form a
self-bound 2D Fermi liquid with an approximate density of 1 nm$^{-2}$ from the
measured density dependence of the $\gamma$-coefficient of heat capacity. We
also show evidence for the first-order transition between the commensurate 4/7
phase and the ferromagnetic incommensurate phase in the second layer in the
density range of 8.1 $\leq \rho \leq$ 9.5 nm$^{-2}$.",0910.5905v1
2012-03-11,Effect of orbital-overlap dependence in density functionals,"The semilocal meta generalized gradient approximation (MGGA) for the
exchange-correlation functional of Kohn-Sham (KS) density functional theory can
yield accurate ground-state energies simultaneously for atoms, molecules,
surfaces, and solids, due to the inclusion of kinetic energy density as an
input. We study for the first time the effect and importance of the dependence
of MGGA on the kinetic energy density through the dimensionless inhomogeneity
parameter, $\alpha$, that characterizes the extent of orbital overlap. This
leads to a simple and wholly new MGGA exchange functional, which interpolates
between the single-orbital regime, where $\alpha=0$, and the slowly varying
density regime, where $\alpha \approx 1$, and then extrapolates to $\alpha \to
\infty$. When combined with a variant of the Perdew-Burke-Erzerhof (PBE) GGA
correlation, the resulting MGGA performs equally well for atoms, molecules,
surfaces, and solids.",1203.2308v2
2012-07-09,Entropy-driven liquid-liquid separation in supercooled water,"Twenty years ago Poole et al. (Nature 360, 324, 1992) suggested that the
anomalous properties of supercooled water may be caused by a critical point
that terminates a line of liquid-liquid separation of lower-density and
higher-density water. Here we present an explicit thermodynamic model based on
this hypothesis, which describes all available experimental data for
supercooled water with better quality and with fewer adjustable parameters than
any other model suggested so far. Liquid water at low temperatures is viewed as
an 'athermal solution' of two molecular structures with different entropies and
densities. Alternatively to popular models for water, in which the
liquid-liquid separation is driven by energy, the phase separation in the
athermal two-state water is driven by entropy upon increasing the pressure,
while the critical temperature is defined by the 'reaction' equilibrium
constant. In particular, the model predicts the location of density maxima at
the locus of a near-constant fraction (about 0.12) of the lower-density
structure.",1207.2101v2
2012-09-05,Saha Equation Normalized to Total Atomic Number Density,"The Saha equation describes the relative number density of consecutive
ionization levels of a given atomic species under conditions of thermodynamic
equilibrium in an ionized gas. Because the number density in the denominator
may be very small, special steps must be taken to ensure numerical stability.
In this paper we recast the equation into a form in which each ionization
fraction is normalized by the total number density of the atomic species,
analogous to the Boltzmann equation describing the distribution of excitation
states for a given ion.",1209.1111v2
2013-07-01,Nuclear Level Densities at High Excitation Energies and for Large Particle Numbers,"Starting from an independent-particle model with a finite and arbitrary set
of single-particle energies, we develop an analytical approximation to the
many-body level density $\rho_A(E)$ and to particle-hole densities. We use
exact expressions for the low-order moments and cumulants to derive approximate
expressions for the coefficients of an expansion of these densities in terms of
orthogonal polynomials. The approach is asymptotically (mass number $A \gg 1$)
convergent and, for large $A$, covers about 20 orders of magnitude near the
maximum of $\rho_A(E)$ (i.e., about half the spectrum). Densities of accessible
states are calculated using the Fermi-gas model.",1307.0400v2
2015-08-24,The thermodynamics of Fermi gases in three dimensional fuzzy space,"We use the recently derived density of states for a particle confined to a
spherical well in three dimensional fuzzy space to compute the thermodynamics
of a gas of non-interacting fermions confined to such a well. Special emphasis
is placed on non-commutative effects and in particular non-commutative
corrections to the thermodynamics at low densities and temperatures are
computed where the non-relativistic approximation used here is valid.
Non-commutative effects at high densities are also identified, the most
prominent being the existence of a minimal volume at which the gas becomes
incompressible. The latter is closely related to a low/high density duality
exhibited by these systems, which in turn is a manifestation of an
infra-red/ultra violet duality in the single particle spectrum. Both
non-rotating and slowly rotating gasses are studied. Approximations are
benchmarked against exact numerical computations for the non-rotating case and
several other properties of the gas are demonstrated with numerical
computations. Finally, a non-commutative gas confined by gravity is studied and
several novel features regarding the mass-radius relation, density and entropy
are highlighted.",1508.05799v1
2016-02-11,Density-Matrix Propagation Driven by Semiclassical Correlation,"Methods based on propagation of the one-body reduced density-matrix hold much
promise for the simulation of correlated many-electron dynamics far from
equilibrium, but difficulties with finding good approximations for the
interaction term in its equation of motion have so far impeded their
application. These difficulties include the violation of fundamental physical
principles such as energy conservation, positivity conditions on the density,
or unchanging natural orbital occupation numbers. We review some of the recent
efforts to confront these problems, and explore a semiclassical approximation
for electron correlation coupled to time-dependent Hartree-Fock propagation. We
find that this approach captures changing occupation numbers, and excitations
to doubly-excited states, improving over TDHF and adiabatic approximations in
density-matrix propagation. However, it does not guarantee $N$-representability
of the density-matrix, consequently resulting sometimes in violation of
positivity conditions, even though a purely semiclassical treatment preserves
these conditions.",1602.03723v1
2016-03-18,Breadth versus depth: Interactions that stabilize particle assemblies to changes in density or temperature,"We use inverse methods of statistical mechanics to explore trade-offs
associated with designing interactions to stabilize self-assembled structures
against changes in density or temperature. Specifically, we find
isotropic,convex-repulsive pair potentials that maximize the density range for
which a two-dimensional square lattice is the stable ground state subject to a
constraint on the chemical potential advantage it exhibits over competing
structures (i.e., 'depth' of the associated minimum on the chemical potential
hypersurface). We formulate the design problem as a non-linear program, which
we solve numerically. This allows us to efficiently find optimized interactions
for a wide range of possible chemical potential constraints. We find that
assemblies designed to exhibit a large chemical potential advantage at a
specified density have a smaller overall range of densities for which they are
stable. This trend can be understood by considering the separation-dependent
features of the pair potential and its gradient required to enhance the
stability of the target structure relative to competitors. Using molecular
dynamics simulations, we further show that potentials designed with larger
chemical potential advantages exhibit higher melting temperatures.",1603.05989v1
2018-07-05,Revisiting Perspective Information for Efficient Crowd Counting,"Crowd counting is the task of estimating people numbers in crowd images.
Modern crowd counting methods employ deep neural networks to estimate crowd
counts via crowd density regressions. A major challenge of this task lies in
the perspective distortion, which results in drastic person scale change in an
image. Density regression on the small person area is in general very hard. In
this work, we propose a perspective-aware convolutional neural network (PACNN)
for efficient crowd counting, which integrates the perspective information into
density regression to provide additional knowledge of the person scale change
in an image. Ground truth perspective maps are firstly generated for training;
PACNN is then specifically designed to predict multi-scale perspective maps,
and encode them as perspective-aware weighting layers in the network to
adaptively combine the outputs of multi-scale density maps. The weights are
learned at every pixel of the maps such that the final density combination is
robust to the perspective distortion. We conduct extensive experiments on the
ShanghaiTech, WorldExpo'10, UCF_CC_50, and UCSD datasets, and demonstrate the
effectiveness and efficiency of PACNN over the state-of-the-art.",1807.01989v3
2018-12-31,A variational approach to London dispersion interactions without density distortion,"We introduce a class of variational wavefunctions that capture the long-range
interaction between neutral systems (atoms and molecules) without changing the
diagonal of the density matrix of each monomer. The corresponding energy
optimization yields explicit expressions for the dispersion coefficients in
terms of the ground-state pair densities of the isolated systems, providing a
clean theoretical framework to build new approximations in several contexts. As
the individual monomer densities are kept fixed, we can also unambiguously
assess the effect of the density distortion on van der Waals interactions: for
example, we obtain virtually exact dispersion coefficients between two hydrogen
atoms up to $C_{10}$, and relative errors below $0.2\%$ in other simple cases.",1812.11840v2
2019-11-17,"Equation of state, structure and diffusion coefficients of Gay-Berne fluids: the cases $κ'$ = 5; 10; 15; 20","We performed extensive molecular dynamics simulations to obtain
pressure-density phase diagram, orientational order parameter, pair correlation
functions and translational diffusion coefficients of Gay-Berne fluids.
Different sets of parameters were employed for the Gay-Berne potential, in
particular we studied the cases $\kappa'=5, 10, 15, 20$ and $\kappa=3$,
$\mu=2$, $\nu=1$ at different conditions of density and temperature. The
structure was analyzed in terms of the order parameter and the pair correlation
functions. We found that for the highest value $\kappa'=20$ the region where
pressure increases with density is significantly reduced at low temperatures;
additionally the pressure shows several decays with density as an indicative
that several structural phases can take place. These effects are discussed in
terms of the pair correlation functions. For higher temperatures the pressure
shows only two decays for all $\kappa'$'s studied. As this parameter increases
its value those decays are shifted to lower densities.",1911.07366v3
2012-01-30,"Fractional calculus, completely monotonic functions, a generalized Mittag-Leffler function and phase-space consistency of separable augmented densities","Under the separability assumption on the augmented density, a distribution
function can be always constructed for a spherical population with the
specified density and anisotropy profile. Then, a question arises, under what
conditions the distribution constructed as such is non-negative everywhere in
the entire accessible subvolume of the phase-space. We rediscover necessary
conditions on the augmented density expressed with fractional calculus. The
condition on the radius part R(r^2) -- whose logarithmic derivative is the
anisotropy parameter -- is equivalent to R(1/w)/w being a completely monotonic
function whereas the condition on the potential part is stated as its
derivative up to the order not greater than 3/2-b being non-negative (where b
is the central limiting value for the anisotropy parameter). We also derive the
set of sufficient conditions on the separable augmented density for the
non-negativity of the distribution, which generalizes the condition derived for
the generalized Cuddeford system by Ciotti & Morganti to arbitrary separable
systems. This is applied for the case when the anisotropy is parameterized by a
monotonic function of the radius of Baes & Van Hese. The resulting criteria are
found based on the complete monotonicity of generalized Mittag-Leffler
functions.",1201.6113v1
2014-06-11,Embedded fragment stochastic density functional theory,"We develop a method in which the electronic densities of small fragments
determined by Kohn-Sham density functional theory (DFT) are embedded using
stochastic DFT to form the exact density of the full system. The new method
preserves the scaling and the simplicity of the stochastic DFT but cures the
slow convergence that occurs when weakly coupled subsystems are treated. It
overcomes the spurious charge fluctuations that impair the applications of the
original stochastic DFT approach. We demonstrate the new approach on a
fullerene dimer and on clusters of water molecules and show that the density of
states and the total energy can be accurately described with a relatively small
number of stochastic orbitals.",1406.2782v1
2016-08-08,Stabilized density gradient theory algorithm for modeling interfacial properties of pure and mixed systems,"Density gradient theory (DGT) allows fast and accurate determination of
surface tension and density profile through a phase interface. Several
algorithms have been developed to apply this theory in practical calculations.
While the conventional algorithm requires a reference substance of the system,
a modified ""stabilized density gradient theory"" (SDGT) algorithm is introduced
in our work to solve DGT equations for multiphase pure and mixed systems. This
algorithm makes it possible to calculate interfacial properties accurately at
any domain size larger than the interface thickness without choosing a
reference substance or assuming the functional form of the density profile. As
part of DGT inputs, the perturbed chain statistical associating fluid theory
(PC-SAFT) equation of state (EoS) was employed for the first time with the SDGT
algorithm. PC-SAFT has excellent performance in predicting liquid phase
properties as well as phase behaviors. The SDGT algorithm with the PC-SAFT EoS
was tested and compared with experimental data for several systems. Numerical
stability analyses were also included in each calculation to verify the
reliability of this approach for future applications.",1608.02535v1
2017-11-06,Distributions of pore sizes and atomic densities in binary glasses revealed by molecular dynamics simulations,"We report on the results of a molecular dynamics simulation study of binodal
glassy systems, formed in the process of isochoric rapid quenching from a
high-temperature fluid phase. The transition to vitreous state occurs due to
concurrent spinodal decomposition and solidification of the matter. The study
is focused on topographies of the porous solid structures and their dependence
on temperature and average density. To quantify the pore-size distributions, we
put forth a scaling relation that provides a robust data collapse in systems
with high porosity. We also find that the local density of glassy phases is
broadly distributed, and, with increasing average glass density, a distinct
peak in the local density distribution is displaced toward higher values.",1711.01689v1
2020-03-19,Is friction essential for dilatancy and shear jamming in granular matter?,"Granular packings display the remarkable phenomenon of dilatancy [1], wherein
their volume increases upon shear deformation. Conventional wisdom and previous
results suggest that dilatancy, as also the related phenomenon of shear-induced
jamming, requires frictional interactions [2, 3]. Here, we investigate the
occurrence of dilatancy and shear jamming in frictionless packings. We show
that the existence of isotropic jamming densities {\phi}j above the minimal
density, the J-point density {\phi}J [4, 5], leads both to the emergence of
shear-induced jamming and dilatancy. Packings at {\phi}J form a significant
threshold state into which systems evolve in the limit of vanishing pressure
under constant pressure shear, irrespective of the initial jamming density
{\phi}j. While packings for different {\phi}j display equivalent scaling
properties under compression [6], they exhibit striking differences in
rheological behaviour under shear. The yield stress under constant volume shear
increases discontinuously with density when {\phi}j > {\phi}J, contrary to the
continuous behavior in generic packings that jam at {\phi}J [4, 7].",2003.08815v1
2020-05-19,Polytropic stars in bootstrapped Newtonian gravity,"We study self-gravitating stars in the bootstrapped Newtonian picture for
polytropic equations of state. We consider stars that span a wide range of
compactness values. Both matter density and pressure are sources of the
gravitational potential. Numerical solutions show that the density profiles can
be well approximated by Gaussian functions. Later we assume Gaussian density
profiles to investigate the interplay between the compactness of the source,
the width of the Gaussian density profile and the polytropic index. We also
dedicate a section to comparing the pressure and density profiles of the
bootstrapped Newtonian stars to the corresponding General Relativistic
solutions. We also point out that no Buchdahl limit is found, which means that
the pressure can in principle support a star of arbitrarily large compactness.
In fact, we find solutions representing polytropic stars with compactness above
the Buchdhal limit.",2005.09378v2
2020-08-24,Effects of the pseudo-gap on the field-induced kinetic energy density of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals,"We report on magnetization experiments from which we obtain the field-induced
kinetic energy density, $E_k$, in the superconducting phase of several
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ single crystal samples. The kinetic energy
magnitude changes according to the characteristic reduction of the
single-electron density of states produced by the pseudogap in the underdoped
limit. Moreover, a remarkable peak of $E_k$ occurring at the specific holes
density $p\sim0.18$ is related to a van Hove singularity due to the pseudogap
closure. We also extracted the superfluid density, $\rho_s$. We conclude that
$E_k$ and $\rho_s$ are related to the pseudogap energy scale. This result is
understood as an evidence of the coexistence between superconductivity and the
pseudogap phenomenon in the Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ cuprate
compound.",2008.10674v1
2020-08-26,Self-consistent screening enhances stability of the nonequilibrium excitonic insulator phase,"The nonequilibrium excitonic insulator (NEQ-EI) is an excited state of matter
characterized by a finite density of coherent excitons and a time-dependent
macroscopic polarization. The stability of this exciton superfluid as the
density grows is jeopardized by the increased screening efficiency of the
looser excitons. In this work we put forward a Hartree plus Screened Exchange
HSEX scheme to predict the critical density at which the transition toward a
free electron-hole plasma occurs. The dielectric function is calculated
self-consistently using the NEQ-EI polarization and found to vanish in the
long-wavelength limit. This property makes the exciton superfluid stable up to
relatively high densities. Numerical results for the MoS$_{2}$ monolayers
indicate that the NEQ-EI phase survives up to densities of the order of
$10^{12}\mathrm{cm}^{-2}$.",2008.11417v1
2021-01-14,Interpreting and Predicting Tactile Signals for the SynTouch BioTac,"In the human hand, high-density contact information provided by afferent
neurons is essential for many human grasping and manipulation capabilities. In
contrast, robotic tactile sensors, including the state-of-the-art SynTouch
BioTac, are typically used to provide low-density contact information, such as
contact location, center of pressure, and net force. Although useful, these
data do not convey or leverage the rich information content that some tactile
sensors naturally measure. This research extends robotic tactile sensing beyond
reduced-order models through 1) the automated creation of a precise
experimental tactile dataset for the BioTac over a diverse range of physical
interactions, 2) a 3D finite element (FE) model of the BioTac, which
complements the experimental dataset with high-density, distributed contact
data, 3) neural-network-based mappings from raw BioTac signals to not only
low-dimensional experimental data, but also high-density FE deformation fields,
and 4) mappings from the FE deformation fields to the raw signals themselves.
The high-density data streams can provide a far greater quantity of
interpretable information for grasping and manipulation algorithms than
previously accessible.",2101.05452v1
2021-08-18,Jeans instability in an expanding universe with dissipation,"Jeans instability is analysed in an expanding universe within the framework
of BGK model of the Boltzmann equation and Poisson equations. The background is
characterized by a comoving Maxwellian distribution function and a space-time
Newtonian gravitational potential which satisfy the BGK model of the Boltzmann
and Poisson equations without the necessity to invoke ""Jeans swindle"". The
perturbations of the distribution function and Newtonian gravitational
potentials from their background states are represented by plane waves of small
amplitudes and a differential equation for the density contrast is determined.
The density contrast differential equation was solved numerically and it is
shown: (i) Jeans instability is characterized by perturbation wavelengths
larger than Jeans wavelength where the density contrast grows with time. The
growth of the density contrast is less accentuated for the case where the
particle collisions are considered due to an energy dissipation; (ii) for
perturbation wavelengths smaller than Jeans wavelength the density contrast has
an oscillatory behavior in time and the oscillations for the case where the
collisions are taken into account fade away in time due to the energy
dissipation.",2108.08068v1
2021-10-13,Constraints on the maximum densities of neutron stars from postmerger gravitational waves with third-generation observations,"Using data from 289 numerical relativity simulations of merging binary
neutron stars, we identify, for the first time, a robust quasi-universal
relation connecting the postmerger peak gravitational-wave frequency and the
value of the density at the center of the maximum mass nonrotating neutron
star. This relation offers a new possibility for precision equation-of-state
constraints with next-generation ground-based gravitational-wave
interferometers. Mock Einstein Telescope observations of fiducial events
indicate that Bayesian inferences can constrain the maximum density to
${\sim}15\%$ ($90\%$ confidence level) for a single signal at the minimum
sensitivity threshold for a detection. If the postmerger signal is included in
a full-spectrum (inspiral-merger-postmerger) analysis of such signal, the
pressure-density function can be tightly constrained up to the maximum density,
and the maximum neutron star mass can be measured with an accuracy better than
$12\%$ ($90\%$ confidence level).",2110.06957v3
2024-01-29,Topological Detection of Phenomenological Bifurcations with Unreliable Kernel Densities,"Phenomenological (P-type) bifurcations are qualitative changes in stochastic
dynamical systems whereby the stationary probability density function (PDF)
changes its topology. The current state of the art for detecting these
bifurcations requires reliable kernel density estimates computed from an
ensemble of system realizations. However, in several real world signals such as
Big Data, only a single system realization is available -- making it impossible
to estimate a reliable kernel density. This study presents an approach for
detecting P-type bifurcations using unreliable density estimates. The approach
creates an ensemble of objects from Topological Data Analysis (TDA) called
persistence diagrams from the system's sole realization and statistically
analyzes the resulting set. We compare several methods for replicating the
original persistence diagram including Gibbs point process modelling, Pairwise
Interaction Point Modelling, and subsampling. We show that for the purpose of
predicting a bifurcation, the simple method of subsampling exceeds the other
two methods of point process modelling in performance.",2401.16563v1
2024-03-02,Driven charge density modulation by spin density wave and their coexistence interplay in SmFeAsO: A first-principles study,"We use density functional theory to investigate effects of spin-orbit
coupling and single-stripe-type antiferromagnetic (sAFM) ordering on the
crystal structure and electronic properties of SmFeAsO. The results indicate
that AFM ordering causes the crystal structure transition from tetragonal to
orthorhombic, along with increase in the height of As atoms from Fe layer due
to magnetostriction. It also leads to the opening of partial band gaps, the
emergence of a prominent peak near Fermi energy (EF) in the density of states
(DOS) and a reduction in Fermi surface nesting. The study finds a correlation
between the calculated area under the DOS curve, spanning from EF to the first
peak above it, and the optimal electron-doped concentration required for
inducing superconductivity in SmFeAsO. The findings suggest that spin and
charge density waves can play important roles in the superconducting mechanism
of Fe-based superconductors. Our calculations demonstrate that spin-orbit
coupling reduces electronic correlation.",2403.01111v1
2000-07-20,On the quantum mechanical nature in liquid NMR quantum computing,"The quantum nature of bulk ensemble NMR quantum computing --the center of
recent heated debate, is addressed. Concepts of the mixed state and
entanglement are examined, and the data in a 2 qubit liquid NMR quantum
computation are analyzed. It is pointed out that the key problem in the current
debate is the understanding of entanglement in a mixed state system. The
following points are concluded in this Letter: 1)Density matrix describes the
""state"" of an average particle in an ensemble. It can not describe the state of
an individual particle in an ensemble in detail; 2) Entanglement is a property
of the wave function of a quantum particle(such as an molecule in a liquid NMR
sample). Separability of the density matrix can not be used to measure the
entanglement of mixed ensemble; 3)The evolution of states in bulk-ensemble NMR
quantum computation is quantum mechanical; 4) The coefficient before the
effective pure state density matrix, $\epsilon$, is an measure of the
simultaneity of the molecules in an ensemble. It reflects the intensity of the
NMR signal and has no significance in quantifying the entanglement in the bulk
ensemble NMR system. We conclude that the liquid NMR quantum computation is
genuine, not just classical simulations.",0007077v1
2009-04-08,Effects of cobalt doping and three-dimensionality in $BaFe_2As_2$,"We investigate the dual roles of a cobalt impurity in the Ba-122
ferropnictide superconductor in the state with coexisting collinear spin
density wave (SDW) order as a dopant and as a scattering center, using first
principles electronic structure methods. The Co atom is found to dope the FeAs
plane where it is located with a single delocalized electron as expected, but
also induces a strong perturbation of the SDW ground state of the system. This
in turn induces a stripe-like modulation of the density of states in nearby
planes which may be observable in STM experiments. The defect is found to have
an intermediate strength nonmagnetic scattering potential with a range of
roughly 1 Angstrom, and the Co gives rise to a smaller but longer range
magnetic scattering potential. The impurity potential in both channels is
highly anisotropic, reflecting the broken symmetry of the SDW ground state. We
give values for the effective Co potentials for each d orbital on the impurity
and nearby sites. The calculation also shows a clear local resonance comprised
of Co states about 200meV above the Fermi level, in quantitative agreement with
a recent report from STM. Finally, we discuss the issue of the effective
dimensionality of the 122 materials, and show that the hybridization of the
out-of-phase As atoms leads to a higher density of states between the FeAs
planes relative to the 1111 counterparts.",0904.1257v2
2014-02-12,Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model,"A multi-reference configuration mixing scheme is used to describe the ground
state, characterized by well defined spin and space group symmetry quantum
numbers as well as doping fractions $N_{e}/N_{sites}$, of one dimensional
Hubbard lattices with nearest-neighbor hopping and periodic boundary
conditions. Within this scheme, each ground state is expanded in a given number
of nonorthogonal and variationally determined symmetry-projected
configurations. The results obtained for the ground state and correlation
energies of half-filled and doped lattices with 30, 34 and 50 sites, compare
well with the exact Lieb-Wu solutions as well as with the ones obtained with
other state-of-the-art approximations. The structure of the intrinsic
symmetry-broken determinants resulting from the variational procedure is
interpreted in terms of solitons whose translational and breathing motions can
be regarded as basic units of quantum fluctuations. It is also shown that in
the case of doped 1D lattices, a part of such fluctuations can also be
interpreted in terms of polarons. In addition to momentum distributions, both
spin-spin and density-density correlation functions are studied as functions of
doping. The spectral functions and density of states, computed with an ansatz
whose quality can be well-controlled by the number of symmetry-projected
configurations used to approximate the $N_{e} \pm 1$ electron systems, display
features beyond a simple quasiparticle distribution, as well as spin-charge
separation trends.",1402.2968v1
2018-11-21,Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids,"The properties of the isotropic incompressible $\nu=5/2$ fractional quantum
Hall (FQH) state are described by a paired state of composite fermions in zero
(effective) magnetic field, with a uniform $p_x+ip_y$ pairing order parameter,
which is a non-Abelian topological phase with chiral Majorana and charge modes
at the boundary. Recent experiments suggest the existence of a proximate
nematic phase at $\nu=5/2$. This finding motivates us to consider an
inhomogeneous paired state - a $p_x+ip_y$ pair-density-wave (PDW) - whose
melting could be the origin of the observed liquid-crystalline phases. This
state can viewed as an array of domain and anti-domain walls of the $p_x+i p_y$
order parameter. We show that the nodes of the PDW order parameter, the
location of the domain walls (and anti-domain walls) where the order parameter
changes sign, support a pair of symmetry-protected counter-propagating Majorana
modes. The coupling behavior of the domain wall Majorana modes crucially
depends on the interplay of the Fermi energy $E_{F}$ and the PDW pairing energy
$E_{\textrm{pdw}}$. The analysis of this interplay yields a rich set of
topological states. The pair-density-wave order state in paired FQH system
provides a fertile setting to study Abelian and non-Abelian FQH phases - as
well as transitions thereof - tuned by the strength of the paired liquid
crystalline order.",1811.08897v5
2010-05-18,"Dynamics of disentanglement, density matrix and coherence in neutrino oscillations","In charged current weak interaction processes, neutrinos are produced in an
entangled state with the charged lepton. This correlated state is disentangled
by the measurement of the charged lepton in a detector at the production site.
We study the dynamical aspects of disentanglement, propagation and detection,
in particular the conditions under which the disentangled state is a coherent
superposition of mass eigenstates. The appearance and disappearance
far-detection processes are described from the time evolution of this
disentangled ""collapsed"" state. The familiar quantum mechanical interpretation
and factorization of the detection rate emerges when the quantum state is
disentangled on time scales \emph{much shorter} than the inverse oscillation
frequency, in which case the final detection rate factorizes in terms of the
usual quantum mechanical transition probability provided the final density of
states is insensitive to the neutrino energy difference. We suggest
\emph{possible} corrections for short-baseline experiments. If the charged
lepton is unobserved, neutrino oscillations and coherence are described in
terms of a reduced density matrix obtained by tracing out an un-observed
charged lepton. The diagonal elements in the mass basis describe the production
of mass eigenstates whereas the off diagonal ones provide a measure of
coherence. It is shown that coherences are of the same order of the diagonal
terms on time scales up to the inverse oscillation frequency, beyond which the
coherences oscillate as a result of the interference between mass eigenstates.",1005.3260v2
2021-04-20,Electrostatic energy of Coulomb crystals with polarized electron background,"Outer crusts of neutron stars and interiors of cool white dwarfs consist of
bare atomic nuclei, arranged in a crystal lattice and immersed in a Fermi gas
of degenerate electrons. We study electrostatic properties of such Coulomb
crystals, taking into account the polarizability of the electron gas and
considering different lattice structures, which can form the ground state. To
take the electron background polarization into account, we use the linear
response theory with the electron dielectric function given either by the
Thomas-Fermi approximation or by the random-phase approximation (RPA). We
compare the widely used nonrelativistic (Lindhard) version of the RPA
approximation with the more general, relativistic (Jancovici) version. The
results of the different approximations are compared to assess the importance
of going beyond the Thomas-Fermi or Lindhard approximations. We also include
contribution of zero-point vibrations of ions into the ground-state energy. We
show that the bcc lattice forms the ground state for any charge number $Z$ of
the atomic nuclei at the densities where the electrons are relativistic
($\rho\gtrsim10^6$ g cm$^{-3}$), while at lower densities the fcc and hcp
lattices can form the ground state. The MgB$_2$-like lattice never forms the
ground state at realistic densities in the crystallized regions of degenerate
stars. The RPA corrections strongly affect the boundaries between the phases.
As a result, transitions between different ground-state structures depend on
$Z$ in a nontrivial way. The relativistic and quantum corrections produce less
dramatic effects, moderately shifting the phase boundaries.",2104.09964v1
2001-03-26,On the Ground State of Electron Gases at Negative Compressibility,"Two- and three-dimensional electron gases with a uniform neutralizing
background are studied at negative compressibility. Parametrized expressions
for the dielectric function are used to access this strong-coupling regime,
where the screened Coulomb potential becomes overall attractive for like
charges. Closely examining these expressions reveals that the ground state with
a periodic modulation of the charge density, albeit exponentially damped,
replaces the homogeneous one at positive compressibility. The wavevector
characterizing the new ground state depends on the density and is complex,
having a positive imaginary part, as does the homogeneous ground state, and
real part, as does the genuine charge density wave.",0103524v2
2018-07-09,Stabilization of the Fulde-Ferrell-Larkin-Ovchinnikov State by Tuning In-plane Magnetic-Field Direction: Application to a Quasi-One-Dimensional Organic Superconductor,"The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in quasi-one-dimensional
systems with warped Fermi surfaces is examined in strong parallel magnetic
fields. It is shown that the state is extremely stable for field directions
around nontrivial optimum directions, at which the upper critical field
exhibits cusps, and that the stabilization is due to a Fermi-surface effect
analogous to the nesting effect for the spin density wave and charge density
wave. Interestingly, the behavior with cusps is analogous to that in a square
lattice system in which the hole density is controlled. For the organic
superconductor (TMTSF)_2ClO_4, when the hopping parameters obtained by previous
authors based on X-ray crystallography results are assumed, the optimum
directions are in quadrants consistent with the previous experimental
observations. Furthermore, near this set of parameters, we also find sets of
hopping parameters that more precisely reproduce the observed optimum in-plane
field directions. These results are consistent with the hypothesis that the
FFLO state is realized in the organic superconductor.",1807.02937v1
2016-12-20,Superconductivity in a two-dimensional repulsive Rashba gas at low electron density,"We study the superconducting instability and the resulting superconducting
states in a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling
at low electron density (namely the Fermi energy $E_F$ is lower than the energy
$E_R$ of the Dirac point induced by Rashba coupling). We find that
superconductivity is enhanced as the dimensionless Fermi energy $\epsilon_F$
($\epsilon_F\equiv E_F/E_R$) decreases, due to the following two reasons.
First, the density of states at $\epsilon_F$ increases as
$1/\sqrt{\epsilon_F}$. Second, the particle-hole bubble becomes more
anisotropic, resulting in an increasing effective attraction. The
superconducting state is always in the total angular momentum $j_z=+2$ (or
$j_z=-2$) channel with Chern number $C=4$ (or $C=-4$), breaking time reversal
symmetry spontaneously. Although a putative Leggett mode is expected due to the
two-gap nature of the superconductivity, we find that it is always damped. More
importantly, once a sufficiently large Zeeman coupling is applied to the
superconducting state, the Chern number can be tuned to be $\pm1$ and Majorana
zero modes exist in the vortex cores.",1612.06613v1
2017-03-14,Singlet Fission in Chiral Carbon Nanotubes: Density Functional Theory Based Computation,"Singlet fission (SF) process, where a singlet exciton decays into a pair of
spin one exciton states which are in the total spin singlet state, is one of
the possible channels for multiple exciton generation (MEG). In chiral
single-wall carbon nanotubes (SWCNTs) efficient SF is present within the solar
spectrum energy range which is shown by the many-body perturbation theory
(MBPT) calculations based on the density functional theory (DFT) simulations.
We calculate SF exciton-to-biexction decay rates ${\rm R}_{1\to 2}$ and
biexciton-to-exction rates ${\rm R}_{2\to1}$ in the (6,2), (6,5), (10,5)
SWCNTs, and in (6,2) SWCNT functionalized with Cl atoms. Within the solar
energy range, we predict ${\rm R}_{1\to2}\sim 10^{14}-10^{15}~s^{-1}$, while
biexciton-to-exction recombination is weak with ${\rm R}_{2\to 1}/{\rm R}_{1\to
2}\leq 10^{-2}.$ SF MEG strength in pristine SWCNTs varies strongly with the
excitation energy, which is due to highly non-uniform density of states at low
energy. However, our results for (6,2) SWCNT with chlorine atoms adsorbed to
the surface suggest that MEG in the chiral SWCNTs can be enhanced by altering
the low-energy electronic states via surface functionalization.",1703.04693v1
1994-12-26,Lyapunov Exponents and KS Entropy for the Lorentz Gas at Low Densities,"The Lyapunov exponents and the KS entropy for a two dimensional Lorentz gas
at low densities are defined for general non-equilibrium states and calculated
with the use of a Lorentz-Boltzmann type equation. In equilibrium the density
dependence of these quantities predicted by Krylov is recovered and explicit
expressions are obtained. The relationship between the KS entropy, Lyapunov
exponents, and escape rate, conjectured by Gaspard and Nicolis for
non-equilibrium systems is confirmed and generalized.",9412012v1
1993-04-08,Uniform Density Theorem for the Hubbard Model,"A general class of hopping models on a finite bipartite lattice is
considered, including the Hubbard model and the Falicov-Kimball model. For the
half-filled band, the single-particle density matrix $\uprho (x,y)$ in the
ground state and in the canonical and grand canonical ensembles is shown to be
constant on the diagonal $x=y$, and to vanish if $x \not=y$ and if $x$ and $y$
are on the same sublattice. For free electron hopping models, it is shown in
addition that there are no correlations between sites of the same sublattice in
any higher order density matrix. Physical implications are discussed.",9304015v1
1994-12-13,Introduction to the Supersymmetry Method for the Gaussian Random-Matrix Ensembles,"This article is intended to provide a pedagogical introduction to the
supersymmetry method for performing ensemble-averaging in Gaussian
random-matrix theory. The method is illustrated by a detailed calculation of
the simplest non-trivial physical quantity, namely, the second-order
correlation in the density of states for two different energies within the
spectrum (commonly known as the density-density correlator) for a system
described by a random Hamiltonian matrix belonging to the Gaussian unitary
ensemble.",9412060v3
1997-07-30,Van der Waals Energies in Density Functional Theory,"In principle, density functional theory yields the correct ground-state
densities and energies of electronic systems under the action of a static
external potential.
  However, traditional approximations fail to include Van der Waals energies
between separated systems. This paper proposes a practical procedure for
remedying this difficulty. Our method allows seamless calculations between
small and large inter-system distances. The asymptotic H-He and He--He
interactions are calculated as a first illustration, with very accurate
results.",9707328v1
1999-02-08,Density Modulations and Addition Spectra of Interacting Electrons in Disordered Quantum Dots,"We analyse the ground state of spinless fermions on a lattice in a weakly
disordered potential, interacting via a nearest neighbour interaction, by
applying the self-consistent Hartree-Fock approximation. We find that charge
density modulations emerge progressively when r_s >1, even away from
half-filling, with only short-range density correlations. Classical geometry
dependent ""magic numbers"" can show up in the addition spectrum which are
remarkably robust against quantum fluctuations and disorder averaging.",9902099v1
1999-05-10,Exchange and Correlation Kernels at the Resonance Frequency -- Implications for Excitation Energies in Density-Functional Theory,"Specific matrix elements of exchange and correlation kernels in
time-dependent density-functional theory are computed. The knowledge of these
matrix elements not only constraints approximate time-dependent functionals,
but also allows to link different practical approaches to excited states,
either based on density-functional theory, or on many-body perturbation theory,
despite the approximations that have been performed to derive them.",9905119v2
2001-07-04,Low density approach to the Kondo-lattice model,"We propose a new approach to the (ferromagnetic) Kondo-lattice model in the
low density region, where the model is thought to give a reasonable frame work
for manganites with perovskite structure exhibiting the ""colossal
magnetoresistance"" -effect. Results for the temperature- dependent
quasiparticle density of states are presented. Typical features can be
interpreted in terms of elementary spin-exchange processes between itinerant
conduction electrons and localized moments. The approach is exact in the zero
bandwidth limit for all temperatures and at T=0 for arbitrary bandwidths,
fulfills exact high-energy expansions and reproduces correctly second order
perturbation theory in the exchange coupling.",0107083v1
1999-09-01,Lattice QCD at Finite Temperature and Density,"We review recent results on QCD at finite temperature and non-vanishing
baryon number density. We focus on observables which are of immediate interest
to experimental searches for the Quark Gluon Plasma, i.e. the phase transition
temperature, the equation of state in two and three flavour QCD and thermal
effects on hadron masses. Some new developments in finite density QCD are also
presented.",9909006v1
2005-10-18,The QCD phase diagram at finite density,"We study the density of states method to explore the phase diagram of the
chiral transition on the tempeature and quark chemical potential plane. Four
quark flavours are used in the analysis. Though the method is quite expensive
small lattices show an indication for a triple-point connecting three different
phases on the phase diagram.",0510087v1
2004-10-06,Auxiliary field method at finite temperature and/or finite density,"We discuss the relation between the effective vector meson mass and equation
of state (EOS) for nuclear matter. In the mean field approximation, the EOS
becomes softer due to the reduction of the effective omega-meson mass, if we
assume that the omega-meson mean field is proportional to the baryon density.
We examine the assumption by using the auxiliary field method at finite
temperature and /or density.",0410025v1
2007-11-07,The $ΣΣ$ interactions in finite-density QCD sum rules,"The properties of $\Sigma$-hyperons in pure $\Sigma$ matter are studied with
the finite-density quantum chromo-dynamics sum rule (QCDSR) approach. The
$\Sigma\Sigma$ nuclear potential $U_\Sigma$ is most likely strongly attractive,
it could be about -50 MeV or even more attractive at normal nuclear density. If
this prediction is the case, the interactions between $\Sigma$-hyperons should
play crucial roles in the strange nuclear matter, when there are multi-$\Sigma$
hyperons. The bound state of double-$\Sigma$ maybe exist.",0711.1003v3
2008-01-24,Trapped p-wave superfluids: a local density approach,"The local density approximation is used to study the ground state superfluid
properties of harmonically trapped p-wave Fermi gases as a function of
fermion-fermion attraction strength. While the density distribution is bimodal
on the weakly attracting BCS side, it becomes unimodal with increasing
attraction and saturates towards the BEC side. This non-monotonic evolution is
related to the topological gapless to gapped phase transition, and may be
observed via radio-frequency spectroscopy since quasi-particle transfer current
requires a finite threshold only on the BEC side.",0801.3795v1
2009-04-30,Chemical potential of quadrupolar two-centre Lennard-Jones fluids by gradual insertion,"The gradual insertion method for direct calculation of the chemical potential
by molecular simulation is applied in the NpT ensemble to different quadrupolar
two-centre Lennard-Jones fluids at high density state points. The results agree
well with Widom's test particle insertion but show at very high densities
significantly smaller statistical uncertainties. The gradual insertion method,
which is coupled here with preferential sampling, extends the density range
where reliable information on the chemical potential can be obtained.
Application details are reported.",0904.4771v1
2010-03-30,Transverse momentum spectra and elliptic flow in ideal hydrodynamics and geometric scaling,"In an ideal hydrodynamic model, with an equation of state where the
confinement-deconfinement transition is a cross-over at $T_{co}=196 MeV$, we
have simulated $\sqrt{s}$=200 GeV Au+Au collisions. Simultaneous description of
the experimental charged particle's $p_T$ spectra and elliptic flow require
that in central (0-10%) Au+Au collisions, initial energy density scales with
the binary collision number density. In less central collisions, experimental
data demand scaling with the participant density. Simulation studies also
indicate that in central collisions viscous effects are minimal.",1003.5791v1
2013-06-19,"Initial Friedmann universe, its spatial flatness, matter creation, and the cosmological term","In the Friedmann equations, an infinite initial density is avoided only when
the universe is spatially flat. With such equations being then valid when the
scale factor $a=0$, the universe must also be in the state of vacuum when $a$
is infinitesimal. Matter creation thus largely comes from nonlinearity of the
Friedmann equations at a finite $a$. For the correspondence between such an
initial vacuum and the Friedmann universe, therefore, a vacuum density is
suggested to be gravitationally significant only when it could also have a
matter phase. The effective cosmological term is then due to such a vacuum
density.",1306.5997v1
2013-12-16,FFTPL: An Analytic Placement Algorithm Using Fast Fourier Transform for Density Equalization,"We propose a flat nonlinear placement algorithm FFTPL using fast Fourier
transform for density equalization. The placement instance is modeled as an
electrostatic system with the analogy of density cost to the potential energy.
A well-defined Poisson's equation is proposed for gradient and cost
computation. Our placer outperforms state-of-the-art placers with better
solution quality and efficiency.",1312.4587v1
2015-09-10,Connection formulas for thermal density functional theory,"The adiabatic connection formula of ground-state density functional theory
relates the correlation energy to a coupling-constant integral over a purely
potential contribution, and is widely used to understand and improve
approximations. The corresponding formula for thermal density functional theory
is cast as an integral over temperatures instead, ranging upward from the
system's physical temperature. We also show how to relate different different
correlation components to each other, either in terms of temperature- or
coupling-constant integrations. We illustrate our results on the uniform
electron gas.",1509.03060v2
2010-05-05,Phase Fluctuations near the Chiral Critical Point,"The Helmholtz free energy density is parametrized as a function of
temperature and baryon density near the chiral critical point of QCD. The
parametrization incorporates the expected critical exponents and amplitudes. An
expansion away from equilibrium states is achieved with Landau theory. This is
used to calculate the probability that the system is found at a density other
than the equilibrium one. Such fluctuations are predicted to be very large in
heavy ion collisions.",1005.0860v1
2010-05-08,Semiclassical Electron Correlation in Density-Matrix Time-Propagation,"Lack of memory (locality in time) is a major limitation of almost all present
time-dependent density functional approximations. By using semiclassical
dynamics to compute correlation effects within a density-matrix functional
approach, we incorporate memory, including initial-state dependence, as well as
changing occupation numbers, and predict more observables in strong-field
applications.",1005.1341v2
2008-07-20,$^{77}$Se NMR investigation of the field-induced spin-density-wave transitions in (TMTSF)$_2$ClO$_4$,"Complementary $^{77}$Se nuclear magnetic resonance (NMR) and electrical
transport have been used to correlate the spin density dynamics with the
subphases of the field-induced spin density wave (FISDW) ground state in \tmt.
We find that the peaks in the spin-lattice relaxation rate 1/T$_1$ appear
within the metal-FISDW phase boundary and/or at first-order subphase
transitions. In the quantum limit above 25 T, the NMR data gives an insight
into the FISDW electronic structure.",0807.3119v1
2015-12-10,Scalar QED Action Density and Schwinger Pair Production in (A)dS_2,"We review the one-loop effective action in scalar QED and the Schwinger
effect in a uniform electric field in a two-dimensional (anti-) de Sitter
space. The Schwinger effect has a thermal interpretation in terms of the
effective temperature introduced by Cai and Kim. We propose a method to find
the density of states for the charged scalar and obtain the QED action density
and the pair-production rate in the in-out formalism.",1512.03142v1
2017-10-10,Dark Matter Freeze-out During Matter Domination,"We highlight the general scenario of dark matter freeze-out whilst the energy
density of the universe is dominated by a decoupled non-relativistic species.
Decoupling during matter domination changes the freeze-out dynamics, since the
Hubble rate is parametrically different for matter and radiation domination.
Furthermore, for successful Big Bang Nucleosynthesis the state dominating the
early universe energy density must decay, this dilutes (or repopulates) the
dark matter. As a result, the masses and couplings required to reproduce the
observed dark matter relic density can differ significantly from radiation
dominated freeze-out.",1710.03758v2
2019-10-17,Autoregressive Models: What Are They Good For?,"Autoregressive (AR) models have become a popular tool for unsupervised
learning, achieving state-of-the-art log likelihood estimates. We investigate
the use of AR models as density estimators in two settings -- as a learning
signal for image translation, and as an outlier detector -- and find that these
density estimates are much less reliable than previously thought. We examine
the underlying optimization issues from both an empirical and theoretical
perspective, and provide a toy example that illustrates the problem.
Overwhelmingly, we find that density estimates do not correlate with perceptual
quality and are unhelpful for downstream tasks.",1910.07737v1
2021-04-21,Quantum variational approach to lattice gauge theory at nonzero density,"The simulation of dense fermionic matters is a long-standing problem in
lattice gauge theory. One hopeful solution would be the use of quantum
computers. In this paper, digital quantum simulation is designed for lattice
gauge theory at nonzero density. The quantum variational algorithm is adopted
to obtain the ground state at nonzero density. A benchmark test is performed in
the lattice Schwinger model.",2104.10669v2
2007-11-05,Inhomogeneous Helium Reionization and the Equation of State of the Intergalactic Medium,"The temperature of the intergalactic medium (IGM) is set by the competition
between photoheating and adiabatic cooling, which are usually assumed to define
a tight equation of state in which the temperature increases monotonically with
density. We use a semi-analytic model, accurate at low to moderate IGM
densities (<5 times the mean), to show that inhomogeneous reionization can
substantially modify these expectations. Because reionization is driven by
biased sources, dense pockets of the IGM are likely to be ionized first. As a
result, voids initially remain cool while dense regions are heated
substantially. However, near the end of reionization, dense regions have
already cooled from their initially large temperature while voids have only
just been heated. Thus, near the end of helium reionization the equation of
state can invert itself, with the hottest gas inside voids. The degree to which
this happens depends on the magnitude of the density bias during reionization:
if rare, bright sources dominate reionization, so that each ionized region
contains a typical volume of the IGM, the equation of state will remain
monotonic. We also show that the distribution of temperatures at a fixed
density has significant scatter and evolves rapidly throughout and even after
reionization. Finally, we show that the observed temperature jump at z ~3.2 is
consistent with the behavior at the end of helium reionization, although it
requires a somewhat larger temperature increase than expected.",0711.0751v2
2014-02-04,Microscopic Coexistence of Magnetism and Superconductivity in charge compensated Ba1-xKx(Fe1-yCoy)2As2,"We present a detailed investigation of the electronic phase diagram of
effectively charge compensated Ba1-xKx(Fe1-yCoy)2As2 with x/2 = y. Our
experimental study by means of x-ray diffraction, M\""ossbauer spectroscopy,
muon spin relaxation and ac susceptibility measurements on polycrystalline
samples is complemented by density functional electronic structure
calculations. For low substitution levels of x/2 = y \< 0.13, the system
displays an orthorhombically distorted and antiferromagnetically ordered ground
state. The low temperature structural and magnetic order parameters are
successively reduced with increasing substitution level. We observe a linear
relationship between the structural and the magnetic order parameter as a
function of temperature and substitution level for x/2 = y \< 0.13. At
intermediate substitution levels in the range between 0.13 and 0.19, we find
superconductivity with a maximum Tc of 15 K coexisting with static magnetic
order on a microscopic length scale. For higher substitution levels x/2 = y \>
0.25 a tetragonal non-magnetic ground state is observed. Our DFT calculations
yield a signifcant reduction of the Fe 3d density of states at the Fermi energy
and a strong suppression of the ordered magnetic moment in excellent agreement
with experimental results. The appearance of superconductivity within the
antiferromagnetic state can by explained by the introduction of disorder due to
non-magnetic impurities to a system with a constant charge carrier density. Our
experimental study by means of x-ray diffraction, M\""ossbauer spectroscopy,
muon spin relaxation and ac susceptibility measurements on polycrystalline
samples is complemented by density functional electronic structure
calculations.",1402.0711v1
2020-09-21,Leaders and obstacles raise cultural boundaries,"We employ an agent-based model for cultural dynamics to investigate the
effects of spatial heterogeneities on the collective behavior of a social
system. We introduce heterogeneity as a random distribution of defects or
imperfections in a two-dimensional lattice. Two types of defects are considered
separately: obstacles that represent geographic features, and opinion leaders,
described as agents exerting unidirectional influence on other agents. In both
cases, we characterize two collective phases on the space of parameters of the
system, given by the density of defects and a quantity expressing the number of
available states: one ordered phase, consisting of a large homogeneous group;
and a disordered phase, where many small cultural groups coexist. In the case
of leaders, the homogeneous state corresponds to their state. We find that a
high enough density of obstacles contributes to cultural diversity in the
system. On the other hand, we find a nontrivial effect when opinion leaders are
distributed in the system: if their density is greater than some threshold
value, leaders are no longer efficient in imposing their state to the
population, but they actually promote multiculturality. In this situation, we
uncover that leaders, as well as obstacles, serve as locations for the
formation of boundaries and segregation between different cultural groups.
Moreover, a lower density of leaders than obstacles is needed to induce
multiculturality in the system.",2009.09591v1
2020-10-15,Visualizing the multifractal wavefunctions of a disordered two-dimensional electron gas,"The wavefunctions of a disordered two-dimensional electron gas at the
quantum-critical Anderson transition are predicted to exhibit multifractal
scaling in their real space amplitude. We experimentally investigate the
appearance of these characteristics in the spatially resolved local density of
states of a two-dimensional mixed surface alloy Bi_xPb_{1-x}/Ag(111), by
combining high-resolution scanning tunneling microscopy with spin and
angle-resolved inverse-photoemission experiments. Our detailed knowledge of the
surface alloy electronic band structure, the exact lattice structure and the
atomically resolved local density of states enables us to construct a realistic
Anderson tight binding model of the mixed surface alloy, and to directly
compare the measured local density of states characteristics with those from
our model calculations. The statistical analyses of these two-dimensional local
density of states maps reveal their log-normal distributions and multifractal
scaling characteristics of the underlying wavefunctions with a finite anomalous
scaling exponent. Finally, our experimental results confirm theoretical
predictions of an exact scaling symmetry for Anderson quantum phase transitions
in the Wigner-Dyson classes.",2010.07554v1
2022-02-04,Electron Spectrum Topology and Giant Density-of-States Singularities in Cubic Lattices,"The topology of isoenergetic surfaces in reciprocal space for simple (sc),
body-centered (bcc), and face-centered (fcc) cubic lattices is investigated in
detail in the tight-binding approximation, taking into account the transfer
integrals between the nearest and next neighbors $t$ and $t'$. It is shown
that, for values $\tau = t'/t = \tau_\ast$ corresponding to a change in the
topology of surfaces, lines and surfaces of $\mathbf k$-van Hove points can be
formed. With a small deviation of $\tau$ from these singular values, the
spectrum in the vicinity of the van Hove line (surface) is replaced by a weak
dependence on $\mathbf k$ in the vicinity of several van Hove points that have
a giant mass proportional to $|\tau - \tau_ \ast|^{-1}$. Singular contributions
to the density of states near peculiar $\tau$ values are considered; analytical
expressions for the density of states being obtained in terms of elliptic
integrals. It is shown that in a number of cases the maximum value of the
density of states is achieved at energies corresponding not to
$\mathbf{k}$-points on the Brillouin zone edges, but to its internal points in
highly symmetrical directions. The corresponding contributions to electron and
magnetic properties are treated, in particular, in application to weak
itinerant magnets.",2202.02133v1
2000-07-04,Comment on ``Composite Fermion Hofstadter Problem: Partially Polarized Density Wave States in the $ν=2/5$ ...'',"In a recent paper [Phys.Rev.Lett. 82, 3665 (1999)], magnetic field driven
spin transitions in fractional quantum Hall (FQH) states were reported, and in
particular, at filling factors 2/3 and 2/5, weak features were observed at half
polarization. This would imply that the ground state energy is non-monotonic at
half polarization. It was proposed in
  Ref.[Phys. Rev. Lett. 84, 350 (2000)] that the system is then a charge
density wave (CDW) state of composite fermions with a subband gap that could
explain the observed plateaus at half polarization. Similar CDW state is also
expected at filling factor 2/3. Here we show that the proposed CDW state is not
the half polirized ground state at these two filling factors.",0007043v1
2005-03-30,Anharmonicity and asymmetry of Landau levels for a two-dimensional electron gas,"We calculate the density of states of a two dimensional electron gas located
at the interface of a GaAlAs/GaAs heterojunction. The disorder potential which
is generally created by a single doping layer behind a spacer, is here enhanced
by the presence of a second delta doped layer of scatterers which can be
repulsive or attractive impurities. We have calculated the density of states by
means of the Klauder's approximation, in the presence of a magnetic field of
arbitrary strength. At low field either band tails or impurity bands are
observed for attractive potentials, depending on the impurity concentration. At
higher field, impurity bands are observed for both repulsive and attractive
potentials. We discuss the effect of such an asymmetrical density of states on
the transport properties in the quantum Hall effect regime.",0503714v2
2006-06-07,Longitudinal fluid dynamics for ultrarelativistic heavy-ion collisions,"We develop a 1+1 dimensional hydrodynamical model for central heavy-ion
collisions at ultrarelativistic energies. Deviations from Bjorken's scaling are
taken into account by implementing finite-size profiles for the initial energy
density. The calculated rapidity distributions of pions, kaons and antiprotons
in central Au+Au collisions at the c.m. energy 200 AGeV are compared with
experimental data of the BRAHMS Collaboration. The sensitivity of the results
to the choice of the equation of state, the parameters of initial state and the
freeze-out conditions is investigated. Experimental constraints on the total
energy of produced particles are used to reduce the number of model parameters.
The best fits of experimental data are obtained for soft equations of state and
Gaussian-like initial profiles of the energy density. It is found that initial
energy densities required for fitting experimental data decrease with
increasing critical temperature of the phase transition.",0606074v2
2003-07-29,Integrated density of states and Wegner estimates for random Schrödinger Operators,"We survey recent results on spectral properties of random Schr\""odinger
operators. The focus is set on the integrated density of states (IDS). First we
present a proof of the existence of a self-averaging IDS which is general
enough to be applicable to random Schr\""odinger and Laplace-Beltrami operators
on manifolds. Subsequently we study more specific models in Euclidean space,
namely of alloy type, and concentrate on the regularity properties of the IDS.
We discuss the role of the integrated density of states and its regularity
properties for the spectral analysis of random Schr\""odinger operators,
particularly in relation to localisation. Proofs of the central results are
given in detail. Whenever there are alternative proofs, the different
approaches are compared.",0307062v2
1997-09-16,Decoherence and Dissipation in Quantum Two-State Systems,"The Brownian dynamics of the density operator for a quantum system
interacting with a classical heat bath is described using a stochastic,
non-linear Liouville equation obtained from a variational principle. The
environment's degrees of freedom are simulated by classical harmonic
oscillators, while the dynamical variables of the quantum system are two
non-hermitian ""square root operators"" defined by a Gauss-like decomposition of
the density operator. The rate of the noise-induced transitions is expressed as
a function of the environmental spectral density, and is discussed for the case
of the white noise and blackbody radiation. The result is compared with the
rate determined by a quantum environment, calculated by partial tracing in the
whole Hilbert space. The time-dependence of the von Neumann entropy and of the
dissipated energy is obtained numerically for a system of two quantum states.
These are the ground and first excited state of the center of mass vibrations
for an ion confined in a harmonic trap.",9709033v2
2003-09-09,Decoherence in strongly coupled quantum oscillators,"In this paper we present a comprehensive analysis of the coherence phenomenon
of two coupled dissipative oscillators. The action of a classical driving field
on one of the oscillators is also analyzed. Master equations are derived for
both regimes of weakly and strongly interacting oscillators from which
interesting results arise concerning the coherence properties of the joint and
the reduced system states. The strong coupling regime is required to achieve a
large frequency shift of the oscillator normal modes, making it possible to
explore the whole profile of the spectral density of the reservoirs. We show
how the decoherence process may be controlled by shifting the normal mode
frequencies to regions of small spectral density of the reservoirs. Different
spectral densities of the reservoirs are considered and their effects on the
decoherence process are analyzed. For oscillators with different damping rates,
we show that the worse-quality system is improved and vice-versa, a result
which could be useful for quantum state protection. State recurrence and swap
dynamics are analyzed as well as their roles in delaying the decoherence
process.",0309082v1
1994-11-08,Density of states of a layered S/N d-wave superconductor,"We calculate the density of states of a layered superconductor in which there
are two layers per unit cell. One of the layers contains a d-wave pairing
interaction while the other is a normal metal. The goal of this article is to
understand how the d-wave behaviour of the system is modified by the coupling
between the layer-types. This coupling takes the form of coherent, single
particle tunneling along the c-axis. We find that there are two physically
different limits of behaviour, which depend on the relative locations of the
Fermi surfaces of the two layer-types. We also discuss the interference between
the interlayer coupling and pairing interaction and we find that this
interference leads to features in the density of states.",9411003v1
2009-04-24,Absorption and Fluorescence Properties of Oligothiophene Biomarkers from Long-Range-Corrected Time-Dependent Density Functional Theory,"The absorption and fluorescence properties in a class of oligothiophene
push-pull biomarkers are investigated with a long-range-corrected (LC) density
functional method. Using linear response time-dependent density functional
theory (TDDFT), we calculate excitation energies, fluorescence energies,
oscillator strengths, and excited-state dipole moments. To benchmark and assess
the quality of the LC-TDDFT formalism, an extensive comparison is made between
LC-BLYP excitation energies and approximate coupled cluster singles and doubles
(CC2) calculations. When using a properly-optimized value of the range
parameter, ""mu"", we find that the LC technique provides an accurate description
of charge-transfer excitations as a function of biomarker size and chemical
functionalization. In contrast, we find that re-optimizing the fraction of
Hartree Fock exchange in conventional hybrid functionals still yields an
inconsistent description of excitation energies and oscillator strengths for
the two lowest excited states in our series of biomarkers. The results of the
present study emphasize the importance of a distance-dependent contribution of
exchange in TDDFT for investigating excited-state properties.",0904.3918v1
2009-09-06,Dense stellar matter with trapped neutrinos under strong magnetic fields,"We investigate the effects of strong magnetic fields on the equation of state
of dense stellar neutrino-free and neutrino-trapped matter. Relativistic
nuclear models both with constant couplings (NLW) and with density dependent
parameters (DDRH) and including hyperons are considered . It is shown that at
low densities neutrinos are suppressed in the presence of the magnetic field.
The magnetic field reduces the strangeness fraction of neutrino-free matter and
increases the strangeness fraction of neutrino-trapped matter. The mass-radius
relation of stars described by these equations of state are determined. The
magnetic field makes the overall equation of state stiffer and the stronger the
field the larger the mass of maximum mass star and the smaller the baryon
density at the center of the star. As a consequence in the presence of strong
magnetic fields the possibility that a protoneutron star evolves to a blackhole
is smaller.",0909.1116v1
2010-09-22,High efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements,"We propose a high efficiency tomographic scheme to reconstruct an unknown
quantum state of the qubits by using a series of quantum nondemolition (QND)
measurements. The proposed QND measurements of the qubits are implemented by
probing the the stationary transmissions of the dispersively-coupled resonator.
It is shown that only one kind of QND measurements is sufficient to determine
all the diagonal elements of the density matrix of the detected quantum state.
The remaining non-diagonal elements of the density matrix can be determined by
other spectral measurements by beforehand transferring them to the diagonal
locations using a series of unitary operations. Compared with the pervious
tomographic reconstructions based on the usual destructively projective (DP)
measurements (wherein one kind of such measurements could only determine one
diagonal element of the density matrix), the present approach exhibits
significantly high efficiency for N-qubit (N > 1). Specifically, our generic
proposal is demonstrated by the experimental circuit-quantumelectrodynamics
(circuit-QED) systems with a few Josephson charge qubits.",1009.4252v1
2010-09-29,Prediction of femtosecond oscillations in the transient current of a quantum dot in the Kondo regime,"We invoke the time-dependent non-crossing approximation in order to study the
effects of the density of states of gold contacts on the instantaneous
conductance of a single electron transistor which is abruply moved into the
Kondo regime by means of a gate voltage. For an asymmetrically coupled system,
we observe that the instantaneous conductance in the Kondo timescale exhibits
beating with distinct frequencies, which are proportional to the separation
between the Fermi level and the sharp features in the density of states of
gold. Increasing the ambient temperature or bias quenches the amplitude of the
oscillations. We attribute the oscillations to interference between the
emerging Kondo resonance and van-Hove singularities in the density of state. In
addition, we propose an experimental realization of this model.",1009.5805v1
2011-01-03,Observation of a first order phase transition in fluid iron at pressures of 3 to 5 GPa,"Direct measurements of resistivity and caloric equation of state have been
performed for fluid iron at pressures of 2 to 12 GPa in a wide density range.
We found that the isochoric temperature coefficient of resistivity becomes
negative, and this is considered as an indication of the metal-to-nonmetal
transition, when density decreased by a factor of 3 to 4 compared to the normal
solid density. We detected also that isentropes plotted in the pressure -
specific volume plane have well-defined kinks localized on a convex curve with
a maximum at about 5 GPa. Such behavior of isentropes evidences about a first
order phase transition with a critical pressure one order of magnitude higher
than the predicted pressure of the liquid-vapor critical point. Arguments are
presented that the observed phase transition is most likely the liquid-vapor
transition rather than an extra first order transition in the fluid state. We
show that the gaseous nonmetallic phase represents dense plasma in the 1-2-th
state of ionization so that it is a plasma phase transition as well.",1101.0487v2
2011-02-11,Quantum mechanics in metric space: wave functions and their densities,"Hilbert space combines the properties of two fundamentally different types of
mathematical spaces: vector space and metric space. While the vector-space
aspects of Hilbert space, such as formation of linear combinations of state
vectors, are routinely used in quantum mechanics, the metric-space aspects of
Hilbert space are much less exploited. Here we show that a suitable metric
stratifies Fock space into concentric spheres. Maximum and minimum distances
between wave functions are derived and geometrically interpreted in terms of
this metric. Unlike the usual Hilbert-space analysis, our results apply also to
the reduced space of only ground-state wave functions and to that of particle
densities, each of which forms a metric space but not a Hilbert space. The
Hohenberg-Kohn mapping between densities and ground-state wave functions, which
is highly complex and nonlocal in coordinate description, is found, for three
different model systems, to be very simple in metric space, where it is
represented by a monotonic mapping of vicinities onto vicinities. Surprisingly,
it is also found to be nearly linear over a wide range of parameters.",1102.2329v1
2011-10-18,Connecting Neutron Star Observations to Three-Body Forces in Neutron Matter and to the Nuclear Symmetry Energy,"Using a phenomenological form of the equation of state of neutron matter near
the saturation density which has been previously demonstrated to be a good
characterization of quantum Monte Carlo simulations, we show that currently
available neutron star mass and radius measurements provide a significant
constraint on the equation of state of neutron matter. At higher densities we
model the equation of state using polytropes and a quark matter model, and we
show that our results do not change strongly upon variation of the lower
boundary density where these polytropes begin. Neutron star observations offer
an important constraint on a coefficient which is directly connected to the
strength of the three-body force in neutron matter, and thus some theoretical
models of the three-body may be ruled out by currently available astrophysical
data. In addition, we obtain an estimate of the symmetry energy of nuclear
matter and its slope that can be directly compared to the experiment and other
theoretical calculations.",1110.4142v2
2012-06-25,The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian,"We consider the density of states measure of the Fibonacci Hamiltonian and
show that, for small values of the coupling constant $V$, this measure is
exact-dimensional and the almost everywhere value $d_V$ of the local scaling
exponent is a smooth function of $V$, is strictly smaller than the Hausdorff
dimension of the spectrum, and converges to one as $V$ tends to zero. The proof
relies on a new connection between the density of states measure of the
Fibonacci Hamiltonian and the measure of maximal entropy for the Fibonacci
trace map on the non-wandering set in the $V$-dependent invariant surface. This
allows us to make a connection between the spectral problem at hand and the
dimension theory of dynamical systems.",1206.5560v1
2015-10-01,Towards an optimal flow: Density-of-states-informed replica-exchange simulations,"Replica exchange (RE) is one of the most popular enhanced-sampling
simulations technique in use today. Despite widespread successes, RE
simulations can sometimes fail to converge in practical amounts of time, e.g.,
when sampling around phase transitions, or when a few hard-to-find
configurations dominate the statistical averages. We introduce a generalized RE
scheme, density-of-states-informed RE (g-RE), that addresses some of these
challenges. The key feature of our approach is to inform the simulation with
readily available, but commonly unused, information on the the density of
states of the system as the RE simulation proceeds. This enables two
improvements, namely, the introduction of resampling moves that actively move
the system towards equilibrium, and the continual adaptation of the optimal
temperature set. As a consequence of these two innovations, we show that the
configuration flow in temperature space is optimized and that the overall
convergence of RE simulations can be dramatically accelerated.",1510.00431v1
2016-01-13,Quantum interference patterns around magnetic impurities in a 2D electron gas with strong Rashba spin-orbit interaction,"Explicit dependencies of the local density of states and the magnetization
local density of states have been obtained around magnetic point defects in a
two-dimensional electron gas with Rashba spin-orbit interaction . The
expressions are given in the Born approximation for arbitrary magnitude and
orientation of the defect magnetic moment, and for arbitrary size of the
constant of spin-orbit interaction alpha/. On the basis of our asymptotically
exact formulas a procedure for the determination of the constant alpha/ in STM
experiments is proposed. The novel analytical results are compared with the
numerical and approximate results of previous work. At variance with earlier
work we find that that magnetic scattering in the presence of spin-orbit
interaction does not modify the local density of states and that the spin
texture resulting from in-plain orientation of the defect magnetic moment, and
elastic scattering, is not a purely in-plane spin texture.",1601.03154v1
2016-10-24,Thermoelectric power as a probe of density of states in correlated actinide materials: the case of PuCoGa$_{5}$ superconductor,"We present measurements of the thermoelectric power of the plutonium-based
unconventional superconductor PuCoGa$_{5}$. The data is interpreted within a
phenomenological model for the quasiparticle density of states of intermediate
valence systems and the results are compared with results obtained from
photoemission spectroscopy. The results are consistent with intermediate
valence nature of 5$f$-electrons, furthermore, we propose that measurements of
the Seebeck coefficient can be used as a probe of density of states in this
material, thereby providing a link between transport measurements and
photoemission in strongly correlated materials. We discuss these results and
their implications for the electronic structure determination of other strongly
correlated systems, especially actinide materials.",1610.07581v1
2019-11-14,Equation of state of QCD matter within the Hagedorn bag-like model,"The QCD equation of state at finite temperature and densities of conserved
charges is considered in the framework of a Hagedorn bag-like model,
incorporating both the finite sizes of hadrons as well as their exponential
mass spectrum. Augmented with non-zero masses of quarks and gluons in the bag
spectrum, the model yields a fair quantitative description of lattice data on
thermodynamic functions, the conserved charges susceptibilities, and Fourier
coefficients of net-baryon density. Both at zero and finite baryon densities a
broad crossover transition between hadronic and quark-gluon matter is observed.
The model thus provides a thermodynamically consistent construction of a
crossover equation of state for finite baryon number, electric charge and
strangeness chemical potentials, which can be used in fluid dynamical
simulations of heavy-ion collisions.",1911.06420v1
2008-07-26,"Instanton sector of correlated electron systems as the origin of populated pseudo-gap and flat ""band"" behavior: analytic solution","Finite temperature instantons between meta-stable vacua of correlated
electronic system are solved analytically for quasi one-dimensional Hubbard
model. The instantons produce dynamic symmetry breaking and connect metallic
state with the dual vacua: superconducting (SC) and spin-density wave (SDW)
states. The instantons spread along the Matsubara's imaginary time and possess
the structure similar to the coordinate-space solitonic lattices previously
discovered in quasi one-dimensional Peierls model. On the microscopic level the
inter-vacua excursion is described by mutual transformations between the
""resonating quartets"" of the couples of electron-hole and Cooper pairs.
Spectral properties of the electrons in the ""instantonic crystal"" reveal
pseudo-gap (PG) behavior, with finite fermionic density of states in the center
of the PG and ``flat-band'' outside of it. Analytically derived inverse
temperature scaling of the pseudo-gap and the densities of the SC and SDW
condensates is discussed in the context of ARPES and STM data in high-Tc
cuprates.",0807.4222v1
2014-05-30,Understanding disorder-induced zero-bias anomalies in systems with short-range interactions: An atomic-limit perspective,"Motivated by the novel electronic behaviors seen in transition metal oxides,
we look for physical insight into disordered, strongly-correlated systems by
exploring the atomic limit. In recent work, the atomic limit has provided a
useful reference point in systems with strong {\em local} interactions. For
comparison with experiments, the exploration of {\em non}local interactions is
of interest. In the atomic limit, both the case of on-site interactions alone
and the case of infinite-range ($1/r$) interactions are well understood;
however, not so the intervening possibilities. Here we study the atomic limit
of the extended Anderson-Hubbard model using classical Monte Carlo to calculate
the single-particle density of states. We show that the combination of
nearest-neighbor interactions and site disorder produce a zero-bias anomaly
caused by residual charge ordering, and the addition of on-site interactions
has a non-monotonic effect on the depth of this zero-bias anomaly. A key
conclusion is that the form of the density of states in this classical system
strongly resembles density of states results obtained for the full extended
Anderson-Hubbard model when $U<4V$.",1405.7932v2
2014-06-25,Impact of nitrogen incorporation on interface states in (100)Si/HfO2,"The influence of nitrogen incorporation on the energy distribution of
interface states in the (100)Si/HfO2 system and their passivation by hydrogen
have been studied. The results are compared to those of nominally N-free
samples. The nitrogen in the (100)Si/HfO2 entity is found to increase the trap
density, most significantly, in the upper part of Si band gap, in which energy
range nitrogen incorporation prevents passivation of interface traps by
hydrogen. At the same time, passivation of fast interface traps in the lower
part of the band gap proceeds efficiently, provided the thickness of the
nitrogen containing interlayer is kept within a few monolayers. The minimal
interface trap density below the midgap achieved after passivation in H2 is
dominated by the presence of slow N-related states, likely located in the
insulator. As inferred from capacitance-voltage and ac conductance analysis,
the lowest density of electrically active defects [(8-9)x10 10 eV-1cm-2 at
0.4-0.5 eV from the top of the Si valence band edge] is achieved both in the
N-free and N-containing (100)Si/HfO2 structuresafter post-deposition anneal at
800C in (N2+5%O2) followed by passivation in molecular hydrogen at 400C for 30
min.",1406.6609v1
2016-12-17,Metal hydrogen sulfide superconducting temperature,"\'Eliashberg theory generalized to the case of the electron-phonon (EP)
systems with the not constant density of electronic states, as well as to the
case of the frequency dependent renormalization of both the electron mass and
the chemical potential, is used to study hydrogen sulphide phase under
pressure. The frequency and the temperature dependences of the electron mass
renormalization ReZ , the density of electronic states , renormalized by the EP
interaction , the spectral function of the electron-phonon interaction,
obtained by calculation are used to calculate the electronic abnormal GF. The
generalized \'Eliashberg equations with the variable density of electronic
states are resolved for the hydrogen sulphide phase under pressure. The
dependence of both the real and the imaginary part of the order parameter on
the frequency in the phase is obtained. The results of the solution of the
Eliashberg equations for the Im-3m (170 GPa), Im-3m (200 GPa), Im-3m (225 GPa)
and R3m (120 GPa) hydrogen sulphide phases are presented. The value in the
hydrogen sulfide phase at the pressure P = 225 GPa has been defined. The value
for the hydrogen sulfide phase at the pressure P = 170 GPa has been predicted.",1612.05790v1
2019-09-20,Optical Enhancement of Superconductivity via Targeted Destruction of Charge Density Waves,"It has been experimentally established that the occurrence of charge density
waves is a common feature of various under-doped cuprate superconducting
compounds. The observed states, which are often found in the form of bond
density waves (BDW), often occur in a temperature regime immediately above the
superconducting transition temperature. Motivated by recent optical experiments
on superconducting materials, where it has been shown that optical irradiation
can transiently improve the superconducting features, here, we propose a new
approach for the enhancement of superconductivity by the targeted destruction
of the BDW order. Since BDW states are usually found in competition with
superconductivity, suppression of the BDW order enhances the tendency of
electrons to form Cooper pairs after reaching a steady-state. By investigating
the optical coupling of gapless, collective fluctuations of the BDW modes, we
argue that the resonant excitation of these modes can melt the underlying BDW
order parameter. We propose an experimental setup to implement such an optical
coupling using 2D plasmon-polariton hybrid systems.",1909.09689v1
2023-10-17,Determination of the Equation of State from Nuclear Experiments and Neutron Star Observations,"With recent advances in neutron star observations, major progress has been
made in determining the pressure of neutron star matter at high density. This
pressure is constrained by the neutron star deformability, determined from
gravitational waves emitted in a neutron-star merger, and measurements of radii
of two neutron stars, using a new X-ray observatory on the International Space
Station. Previous studies have relied on nuclear theory calculations to provide
the equation of state at low density. Here we use a combination of 15
constraints composed of three astronomical observations and twelve nuclear
experimental constraints that extend over a wide range of densities. Bayesian
Inference is then used to obtain a comprehensive nuclear equation of state.
This data-centric result provides benchmarks for theoretical calculations and
modeling of nuclear matter and neutron stars. Furthermore, it provides insights
on the composition of neutron stars and their cooling via neutrino radiation.",2310.11588v2
1999-12-17,Models of the Pseudogap State in Cuprates,"We review a certain class of (""nearly"") exactly solvable models of electronic
spectrum of two-dimensional systems with fluctuations of short range order of
""dielectric"" (e.g. antiferromagnetic) or ""superconducting"" type, leading to the
formation of anisotropic pseudogap state on certain parts of the Fermi surface.
The models are based on recurrence procedure for one- and two-electron Green's
functions which takes into account of all Feynman diagrams in perturbation
series with the use of the approximate Ansatz for higher-order terms in this
series. These models can be applied to calculation of spectral density, density
of states and conductivity in the normal state, as well as to calculation of
some properties of superconducting state.",9912318v1
2009-08-14,Splitting of critical energies in the $n$=0 Landau level of graphene,"The lifting of the degeneracy of the states from the graphene $n$=0 Landau
level (LL) is investigated through a non-interacting tight-binding model with
random hoppings. A disorder-driven splitting of two bands and of two critical
energies is observed by means of density of states and participation ratio
calculations. The analysis of the probability densities of the states within
the $n$=0 LL provides some insights into the interplay of lattice and disorder
effects on the splitting process. An uneven spatial distribution of the wave
function amplitudes between the two graphene sublattices is found for the
states in between the two split peaks. It is shown that as the splitting is
increased (linear increasing with disorder and square root increasing with
magnetic field), the two split levels also get increasingly broadened, in such
a way that the proportion of the overlapped states keeps approximately constant
for a wide range of disorder or magnetic field variation.",0908.2120v1
2014-11-23,On the rate of convergence for the mean field approximation of many-body quantum dynamics,"We consider the time evolution of quantum states by many-body Schr\""odinger
dynamics and study the rate of convergence of their reduced density matrices in
the mean field limit. If the prepared state at initial time is of coherent or
factorized type and the number of particles $n$ is large enough then it is
known that $1/n$ is the correct rate of convergence at any time. We show in the
simple case of bounded pair potentials that the previous rate of convergence
holds in more general situations with possibly correlated prepared states. In
particular, it turns out that the coherent structure at initial time is
unessential and the important fact is rather the speed of convergence of all
reduced density matrices of the prepared states. We illustrate our result with
several numerical simulations and examples of multi-partite entangled quantum
states borrowed from quantum information.",1411.6284v1
2021-07-28,Quantum state tomography of molecules by ultrafast diffraction,"Ultrafast electron diffraction and time-resolved serial crystallography are
the basis of the ongoing revolution in capturing at the atomic level of detail
the structural dynamics of molecules. However, most experiments employ the
classical ""ball-and-stick"" depictions, and the information of molecular quantum
states, such as the density matrix, is missing. Here, we introduce a framework
for the preparation and ultrafast coherent diffraction from rotational wave
packets of molecules, and we establish a new variant of quantum state
tomography for ultrafast electron diffraction to characterize the molecular
quantum states. The ability to reconstruct the density matrix of molecules of
arbitrary degrees of freedom will provide us with an unprecedentedly clear view
of the quantum states of molecules, and enable the visualization of effects
dictated by the quantum dynamics of molecules.",2107.13310v1
2023-04-12,A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density,"Lattice gauge theories coupled to fermionic matter account for many
interesting phenomena in both high energy physics and condensed matter physics.
Certain regimes, e.g. at finite fermion density, are difficult to simulate with
traditional Monte Carlo algorithms due to the so-called sign-problem. We
present a variational, sign-problem-free Monte Carlo method for lattice gauge
theories with continuous gauge groups and apply it to (2+1)-dimensional compact
QED with dynamical fermions at finite density. The variational ansatz is
formulated in the full gauge field basis, i.e. without having to resort to
truncation schemes for the $U(1)$ gauge field Hilbert space. The ansatz
consists of two parts: first, a pure gauge part based on Jastrow-type ansatz
states (which can be connected to certain neural-network ansatz states) and
secondly, on a fermionic part based on gauge-field dependent fermionic Gaussian
states. These are designed in such a way that the gauge field integral over all
fermionic Gaussian states is gauge-invariant and at the same time still
efficiently tractable. To ensure the validity of the method we benchmark the
pure gauge part of the ansatz against another variational method and the full
ansatz against an existing Monte Carlo simulation where the sign-problem is
absent. Moreover, in limiting cases where the exact ground state is known we
show that our ansatz is able to capture this behavior. Finally, we study a
sign-problem affected regime by probing density-induced phase transitions.",2304.05916v1
2016-01-14,Mixed-state form factors of $U(1)$ twist fields in the Dirac theory,"Using the ""Liouville space"" (the space of operators) of the massive Dirac
theory, we define mixed-state form factors of $U(1)$ twist fields. We consider
mixed states with density matrices diagonal in the asymptotic particle basis.
This includes the thermal Gibbs state as well as all generalized Gibbs
ensembles of the Dirac theory. When the mixed state is specialized to a thermal
Gibbs state, using a Riemann-Hilbert problem and low-temperature expansion, we
obtain finite-temperature form factors of $U(1)$ twist fields. We then propose
the expression for form factors of $U(1)$ twist fields in general diagonal
mixed states. We verify that these form factors satisfy a system of nonlinear
functional differential equations, which is derived from the trace definition
of mixed-state form factors. At last, under weak analytic conditions on the
eigenvalues of the density matrix, we write down the large distance form factor
expansions of two-point correlation functions of these twist fields. Using the
relation between the Dirac and Ising models, this provides the large-distance
expansion of the R$\acute{\text{e}}$nyi entropy (for integer
R$\acute{\text{e}}$nyi parameter) in the Ising model in diagonal mixed states.",1601.03702v3
2003-08-19,Anisotropic Cosmological Models with Energy Density Dependent Bulk Viscosity,"An analysis is presented of the Bianchi type I cosmological models with a
bulk viscosity when the universe is filled with the stiff fluid $p = \epsilon$
while the viscosity is a power function of the energy density, such as $\eta =
\alpha |\epsilon|^n$. Although the exact solutions are obtainable only when the
$2n$ is an integer, the characteristics of evolution can be clarified for the
models with arbitrary value of $n$. It is shown that, except for the $n = 0$
model that has solutions with infinite energy density at initial state, the
anisotropic solutions that evolve to positive Hubble functions in the later
stage will begin with Kasner-type curvature singularity and zero energy density
at finite past for the $n> 1$ models, and with finite Hubble functions and
finite negative energy density at infinite past for the $n < 1$ models. In the
course of evolution, matters are created and the anisotropies of the universe
are smoothed out. At the final stage, cosmologies are driven to infinite
expansion state, de Sitter space-time, or Friedman universe asymptotically.
However, the de Sitter space-time is the only attractor state for the $n <1/2 $
models. The solutions that are free of cosmological singularity for any finite
proper time are singled out. The extension to the higher-dimensional models is
also discussed.",0308059v2
2021-06-02,Phase Transitions of Repulsive Two-Component Fermi Gases in Two Dimensions,"We predict the phase separations of two-dimensional Fermi gases with
repulsive contact-type interactions between two spin components. Using
density-potential functional theory with systematic semiclassical
approximations, we address the long-standing problem of itinerant
ferromagnetism in realistic settings. We reveal a universal transition from the
paramagnetic state at small repulsive interactions towards ferromagnetic
density profiles at large interaction strengths, with intricate particle-number
dependent phases in between. Building on quantum Monte Carlo results for
uniform systems, we benchmark our simulations against Hartree-Fock calculations
for a small number of trapped fermions. We thereby demonstrate that our
employed corrections to the mean-field interaction energy and especially to the
Thomas-Fermi kinetic energy functional are necessary for reliably predicting
properties of trapped mesoscopic Fermi gases. The density patterns of the
ground state survive at low finite temperatures and confirm the Stoner-type
polarization behavior across a universal interaction parameter, albeit with
substantial quantitative differences that originate in the trapping potential
and the quantum-corrected kinetic energy. We also uncover a zoo of metastable
configurations that are energetically comparable to the ground-state density
profiles and are thus likely to be observed in experiments. We argue that our
density-functional approach can be easily applied to interacting
multi-component Fermi gases in general.",2106.01068v2
2023-01-19,Illuminating trap density trends in amorphous oxide semiconductors with ultrabroadband photoconduction,"Under varying growth and device processing conditions, ultrabroadband
photoconduction (UBPC) reveals strongly evolving trends in the defect density
of states (DoS) for amorphous oxide semiconductor thin-film transistors (TFTs).
Spanning the wide bandgap of amorphous InGaZnO$_x$ (a-IGZO), UBPC identifies
seven oxygen-deep donor vacancy peaks that are independently confirmed by
energetically matching to photoluminescence emission peaks. The sub-gap DoS
from 15 different types of a-IGZO TFTs all yield similar DoS, except only
back-channel etch TFTs can have a deep acceptor peak seen at 2.2 eV below the
conduction band mobility edge. This deep acceptor is likely a zinc vacancy,
evidenced by trap density which becomes 5-6x larger when TFT wet-etch methods
are employed. Certain DoS peaks are strongly enhanced for TFTs with active
channel processing damage caused by plasma exposure. While Ar implantation and
He plasma processing damage are similar, Ar plasma yields more disorder showing
a 2x larger valence-band Urbach energy and two orders of magnitude increase in
the deep oxygen vacancy trap density. Changing the growth conditions of a-IGZO
also impacts the DoS, with zinc-rich TFTs showing much poorer electrical
performance compared to 1:1:1 molar ratio a-IGZO TFTs owing to the former
having a ~10xlarger oxygen vacancy trap density. Finally, hydrogen is found to
behave as a donor in amorphous indium tin gallium zinc oxide TFTs.",2301.08196v1
1996-01-23,Thermodynamics for Fractional Exclusion Statistics,"We discuss the thermodynamics of a gas of free particles obeying Haldane's
exclusion statistics, deriving low temperature and low density expansions. For
gases with a constant density of states, we derive an exact equation of state
and find that temperature-dependent quantities are independent of the
statistics parameter.",9601108v2
1996-04-22,Periodic Orbit Theory of the Transition to Chaos in Quantum Wells,"An analytic theory is developed for the density of states oscillations in
quantum wells in a magnetic field which is tilted with respect to the barrier
planes. The main oscillations are found to come from the simplest one or
two-bounce periodic orbits. We calculate their period and stability
analytically and find an infinite sequence of destabilizations followed by
restabilizations as the chaos parameter increases. This phenomenon explains the
re-entrant frequency-doubling of the density of states peaks observed in recent
magnetotunneling experiments.",9604140v1
1997-09-23,Density of states and reflectionless tunneling in NS junction with a barrier,"The effect of the barrier on the proximity effect in normal-superconductor
junction is analyzed. A general criterion for the barrier, though large, to be
effectively transparent, is given. This criterion is applied to both the
conductance of a disordered NS junction (reflectionless tunneling) and the
density of states across it, showing that both phenomena stem from the same
physical effect.",9709248v2
1998-07-28,Disorder-Induced Topological Defects in a d=2 Elastic Medium at Zero Temperature,"The density and correlations of topological defects are investigated
numerically in a model of a d=2 elastic medium subject to a periodic quenched
random potential. The computed density of defects decreases approximately
exponentially with the defect core energy. Comparing the defect-free ground
state with the ground state with defects, it is found that the difference is
described by string-like excitations, bounded by defect pairs, which have a
fractal dimension of 1.250(3). At zero temperature, the disorder-induced
defects screen the interaction of introduced vortex pairs.",9807374v1
1999-02-12,Ground state of a homogeneous Bose gas: a diffusion Monte Carlo calculation,"We use a diffusion Monte Carlo method to calculate the lowest energy state of
a uniform gas of bosons interacting through different model potentials, both
strictly repulsive and with an attractive well. We explicitly verify that at
low density the energy per particle follows a universal behavior fixed by the
gas parameter na^3. In the regime of densities typical for experiments in
trapped Bose-condensed gases, the corrections to the mean-field energies
greatly exceed the differences due to the details of the potential.",9902185v1
1999-04-14,Density of states in coupled chains with off-diagonal disorder,"We compute the density of states (d.o.s.) in N coupled chains with random
hopping. At zero energy, the d.o.s. shows a singularity that strongly depends
on the parity of N. For odd N, the d.o.s. is proportional to 1/(E (\ln |E|)^3),
with and without time-reversal symmetry. For even N, the d.o.s. is proportional
to \ln |E| in the presence of time-reversal symmetry, while there is a
pseudogap, d.o.s. proportional to E \ln |E|, in the absence of time-reversal
symmetry.",9904200v1
1999-07-19,Correlation Effects on Optical Conductivity of FeSi,"Effects of electron correlation in FeSi are studied in terms of the two-band
Hubbard model with the density of states obtained from the band calculation.
Using the self-consistent second-order perturbation theory combined with the
local approximation, the correlation effects are investigated on the density of
states and the optical conductivity spectrum, which are found to reproduce the
experiments done by Damascelli et al. semiquantitatively. It is also found that
the peak at the gap edge shifts to lower energy region by correlation effects,
as is seen in the experiments.",9907264v2
1999-08-28,Thermodynamics of the s=1/2 transverse XX chain with Dzyaloshinskii-Moriya interaction in the presence of correlated Lorentzian disorder,"The spin-1/2 transverse XY chain with correlated disorder may exhibit the
nonzero averaged transverse magnetization at zero averaged transverse field. We
discuss this peculiarity connected with asymmetry in the density of states and
induced by the correlated disorder analysing the moments of the density of
states.",9908425v1
2000-05-26,Spin and charge excitations in incommensurate spin density waves,"Collective excitations both for spin- and charge-channels are investigated in
incommensurate spin density wave (or stripe) states on two-dimensional Hubbard
model. By random phase approximation, the dynamical susceptibility
\chi(q,\omega) is calculated for full range of (q,\omega) with including all
higher harmonics components. An intricate landscape of the spectra in
\chi(q,\omega) is obtained. We discuss the anisotropy of the dispersion cones
for spin wave excitations, and for the phason excitation related to the motion
of the stripe line. Inelastic neutron experiments on Cr and its alloys and
stripe states of underdoped cuprates are proposed.",0005466v1
2000-09-29,Density-correlator signatures of the vulcanization transition,"Certain density correlators, measurable via various experimental techniques,
are studied in the context of the vulcanization transition. It is shown that
these correlators contain essential information about both the vulcanization
transition and the emergent amorphous solid state. Contact is made with various
physical ingredients that have featured in experimental studies of amorphous
colloidal and gel systems and in theoretical studies of the glassy state.",0009479v1
2001-02-12,Comment on ``Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band'',"In a recent letter (PRL 84, 3930 (2000)) Nakhmedov et al. claimed that the
Van Hove singularity at $\epsilon=0$ in the density of states (DoS) of the
two-dimensional crystal with half-filled tight-binding band survives the
addition of substitutional impurities. This derivation suffers from several
inconsistencies. We resolve them and show that the DoS at the band center is
finite, as one might naively expect.",0102197v1
2001-03-02,Phonon Density-of-States in MgB2,"We report inelastic neutron scattering measurements of the phonon
density-of-states in Mg11B2, which has a superconducting transition at 39.2 K.
The acoustic phonons extend in energy to 36 meV, and there are highly
dispersive optic branches peaking at 54, 78, 89 and 97 meV. A simple Born-von
Karman model is able to reproduce the mode energies, and provides an estimate
of the electron-phonon coupling of lambda~0.9. The estimated boron and
magnesium contributions to the isotope effect are in qualitative agreement with
experiment. The data confirm that a conventional phonon mechanism, with
moderately strong electron-phonon coupling, can explain the observed
superconductivity.",0103064v1
2001-04-09,Phase diagram regions deduced for strongly correlated systems via unitary transformation,"From known phase diagram regions of different model Hamiltonians describing
strongly correlated systems we deduced new domains of the ground state phase
diagram of the same model by an unitary transformation. Different types of
extended Hubbard Hamiltonians were used for the starting point and the
existence of new stable spin-density wave, charge-density wave, ferromagnetic
state and a paramagnetic insulator is demonstrated. The used procedure itself
is dimension independent.",0104143v1
2001-09-06,Replica treatment of non-Hermitian disordered Hamiltonians,"We employ the fermionic and bosonic replicated nonlinear sigma models to
treat Ginibre unitary, symplectic, and orthogonal ensembles of non-Hermitian
random matrix Hamiltonians. Using saddle point approach combined with Borel
resummation procedure we derive the exact large-N results for microscopic
density of states in all three ensembles. We also obtain tails of the density
of states as well the two-point function for the unitary ensemble.",0109126v2
2002-01-17,Critical magnetic fluctuations induced superconductivity and residual density of states in $CeRhIn_5$ superconductor,"We propose the multiband extension of the spin-fermion model to address the
superconducting d-wave pairing due to magnetic interaction near critical point.
We solve the unrestricted gap equation with a general d-wave symmetry gap and
find that divergent magnetic correlation length $\xi$ leads to the very
unharmonic shape of the gap function with shallow gap regions near nodes. These
regions are extremely sensitive to disorder. Small impurity concentration
induces substantial residual density of states. We argue that we can understand
the large $N_{res}(0) = \lim_{T\to 0} C_p(T)/T$ value and its pressure
dependence of the recently discovered $CeRhIn_5$ superconductor under pressure
within this approach.",0201315v1
2002-06-15,Signature of Spin Collective Mode in Local Tunneling Spectra of a d-wave Superconductor,"We consider the influence of magnetic excitations on the local density of
states in the d-wave superconductor. The magnetic susceptibility is calculated
within the renormalized $t-t'-J$ model and its influence on the quasiparticle
self-energy is considered using a minimal model originally proposed by
Polkovnikov {\it et al.}[cond-mat/0203176]. We find the local density of states
possess periodic components both along $(\pi,0)$ and $(\pi,\pi)$ directions
with the associated wavevectors changing in magnitude as the quasiparticle
energy is varied. Comparison with the STM experiment reveals that the
calculated LDOS modulation is inconsistent with the measured data.",0206284v1
2002-09-27,Local Density of States in the Antiferromagnetic and Ferromagnetic Kondo Models,"Based on a simple approximation scheme we have computed the local density of
states (LDOS) of the antiferromagnetic and ferromagnetic Kondo models for the
full range of band occupations and coupling strengths. For both models the LDOS
with its full energy dependence has not been calculated before. Arguments are
given for the results to be qualitatively trustworthy despite the simplicity of
the approximation scheme.",0209639v1
2002-10-04,Electron-Phonon Interaction in NbB_2 : A Comparison with MgB_2,"We present a comparison of electron-phonon interaction in NbB_2 and MgB_2,
calculated using full-potential, density-functional-based methods in P6/mmm
crystal structure. Our results, described in terms of (i) electronic structure,
(ii) phonon density of states F(\omega), (iii) Eliashberg function \alpha
^2F(\omega), and (iv) the solutions of the isotropic Eliashberg gap equation,
clearly show significant differences in the electron-phonon interaction in
NbB_2 and MgB_2. We find that the average electron-phonon coupling constant
\lambda is equal to 0.59 for MgB_2 and 0.43 for NbB_2, leading to
superconducting transition temperature T_c of around 22 K for MgB_2 and 3 K for
NbB_2.",0210091v1
2003-01-13,"Low-density, one-dimensional quantum gases in a split trap","We investigate degenerate quantum gases in one dimension trapped in a
harmonic potential that is split in the centre by a pointlike potential. Since
the single particle eigenfunctions of such a system are known for all strengths
of the central potential, the dynamics for non-interacting fermionic gases and
low-density, strongly interacting bosonic gases can be investigated exactly
using the Fermi-Bose mapping theorem. We calculate the exact many-particle
ground-state wave-functions for both particle species, investigate soliton-like
solutions, and compare the bosonic system to the well-known physics of Bose
gases described by the Gross-Pitaevskii equation. We also address the
experimentally important questions of creation and detection of such states.",0301200v1
2003-02-19,"Random hopping fermions on bipartite lattices: Density of states, inverse participation ratios, and their correlations in a strong disorder regime","We study Anderson localization of non-interacting random hopping fermions on
bipartite lattices in two dimensions, focusing our attention to strong disorder
features of the model. We concentrate ourselves on specific models with a
linear dispersion in the vicinity of the band center, which can be described by
a Dirac fermion in the continuum limit. Based on the recent renormalization
group method developed by Carpentier and Le Doussal for the XY gauge glass
model, we calculate the density of states, inverse participation ratios, and
their spatial correlations. It turns out that their behavior is quite different
from those expected within naive weak disorder approaches.",0302376v1
2003-02-24,Defect and anisotropic gap induced quasi-one-dimensional modulation of local density of states in YBa$_2$Cu$_3$O$_{7-δ}$,"Motivated by recent angle-resolved photoemission spectroscopy (ARPES)
measurement that superconducting YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) exhibits a
$d_{x^2-y^2} + s$-symmetry gap, we show possible quasi-one-dimensional
modulations of local density of states in YBCO. These aniostropic gap and
defect induced stripe structures are most conspicuous at higher biases and
arise due to the nesting effect associated with a Fermi liquid. Observation of
these spectra by scanning tunneling microscopy (STM) would unify the picture
among STM, ARPES, and inelastic neutron scattering for YBCO.",0302473v1
2003-04-23,Generalized Coherent State Derivation of TDDFT Equations for Superconductors,"Equations of motion are derived for the normal and the anomalous
single-electron density matrices of a Fermi liquid using a time dependent
finite temperature generalized coherent state (GCS) variational ansatz for the
many-body density matrix. Self-consistent equations for the order parameter
$\Delta$ allow to investigate the interplay of Coulomb repulsion and pairing
attraction in homogeneous and inhomogeneous Fermi-liquids with spontaneously
broken symmetry such as high temperature superconductors. The temperature of
the Kosterlitz-Thouless transition to the two-dimensional superfluidity is
calculated.",0304531v1
2003-10-20,Density of states of the interacting two-dimensional electron gas,"We study the influence of electron-electron interactions on the density of
states (DOS) of clean 2D electron gas. We confirm the linear cusp in the DOS
around the Fermi level, which was obtained previously. The cusp crosses over to
a pure logarithmic dependence further away from the Fermi surface.",0310448v4
2003-11-13,Density of states of disordered Dirac particles: Infinitely many operators with negative scaling dimensions and freezing transitions,"The global density of states (GDOS) close to the band center $\epsilon=0$ for
a particle hopping on a square lattice and subjected to disorder that preserves
the bipartite symmetry of the lattice is computed using field theoretical
methods. The GDOS diverges like $ |\epsilon|^{-1}\exp (-c|\ln\epsilon|^{\kappa}
) $ with $\kappa=2/3$ in agreement with a prediction by Motrunich \textit{et
al.} and in disagreement with an older prediction by Gade ($\kappa=1/2$).",0311302v1
2004-01-22,Nonmagnetic impurity effects in MgB$_{2}$,"We study nonmagnetic impurity effects in MgB$_{2}$ using the quasiclassical
equations of superconductivity for a weak-coupling two-band model. Parameters
in the model are fixed so as to reproduce experiments on MgB$_{2}$ as closely
as possible. The quasiparticle density of states and the specific heat are
calculated for various values of the interband impurity scattering. The density
of states changes gradually from a two-gap structure into the conventional
single-gap structure as the interband scattering increases. It is found that
the excitation threshold is not a monotonic function of the interband
scattering. Calculated results for the specific heat are in good agreements
with experiments on samples after irradiation.",0401410v1
2004-07-20,Inhomogeneously doped thermoelectric nanomaterials,"Inhomogeneously doped thermoelectric nanomaterials with a delta-function
electronic density of states can operate with Carnot efficiency in the absence
of phonon heat leaks. Here we self-consistently calculate the efficiency and
power from open-circuit to short-circuit of a simple model of a thermoelectric
nanomaterial with a narrow peak in the electronic density of states and finite
lattice thermal conductivity, comparing the results for inhomogeneous and
homogeneous doping. For power generation between 800K and 300K, we find that
not only does inhomogeneous doping increase the maximum efficiency by 10%, but
it also increases the maximum power by up to 60%.",0407506v1
2004-07-28,STM Studies of Near-Optimal Doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$,"In this paper we summarize our STM studies of the density of electronic
states in nearly optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ in zero
field. We report on the inhomogeneity of the gap structure, density of states
modulations with four-lattice constant period, and coherence peak modulation.",0407743v1
2004-09-21,Pinning and Dynamics of Colloids on One Dimensional Periodic Potentials,"Using numerical simulations we study the pinning and dynamics of interacting
colloids on periodic one-dimensional substrates. As a function of colloid
density, temperature, and substrate strength, we find a variety of pinned and
dynamic states including pinned smectic, pinned buckled, two-phase flow, and
moving partially ordered structures. We show that for increasing colloid
density, peaks in the depinning threshold occur at commensurate states. The
scaling of the pinning threshold versus substrate strength changes when the
colloids undergo a transition from one-dimensional chains to a buckled
configuration.",0409561v1
2005-01-03,Rashba-control for the spin excitation of a fully spin polarized vertical quantum dot,"Far infrared radiation absorption of a quantum dot with few electrons in an
orthogonal magnetic field could monitor the crossover to the fully spin
polarized state. A Rashba spin-orbit coupling can tune the energy and the spin
density of the first excited state which has a spin texture carrying one extra
unit of angular momentum. The spin orbit coupling can squeeze a flipped spin
density at the center of the dot and can increase the gap in the spectrum.",0501021v1
2005-05-04,Probing the Kondo density of states in a three-terminal quantum ring,"We have measured the Kondo effect in a quantum ring connected to three
terminals. In this configuration non-linear transport measurements allow to
check which lead contributes to the Kondo density of states (DOS) and which
does not. When the ring is connected to two strongly and one weakly coupled
leads, the measurement of the differential conductance through the weakly
coupled lead allows to probe directly the Kondo DOS. In addition, by applying a
bias between the two strongly coupled leads, we show the splitting of the
out-of-equilibrium DOS.",0505111v1
2006-06-28,Evidence for the Luttigger liquid density of states in transport across the incompressible stripe at fractional filling factors,"We experimentally investigate transport across the incompressible stripe at
the sample edge in the fractional quantum Hall effect regime at bulk filling
factors $\nu=2/3$ and $\nu=2/5$. We obtain the dependence of the equilibration
length, that is a phenomenological characteristics of the transport, on the
voltage imbalance and the temperature, at high voltage imbalances. These
dependencies are found to be of the power-law form, which is a strong evidence
for the Luttigger liquid density of states.",0606741v2
2006-12-13,"Sampling the two-dimensional density of states g(E,M) of a giant magnetic molecule using the Wang-Landau method","The Wang-Landau method is used to study the magnetic properties of the giant
paramagnetic molecule Mo_72Fe_30 in which 30 Fe3+ ions are coupled via
antiferromagnetic exchange. The two-dimensional density of states g(E,M) in
energy and magnetization space is calculated using a self-adaptive version of
the Wang-Landau method. From g(E,M) the magnetization and magnetic
susceptibility can be calculated for any temperature and external field.",0612320v1
1997-05-12,Vacuum properties of a Non-Local Thirring-Like Model,"We use path-integral methods to analyze the vacuum properties of a recently
proposed extension of the Thirring model in which the interaction between
fermionic currents is non-local. We calculate the exact ground state wave
functional of the model for any bilocal potential, and also study its
long-distance behavior. We show that the ground state wave functional has a
general factored Jastrow form. We also find that it posess an interesting
symmetry involving the interchange of density-density and current-current
interactions.",9705077v1
2003-04-17,Asymptotic Density of Open p-brane States with Zero-modes included,"We obtain the asymptotic density of open p-brane states with zero-modes
included. The resulting logarithmic correction to the p-brane entropy has a
coefficient - \frac{p + 2}{2 p}, and is independent of the dimension of the
embedding spacetime. Such logarithmic corrections to the entropy, with
precisely this coefficient, appear in two other contexts also: a gas of
massless particles in p-dimensional space, and a Schwarzschild black hole in (p
+ 2)-dimensional anti de Sitter spacetime.",0304152v2
2002-10-25,Integrated density of states for ergodic random Schrödinger operators on manifolds,"We consider the Riemannian universal covering of a compact manifold $M = X /
\Gamma$ and assume that $\Gamma$ is amenable. We show for an ergodic random
family of Schr\""odinger operators on $X$ the existence of a (non-random)
integrated density of states.",0210047v1
2003-12-02,Quantum electrodynamics of relativistic bound states with cutoffs,"We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing
the interaction of relativistic electrons and positrons in the Coulomb
potential with photons in Coulomb gauge. The interaction includes both
interaction of the current density with transversal photons and the Coulomb
interaction of charge density with itself. We prove that the Hamiltonian is
self-adjoint and has a ground state for sufficiently small coupling constants.",0312011v1
2004-03-31,Hölder equicontinuity of the integrated density of states at weak disorder,"H\""older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, with
a constant $C$ independent of the disorder strength $\lambda$ is proved for the
integrated density of states $N_\lambda(E)$ associated to a discrete random
operator $H = H_o + \lambda V$ consisting of a translation invariant hopping
matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely
continuous distribution, under a regularity assumption for the hopping term.",0403063v2
2004-09-03,Continuity with respect to Disorder of the Integrated Density of States,"We prove that the integrated density of states (IDS) associated to a random
Schroedinger operator is locally uniformly Hoelder continuous as a function of
the disorder parameter lambda. In particular, we obtain convergence of the IDS,
as lambda tends to 0, to the IDS for the unperturbed operator at all energies
for which the IDS for the unperturbed operator is continuous in energy.",0409007v1
2001-05-21,Exact limiting solutions for certain deterministic traffic rules,"We analyze the steady-state flow as a function of the initial density for a
class of deterministic cellular automata rules (``traffic rules'') with
periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1
(1998)]. We are able to predict from simple considerations the observed,
unexpected cutoff of the average flow at unity. We also present an efficient
algorithm for determining the exact final flow from a given finite initial
state. We analyze the behavior of this algorithm in the infinite limit to
obtain for R_m,k an exact polynomial equation maximally of 2(m+k)th degree in
the flow and density.",0105045v1
1998-06-29,Relativistic Equation of State of Nuclear Matter for Supernova Explosion,"We construct the equation of state (EOS) of nuclear matter at finite
temperature and density with various proton fractions within the relativistic
mean field (RMF) theory for the use in the supernova simulations. The
Thomas-Fermi approximation is adopted to describe the non-uniform matter where
we consider nucleus, alpha-particle, proton and neutron in equilibrium. We
treat the uniform matter and non-uniform matter consistently using the RMF
theory. We tabulate the outcome as the pressure, free energy, entropy etc, with
enough mesh points in wide ranges of the temperature, proton fraction, and
baryon mass density.",9806095v1
2004-03-11,Ground state properties of rare-earth nuclei in the relativistic Hartree-Bogoliubov model with density-dependent meson-nucleon couplings,"The relativistic mean-field effective interaction with density-dependent
meson-nucleon couplings DD-ME1 is tested in the calculation of deformed nuclei.
Ground-state properties of six isotopic chains ($60\le Z \le 70$) in the region
of rare-earth nuclei are calculated by using the relativistic
Hartree-Bogoliubov (RHB) model with the DD-ME1 mean-field interaction, and with
the Gogny D1S force for the pairing interaction. Results of fully
self-consistent RHB calculations for the total binding energies, charge isotope
shifts and quadrupole deformation parameters are compared with the available
empirical data.",0403027v1
2004-08-06,Spin-orbit term and spin-fields: extension of Skyrme-force induced local energy density approach,"A systematic study of terminating states in A$\sim$50 mass region using the
self-consistent Skyrme-Hartree-Fock model is presented. The objective is to
demonstrate that the terminating states, due to their intrinsic simplicity,
offer unique and so far unexplored opportunities to study different aspects of
the effective NN interaction or nuclear local energy density functional. In
particular, we demonstrate that the agreement of the calculations to the data
depend on the spin fields and the spin-orbit term which, in turn, allows to
constrain the appropriate Landau parameters and the strength of the spin-orbit
potential.",0408018v1
2005-04-05,The phases of isospin asymmetric matter in the two flavor NJL model,"We investigate the phase diagram of isospin asymmetric matter at T=0 in the
two flavor Nambu-Jona-Lasinio model. Our approach describes the single nucleon
as a confined quark-diquark state, the saturation properties of nuclear matter
at normal densities, and the phase transition to normal or color
superconducting quark matter at higher densities. The resulting equation of
state of charge neutral matter is discussed.",0504020v2
2006-01-16,Density Matrix Renormalization Group and the Nuclear Shell Model,"We describe the use of the Density Matrix Renormalization Group method as a
means of approximately solving large-scale nuclear shell-model problems. We
focus on an angular-momentum-conserving variant of the method and report test
results for the nucleus $^{48}Cr$. The calculation is able to reproduce both
the ground state energy and the energy of the first excited state, by
diagonalizing matrices much smaller than those of the full shell model.",0601044v1
2002-12-19,Efficient Quantum State Tomography for Quantum Information Processing using a two-dimensional Fourier Transform Technique,"A new method of quantum state tomography for quantum information processing
is described. The method based on two-dimensional Fourier transform technique
involves detection of all the off-diagonal elements of the density matrix in a
two-dimensional experiment. All the diagonal elements are detected in another
one-dimensional experiment. The method is efficient and applicable to a wide
range of spin systems. The proposed method is explained using a 2 qubit system
and demonstrated by tomographing arbitrary complex density matrices of 2 and 4
qubit systems using simulations.",0212116v1
2006-06-12,Photon States from Propagating Complex Electromagnetic Fields,"A wavefunction for single- and many-photon states is defined by associating
photons with different momenta to different spectral and polarization
components of the classical, generally complex, electromagnetic field that
propagates in a definite direction. By scaling each spectral component of the
classical field to the square root of the photon energy, the appropriately
normalized photon wavefunction acquires the desired interpretation of
probability density amplitude, in contradistinction to the Riemann-Silbertsein
wavefunction that can be considered as the amplitude of the photon probability
energy density.",0606096v1
2007-08-24,Interacting holographic dark energy in the scalar-Gauss-Bonnet gravity,"In this paper we study cosmological application of interacting holographic
dark energy density in the scalar-Gauss-Bonnet framework. We employ the
interacting holographic model of dark energy to obtain the equation of state
for the interacting holographic energy density in spatially flat universe. Our
calculation show, taking $\Omega_{\Lambda}=0.73$ for the present time, it is
possible to have $w_{\rm \Lambda}^{eff}$ crossing -1. This implies that one can
generate phantom-like equation of state from the interacting holographic dark
energy model in flat universe in the scalar-Gauss-Bonnet cosmology framework.
Then we reconstruct the potential of the scalar field.",0708.3284v1
2008-04-30,Localization and interaction of indirect excitons in GaAs coupled quantum wells,"We introduced an elevated trap technique and exploited it for lowering the
effective temperature of indirect excitons. We observed narrow
photoluminescence lines which correspond to the emission of individual states
of indirect excitons in a disorder potential. We studied the effect of
exciton-exciton interaction on the localized and delocalized exciton states and
found that the homogeneous line broadening increases with density and dominates
the linewidth at high densities.",0804.4886v1
2008-11-07,Neutron scattering Measurements of the phonon density of states of FeSe$_{1-x}$ superconductors,"Inelastic neutron-scattering experiments have been carried out on
polycrystalline samples of the FeSe$_{1-x}$ superconductors. We report the
phonon density of states for FeSe$_{1-x}$ with Tc$\approx$8 K. The phonon
cutoff frequency is observed around 40 meV. No significant change is observed
across the superconducting transition. The measurements support the published
first-principles calculations [A. Subedi et al., Phys. Rev. B \textbf{78},
134514 (2008)].",0811.1215v3
2008-11-27,Density of states governs light scattering in photonic crystals,"We describe a smooth transition from (fully ordered) photonic crystal to
(fully disordered) photonic glass that enables us to make an accurate
measurement of the scattering mean free path in nanostructured media and, in
turn, establishes the dominant role of the density of states. We have found one
order of magnitude chromatic variation in the scattering mean free path in
photonic crystals for just $\sim 3%$ shift around the band-gap ($\sim 27$ nm in
wavelength).",0811.4494v1
2009-05-08,Hyperfine tensors of nitrogen-vacancy center in diamond from \emph{ab initio} calculations,"We determine and analyze the charge and spin density distributions of
nitrogen-vacancy (N-V) center in diamond for both the ground and excited states
by \emph{ab initio} supercell calculations. We show that the hyperfine tensor
of $^{15}$N nuclear spin is negative and strongly anisotropic in the excited
state, in contrast to previous models used extensively to explain electron spin
resonance measurements. In addition, we detect a significant redistribution of
the spin density due to excitation that has serious implications for the
quantum register applications of N-V center.",0905.1169v1
2009-10-17,Yang-Lee Zeros of the Triangular Ising Antiferromagnets,"Using both the exact enumeration method (microcanonical transfer matrix) for
a small system (L = 9) and the Wang-Landau Monte Carlo algorithm for large
systems to L = 30, we obtain the exact and approximate densities of states
g(M,E), as a function of magnetization M and exchange energy E, for the
triangular-lattice Ising model. Based on the density of states g(M,E), we
investigate the phase transition properties of Yang-Lee zeros for the
triangular Ising antiferromagnets and obtain the magnetic exponents at various
temperatures.",0910.3255v1
2010-01-19,Generalized Cramer-Rao relations for non-relativistic quantum systems,"The Cramer-Rao product of the Fisher information and the variance of a
probability density \rho(x), defined on a domain \Delta \in R^D, is found to
have a minimum value reached by the density associated with the ground state of
the harmonic oscillator in \Delta, when \Delta is an unbounded domain. If
\Delta is bounded, the minimum value of the Fisher information is achieved by
the ground state of the quantum box described itself by this domain.",1001.3376v1
2010-02-10,Spin-orbit coupling induced anisotropy effects in bimetallic antiferromagnets: A route towards antiferromagnetic spintronics,"Magnetic anisotropy phenomena in bimetallic antiferromagnets Mn$_2$Au and
MnIr are studied by first-principles density functional theory calculations. We
find strong and lattice-parameter dependent magnetic anisotropies of the ground
state energy, chemical potential, and density of states, and attribute these
anisotropies to combined effects of large moment on the Mn 3$d$ shell and large
spin-orbit coupling on the 5$d$ shell of the noble metal. Large magnitudes of
the proposed effects can open a route towards spintronics in compensated
antiferromagnets without involving ferromagnetic elements.",1002.2151v1
2010-08-27,Interface Landau levels in graphene monolayer-bilayer junction,"Electronic structure of graphene monolayer-bilayer junction in a magnetic
field is studied within an effective-mass approximation. The energy spectrum is
characterized by interface Landau levels, i.e., the locally flat bands
appearing near the boundary region, resulting in a series of characteristic
peaks in the local density of states. Their energies are independent of
boundary types such as zigzag or armchair. In the atomic scale, the local
density of states shows a Kekul\'{e} pattern due to the valley mixing in the
armchair boundary, while does not in the zigzag boundary.",1008.4679v1
2010-11-26,Effect of boron dimers on the superconducting critical temperature in boron-doped diamond,"We study how attractive boron correlations in boron-doped diamond affect the
superconducting critical temperature. The critical temperature is obtained from
the McMillan formula for strong coupling superconductors with the density of
states evaluated in the dynamical cluster approximation. Numerical results for
the cluster of $2\times 2\times 2$ atoms show that attractive correlations
lower the density of states at the Fermi level. We argue that this might
explain experimentally observed differences in critical temperatures of 100 and
111 oriented films.",1011.5824v2
2011-06-28,Uniform existence of the integrated density of states on metric Cayley graphs,"Given a finitely generated amenable group we consider ergodic random
Schr\""odinger operators on a Cayley graph with random potentials and random
boundary conditions. We show that the normalised eigenvalue counting functions
of finite volume parts converge uniformly. The integrated density of states as
the limit can be expressed by a Pastur-Shubin formula. The spectrum supports
the corresponding measure and discontinuities correspond to the existence of
compactly supported eigenfunctions.",1106.5724v2
2011-08-12,Quantum Uncertainties in the Schmidt Basis Given by Decoherence,"A common misconception is that decoherence gives the eigenstates that we
observe to be fairly definite about a subsystem (e.g., approximate eigenstates
of position) as the elements of the Schmidt basis in which the density matrix
of the subsystem is diagonal. Here I show that in simple examples of linear
systems with gaussian states, the Schmidt basis states have as much mean
uncertainty about position as the full density matrix with its combination of
different possibilities.",1108.2709v2
2011-08-30,Signatures of Delocalization in the Fermionic 1D Hubbard Model with Box Disorder: Comparative Study with DMRG and R-DMFT,"We investigate the 1D Anderson-Hubbard model at half filling with
box-disorder. The ground state phase diagram is obtained by means of real-space
dynamical mean-field theory (R-DMFT) and the density matrix renormalization
group (DMRG). We find Mott insulating and Anderson localized regimes as well as
a strong indication of a delocalized phase for intermediate interaction and
disorder strength within accessible system sizes. These phases are
characterized and distinguished by qualitatively different scaling behavior of
the local density of states, the energy gap in the excitation spectrum and the
inverse participation number.",1108.6057v1
2012-03-16,Perturbative Analysis of Nonequilibrium Steady States in Quantum Systems,"We study the nonequilibrium steady state (NESS) in a quantum system in
contact with two heat baths at different temperatures. We use a
time-independent perturbative expansion with respect to the coupling with the
two heat baths to obtain the density matrix for the NESS. In particular, we
show an explicit representation of the density matrix for the reflection
symmetric and weakly nonequilibrium case. We also calculate the expectation
value of the energy current and show that the Kubo formula holds in this case.",1203.3817v1
2012-05-01,A Note on the Analyticity of Density of States,"We consider the $d$-dimensional Anderson model, and we prove the density of
states is locally analytic if the single site potential distribution is locally
analytic and the disorder is large. We employ the random walk expansion of
resolvents and a simple complex function theory trick. In particular, we
discuss the uniform distribution case, and we obtain a sharper result using
more precise computations. The method can be also applied to prove the
analyticity of the correlation functions.",1205.0077v2
2012-05-15,A Correction Method for the Density of States,"We present a correction method for the density of states (DOS) obtained from
the generalized ensemble simulations. The DOS is proportionally corrected to
match the exact values and/or good approximations known for the system. We
demonstrate the validity of the method by applying it to the DOS of 2D Potts
model calculated from various generalized ensemble simulations. It is shown
that the root-mean-square error of the DOS is reduced by ~50% or more without
additional heavy calculations.",1205.3244v1
2012-05-23,Quantum Coulomb gap in low dimensions,"We study the single-particle density of states of one-dimensional and
two-dimensional quantum disordered systems with long-range interactions. We
consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction
in two dimensions, which produce linear gaps in the density of states in both
cases. We focus on the strong localization regime where the localization length
is small but non-zero. We use an exact diagonalization technique for small
system sizes and a perturbation approach for larger sizes. We find that, with
both methods, the inclusion of a finite hopping contribution does not change
the linear character of the gap, but reduces its slope, widening the gap.",1205.5186v1
2012-06-08,"Effect of Ni, Fe Intercalation on the Superconducting Properties of ZrTe3","We report the superconductivity at enhanced temperature of 5.2 K in the
polycrystalline sample of ZrTe3 and Ni intercalated ZrTe3. ZrTe3 is a Charge
Density Wave (T = 63K) compound, which is known to superconduct only below 2K
in single crystalline form. We discuss that the intergrain strains in the
polycrystalline samples induces an intrinsic pressure and thus enhances the
transition temperature. Fe intercalation of ZrTe3 kills both the charge density
wave and superconducting states, gives rise to the magnetic ordering in the
compound.",1206.1716v1
2012-07-10,Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs,"In this paper we consider random Hamiltonians defined on long-range
percolation graphs over $\ZZ^d$. The Hamiltonian consists of a randomly
weighted Laplacian plus a random potential. We prove uniform existence of the
integrated density of states and express the IDS using a Pastur-Shubin trace
formula.",1207.2445v2
2012-09-04,The effect of point split regularization on the sign of the Casimir energy,"In a recent paper [1] the Casimir energy was calculated for a massive dirac
field in (1+1) dimensional space-time in the presence of an inverse square well
potential and shown to be positive. It will be shown that this result violates
a key assumption of quantum field theory which is that the vacuum state is the
state of minimum energy. The reason for this discrepancy is examined and is
shown to be related to the way the charge density operator is defined. If the
charge density operator is defined using point splitting then an extra term
will be added to the charge which will result in the Casimir energy being
negative.",1209.0508v1
2012-11-28,Averaged collision and reaction rates in a two-species gas of ultracold fermions,"Reactive or elastic two-body collisions in an ultracold gas are affected by
quantum statistics. In this paper, we study ensemble-averaged collision rates
for a two-species fermionic gas. The two species may have different masses,
densities and temperatures. We investigate how averaged collision rates are
affected by the presence of Fermi spheres in the initial states; Pauli blocking
of final states is not considered. It is shown that, independently on the
details of the collision, Fermi-averaged collision rates deviate from
Boltzmann-averaged ones, particularly for a gas with strong imbalance of masses
or densities.",1211.6613v1
2013-03-29,Double Dressing and Manipulation of the Photonic Density of States in Nanostructured Qubits,"In this work, a model to study the coupling between a semiconductor qubit and
two timedependent electric fields is developed. By using it in the resonantly
monochromatic double dressing regime, control of the local density of optical
states is theoretically and numerically demonstrated for a strongly confined
exciton. Drastic changes in the allowed energy transitions yielding tunable
broadening of the optically active frequency ranges, are observed in the
simulated emission spectra. The presented results are in excellent qualitative
and quantitative agreement with recent experimental observations.",1303.7411v2
2013-06-08,Wide range equation of state for fluid hydrogen within density functional theory,"Wide range equation of state (EOS) for liquid hydrogen is ultimately built by
combining two kinds of density functional theory (DFT) molecular dynamics
simulations, namely, first-principles molecular dynamics simulations and
orbital-free molecular dynamics simulations. Specially, the present
introduction of short cutoff radius pseudopotentials enables the hydrogen EOS
to be available in the range $9.82\times10^{-4}$ to $1.347\times10^{3}$
g/cm$^{3}$ and up to $5\times10^{7}$ K. By comprehensively comparing with
various attainable experimental and theoretical data, we derive the conclusion
that our DFT-EOS can be readily and reliably conducted to hydrodynamic
simulations of the inertial confinement fusion.",1306.1902v1
2014-01-10,Nonequilibrium thermal entanglement for three-spin chain,"The dynamics of a chain of three spins coupled at both ends to separate
bosonic baths at different temperatures is studied. An exact analytical so-
lution of the master equation in the Born-Markov approximation for the reduced
density matrix of the chain is constructed. It is shown that for long times the
reduced density matrix converges to the non-equilibrium steady- state.
Dynamical and steady state properties of the concurrence between the first and
the last spin are studied.",1401.2302v1
2014-02-02,Current states in superconducting films: numerical results and approximations,"We present numerical solution of equations by Aslamazov and Lempitskiy (AL)
for the distribution of the transport current density in thin superconducting
films in the absence of external magnetic field, in both the Meissner and the
vortex states. This solution describes smooth transition between the regimes of
a wide film and a narrow channel and enables us to find the critical currents
and current-voltage characteristics within a wide range of the film width and
temperatures. We propose simple approximating formulas for the current density
distributions and critical currents.",1402.0230v2
2015-11-25,Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit,"We consider the Bogolubov-Hartree-Fock functional for a fermionic many-body
system with two-body interactions. For suitable interaction potentials that
have a strong enough attractive tail in order to allow for two-body bound
states, but are otherwise sufficiently repulsive to guarantee stability of the
system, we show that in the low-density limit the ground state of this model
consists of a Bose-Einstein condensate of fermion pairs. The latter can be
described by means of the Gross-Pitaevskii energy functional.",1511.08047v1
2016-01-22,Screening of magnetic moment at Co impurity in Cu host,"Cobalt impurity located in the bulk copper is described making use of the
multi-orbital Anderson impurity model that is parametrized to match the
electronic structure from the local density approximation, and solved using the
Lanczos method. We concentrate on the many-body description of the ground state
and excitation spectra. The calculations yield a nonmagnetic ground state for
the impurity atom. The computed spectral densities are in a good agreement with
those obtained using the quantum Monte Carlo method.",1601.06022v1
2017-08-15,Strong and weak single particle nonlocality induced by time-dependent boundary conditions,"We investigate the issue of single particle nonlocality in a quantum system
subjected to time-dependent boundary conditions. We first prove that contrary
to earlier claims, there is no strong nonlocality: a quantum state localized at
the center of a well with infinitely high moving walls is not modified by the
wall's motion. We then show the existence of a weak form of nonlocality: when a
quantum state is extended over the well, the wall's motion induces a current
density all over the box instantaneously. We indicate how this current density
can in principle be measured by performing weak measurements of the particle's
momentum.",1708.05293v1
2018-04-30,Spectral theory of Liouvillians for dissipative phase transitions,"A state of an open quantum system is described by a density matrix, whose
dynamics is governed by a Liouvillian superoperator. Within a general
framework, we explore fundamental properties of both first-order dissipative
phase transitions and second-order dissipative phase transitions associated
with a symmetry breaking. In the critical region, we determine the general form
of the steady-state density matrix and of the Liouvillian eigenmatrix whose
eigenvalue defines the Liouvillian spectral gap. We illustrate our exact
results by studying some paradigmatic quantum optical models exhibiting
critical behavior.",1804.11293v2
2010-05-26,Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder,"We theoretically demonstrate features of Anderson localization in the
Tonks-Girardeau gas confined in one-dimensional (1D) potentials with controlled
disorder. That is, we investigate the evolution of the single particle density
and correlations of a Tonks-Girardeau wave packet in such disordered
potentials. The wave packet is initially trapped, the trap is suddenly turned
off, and after some time the system evolves into a localized steady state due
to Anderson localization. The density tails of the steady state decay
exponentially, while the coherence in these tails increases. The latter
phenomenon corresponds to the same effect found in incoherent optical solitons.",1005.4726v1
2010-05-26,Monte Carlo simulation of joint density of states of two continuous spin models using Wang-Landau-Transition-Matrix Algorithm,"Monte Carlo simulation has been performed in one-dimensional Lebwohl-Lasher
model and two dimensional XY-model using the Wang-Landau and the
Wang-Landau-Transition-Matrix Monte Carlo methods. Random walk has been
performed in the two-dimensional space comprising of energy-order parameter and
energy-correlation function and the joint density of states (JDOS) were
obtained. From the JDOS the order parameter, susceptibility and correlation
function are calculated. Agreement between the results obtained from the two
algorithms is very good.",1005.4847v1
2014-03-26,Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations,"In this paper, we are concerned with the compressible Euler-Maxwell equations
with a nonconstant background density (e.g. of ions) in three dimensional
space. There exist stationary solutions when the background density is a small
perturbation of a positive constant state. We first show the asymptotic
stability of solutions to the Cauchy problem near the stationary state provided
that the initial perturbation is sufficiently small. Moreover the convergence
rates are obtained by combining the $L^p$-$L^q$ estimates for the linearized
equations with time-weighted estimate.",1403.6595v1
2017-06-07,Semi-classical limit of the Levy-Lieb functional in Density Functional Theory,"In a recent work, Bindini and De Pascale have introduced a regularization of
$N$-particle symmetric probabilities which preserves their one-particle
marginals. In this short note, we extend their construction to mixed quantum
fermionic states. This enables us to prove the convergence of the Levy-Lieb
functional in Density Functional Theory , to the corresponding multi-marginal
optimal transport in the semi-classical limit. Our result holds for mixed
states of any particle number $N$, with or without spin.",1706.02199v4
2017-06-22,Oscillation theory for the density of states of high dimensional random operators,"Sturm-Liouville oscillation theory is studied for Jacobi operators with block
entries given by covariant operators on an infinite dimensional Hilbert space.
It is shown that the integrated density of states of the Jacobi operator is
approximated by the winding of the Pruefer phase w.r.t. the trace per unit
volume. This rotation number can be interpreted as a spectral flow in a von
Neumann algebra with finite trace.",1706.07498v2
2017-09-25,Delta shocks in the relativistic full Euler equations for a Chaplygin gas,"The relativistic full Euler equations for a Chaplygin gas are studied. The
Riemann problem is solved constructively. There are two kinds of Riemann
solutions, in which one consists of three contact discontinuities and the other
involves a delta shock wave on which both state variables the rest mass density
and the proper energy density simultaneously contain the Dirac delta functions.
It is quite different from the previous ones on which only one state variable
contains the Dirac delta function. The formation mechanism, generalized
Rankine-Hugoniot relation and entropy condition are clarified for this type of
delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy
condition, the existence and uniqueness of delta shock solutions are also
established.",1709.08445v1
2017-09-26,Eigenstate entanglement in the Sachdev-Ye-Kitaev model,"We study the entanglement entropy of eigenstates (including the ground state)
of the Sachdev-Ye-Kitaev model. We argue for a volume law, whose coefficient
can be calculated analytically from the density of states. The coefficient
depends on not only the energy density of the eigenstate but also the subsystem
size. Very recent numerical results of Liu, Chen, and Balents confirm our
analytical results.",1709.09160v2
2017-10-19,Tailoring symmetric metallic and magnetic edge states of nanoribbon in semiconductive monolayer PtS2,"Fabrication of atomic scale of metallic wire remains challenging. In present
work, a nanoribbon with two parallel symmetric metallic and magnetic edges was
designed from semiconductive monolayer PtS2 by employing first-principles
calculations based on density functional theory. Edge energy, bonding charge
density, band structure and simulated STM of possible edges states of PtS2 were
systematically studied. It was found that Pt-terminated edge nanoribbons were
the relatively stable metallic and magnetic edge tailored from a noble
transition metal dichalcogenides PtS2. The nanoribbon with two atomic metallic
wires may have promising application as nano power transmission lines, which at
least two lines are needed.",1710.07008v1
2019-01-30,Vortex patterns in the almost-bosonic anyon gas,"We study theoretically and numerically the ground state of a gas of 2D
abelian anyons in an external trapping potential. We treat anyon statistics in
the magnetic gauge picture, perturbatively around the bosonic end. This leads
to a mean-field energy functional, whose ground state displays vortex lattices
similar to those found in rotating Bose-Einstein condensates. A crucial
difference is however that the vortex density is proportional to the underlying
matter density of the gas.",1901.10739v2
2020-03-31,Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators,"We study discrete random Schr\""odinger operators via the supersymmetric
formalism. We develop a cluster expansion that converges at both strong and
weak disorder. We prove the exponential decay of the disorder-averaged Green's
function and the smoothness of the local density of states either at weak
disorder and at energies in proximity of the unperturbed spectrum or at strong
disorder and at any energy. As an application, we establish Lifshitz-tail-type
estimates for the local density of states and thus localization at weak
disorder.",2004.00145v2
2020-05-04,Correlation-induced orbital angular momentum changes,"We demonstrate that the orbital angular momentum flux density of a paraxial
light beam can change on propagation in free space. These changes are entirely
due to the spatial coherence state of the source, and the effect is analogous
to correlation-induced changes in the intensity, spectrum and polarization of a
beam. The use of the source coherence state to control the width, shape, and
transverse shifts of the OAM flux density is demonstrated with numerical
examples.",2005.01667v1
2020-10-21,Evidence for direct and indirect gap in FeSi from electron tunneling spectroscopy,"We report electron tunneling spectroscopy studies on single crystalline FeSi
sample performed for the case of homogeneous tunnel junction contacts and for
the case of counter electrodes made from Pt-Rh alloy. Our results reveal that
while the tunneling spectroscopy in the configuration with Pt-Rh tip is
preferably sensitive to the d-partial density of states and to the indirect
energy gap, the FeSi-FeSi type of tunnel junction yields spectroscopic
information on the c-partial density of states and on the direct gap in FeSi.",2010.10838v1
2021-08-13,The Integrated Density of States of the 1D Discrete Anderson-Bernoulli Model at Rational Energies,"We show there is a countable dense set of energies at which the integrated
density of states of the 1D discrete Anderson-Bernoulli model can be given
explicitly and does not depend on the disorder parameter, provided the latter
is above an energy-dependent threshold.",2108.06311v2
2022-05-31,Detection of multipartite entanglement based on Heisenberg-Weyl representation of density matrices,"We study entanglement and genuine entanglement of tripartite and four-partite
quantum states by using Heisenberg-Weyl (HW) representation of density
matrices. Based on the correlation tensors in HW representation, we present
criteria to detect entanglement and genuine tripartite and four-partite
entanglement. Detailed examples show that our method can detect more entangled
states than previous criteria.",2205.15493v1
2022-12-19,Progress applying density of states for gravitational waves,"Many models of composite dark matter feature a first-order confinement
transition in the early Universe, which would produce a stochastic background
of gravitational waves that will be searched for by future gravitational-wave
observatories. We present work in progress using lattice field theory to
predict the properties of such first-order transitions. Targeting SU(N)
Yang--Mills theories, this work employs the Logarithmic Linear Relaxation (LLR)
density of states algorithm to avoid super-critical slowing down at the
transition.",2212.09199v1
2023-03-10,Density of states for the Anderson model on nested fractals,"We prove the existence and establish the Lifschitz singularity of the
integrated density of states for certain random Hamiltonians
$H^\omega=H_0+V^\omega$ on fractal spaces of infinite diameter. The kinetic
term $H_0$ is given by $\phi(-\mathcal L),$ where $\mathcal L$ is the Laplacian
on the fractal and $\phi$ is a completely monotone function satisfying some
mild regularity conditions. The random potential $V^\omega$ is of alloy-type.",2303.05980v1
2023-07-30,Non-Equilibrium Nature of Fracture Determines the Crack Paths,"A high-fidelity neural network-based force field, NN-F$^{3}$, is developed to
cover the strain states up to material failure and the non-equilibrium,
intermediate nature of fracture. Simulations of fracture in 2D crystals using
NN-F$^{3}$ reveal spatial complexities from lattice-scale kinks to sample-scale
patterns. We find that the fracture resistance cannot be quantified by the
energy densities of relaxed edges as in the literature. Instead, the fracture
patterns, critical stress intensity factors at the kinks, and energy densities
of edges in the intermediate, unrelaxed states offer reasonable measures for
the fracture toughness and its anisotropy.",2307.16126v1
2023-10-09,Second Order Expansion of Gibbs State Reduced Densities in the Gross-Pitaevskii Regime,"We consider a translation-invariant system of $N$ bosons in $\mathbb{T}^{3}$
that interact through a repulsive two-body potential with scattering length of
order $N^{-1}$ in the limit $N\to \infty$. We derive second order expressions
for the one- and two-particle reduced density matrices of the Gibbs state at
fixed positive temperatures, thus obtaining a justification of Bogoliubov's
prediction on the fluctuations around the condensate.",2310.05448v1
2019-01-15,Turbulence decay in the density-stratified intracluster medium,"Turbulence evolution in a density-stratified medium differs from that of
homogeneous isotropic turbulence described by the Kolmogorov picture. We
evaluate the degree of this effect in the intracluster medium (ICM) with
hydrodynamical simulations. We find that the buoyancy effect induced by ICM
density stratification introduces qualitative changes to the turbulence energy
evolution, morphology, and the density fluctuation - turbulence Mach number
relation, and likely explains the radial dependence of the ICM turbulence
amplitude as found previously in cosmological simulations. A new channel of
energy flow between the kinetic and the potential energy is opened up by
buoyancy. When the gravitational potential is kept constant with time, this
energy flow leaves oscillations to the energy evolution, and leads to a
balanced state of the two energies where both asymptote to power-law time
evolution with slopes shallower than that for the turbulence kinetic energy of
homogeneous isotropic turbulence. We discuss that the energy evolution can
differ more significantly from that of homogeneous isotropic turbulence when
there is a time variation of the gravitational potential. Morphologically, ICM
turbulence can show a layered vertical structure and large horizontal vortical
eddies in the central regions with the greatest density stratification. In
addition, we find that the coefficient in the linear density fluctuation -
turbulence Mach number relation caused by density stratification is in general
a variable with position and time.",1901.04666v2
2022-06-28,Electronic-structure properties from atom-centered predictions of the electron density,"The electron density of a molecule or material has recently received major
attention as a target quantity of machine-learning models. A natural choice to
construct a model that yields transferable and linear-scaling predictions is to
represent the scalar field using a multi-centered atomic basis analogous to
that routinely used in density fitting approximations. However, the
non-orthogonality of the basis poses challenges for the learning exercise, as
it requires accounting for all the atomic density components at once. We devise
a gradient-based approach to directly minimize the loss function of the
regression problem in an optimized and highly sparse feature space. In so
doing, we overcome the limitations associated with adopting an atom-centered
model to learn the electron density over arbitrarily complex datasets,
obtaining extremely accurate predictions. The enhanced framework is tested on
32-molecule periodic cells of liquid water, presenting enough complexity to
require an optimal balance between accuracy and computational efficiency. We
show that starting from the predicted density a single Kohn-Sham
diagonalization step can be performed to access total energy components that
carry an error of just 0.1 meV/atom with respect to the reference density
functional calculations. Finally, we test our method on the highly
heterogeneous QM9 benchmark dataset, showing that a small fraction of the
training data is enough to derive ground-state total energies within chemical
accuracy.",2206.14087v1
2007-02-01,Effect of the Inverse Volume Modification in Loop Quantum Cosmology,"It is known that in loop quantum cosmology (LQC) the universe avoids the
singularity by a bounce when the matter density approaches the critical density
$\rho_c$ (the order of Planck density). After incorporating the inverse volume
modifications both in the gravitational and matter part in the improved
framework of LQC, we find that the inverse volume modification can decrease the
bouncing energy scale, and the presence of nonsingular bounce is generic. For
the backward evolution in the expanding branch, in terms of different initial
states the evolution trajectories classify into two classes. One class with
larger initial energy density leads to the occurrence of bounce in the region
$a>a_{ch}$ where $a_{ch}$ marks the different inverse volume modification
region. The other class with smaller initial energy density evolves back into
the region $a<a_{ch}$. In this region, both the energy density for the scalar
field and the bouncing energy scale decrease with the backward evolution.
However, in the deep modification region, because of the inverse volume
modification the scalar field is frozen, such that the bounce is present when
the bouncing energy scale decreases to be equal to the energy density of the
scalar field. Using numerical method, we show the evolution picture for the
second class bounce.",0702002v2
2009-02-25,Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism,"We consider a periodic lattice loaded with pairs of bosonic atoms tightly
bound to each other via strong attractive on-site interaction that exceeds the
inter-site tunneling rate. An ensemble of such lattice-dimers is accurately
described by an effective Hamiltonian of hard core bosons with strong
nearest-neighbor repulsion which is equivalent to the $XXZ$ model with
Ising-like anisotropy. We calculate the ground-state phase diagram for a
one-dimensional system which exhibits incompressible phases, corresponding to
an empty and a fully filled lattice (ferromagnetic phases) and a half-filled
alternating density crystal (anti-ferromagnetic phase), separated from each
other by compressible phases. In a finite lattice the compressible phases show
characteristic oscillatory modulations on top of the anti-ferromagnetic density
profile and in density-density correlations. We derive a kink model which
provides simple quantitative explanation of these features. To describe the
long-range correlations of the system we employ the Luttinger liquid theory
with the relevant Luttinger parameter $K$ obtained exactly using the Bethe
Ansatz solution. We calculate the density-density as well as first-order
correlations and find excellent agreement with numerical results obtained with
density matrix renormalization group (DMRG) methods. We also present a
perturbative treatment of the system in higher dimensions.",0902.4442v1
2012-07-07,"Vortex creep and critical current densities in superconducting (Ba,K)Fe$_{2}$As$_{2}$ single crystals","The surprisingly rapid relaxation of the sustainable current density in the
critical state of single crystalline Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ is
investigated for magnetic fields oriented parallel to the c-axis and to the
$ab$--plane respectively. Due to the inadequacy of standard analysis procedures
developed for flux creep in the high temperature superconducting cuprates, we
develop a simple, straightforward data treatment technique that reveals the
creep mechanism and the creep exponent $\mu$. At low magnetic fields, below the
second magnetization peak, $\mu$ varies only slightly as function of
temperature and magnetic flux density $B$. From the data, we determine the
temperature- and field dependence of the effective activation barrier for
creep. At low temperatures, the measured current density approaches the
zero--temperature critical current density (in the absence of creep) to within
a factor 2, thus lending credence to earlier conclusions drawn with respect to
the pinning mechanism. The comparable values of the experimental screening
current density and the zero-temperature critical current density reveals the
limited usefulness of the widely used ""interpolation formula"".",1207.1796v1
2012-04-03,Interacting fermions in 1D disordered lattices: Exploring localization and transport properties with lattice density-functional theories,"We investigate the static and dynamical behavior of 1D interacting fermions
in disordered Hubbard chains, contacted to semi-infinite leads. The chains are
described via the repulsive Anderson-Hubbard Hamiltonian, using static and
time-dependent lattice density-functional theory. The dynamical behavior of our
quantum transport system is performed via an integration scheme available in
the literature, which we modify via the recursive Lanczos method, to increase
its efficiency. To quantify the degree of localization due to disorder and
interactions, we adapt the definition of the inverse participation ratio to
obtain an indicator which is both suitable for quantum transport geometries and
which can be obtained within density-functional theory. Lattice density
functional theories are reviewed and, for contacted chains, we analyze the
merits and limits of the coherent-potential approximation in describing the
spectral properties, with interactions included via lattice density functional
theory. Our approach appears to able to capture complex features due to the
competition between disorder and interactions. Specifically, we find a
dynamical enhancement of delocalization in presence of a finite bias, and an
increase of the steady-state current induced by inter-particle interactions.
This behavior is corroborated by results for the time-dependent densities and
for the inverse participation ratio. Using short isolated chains with
interaction and disorder, a brief comparative analysis between time-dependent
density-functional theory and exact results is then given, followed by general
conclusive remarks.",1204.0672v2
2022-06-10,In Defense of Core-set: A Density-aware Core-set Selection for Active Learning,"Active learning enables the efficient construction of a labeled dataset by
labeling informative samples from an unlabeled dataset. In a real-world active
learning scenario, considering the diversity of the selected samples is crucial
because many redundant or highly similar samples exist. Core-set approach is
the promising diversity-based method selecting diverse samples based on the
distance between samples. However, the approach poorly performs compared to the
uncertainty-based approaches that select the most difficult samples where
neural models reveal low confidence. In this work, we analyze the feature space
through the lens of the density and, interestingly, observe that locally sparse
regions tend to have more informative samples than dense regions. Motivated by
our analysis, we empower the core-set approach with the density-awareness and
propose a density-aware core-set (DACS). The strategy is to estimate the
density of the unlabeled samples and select diverse samples mainly from sparse
regions. To reduce the computational bottlenecks in estimating the density, we
also introduce a new density approximation based on locality-sensitive hashing.
Experimental results clearly demonstrate the efficacy of DACS in both
classification and regression tasks and specifically show that DACS can produce
state-of-the-art performance in a practical scenario. Since DACS is weakly
dependent on neural architectures, we present a simple yet effective
combination method to show that the existing methods can be beneficially
combined with DACS.",2206.04838v3
2021-07-21,The Fluid Dynamics of the One-Body Stationary States of Quantum Mechanics with Real Valued Wavefunctions,"It is demonstrated that the probability density function, given by the square
of a quantum mechanical wavefunction that is a real-valued eigenvector of a
time-independent, one-body Schroedinger equation, satisfies a compressible-flow
generalization of the Bernoulli equation, where the mass density is the
probability density times the mass of the system; the pressure and velocity
fields are defined by functions depending on the probability density, and the
gradient and the Laplacian of the probability density, where there are two
possible directions of the velocity on a streamline. The velocity given
definition implies a generalization of the steady-flow continuity equation
where mass is not locally conserved. The gradient of the Bernoullian equation
is demonstrated to be equivalent to the steady flow Euler equation for variable
mass and irrotational flow. A speed of sound quadratic equation is obtained
from a spherical wave-pulse. One of the solutions indicates that the wave-pulse
velocity on a streamline is equal in magnitude but opposite in direction of the
fluid velocity on the streamline. The other solution is the focus of attention
from that point on. It is proven that the extremums of the momentum per volume
on a streamline occur at points that are Mach 1 speed. The developed formalism
is applied to a particle in a one-dimensional box, the ground and first
excited-states of the one-dimensional harmonic oscillator, and the hydrogen 1s
and 2s states. Some behavior is repeated in all the applications examined. For
example, an antinode, a point of local-maximum density, has zero velocity and
zero Mach speed on the streamline, while a node, a point of minimum density,
has infinite velocity and Mach 2. In between the node and antinode is an
extremum of the momentum, and Mach 1. (This is a short version of the
abstract.)",2107.10315v1
2003-06-11,Hadronic Density of States from String Theory,"Exactly soluble string theories describing a particular hadronic sector of
certain confining gauge theories have been obtained recently as Penrose-Gueven
limits of the dual supergravity backgrounds. The effect of taking the
Penrose-Gueven limit on the gravity side translates, in the gauge theory side,
into an effective truncation to hadrons of large U(1) charge (annulons). We
present an exact calculation of the finite temperature partition function for
the hadronic states corresponding to a Penrose-Gueven limit of the
Maldacena-Nunez embedding of N=1 SYM into string theory. It is established that
the theory exhibits a Hagedorn density of states.
  Motivated by this exact calculation we propose a semiclassical string
approximation to the finite temperature partition function for confining gauge
theories admitting a supergravity dual, by performing an expansion around
classical solutions characterized by temporal windings. This semiclassical
approximation reveals a hadronic energy density of states of Hagedorn type,
with the coefficient determined by the gauge theory string tension as expected
for confining theories. We argue that our proposal captures primarily
information about states of pure N=1 SYM, given that this semiclassical
approximation does not entail a projection onto states of large U(1) charge.",0306107v1
2009-02-01,Band terminations in density functional theory,"The analysis of the terminating bands has been performed in the relativistic
mean field framework. It was shown that nuclear magnetism provides an
additional binding to the energies of the specific configuration and this
additional binding increases with spin and has its {\it maximum} exactly at the
terminating state. This suggests that the terminating states can be an
interesting probe of the time-odd mean fields {\it provided that other effects
can be reliably isolated.} Unfortunately, a reliable isolation of these effects
is not that simple: many terms of the density functional theories contribute
into the energies of the terminating states and the deficiencies in the
description of those terms affect the result. The recent suggestion
\cite{ZSW.05} that the relative energies of the terminating states in the $N
\neq Z, A\sim 44$ mass region given by $\Delta E$ {\it provide unique and
reliable constraints on time-odd mean fields and the strength of spin-orbit
interaction} in density functional theories has been reanalyzed. The current
investigation shows that the $\Delta E$ value is affected also by the relative
placement of the states with different orbital angular momentum ${\it l}$,
namely, the placement of the $d$ (${\it l}=2$) and $f$ (${\it l}=3$) states.
This indicates the dependence of the $\Delta E$ value on the properties of the
central potential.",0902.0098v1
2020-03-07,Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform,"In this work, we consider the problem of steering the first two moments of
the uncertain state of a discrete time nonlinear stochastic system to
prescribed goal quantities at a given final time. In principle, the latter
problem can be formulated as a density tracking problem, which seeks for a
feedback policy that will keep the probability density function of the state of
the system close, in terms of an appropriate metric, to the goal density. The
solution to the latter infinite-dimensional problem can be, however, a complex
and computationally expensive task. Instead, we propose a more tractable and
intuitive approach which relies on a greedy control policy. The latter control
policy is comprised of the first elements of the control policies that solve a
sequence of corresponding linearized covariance steering problems. Each of
these covariance steering problems relies only on information available about
the state mean and state covariance at the current stage and can be formulated
as a tractable (finite-dimensional) convex program. At each stage, the
information on the state statistics is updated by computing approximations of
the predicted state mean and covariance of the resulting closed-loop nonlinear
system at the next stage by utilizing the (scaled) unscented transform.
Numerical simulations that illustrate the key ideas of our approach are also
presented.",2003.03679v2
2021-10-22,Multipartitioning topological phases by vertex states and quantum entanglement,"We discuss multipartitions of the gapped ground states of (2+1)-dimensional
topological liquids into three (or more) spatial regions that are adjacent to
each other and meet at points. By considering the reduced density matrix
obtained by tracing over a subset of the regions, we compute various
correlation measures, such as entanglement negativity, reflected entropy, and
associated spectra. We utilize the bulk-boundary correspondence to show that
such multipartitions can be achieved by using what we call vertex states in
(1+1)-dimensional conformal field theory -- these are a type of state used to
define an interaction vertex in string field theory and can be thought of as a
proper generalization of conformal boundary states. This approach allows an
explicit construction of the reduced density matrix near the entangling
boundaries. We find the fingerprints of topological liquid in these quantities,
such as (universal pieces in) the scaling of the entanglement negativity, and a
non-trivial distribution of the spectrum of the partially transposed density
matrix. For reflected entropy, we test the recent claim that states the
difference between reflected entropy and mutual information is given, once
short-range correlations are properly removed, by $(c/3)\ln 2$ where $c$ is the
central charge of the topological liquid that measures ungappable edge degrees
of freedom. As specific examples, we consider topological chiral $p$-wave
superconductors and Chern insulators. We also study a specific lattice fermion
model realizing Chern insulator phases and calculate the correlation measures
numerically, both in its gapped phases and at critical points separating them.",2110.11980v1
2013-09-20,Probing the high-density behavior of symmetry energy with gravitational waves,"Gravitational wave (GW) astronomy opens up an entirely new window on the
Universe to probe the equations of state (EOS) of neutron-rich matter. With the
advent of next generation GW detectors, measuring the gravitational radiation
from coalescing binary neutron star systems, mountains on rotating neutron
stars, and stellar oscillation modes may become possible in the near future.
Using a set of model EOSs satisfying the latest constraints from terrestrial
nuclear experiments, state of the art nuclear many-body calculations of the
pure neutron matter EOS, and astrophysical observations consistently, we study
various GW signatures of the high-density behavior of the nuclear symmetry
energy, which is considered among the most uncertain properties of dense
neutron-rich nucleonic matter. In particular, we find the tidal polarizability
of neutron stars, potentially measurable in binary systems just prior to
merger, is more sensitive to the high density component of the nuclear symmetry
energy than the symmetry energy at nuclear saturation density. We also find
that the upper limit on the GW strain amplitude from elliptically deformed
stars is very sensitive to the density dependence of the symmetry energy. This
suggests that future developments in modeling of the neutron star crust, and
direct gravitational wave signals from accreting binaries will provide a wealth
of information on the EOS of neutron-rich matter. We also review the
sensitivity of the $r$-mode instability window to the density dependence of the
symmetry energy. Whereas models with larger values of the density slope of the
symmetry energy at saturation seem to be disfavored by the current
observational data, within a simple $r$-mode model, we point out that a
subsequent softer behavior of the symmetry energy at high densities (hinted at
by recent observational interpretations) could rule them in.",1309.5153v1
2002-04-14,Observation of large many-body Coulomb interaction effects in a doped quantum wire,"We demonstrate strong one dimensional (1-D) many-body interaction effects in
photoluminescence (PL) in a GaAs single quantum wire of unprecedented optical
quality, where 1-D electron plasma densities are controlled via electrical
gating. We observed PL of 1-D charged excitons with large binding energy of 2.3
meV relative to the neutral excitons, and its evolution to a Fermi-edge
singularity at high electron density. Furthermore, we find a strong band-gap
renormalization in the 1-D wire, or a large red-shift of PL with increased
electron plasma density. Such a large PL red-shift is not observed when we
create a high density neutral electron-hole plasma in the same wire, due
probably to cancellation of the Coulomb interaction energy in the neutral
plasma.",0204301v1
2003-12-03,Electronic Raman scattering in unconventional density waves,"We investigate the electronic Raman scattering in pure, quasi-one dimensional
conductors with density wave ground state. In particular, we develop the theory
of light-scattering on spin and charge density waves, both conventional and
unconventional. We calculate the electronic Raman response of the interacting
electron system with a single, highly anisotropic conduction band. The
calculation is carried out in the mean field approximation. Beside the
quasiparticle contribution, the electron-electron interaction is also included
on RPA level. The contribution of collective modes and the effect of Coulomb
screening are investigated. In analogy with unconventional superconductivity,
the obtained Raman spectra - which are finite in the low temperature phase
possessing a gap, and vanish identically in the normal state - show unique and
strong dependence on the polarization of the incoming and scattered light. We
have found distinct, characteristic lineshapes, especially in the
unconventional situation, depending on the various scattering geometries and
the particular momentum dependence of the density wave order parameter.",0312093v2
2005-06-28,A macroscopic persistent current generation by merons in a spin density wave ordered state,"We show that a stable spontaneous current appears in a system of a spin
density wave order with merons, vortices in the spin configuration with winding
number +1. A meron in the spin density wave order modifies the boundary
condition for eigenfunctions around it to a sign-change one. As a consequence,
two types of stable current states, one with a clockwise circulation and the
other with a counterclockwise one, arise. When a magnetic field is present, one
produces a diamagnetic current is chosen. A collection of such currents results
in a large diamagnetic current; and if the meron density is sufficiently large,
a perfect diamagnetism is realized. The stability of this diamagnetic current
is attributed to the topological nature of the merons, and as long as the
distribution of the merons remains the same the current will persist even in a
macroscopic system.",0506747v1
2006-03-07,Quantum dot with ferromagnetic leads: a density-matrix renormalization group study,"A quantum dot coupled to ferromagnetically polarized one-dimensional leads is
studied numerically using the density matrix renormalization group method.
Several real space properties and the local density of states at the dot are
computed. It is shown that this local density of states is suppressed by the
parallel polarization of the leads. In this case we are able to estimate the
length of the Kondo cloud, and to relate its behavior to that suppression.
Another important result of our study is that the tunnel magnetoresistance as a
function of the quantum dot on-site energy is minimum and negative at the
symmetric point.",0603168v2
2001-09-10,Transition from BCS pairing to Bose-Einstein condensation in low-density asymmetric nuclear matter,"We study the isospin-singlet neutron-proton pairing in bulk nuclear matter as
a function of density and isospin asymmetry within the BCS formalism. In the
high-density, weak-coupling regime the neutron-proton paired state is strongly
suppressed by a minor neutron excess. As the system is diluted, the BCS state
with large, overlapping Cooper pairs evolves smoothly into a Bose-Einstein
condensate of tightly bound neutron-proton pairs (deuterons). In the resulting
low-density system a neutron excess is ineffective in quenching the pair
correlations because of the large spatial separation of the deuterons and
neutrons. As a result, the Bose-Einstein condensation of deuterons is weakly
affected by an additional gas of free neutrons even at very large asymmetries.",0109024v1
2007-06-01,Recent progress constraining the nuclear equation of state from astrophysics and heavy ion reactions,"The quest for the nuclear equation of state (EoS) at high densities and/or
extreme isospin is one of the longstanding problems of nuclear physics. Ab
initio calculations for the nuclear many-body problem make predictions for the
density and isospin dependence of the EoS far away from the saturation point of
nuclear matter. On the other hand, in recent years substantial progress has
been mode to constrain the EoS both, from the astrophysical side and from
accelerator based experiments. Heavy ion experiments support a soft EoS at
moderate densities while recent neutron star observations require a ``stiff''
high density behavior. Both constraints are discussed and shown to be in
agreement with the predictions from many-body theory.",0706.0130v1
2007-10-23,BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter,"We propose new types of density dependent contact pairing interaction which
reproduce the pairing gaps in symmetric and neutron matter obtained by a
microscopic treatment based on the nucleon-nucleon interaction. These
interactions are able to simulate the pairing gaps of either the bare
interaction or the interaction screened by the medium polarization effects. It
is shown that the medium polarization effects cannot be cast into the density
power law function usually introduced together with the contact interaction and
require the introduction of another isoscalar term. The BCS-BEC crossover of
neutrons pairs in symmetric and symmetric nuclear matter is studied by using
these contact interactions. It is shown that the bare and screened pairing
interactions lead to different features of the BCS-BEC crossover in symmetric
nuclear matter. For the screened pairing interaction, a two-neutron BEC state
is formed in symmetric matter at $k_{Fn}\sim 0.2$ fm$^{-1}$ (neutron density
$\rho_n/\rho_0\sim 10^{-3}$). Contrary the bare interaction does not form the
BEC state at any neutron density.",0710.4241v2
2007-11-21,The high density equation of state: constraints from accelerators and astrophysics,"The nuclear equation of state (EoS) at high densities and/or extreme isospin
is one of the longstanding problems of nuclear physics. In the last years
substantial progress has been made to constrain the EoS both, from the
astrophysical side and from accelerator based experiments. Heavy ion
experiments support a soft EoS at moderate densities while the possible
existence of high mass neutron star observations favors a stiff EoS. Ab initio
calculations for the nuclear many-body problem make predictions for the density
and isospin dependence of the EoS far away from the saturation point. Both, the
constraints from astrophysics and accelerator based experiments are shown to be
in agreement with the predictions from many-body theory.",0711.3367v1
2009-06-10,Polarized Fermi gases in asymmetric optical lattices,"The zero-temperature phase diagrams of imbalanced two-species Fermi gases are
investigated in asymmetric optical lattices with arbitrary potential depths,
based on the exact spectrum instead of the Fermi-Hubbard model. We study the
effect of lattice potentials and atomic densities to the fully paired
Bardeen-Cooper-Schrieffer (BCS) state and particularly the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. It is found that the increasing
lattice potential favors BCS at low densities because of the enhanced effective
coupling; whereas FFLO is favored at intermediate densities when the system
undergoes a dimensional crossover. Finally using local density approximation we
study the evolution of phase profile in the presence of external harmonic traps
by merely tuning the lattice potentials.",0906.1937v2
2013-11-16,A thermodynamically consistent quasi-particle model without density-dependent infinity of the vacuum zero point energy,"In this paper, we generalize the improved quasi-particle model proposed in J.
Cao et al., [ Phys. Lett. B {\bf711}, 65 (2012)] from finite temperature and
zero chemical potential to the case of finite chemical potential and zero
temperature, and calculate the equation of state (EOS) for (2+1) flavor Quantum
Chromodynamics (QCD) at zero temperature and high density. We first calculate
the partition function at finite temperature and chemical potential, then go to
the limit $T=0$ and obtain the equation of state (EOS) for cold and dense QCD,
which is important for the study of neutron stars. Furthermore, we use this EOS
to calculate the quark-number density, the energy density, the quark-number
susceptibility and the speed of sound at zero temperature and finite chemical
potential and compare our results with the corresponding ones in the existing
literature.",1311.4017v2
2014-11-16,Semiclassical time crystal in the chiral Gross-Neveu model,"In the limit of a large number of flavors, the ground state of the chiral
Gross-Neveu model at finite fermion density exhibits a spatially periodic mean
field in the form of the chiral spiral, thereby breaking translational
invariance. Here we show that the ground state of the same model at finite
fermion current density gives rise to a mean field which is periodic in time, a
temporal chiral spiral. Since the current density is the same as axial charge
density in two dimensions and axial charge is conserved, this may serve as an
example of a time crystal. More specifically, as mean field theory is invoked
in the large N limit, we are dealing with a semiclassical time crystal.",1411.4236v1
2014-12-12,"Effect of dilute, strongly pinning impurities on charge density waves","We study theoretically the effects of strong pinning centers on a charge
density wave in the limit that the charge density wave coherence length is
shorter than the average inter-impurity distance. An analysis based on a
Ginzburg-Landau model shows that long range forces arising from the elastic
response of the charge density wave induce a kind of collective pinning which
suppresses impurity-induced phase fluctuations leading to a long ranged ordered
ground state. The effective correlations among impurities are characterized by
a length scale parametrically longer than the average inter-impurity distance.
The thermal excitations are found to be gapped implying the stability of the
ground state. We also present Monte Carlo simulations that confirm the basic
features of the analytical results.",1412.3965v1
2015-10-01,Microscopically constrained mean field models from chiral nuclear thermodynamics,"We explore the use of mean field models to approximate microscopic nuclear
equations of state derived from chiral effective field theory across the
densities and temperatures relevant for simu- lating astrophysical phenomena
such as core-collapse supernovae and binary neutron star mergers. We consider
both relativistic mean field theory with scalar and vector meson exchange as
well as energy density functionals based on Skyrme phenomenology and compare to
thermodynamic equa- tions of state derived from chiral two- and three-nucleon
forces in many-body perturbation theory. Quantum Monte Carlo simulations of
symmetric nuclear matter and pure neutron matter are used to determine the
density regimes in which perturbation theory with chiral nuclear forces is
valid. Within the theoretical uncertainties associated with the many-body
methods, we find that select mean field models describe well microscopic
nuclear thermodynamics. As an additional consistency requirement, we study as
well the single-particle properties of nucleons in a hot/dense environment,
which affect e.g., charged-current weak reactions in neutron-rich matter. The
identified mean field models can be used across a larger range of densities and
temperatures in astrophysical simulations than more computationally expensive
microscopic models.",1510.00444v2
2015-11-16,Ground-state densities of repulsive two-component Fermi gases,"We investigate separations of trapped balanced two-component atomic Fermi
gases with repulsive contact interaction. Candidates for ground-state densities
are obtained from the imaginary-time evolution of a nonlinear
pseudo-Schr\""odinger equation in three dimensions, rather than from the
cumbersome variational equations. With the underlying hydrodynamical approach,
gradient corrections to the Thomas-Fermi approximation are conveniently
included and are shown to be vital for reliable density profiles. We provide
critical repulsion strengths that mark the onset of phase transitions in a
harmonic trap. We present transitions from identical density profiles of the
two fermion species towards isotropic and anisotropic separations for various
confinements, including harmonic and double-well-type traps. Our proposed
method is suited for arbitrary trap geometries and can be straightforwardly
extended to study dynamics in the light of ongoing experiments on degenerate
Fermi gases.",1511.04873v1
2010-05-04,The universal viscosity to entropy density ratio from entanglement,"We present evidence that the universal Kovtun-Son-Starinets shear viscosity
to entropy density ratio of 1/4\pi can be associated with a Rindler causal
horizon in flat spacetime. Since there is no known holographic (gauge/gravity)
duality for this spacetime, a natural microscopic explanation for this
viscosity is in the peculiar properties of quantum entanglement. In particular,
it is well-known that the Minkowski vacuum state is a thermal state and carries
an area entanglement entropy density in the Rindler spacetime. Based on the
fluctuation-dissipation theorem, we expect a similar notion of viscosity
arising from vacuum fluctuations. Therefore, we propose a holographic Kubo
formula in terms of a two-point function of the stress tensor of matter fields
in the bulk. We calculate this viscosity assuming a minimally coupled scalar
field theory and find that the ratio with respect to the entanglement entropy
density is exactly 1/4\pi in four dimensions. The issues that arise in
extending this result to non-minimally coupled scalar fields, higher spins, and
higher dimensions provide interesting hints about the relationship between
entanglement entropy and black hole entropy.",1005.0475v2
2017-04-18,First-Principles Simulations of Warm Dense Lithium Fluoride,"We perform first-principles path integral Monte Carlo (PIMC) and density
functional theory molecular dynamics (DFT-MD) calculations to explore warm
dense matter states of LiF. Our simulations cover a wide density-temperature
range of $2.08-15.70$~g$\,$cm$^{-3}$ and $10^4-10^9$~K. Since PIMC and DFT-MD
accurately treat effects of atomic shell structure, we find a pronounced
compression maximum and a shoulder on the principal Hugoniot curve attributed
to K-shell and L-shell ionization. The results provide a benchmark for
widely-used EOS tables, such as SESAME, LEOS, and models. In addition, we
compute pair-correlation functions that reveal an evolving plasma structure and
ionization process that is driven by thermal and pressure ionization. Finally,
we compute electronic density of states of liquid LiF from DFT-MD simulations
and find that the electronic gap can remain open with increasing density and
temperature to at least 15.7 g$~$cm$^{-3}$.",1704.05197v1
2008-07-27,"Density functional study of FeS, FeSe and FeTe: Electronic structure, magnetism, phonons and superconductivity","We report density functional calculations of the electronic structure, Fermi
surface, phonon spectrum, magnetism and electron-phonon coupling for the
superconducting phase FeSe, as well as the related compounds FeS and FeTe. We
find that the Fermi surface structure of these compounds is very similar to
that of the Fe-As based superconductors, with cylindrical electron sections at
the zone corner, cylindrical hole surface sections, and depending on the
compound, other small hole sections at the zone center. As in the Fe-As based
materials, these surfaces are separated by a 2D nesting vector at
($\pi$,$\pi$). The density of states, nesting and Fermi surface size increase
going from FeSe to FeTe. Both FeSe and FeTe show spin density wave ground
states, while FeS is close to an instability. In a scenario where
superconductivity is mediated by spin fluctuations at the SDW nesting vector,
the strongest superconductor in this series would be doped FeTe.",0807.4312v2
2016-05-16,Quantum Phase Transition of the Electron-Hole Liquid In the Coupled Quantum Wells,"Many-component electron-hole plasma is considered in the Coupled Quantum
Wells (CQW). It is found that the homogeneous state of the plasma is unstable
if the carrier density is sufficiently small. The instability results in the
breakdown into two coexisting phase - a low-density gas phase and a
high-density electron-hole liquid. The homogeneous state of the electron-hole
liquid is stable if the distance between the quantum wells l is sufficiently
small. However, as the distance l increases and reaches a certain critical
value, the plasmon spectrum of the electron-hole liquid becomes unstable.
Hereupon, a quantum phase transition occurs, resulting in the appearance of the
charge density waves of finite amplitude in both quantum wells. The strong mass
renormalization and the strong Z-factor renormalization are found for the
electron-hole liquid as the quantum phase transition occurs.",1605.04748v1
2017-10-16,Transmission and reflection of charge density waves in a quantum Hall edge controlled by a metal gate,"Quantum energy teleportation (QET) is a proposed protocol related to the
quantum vacuum. The edge channels in a quantum Hall system is well suited for
the experimental verification of QET. For this purpose, we examine a charge
density wave excited and detected by capacitively coupled front gate
electrodes. We observe the waveform of the charge density wave, which is
proportional to the time derivative of the applied square voltage wave.
Further, we study the transmission and reflection behaviors of the charge
density wave by applying a voltage to another front gate electrode to control
the path of the edge state. We show that the threshold voltages where the
dominant direction is switched in either transmission or reflection for dense
and sparse waves are different from the threshold voltage where the current
stops flowing in an equilibrium state.",1710.05530v1
2020-01-21,Negative Energy States in Quantum Theory,"We analyze the Lagrangian density and canonical stress-energy tensor for the
Dirac equation, where the Dirac bispinor has been recast as a multivector set
of fields. For the massless Dirac field, the sign of the energy density is
determined by the relative phase of uncoupled even- and odd-grade field
components. These components become coupled in the massive Dirac equation, and
the sign of the energy is determined by their spatial parity. The corresponding
stress-energy tensors for the second-order equations also admit negative energy
states, with the sign of the energy density again dependent on field parity. We
apply the same multivector approach to electromagnetism, constructing new
Lagrangian and energy densities in which the vector potential and the
electromagnetic field are treated as independent field degrees of freedom.",2001.11345v1
2020-05-06,Skyrmion crystal phases in antiferromagnetic itinerant triangular magnets,"Very often the skyrmions form a triangular crystal in chiral magnets. Here we
study the effect of itinerant electrons on the structure of skyrmion crystal
(SkX) on triangular lattice using Kondo lattice model in the large coupling
limit and treating the localized spins as classical vectors. To simulate the
system, we employ hybrid Markov Chain Monte Carlo method (hMCMC) which includes
electron diagonalization in each MCMC update for classical spins. We present
the low temperature results for $12\times 12$ system at electron density
$n=1/3$ which show a sudden jump in skyrmion number when we increase the
hopping strength of the itinerant electrons. We find that this high skyrmion
number SkX phase is stabilized by combined effects: lowering of density of
states at electron filling $n=1/3$ and also pushing the bottom energy states
further down. We show that these results hold for larger system using
travelling cluster variation of hMCMC. We expect that itinerant triangular
magnets might exhibit the possible transition between low density to high
density SkX phases by applying external pressure.",2005.02724v1
2020-06-24,Crossover transitions in a bus-car mixed-traffic cellular automata model,"We modify the Nagel-Schreckenberg (NaSch) cellular automata model to study
mixed-traffic dynamics. We focus on the interplay between passenger
availability and bus-stopping constraints. Buses stop next to occupied cells of
a discretized sidewalk model. By parametrizing the spacing distance between
designated stops, our simulation covers the range of load-anywhere behavior to
that of well-spaced stops. The interplay of passenger arrival rates and bus
densities drives crossover transitions from platooning to non-platooned
(free-flow and congested) states. We show that platoons can be dissolved by
either decreasing the passenger arrival rate or increasing the bus density. The
critical passenger arrival rate at which platoons are dissolved is an
exponential function of vehicle density. We also find that at low densities,
spacing stops close together induces platooned states, which reduces system
speeds and increases waiting times of passengers.",2006.13532v1
2021-01-05,Chiral Effective Field Theory and the High-Density Nuclear Equation of State,"Born in the aftermath of core collapse supernovae, neutron stars contain
matter under extraordinary conditions of density and temperature that are
difficult to reproduce in the laboratory. In recent years, neutron star
observations have begun to yield novel insights into the nature of strongly
interacting matter in the high-density regime where current theoretical models
are challenged. At the same time, chiral effective field theory has developed
into a powerful framework to study nuclear matter properties with quantified
uncertainties in the moderate-density regime for modeling neutron stars. In
this article, we review recent developments in chiral effective field theory
and focus on many-body perturbation theory as a computationally efficient tool
for calculating the properties of hot and dense nuclear matter. We also
demonstrate how effective field theory enables statistically meaningful
comparisons between nuclear theory predictions, nuclear experiments, and
observational constraints on the nuclear equation of state.",2101.01709v2
2022-02-03,On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet,"Using finite temperature strong coupling expansions for the SU(N) Hubbard
Model, we calculate the thermodynamic properties of the model in the
infinite-$U$ limit for arbitrary density $0\leq \rho \leq 1$ and all $N$. We
express the ferromagnetic susceptibility of the model as a Curie term plus a
$\Delta \chi$, an excess susceptibility above the Curie-behavior. We show that,
on a bipartite lattice, graph by graph the contributions to $\Delta \chi$ are
non-negative in the limit that the hole density $\delta=1-\rho$ goes to zero.
By summing the contributions from all graphs consisting of closed loops we find
that the low hole-density ferromagnetic susceptibility diverges exponentially
as $\exp{\Delta /T}$ as $T \to 0$ in two and higher dimensions. This
demonstrates that Nagaoka-Thouless ferromagnetic state exists as a
thermodynamic state of matter at low enough density of holes and sufficiently
low temperatures. The constant $\Delta$ scales with the SU(N) parameter $N$ as
$1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as
the characteristic temperature scale for ferromagnetic order goes down.",2202.01611v1
2022-05-24,"EBM Life Cycle: MCMC Strategies for Synthesis, Defense, and Density Modeling","This work presents strategies to learn an Energy-Based Model (EBM) according
to the desired length of its MCMC sampling trajectories. MCMC trajectories of
different lengths correspond to models with different purposes. Our experiments
cover three different trajectory magnitudes and learning outcomes: 1) shortrun
sampling for image generation; 2) midrun sampling for classifier-agnostic
adversarial defense; and 3) longrun sampling for principled modeling of image
probability densities. To achieve these outcomes, we introduce three novel
methods of MCMC initialization for negative samples used in Maximum Likelihood
(ML) learning. With standard network architectures and an unaltered ML
objective, our MCMC initialization methods alone enable significant performance
gains across the three applications that we investigate. Our results include
state-of-the-art FID scores for unnormalized image densities on the CIFAR-10
and ImageNet datasets; state-of-the-art adversarial defense on CIFAR-10 among
purification methods and the first EBM defense on ImageNet; and scalable
techniques for learning valid probability densities. Code for this project can
be found at https://github.com/point0bar1/ebm-life-cycle.",2205.12243v1
2001-12-12,Role of disorder in half-filled high Landau levels,"We study the effects of disorder on the quantum Hall stripe phases in
half-filled high Landau levels using exact numerical diagonalization. We show
that, in the presence of weak disorder, a compressible, striped charge density
wave, becomes the true ground state. The projected electron density profile
resembles that of a smectic liquid. With increasing disorder strength W, we
find that there exists a critical value, W_c \sim 0.12 e^2/\epsilon l, where a
transition/crossover to an isotropic phase with strong local electron density
fluctuations takes place. The many-body density of states are qualitatively
distinguishable in these two phases and help elucidate the nature of the
transition.",0112233v2
2007-12-22,"A Raman study of the Charge-Density-Wave State in A$_{0.3}$MoO$_3$ (A = K,Rb)","We report a comparative Raman spectroscopic study of the
quasi-one-dimensional charge-density-wave systems \ab (A = K, Rb). The
temperature and polarization dependent experiments reveal charge-coupled
vibrational Raman features. The strongly temperature-dependent collective
amplitudon mode in both materials differ by about 3 cm, thus revealing the role
of alkali atom. We discus the observed vibrational features in terms of
charge-density-wave ground state accompanied by change in the crystal symmetry.
A frequency-kink in some modes seen in \bb between T = 80 K and 100 K supports
the first-order lock-in transition, unlike \rb. The unusually sharp Raman
lines(limited by the instrumental response) at very low temperatures and their
temperature evolution suggests that the decay of the low energy phonons is
strongly influenced by the presence of the temperature dependent charge density
wave gap.",0712.3880v1
2022-04-11,Interplay between Pair Density Wave and a Nested Fermi Surface,"We show that spontaneous time-reversal-symmetry (TRS) breaking can naturally
arise from the interplay between pair density wave (PDW) ordering at multiple
momenta and nesting of Fermi surfaces (FS). Concretely, we consider
pair-density-wave superconductivity on a hexagonal lattice with nested FS at
$3/4$ electron filling, which is related to a recently discovered
superconductor CsV$_3$Sb$_5$. Because of nesting of the FS, each momentum $\bk$
on the FS has at least two counterparts $-\bk\pm\mathbf{Q}_{\alpha}$
($\alpha=1,2,3$) on the FS to form finite momentum ($\pm\mathbf{Q}_{\alpha}$)
Cooper pairs, resulting in a TRS and inversion broken PDW state with stable
Bogoliubov Fermi pockets. Various spectra, including (local) density of states,
electron spectral function and the effect of quasi-particle interference, have
been investigated. The partial melting of the PDW will give rise to
$4\times{}4$ and $\frac{4}{\sqrt{3}}\times\frac{4}{\sqrt{3}}$ CDW orders, in
addition to the $2\times2$ CDW. Possible implications to real materials such as
CsV$_3$Sb$_5$ and future experiments have been further discussed.",2204.05029v2
2021-05-17,Continuum random-phase approximation for gamma transition between excited states in neutron-rich nuclei,"A characteristic feature of collective and particle-hole excitations in
neutron-rich nuclei is that many of them couple to unbound neutron in continuum
single-particle orbits. The continuum random phase approximation (cRPA) is a
powerful many-body method that describes such excitations, and it provides a
scheme to evaluate transition strengths from the ground state. In an attempt to
apply cRPA to the radiative neutron capture reaction, we formulate in the
present study an extended scheme of cRPA that describes gamma-transitions from
the excited states under consideration, which decay to low-lying excited states
as well as the ground state. This is achieved by introducing a non-local
one-body operator which causes transitions to a low-lying excited state, and
describing a density-matrix response against this operator. As a demonstration
of this new scheme, we perform numerical calculation for dipole, quadrupole,
and octupole excitations in $^{140}$Sn, and discuss E1 and E2 transitions
decaying to low-lying $2^{+}_{1,2}$ and $3^{-}_{1}$ states. The results point
to cases where the branching ratio to the low-lying states is larger than or
comparable with that to the ground state. We discuss key roles of collectivity
and continuum orbits in both initial and final states.",2105.07586v1
1996-11-30,Symmetrized DMRG studies of the properties of Low-lying states of Poly-para-phenylene (PPP) system,"We report the symmetrized density matrix renormalization group (DMRG) study
of neutral and doped oligomers of PPP system within an extended Hubbard model.
Model parameters are determined by comparing the existing results for
interacting small system. We compute a number of properties in the ground state
as well as in the one-photon, two-photon and triplet states to completely
characterize these states. Based on the relative positions of the one-photon
and two-photon states in long oligomers, we suggest that invoking interchain
interactions is essential for explaining strong fluorescence in this system.
Bond-order studies show that the lowest two-photon state corresponds to a
localized excitation while one-photon and triplet excitations are extended in
nature. The bipolaronic state shows clear evidence for charge separation and
disproportionation into two polarons. We find that the extended nature of
one-photon and triplet states of neutral system are very similar to those of
the bipolaronic ground states.",9612012v1
2004-04-27,"Unknown Quantum States and Operations, a Bayesian View","The classical de Finetti theorem provides an operational definition of the
concept of an unknown probability in Bayesian probability theory, where
probabilities are taken to be degrees of belief instead of objective states of
nature. In this paper, we motivate and review two results that generalize de
Finetti's theorem to the quantum mechanical setting: Namely a de Finetti
theorem for quantum states and a de Finetti theorem for quantum operations. The
quantum-state theorem, in a closely analogous fashion to the original de
Finetti theorem, deals with exchangeable density-operator assignments and
provides an operational definition of the concept of an ""unknown quantum state""
in quantum-state tomography. Similarly, the quantum-operation theorem gives an
operational definition of an ""unknown quantum operation"" in quantum-process
tomography. These results are especially important for a Bayesian
interpretation of quantum mechanics, where quantum states and (at least some)
quantum operations are taken to be states of belief rather than states of
nature.",0404156v1
2018-03-22,Joint Quantum-State and Measurement Tomography with Incomplete Measurements,"Estimation of quantum states and measurements is crucial for the
implementation of quantum information protocols. The standard method for each
is quantum tomography. However, quantum tomography suffers from systematic
errors caused by imperfect knowledge of the system. We present a procedure to
simultaneously characterize quantum states and measurements that mitigates
systematic errors by use of a single high-fidelity state preparation and a
limited set of high-fidelity unitary operations. Such states and operations are
typical of many state-of-the-art systems. For this situation we design a set of
experiments and an optimization algorithm that alternates between maximizing
the likelihood with respect to the states and measurements to produce estimates
of each. In some cases, the procedure does not enable unique estimation of the
states. For these cases, we show how one may identify a set of density matrices
compatible with the measurements and use a semi-definite program to place
bounds on the state's expectation values. We demonstrate the procedure on data
from a simulated experiment with two trapped ions.",1803.08245v2
2002-01-26,Equation of state of dense matter and the minimum mass of cold neutron stars,"Equilibrium configurations of cold neutron stars near the minimum mass are
studied, using the recent equation of state SLy, which describes in a unified,
physically consistent manner, both the solid crust and the liquid core of
neutron stars. Results are compared with those obtained using an older FPS
equation of state of cold catalyzed matter. The value of M_min\simeq 0.09M_sun
depends very weakly on the equation of state of cold catalyzed matter: it is
0.094 M_sun for the SLy model, and 0.088 M_sun for the FPS one. Central density
at M_min is significantly lower than the normal nuclear density: for the SLy
equation of state we get central density 1.7 10^{14} g/cm^3, to be compared
with 2.3 10^{14} g/cm^3 obtained for the FPS one. Even at M_min, neutron stars
have a small liquid core of radius of about 4 km, containing some 2-3% of the
stellar mass. Neutron stars with 0.09 M_sun <M<0.17 M_sun are bound with
respect to dispersed configuration of the hydrogen gas, but are unbound with
respect to dispersed Fe^56. The effect of uniform rotation on the minimum-mass
configuration of cold neutron stars is studied. Rotation increases the value of
M_min; at rotation period of 10 ms the minimum mass of neutron stars increases
to 0.13 M_sun, and corresponds to the mass-shedding (Keplerian) configuration.
In the case of the shortest observed rotation period of radio pulsars 1.56 ms,
minimum mass of uniformly rotating cold neutron stars corresponds to the
mass-shedding limit, and is found at 0.61 M_sun for the SLy EOS and 0.54 M_sun
for the FPS EOS.",0201434v1
1997-10-06,Density matrix renormalization group study of the polaron problem in the Holstein model,"We propose a new density matrix renormalization group (DMRG) approach to
study lattices including bosons. The key to the new approach is an exact
mapping of a boson site containing 2^N states to N pseudo-sites, each with 2
states. The pseudo-sites can be viewed as the binary digits of a boson level.
We apply the pseudo-site DMRG method to the polaron problem in the one- and
two-dimensional Holstein models. Ground state results are presented for a wide
range of electron-phonon coupling strengths and phonon frequencies on lattices
large enough (up to 80 sites in one dimension and up to 20x20 sites in two
dimensions) to eliminate finite size effects, with up to 128 phonon states per
phonon mode. We find a smooth but quite abrupt crossover from a quasi-free
electron ground state with a slightly renormalized mass at weak electron-phonon
coupling to a polaronic ground state with a large effective mass at strong
coupling, in agreement with previous studies.",9710058v1
2003-02-16,Polar type density of states in non-unitary odd-parity superconducting states of gap with point nodes,"It is shown that the density of states (DOS) proportional to the excitation
energy, the so-called polar like DOS, can arise in the odd-parity states with
the superconducting gap vanishing at points even if the spin-orbit interaction
for Cooper pairing is strong enough. Such gap stuructures are realized in the
non-unitary states, F_{1u}(1,i,0), F_{1u}(1,varepsilon,varepsilon^{2}), and
F_{2u}(1,i,0), classified by Volovik and Gorkov, Sov. Phys.-JETP Vol.61 (1985)
843. This is due to the fact that the gap vanishes in quadratic manner around
the point on the Fermi surface. It is also shown that the region of quadratic
energy dependence of DOS, in the state F_{2u}(1,varepsilon,varepsilon^{2}), is
restricted in very small energy region making it difficult to distinguish from
the polar-like DOS.",0302318v1
2010-03-18,Cold Nuclear Matter Effects on J/psi and Upsilon Production at the LHC,"The charmonium yields are expected to be considerably suppressed if a
deconfined medium is formed in high-energy heavy-ion collisions. In addition,
the bottomonium states, with the possible exception of the Upsilon(1S) state,
are also expected to be suppressed in heavy-ion collisions. However, in
proton-nucleus collisions the quarkonium production cross sections, even those
of the Upsilon(1S), are also suppressed. These ""cold nuclear matter"" effects
need to be accounted for before signals of the high density QCD medium can be
identified in the measurements made in nucleus-nucleus collisions. We identify
two cold nuclear matter effects important for midrapidity quarkonium
production: ""nuclear absorption"", typically characterized as a final-state
effect on the produced quarkonium state and shadowing, the modification of the
parton densities in nuclei relative to the nucleon, an initial-state effect. We
characterize these effects and study the energy, rapidity, and impact-parameter
dependence of initial-state shadowing in this paper.",1003.3497v1
2011-05-23,State-Observation Sampling and the Econometrics of Learning Models,"In nonlinear state-space models, sequential learning about the hidden state
can proceed by particle filtering when the density of the observation
conditional on the state is available analytically (e.g. Gordon et al., 1993).
This condition need not hold in complex environments, such as the
incomplete-information equilibrium models considered in financial economics. In
this paper, we make two contributions to the learning literature. First, we
introduce a new filtering method, the state-observation sampling (SOS) filter,
for general state-space models with intractable observation densities. Second,
we develop an indirect inference-based estimator for a large class of
incomplete-information economies. We demonstrate the good performance of these
techniques on an asset pricing model with investor learning applied to over 80
years of daily equity returns.",1105.4519v1
2015-05-25,Unavoidable Gapless Boundary State and Boundary Superfluidity of Trapped Bose Mott States in Two-Dimensional Optical Lattices,"We study the boundary nature of trapped bosonic Mott insulators in optical
square lattices, by performing quantum Monte Carlo simulation. We show that a
finite superfluid density generally emerges in the incommensurate-filling (IC)
boundary region around the bulk Mott state, irrespectively of the width of the
IC region. Both off-diagonal and density correlation functions in the IC
boundary region exhibit a nearly power-law decay. The power-law behavior and
superfluidity are well developed below a characteristic temperature. These
results indicate that a gapless boundary mode always emerges in any atomic Mott
insulators on optical lattices. This further implies that if we consider a
topological insulating state in Bose or Fermi atomic systems, its boundary
possesses at least two gapless modes (or coupled modes) of an above IC edge
state and the intrinsic topologically-protected edge state.",1505.06592v1
2015-06-12,Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux,"The phase diagram of a half-filled hard core boson two-leg ladder in a flux
is investigated by means of numerical simulations based on the Density Matrix
Renormalization Group (DMRG) algorithm and bosonization. We calculate
experimentally accessible observables such as the momentum distribution, as
well as rung current, density wave and bond-order wave correlation functions,
allowing us to identify the Mott Meissner and Mott Vortex states. We follow the
transition from commensurate Meissner to incommensurate Vortex state at
increasing interchain hopping till the critical value [Piraud et al. Phys. Rev.
B v. 91, p. 140406 (2015)] above which the Meissner state is stable at any
flux. For flux close to $\pi$, and below the critical hopping, we observe the
formation of a second incommensuration in the Mott Vortex state that could be
detectable in current experiments.",1506.03986v2
2016-10-03,Quench dynamics of spin-imbalanced Fermi-Hubbard model in one dimension,"We study a nonequilibrium dynamics of a one-dimensional spin-imbalanced
Fermi-Hubbard model following a quantum quench of on-site interaction,
realizable, for example, in Feshbach-resonant atomic Fermi gases. We focus on
the post-quench evolution starting from the initial BCS and
FuldeFerrell-Larkin-Ovchinnikov (FFLO) ground states and analyze the
corresponding spin-singlet, spin-triplet, density-density, and
magnetization-magnetization correlation functions. We find that beyond a
light-cone crossover time, rich post-quench dynamics leads to thermalized and
pre-thermalized stationary states that display strong dependence on the initial
ground state. For initially gapped BCS state, the long-time stationary state
resembles thermalization with the effective temperature set by the initial
value of the Hubbard interaction. In contrast, while the initial gapless FFLO
state reaches a stationary pre-thermalized form, it remains far from
equilibrium. We suggest that such post-quench dynamics can be used as a
fingerprint for identification and study of the FFLO phase.",1610.00670v2
2011-11-22,Localized end states in density modulated quantum wires and rings,"We study finite quantum wires and rings in the presence of a charge density
wave gap induced by a periodic modulation of the chemical potential. We show
that the Tamm-Shockley bound states emerging at the ends of the wire are stable
against weak disorder and interactions, for discrete open chains and for
continuum systems. The low-energy physics can be mapped onto the Jackiw-Rebbi
equations describing massive Dirac fermions and bound end states. We treat
interactions via the continuum model and show that they increase the charge gap
and further localize the end states. In an Aharonov-Bohm ring with weak link,
the bound states give rise to an unusual $4\pi$-peridodicity in the spectrum
and persistent current as function of an external flux. The electrons placed in
the two localized states on the opposite ends of the wire can interact via
exchange interactions and this setup can be used as a double quantum dot
hosting spin-qubits.",1111.5273v1
2018-10-16,"A spectral and timing study of MAXI J1535-571, based on Swift/XRT, XMM-Newton and NICER observations obtained in fall 2017","We present a spectral-timing analysis of observations taken in fall 2017 of
the newly detected X-ray transient MAXI J1535-571. We included 38 Swift/XRT
window timing mode observations, three XMM-Newton observations and 31 NICER
observations in our study. We computed the fundamental diagrams commonly used
to study black hole transients, and fitted power density and energy spectra to
study the evolution of spectral and timing parameters. The observed properties
are consistent with a bright black hole X-ray binary ($F_{\mathrm{0.6-10
keV}}^{\mathrm{max}}=3.71\pm0.02\times10^{-7}$ erg cm$^{-2}$ s$^{-1}$) that
evolves from the low-hard-state to the high-soft state and back to the
low-hard-state. In some observations the power density spectra showed type-C
quasi-periodic oscillations, giving additional evidence that MAXI J1535-571 is
in a hard state during these observations. The duration of the soft state with
less than ten days is unusually short and observations taken in spring 2018
show that MAXI J1535-571 entered a second (and longer) soft state.",1810.07203v1
2022-04-26,Density matrix reconstruction using non-negative matrix product states,"Quantum state tomography is a key technique for quantum information
processing, but is challenging due to the exponential growth of its complexity
with the system size. In this work, we propose an algorithm which iteratively
finds the best non-negative matrix product state approximation based on a set
of measurement outcomes whose size does not necessarily grow exponentially.
Compared to the tomography method based on neural network states, our scheme
utilizes a so-called tensor train representation that allows straightforward
recovery of the unknown density matrix in the matrix product state form. As
applications, the effectiveness of our algorithm is numerically demonstrated to
reconstruct the ground state of the XXZ spin chain under depolarizing noise.",2204.12383v2
2022-05-19,IL-flOw: Imitation Learning from Observation using Normalizing Flows,"We present an algorithm for Inverse Reinforcement Learning (IRL) from expert
state observations only. Our approach decouples reward modelling from policy
learning, unlike state-of-the-art adversarial methods which require updating
the reward model during policy search and are known to be unstable and
difficult to optimize. Our method, IL-flOw, recovers the expert policy by
modelling state-state transitions, by generating rewards using deep density
estimators trained on the demonstration trajectories, avoiding the instability
issues of adversarial methods. We demonstrate that using the state transition
log-probability density as a reward signal for forward reinforcement learning
translates to matching the trajectory distribution of the expert
demonstrations, and experimentally show good recovery of the true reward signal
as well as state of the art results for imitation from observation on
locomotion and robotic continuous control tasks.",2205.09251v1
2023-06-09,Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states,"We consider the relation between three different approaches to defining
quantum states across several times and locations: the pseudo-density matrix
(PDM), the process matrix, and the multiple-time state approaches. Previous
studies have shown that bipartite two-time states can reproduce the statistics
of bipartite process matrices. Here, we show that the operational scenarios
underlying two-time states can be represented as PDMs, and thereby construct a
mapping from process matrices with measurements to PDMs. The existence of this
mapping implies that PDMs can, like the process matrix, model processes with
indefinite causal orders. The results contribute to the unification of quantum
models of spatiotemporal states.",2306.05958v3
2023-08-29,Nematic and stripe orders within the charge density wave state of doped TiSe$_2$,"In this work, we present a theory to reconcile conflicting experimental
claims regarding the charge density wave (CDW) state in TiSe$_2$, including
whether there is a single or multiple CDW transitions and the occasional
observation of rotation symmetry breaking. Using a
$\boldsymbol{k}\cdot\boldsymbol{p}$ model coupled to the CDW order parameter,
we show how commonplace conduction band doping $x$ must cause a transition from
the $C_3$-symmetric $3Q$ state to a $C_3$-breaking $1Q$ stripe state at a
critical doping $x_{1Q}$. In addition, for sufficient ellipticity of the
conduction bands, as displayed by the realistic band stucture of TiSe$_2$, a
new nematic $3Q$ state also emerges in a region with $x < x_{1Q}$. We then show
how both stripe and nematic states emerge from a minimal interacting
tight-binding model, for both positive and negative initial gaps. Our theory
clarifies a long-standing puzzle and its predictions can be verified with a
variety of probes including transport, photoemission and tunneling.",2308.15541v1
2023-09-13,Real-time quantum dynamics of thermal states with neural thermofields,"Solving the time-dependent quantum many-body Schr\""odinger equation is a
challenging task, especially for states at a finite temperature, where the
environment affects the dynamics. Most existing approximating methods are
designed to represent static thermal density matrices, 1D systems, and/or
zero-temperature states. In this work, we propose a method to study the
real-time dynamics of thermal states in two dimensions, based on thermofield
dynamics, variational Monte Carlo, and neural-network quantum states. To this
aim, we introduce two novel tools: (i) a procedure to accurately simulate the
cooling down of arbitrary quantum variational states from infinite temperature,
and (ii) a generic thermal (autoregressive) recurrent neural-network (ARNNO)
Ansatz that allows for direct sampling from the density matrix using
thermofield basis rotations. We apply our technique to the transverse-field
Ising model subject to an additional longitudinal field and demonstrate that
the time-dependent observables, including correlation operators, can be
accurately reproduced for a 4x4 spin lattice. We provide predictions of the
real-time dynamics on a 6x6 lattice that lies outside the reach of exact
simulations.",2309.07063v1
2024-04-07,Nonreciprocal Nonlinear Responses in the Nonequilibrium States: Moving Charge Density Waves,"The incommensurate charge density wave states (CDWs) can exhibit steady
motion in the flow limit after depinning, behaving as a nonequilibrium system
with time-dependent states. Since the moving CDW, like an electric current,
breaks both time-reversal and inversion symmetries, one may speculate the
emergence of nonreciprocal nonlinear responses from such motion. However, the
moving CDW order parameter is intrinsically time-dependent in the lab frame,
and it is known to be challenging to evaluate the responses of such a
time-varying system. In this work, following the principle of Galilean
relativity, we resolve this time-dependent hard problem in the lab frame by
mapping the system to the comoving frame with static CDW states through the
Galilean transformation. We explicitly show that the nonreciprocal nonlinear
responses would be generated by the movement of CDW states through violating
Galilean relativity. Our work demonstrates not only nonreciprocal nonlinear
responses in nonequilibrium states but also the application of Galilean
transformation in simplifying time-dependent problems.",2404.04789v1
2014-12-22,Algebraic Structure of the Minimum Error Discrimination Problem for Linearly Independent Density Matrices,"The minimum error discrimination problem for ensembles of linearly
independent pure states are known to have an interesting structure; for such a
given ensemble the optimal POVM is given by the pretty good measurment of
another ensemble which can be related to the former ensemble by a bijective
mapping $\mathscr{R}$ on the ""space of ensembles"". In this paper we generalize
this result to ensembles of general linearly independent states (not
necessarily pure) and also give an analytic expression for the inverse of the
map, i.e., for $\mathscr{R}^{-1}$. In the process of proving this we also
simplify the necessary and sufficient conditions that a POVM needs to satisfy
to maximize the probability of success for the MED of an LI ensemble of states.
This simplification is then employed to arrive at a rotationally invariant
necessary and sufficient conditions of optimality. Using these rotationally
invariant conditions it is established that every state of a LI mixed state
ensemble can be resolved to a pure state decomposition so that the
corresponding pure state ensemble (corresponding to pure states of all mixed
states together) has as its optimal POVM a pure state decomposition of the
optimal POVM of mixed state ensemble. This gives the necessary and sufficient
conditions for the PGM of a LI ensemble to be its optimal POVM; another
generalization for the pure state case. Also, these rotationally invariant
conditions suggest a technique to give the optimal POVM for an ensemble of LI
states. This technique is polynomial in time and outpeforms standard
barrier-type interior point SDP in terms of computational complexity.",1412.7174v1
2023-10-09,NEATH II: N$_2$H$^+$ as a tracer of imminent star formation in quiescent high-density gas,"Star formation activity in molecular clouds is often found to be correlated
with the amount of material above a column density threshold of $\sim 10^{22}
\, {\rm cm^{-2}}$. Attempts to connect this column density threshold to a ${\it
volume}$ density above which star formation can occur are limited by the fact
that the volume density of gas is difficult to reliably measure from
observations. We post-process hydrodynamical simulations of molecular clouds
with a time-dependent chemical network, and investigate the connection between
commonly-observed molecular species and star formation activity. We find that
many molecules widely assumed to specifically trace the dense, star-forming
component of molecular clouds (e.g. HCN, HCO$^+$, CS) actually also exist in
substantial quantities in material only transiently enhanced in density, which
will eventually return to a more diffuse state without forming any stars. By
contrast, N$_2$H$^+$ only exists in detectable quantities above a volume
density of $10^4 \, {\rm cm^{-3}}$, the point at which CO, which reacts
destructively with N$_2$H$^+$, begins to deplete out of the gas phase onto
grain surfaces. This density threshold for detectable quantities of N$_2$H$^+$
corresponds very closely to the volume density at which gas becomes
irreversibly gravitationally bound in the simulations: the material traced by
N$_2$H$^+$ never reverts to lower densities, and quiescent regions of molecular
clouds with visible N$_2$H$^+$ emission are destined to eventually form stars.
The N$_2$H$^+$ line intensity is likely to directly correlate with the star
formation rate averaged over timescales of around a Myr.",2310.06037v1
2019-08-10,Bayesian Loss for Crowd Count Estimation with Point Supervision,"In crowd counting datasets, each person is annotated by a point, which is
usually the center of the head. And the task is to estimate the total count in
a crowd scene. Most of the state-of-the-art methods are based on density map
estimation, which convert the sparse point annotations into a ""ground truth""
density map through a Gaussian kernel, and then use it as the learning target
to train a density map estimator. However, such a ""ground-truth"" density map is
imperfect due to occlusions, perspective effects, variations in object shapes,
etc. On the contrary, we propose \emph{Bayesian loss}, a novel loss function
which constructs a density contribution probability model from the point
annotations. Instead of constraining the value at every pixel in the density
map, the proposed training loss adopts a more reliable supervision on the count
expectation at each annotated point. Without bells and whistles, the loss
function makes substantial improvements over the baseline loss on all tested
datasets. Moreover, our proposed loss function equipped with a standard
backbone network, without using any external detectors or multi-scale
architectures, plays favourably against the state of the arts. Our method
outperforms previous best approaches by a large margin on the latest and
largest UCF-QNRF dataset. The source code is available at
\url{https://github.com/ZhihengCV/Baysian-Crowd-Counting}.",1908.03684v1
2016-12-10,Density phase separation and order-disorder transition in a collection of polar self-propelled particles,"We study the order-disorder transition in a collection of polar
self-propelled particles, interacting through a distance dependent short range
alignment interaction. A distance dependent interaction parameter $a_0$ is
introduced such that on decreasing $a_0$ interaction decay faster with distance
$d$ and for $a_0=1.0$ model reduces to Vicsek's type. For all $a_0>0.0$, system
shows a transition from disorder to long ranged ordered state. We find another
phase transition from phase separated to nonphase separated state with
decreasing $a_0$: at the same time order-disorder transition changes from
discontinuous to continuous type. Hence density phase separation plays an
important role in predicting the nature of order-disorder transition. We also
calculate the two-point density structure factor using coarse-grained
hydrodynamic equations of motion with an introduction of a density dependent
alignment term in the equation introduced by Toner and Tu \cite{tonertu}.
Density structure factor shows a divergence at a critical wave-vector $q_c$,
which decreases with decreasing density dependent alignment term. Alignment
term in the coarse-grained equation plays the same role as the distance
dependent parameter $a_0$ in the microscopic simulation. Our results can be
tested in many biological systems: where particle have tendency to interact
strongly with their closest neighbours.",1612.03258v1
2021-12-04,Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density,"We study the ground-state properties of ferromagnetic quasi-one-dimensional
quantum wires using the quantum Monte Carlo (QMC) method for various wire
widths $b$ and density parameters $r_\text{s}$. The correlation energy,
pair-correlation function, static structure factor, and momentum density are
calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in
the static structure factor at $k=2k_\text{F}$ grows as the wire width
decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the
momentum density. It is found that $K_\rho$ increases by about $10$\% between
wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of
finite thickness wires theoretically using the first-order random phase
approximation (RPA) with exchange and self-energy contributions, which is exact
in the high-density limit. Analytical expressions for the static structure
factor and correlation energy are derived for $b \ll r_\text{s}<1$. It is found
that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ from its
value for an infinitely thin wire. It is observed that the correlation energy
depends significantly on the wire model used (harmonic versus cylindrical
confinement). The first-order RPA expressions for the structure factor,
pair-correlation function, and correlation energy are numerically evaluated for
several values of $b$ and $r_\text{s} \leq 1$. These are compared with the QMC
results in the range of applicability of the theory.",2112.12064v2
2020-04-21,Incoherent charge transport in an organic polariton condensate,"We study how polariton condensation modifies charge transport in organic
materials. In typical organic materials, charge transport proceeds via
incoherent hopping. We therefore provide an approach to determine how the rate
and final state of this hopping process is affected by strong matter-light
coupling and polariton condensation. We show how the hopping process may create
excitations when starting from a state with a finite excitation density. That
is, how hopping can change the state of a lower polariton condensate by
creating upper polaritons, optically inactive excitonic dark states, or by
exciting vibrational sidebands. While the matrix elements for these processes
can be large, for typical materials at room temperature, such excitations are
suppressed by thermal factors, and ground state processes dominate. We thus
study how the ground state hopping rate depends on condensate density,
matter-light coupling, and cavity photon detuning. All these factors change the
vibrational configuration associated with the optically active molecules, which
can enhance or suppress hopping by increasing or decreasing the vibrational
overlap with the state of a charged molecule. We show that hopping rates can be
exponentially sensitive to detuning and condensate density, allowing an
increase or decrease of hopping rate by two orders of magnitude.",2004.09790v2
2017-12-01,Dynamics of expansion of the Universe in model with the additional coupling between dark energy and dark matter,"We study the dynamics of expansion of the homogeneous isotropic Universe and
the evolution of its components in the model with nonminimally coupled
dynamical dark energy. Dark energy, like the other components of the Universe,
is described by the perfect fluid approximation with the equation of state
(EoS) $p_ {de}=w\rho_{de}$, where the EoS parameter $w$ depends on time and is
parameterized via the squared adiabatic sound speed $c_{ a}^2$ which is assumed
to be constant. On basis of the general covariant conservation equations for
the interacting dark energy and dark matter and Einstein equations in
Friedmann-Lemaitre-Robertson-Walker metric we analyze the evolution of energy
densities of the hidden components and the dynamics of expansion of the
Universe with two types of interaction: proportional to the sum of densities of
the hidden components and proportional to their product. For the first
interaction the analytical expressions for the densities of dark energy and
dark matter were obtained and analyzed in detail. For the second one the
evolution of densities of hidden components of the Universe was analyzed on
basis of the numerical solutions of their energy-momentum conservation
equations. For certain values of the parameters of these models the energy
densities of dark components become negative. So to ensure that the densities
are always positive we put constraints on the interaction parameter for both
models.",1712.01128v1
2005-06-22,A new intermediate mass protostar in the Cepheus A HW2 region,"We present the discovery of the first molecular hot core associated with an
intermediate mass protostar in the CepA HW2 region. The hot condensation was
detected from single dish and interferometric observations of several high
excitation rotational lines (from 100 to 880K above the ground state) of SO2 in
the ground vibrational state and of HC3N in the vibrationally excited states
v7=1 and v7=2. The kinetic temperature derived from both molecules is 160K. The
high-angular resolution observations (1.25'' x 0.99'') of the SO2
J=28(7,21)-29(6,24) line (488K above the ground state) show that the hot gas is
concentrated in a compact condensation with a size of 0.6''(430AU), located
0.4'' (300AU) east from the radio-jet HW2. The total SO2 column density in the
hot condensation is 10E18cm-2, with a H2 column density ranging from 10E23 to 6
x 10E24cm-2. The H2 density and the SO2 fractional abundance must be larger
than 10E7cm-3 and 2 x 10E-7 respectively. The most likely alternatives for the
nature of the hot and very dense condensation are discussed. From the large
column densities of hot gas, the detection of the HC3N vibrationally excited
lines and the large SO2 abundance, we favor the interpretation of a hot core
heated by an intermediate mass protostar of 10E3 Lo. This indicates that the
CepA HW2 region contains a cluster of very young stars.",0506533v1
1998-09-01,Magnetic properties of periodic nonuniform spin-1/2 $XX$ chains in a random Lorentzian transverse field,"Using continued fractions we examine the density of states, transverse
magnetization and static transverse linear susceptibility of a few periodic
nonuniform spin-1/2 $XX$ chains in a random Lorentzian transverse field.",9809018v1
2001-06-13,Numerical study of quantum percolation,"We study the density of states and the optical conductivity of the classical
double-exchange model on a site percolated cluster.",0106247v1
2006-09-28,Entangled Graphs,"In this paper we prove a separability criterion for mixed states in $\mathbb
C^p\otimes\mathbb C^q$. We also show that the density matrix of a graph with
only one entangled edge is entangled.",0609156v1
1999-09-10,On a possibility of adjoint colored states condensation at finite temperatures in lattice gauge model,"Cooled down and diluted quark-gluon matter is considered. A possibility of
condensation of multiquark clusters with zero N-alities is discussed.",9909089v1
2004-09-22,QCD Thermodynamics on lattice,"I discuss recent developments in lattice QCD thermodynamics on the nature of
the transition at finite temperature and density, equation of state, screening
of static charges and meson spectral functions at high temperatures.",0409139v1
2005-11-11,On the SU(3) parametrization of qutrits,"Parametrization of qutrits on the complex projective plane CP^2 = SU(3)/U(2)
is given explicitly. A set of constraints that characterize mixed state density
matrices is found.",0511111v1
2007-11-26,The q-analogue of the wild fundamental group (II),"In [RS1], we defined q-analogues of alien derivations and stated their basic
properties. In this paper, we prove the density theorem and the freeness
theorem announced in loc. cit.
  [RS1] Ramis J.-P. and Sauloy J., 2007. The q-analogue of the wild fundamental
group (I)",0711.4034v1
2010-11-05,Ab-initio Electronic and Structural Properties of Rutile Titanium Dioxide,"Ab-initio, self-consistent electronic energy bands of rutile TiO2 are
reported within the local density functional approximation (LDA). Our first
principle, non-relativistic and ground state calculations employed a local
density functional approximation (LDA) potential and the linear combination of
atomic orbitals (LCAO). Within the framework of the Bagayoko, Zhao, and
Williams (BZW) method, we solved self-consistently both the Kohn-Sham equation
and the equation giving the ground state charge density in terms of the wave
functions of the occupied states. Our calculated band structure shows that
there is significant O2p-Ti3d hybridization in the valence bands. These bands
are well separated from the conduction bands by an indirect band gap of 2.95
eV, from {\Gamma} to R. Consequently, this work predicts that rutile TiO2 is an
indirect band gap material, as all other gaps from our calculations are larger
than 2.95 eV. We found a slightly larger, direct band gap of 3.05 eV, at the
{\Gamma} point, in excellent agreement with experiment. Our calculations
reproduced the peaks in the measured conduction and valence bands densities of
states, within experimental uncertainties. We also calculated electron
effective mass. Our structural optimization led to lattice parameters of 4.65
{\AA} and 2.97 {\AA} for a_{0} and c_{0}, respectively with a u parameter of
0.3051 and a bulk modulus of 215 GPa.",1011.1315v3
2010-12-30,Simple Impurity Embedded in a Spherical Jellium: Approximations of Density Functional Theory compared to Quantum Monte Carlo Benchmarks,"We study the electronic structure of a spherical jellium in the presence of a
central Gaussian impurity. We test how well the resulting inhomogeneity effects
beyond spherical jellium are reproduced by several approximations of density
functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals,
namely local density approximation (LDA), generalized gradient approximation
(GGA), meta-GGA and orbital-dependent hybrid functionals are compared against
our quantum Monte Carlo (QMC) benchmarks. We identify several distinct
transitions in the ground state of the system as the electronic occupation
changes between delocalized and localized states. We examine the parameter
space of realistic densities ($1 \le r_s\le 5$) and moderate depths of the
Gaussian impurity ($Z<7$). The selected 18 electron system (with closed-shell
ground state) presents $1d \to 2s$ transitions while the 30 electron system
(with open-shell ground state) exhibits $1f \to 2p$ transitions. For the former
system, the accuracy for the transitions is clearly improving with increasing
sophistication of functionals with meta-GGA and hybrid functionals having only
small deviations from QMC. However, for the latter system, we find much larger
differences for the underlying transitions between our pool of DFT functionals
and QMC. We attribute this failure to treatment of the exact exchange within
these functionals. Additionally, we amplify the inhomogeneity effects by
creating the system with spherical shell which leads to even larger errors in
DFT approximations.",1101.0102v2
2014-02-17,Time-dependent density-matrix functional theory for trion excitations: application to monolayer MoS2,"We study possible optically excited bound states in monolayer MoS2: excitons
and trions. For this purpose we formulate and apply a generalized
time-dependent density-matrix functional approach for bound states of multiple
excitations. The approach was used in the cases of three different types of the
exchange-correlation (XC) kernel: 1) two local kernels: a phenomenological
contact and the adiabatic local-density approximation (ALDA) (X and XC); 2)
gradient-corrected X kernels: GEA, PW91 and PBE; and 3) two long-range (LR)
kernels: a phenomenological (Coulomb) and Slater kernels. In the case of
exciton, we find that LDA and its gradient-corrected kernels lead to too weak
binding energy comparing to the experimental data, while the LR kernels are
capable to reproduce the experimental results. Similarly, in the LR case (as
well as in the case of local kernel), one can obtain the experimental value of
the trion binding energy by taking into account the screening effects. Our
results suggest that similar to the excitons, the LR structure of the XC kernel
is necessary to describe the trion bound states. Our calculations for the first
time confirm theoretically with time-dependent density-functional theory
approach that in agreement with experimental data the exciton and trion binding
energies are of order of hundreds (excitons) and tenth (trions) meVs, which can
be used in different technological applications at the room temperature regime.
The approach can be straightforwardly extended on the case of bound states and
nonequilibrium response of systems with larger number of bound electrons and
holes, including biexcitons.",1402.4041v1
2017-02-21,Equation of state and shock compression of warm dense sodium - a first-principles study,"As one of the simple alkali metals, sodium has been of fundamental interest
for shock physics experiments, but knowledge of its equation of state (EOS) in
hot, dense regimes is not well known. By combining path integral Monte Carlo
(PIMC) results for partially-ionized states [B. Militzer and K. P. Driver,
Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density
functional theory molecular dynamics (DFT-MD) results at lower temperatures, we
have constructed a coherent equation of state for sodium over a wide
density-temperature range of $1.93-11.60$ g/cm$^{3}$ and $10^3-1.29\times10^8$
K. We find that a localized, Hartree-Fock nodal structure in PIMC yields
pressures and internal energies that are consistent with DFT-MD at intermediate
temperatures of $2\times10^6$ K. Since PIMC and DFT-MD provide a
first-principles treatment of electron shell and excitation effects, we are
able to identify two compression maxima in the shock Hugoniot curve
corresponding to $K$-shell and $L$-shell ionization. Our Hugoniot curves
provide a benchmark for widely-used EOS models, SESAME, LEOS, and Purgatorio.
Due to the low ambient density, sodium has an unusually high first compression
maximum along the shock Hugoniot curve. At beyond 10$^7$ K, we show that the
radiation effect leads to very high compression along the Hugoniot curve,
surpassing relativistic corrections, and observe an increasing deviation of the
shock and particle velocities from a linear relation. We also compute the
temperature-density dependence of thermal and pressure ionization processes.",1702.06572v1
2018-12-10,"Reversibility, Pattern Formation and Edge Transport in Active Chiral and Passive Disk Mixtures","We numerically examine mixtures of circularly moving and passive disks as a
function of density and active orbit radius. For low or intermediate densities
and/or small orbit radii, the system can organize into a reversible partially
phase separated labyrinth state in which there are no collisions between disks,
with the degree of phase separation increasing as the orbit radius increases.
As a function of orbit radius, we find a divergence in the number of cycles
required to reach a collision-free steady state at a critical radius, while
above this radius the system remains in a fluctuating liquid state. For high
densities, the system can organize into a fully phase separated state that is
mostly reversible, but collisions at the boundaries between the phases lead to
a net transport of disks along the boundary edges in a direction determined by
the chirality of the active disk orbits. We map the dynamic phases as a
function of density and orbit radii, and discuss the results in terms of the
reversible-irreversible transition found in other periodically driven
non-thermal systems. We also consider mixtures of circularly driven disks and
ac driven disks where the ac drive is either in or out of phase with the
circular motion, and find a rich variety of pattern forming and reentrant
disordered phases.",1812.04150v1
2017-07-26,Constraining the equation of state with identified particle spectra,"We show that in a central nucleus-nucleus collision, the variation of the
mean transverse mass with the multiplicity is determined, up to a rescaling, by
the variation of the energy over entropy ratio as a function of the entropy
density, thus providing a direct link between experimental data and the
equation of state. Each colliding energy thus probes the equation of state at
an effective entropy density, whose approximate value is $19$ fm$^{-3}$ for
Au+Au collisions at 200 GeV and $41$ fm$^{-3}$ for Pb+Pb collisions at 2.76
TeV, corresponding to temperatures of $227$ MeV and $279$ MeV if the equation
of state is taken from lattice calculations. The relative change of the mean
transverse mass as a function of the colliding energy gives a direct measure of
the pressure over energy density ratio $P/\epsilon$, at the corresponding
effective density. Using RHIC and LHC data, we obtain $P/\epsilon=0.21\pm
0.10$, in agreement with the lattice value $P/\epsilon=0.23$ in the
corresponding temperature range. Measurements over a wide range of colliding
energies using a single detector with good particle identification would help
reducing the error.",1707.08466v2
2019-01-22,Fate of the doubly heavy spin$-3/2$ baryons in a dense medium,"We investigate the behavior of the doubly heavy spin$-3/2$ baryons in cold
nuclear matter. In particular, we study the variations of the spectroscopic
parameters of the ground state $\Xi^*_{QQ'}$ and $\Omega^*_{QQ'}$ particles,
with $ Q $ and $ Q' $ being $b $ or $ c $ quark, with respect to the changes in
the density of the nuclear medium. We find the shifts on the parameters under
question at saturation medium density compared to their vacuum values. It is
observed that the parameters of the $\Xi^*_{QQ'}$ states containing two heavy
quarks and one up or down quark are affected by the medium, considerably. The
parameters of the $\Omega^*_{QQ'}$ states containing two heavy quarks and one
strange quark, however, do not show any sensitivity to the density of the cold
nuclear medium. We also discuss the variations of the vector self-energy at
each channel with respect to the changes in the density. The negative shifts in
the mass of $\Xi^*_{QQ'}$ states due to nucleons in the medium can be used to
study the doubly heavy baryons' interactions with the nucleons. The results
obtained can also be used in analyses of the results of the future in-medium
experiments.",1901.07399v4
2019-02-25,A variational lower bound on the ground state of a many-body system and the squaring parametrization of density matrices,"A variational upper bound on the ground state energy $E_{\rm gs}$ of a
quantum system, $E_{\rm gs} \leqslant \langle \Psi|H| \Psi \rangle$, is
well-known (here $H$ is the Hamiltonian of the system and $\Psi$ is an
arbitrary wave function). Much less known are variational {\it lower} bounds on
the ground state. We consider one such bound which is valid for a many-body
translation-invariant lattice system. Such a lattice can be divided into
clusters which are identical up to translations. The Hamiltonian of such a
system can be written as $H=\sum_{i=1}^M H_i$, where a term $H_i$ is supported
on the $i$'th cluster. The bound reads $E_{\rm gs}\geqslant M
\inf\limits_{\rho_{cl} \in {\mathbb S_{cl}^G}} {\rm tr}_{cl}\rho_{cl} \, H_{cl}
$, where ${\mathbb S_{cl}^G}$ is some wisely chosen set of reduced density
matrices of a single cluster. The implementation of this latter variational
principle can be hampered by the difficulty of parameterizing the set $\mathbb
M$, which is a necessary prerequisite for a variational procedure. The root
cause of this difficulty is the nonlinear positivity constraint $\rho>0$ which
is to be satisfied by a density matrix. The squaring parametrization of the
density matrix, $\rho=\tau^2/{\rm tr}\,\tau^2$, where $\tau$ is an arbitrary
(not necessarily positive) Hermitian operator, accounts for positivity
automatically. We discuss how the squaring parametrization can be utilized to
find variational lower bounds on ground states of translation-invariant
many-body systems. As an example, we consider a one-dimensional Heisenberg
antiferromagnet.",1902.09246v1
2010-07-07,Evaluating Systematic Dependencies of Type Ia Supernovae: The Influence of Deflagration to Detonation Density,"We explore the effects of the deflagration to detonation transition (DDT)
density on the production of Ni-56 in thermonuclear supernova explosions (type
Ia supernovae). Within the DDT paradigm, the transition density sets the amount
of expansion during the deflagration phase of the explosion and therefore the
amount of nuclear statistical equilibrium (NSE) material produced. We employ a
theoretical framework for a well-controlled statistical study of
two-dimensional simulations of thermonuclear supernovae with randomized initial
conditions that can, with a particular choice of transition density, produce a
similar average and range of Ni-56 masses to those inferred from observations.
Within this framework, we utilize a more realistic ""simmered"" white dwarf
progenitor model with a flame model and energetics scheme to calculate the
amount of Ni-56 and NSE material synthesized for a suite of simulated
explosions in which the transition density is varied in the range 1-3x10^7
g/cc. We find a quadratic dependence of the NSE yield on the log of the
transition density, which is determined by the competition between plume rise
and stellar expansion. By considering the effect of metallicity on the
transition density, we find the NSE yield decreases by 0.055 +/- 0.004 solar
masses for a 1 solar metallicity increase evaluated about solar metallicity.
For the same change in metallicity, this result translates to a 0.067 +/- 0.004
solar mass decrease in the Ni-56 yield, slightly stronger than that due to the
variation in electron fraction from the initial composition. Observations
testing the dependence of the yield on metallicity remain somewhat ambiguous,
but the dependence we find is comparable to that inferred from some studies.",1007.1138v1
2019-09-14,New Perspectives on the Schr{ö}dinger-Pauli Theory of Electrons: Part II: Application to the Triplet State of a Quantum Dot in a Magnetic Field,"The Schr\""odinger-Pauli theory of electrons in the presence of a static
electromagnetic field can be described from the perspective of the individual
electron via its equation of motion or `Quantal Newtonian' first law. The law
is in terms of `classical' fields whose sources are quantum-mechanical
expectation values of Hermitian operators taken with respect to the wave
function. The law states that the sum of the external and internal fields
experienced by each electron vanishes. The external field is the sum of the
binding electrostatic and Lorentz fields. The internal field is the sum of
fields representative of properties of the system: electron correlations due to
the Pauli exclusion principle and Coulomb repulsion; the electron density;
kinetic effects; the current density. Thus, the internal field is a sum of the
electron-interaction, differential density, kinetic, and internal magnetic
fields. The energy can be expressed in integral virial form in terms of these
fields. Via this perspective, the Schr\""odinger-Pauli equation can be written
in a generalized form which then shows it to be intrinsically self-consistent.
This new perspective is explicated by application to the triplet $2^{3}S$ state
of a 2-D 2-electron quantum dot in a magnetic field. The quantal sources of the
density; the paramagnetic, diamagnetic, and magnetization current densities;
pair-correlation density; the Fermi-Coulomb hole charge; and the
single-particle density matrix are obtained, and from them the corresponding
fields determined. The fields are shown to satisfy the `Quantal Newtonian'
first law. The components of the energy too are determined from these fields.
Finally, the example is employed to demonstrate the intrinsic self-consistent
nature of the Schr\""odinger-Pauli equation.",1909.09701v1
2005-05-05,Matrix product states represent ground states faithfully,"We quantify how well matrix product states approximate exact ground states of
1-D quantum spin systems as a function of the number of spins and the entropy
of blocks of spins. We also investigate the convex set of local reduced density
operators of translational invariant systems. The results give a theoretical
justification for the high accuracy of renormalization group algorithms, and
justifies their use even in the case of critical systems.",0505140v6
1997-11-28,On the nature of the quantum states of macroscopic systems,"It is assumed that the quantum state that may describe a macroscopic system
at a given instant of time is one of the eigenstates of the reduced density
matrix calculated from the wave function of the system plus its environment.
This implies that the above quantum state is a member of a special orthonormed
set of states. Using a suitable Monte-Carlo simulation, this property is shown
to be consistent with the extremely small standard deviation for the
coordinates and the momenta of macroscopic systems. Consequences for
statistical mechanics and possible observable effects are discussed.",9711072v1
1998-11-13,Stationary States in Saturated Two-Photon Processes and Generation of Phase-Averaged Mixtures of Even and Odd Quantum States,"We consider a relaxation of a single mode of the quantized field in a
presence of one- and two-photon absorption and emission processes. Exact
stationary solutions of the master equation for the diagonal elements of the
density matrix in the Fock basis are found in the case of completely saturated
two-photon emission. If two-photon processes dominate over single-photon ones,
the stationary state is a mixture of phase averaged even and odd coherent
states.",9811031v1
2006-10-16,Point Estimation of States of Finite Quantum Systems,"The estimation of the density matrix of a $k$-level quantum system is studied
when the parametrization is given by the real and imaginary part of the entries
and they are estimated by independent measurements. It is established that the
properties of the estimation procedure depend very much on the invertibility of
the true state. In particular, in case of a pure state the estimation is less
efficient. Moreover, several estimation schemes are compared for the unknown
state of a qubit when one copy is measured at a time. It is shown that the
average mean quadratic error matrix is the smallest if the applied observables
are complementary. The results are illustrated by computer simulations.",0610124v1
2007-11-14,Breakdown of universal transport in correlated d-wave superconductors,"The prediction and observation of low-temperature universal thermal
conductivity in cuprates has served as a keystone of theoretical approaches to
the superconducting state, but recent measurements on underdoped samples show
strong violations of this apparently fundamental property of d-wave nodal
quasiparticles. Here, we show that the breakdown of universality may be
understood as the consequence of disorder-induced magnetic states in the
presence of increasing antiferromagnetic correlations in the underdoped state,
even as these same correlations protect the nodal low-energy density of states
in agreement with recent scanning tunneling experiments.",0711.2294v2
2012-09-12,Pedagogical introduction to the entropy of entanglement for Gaussian states,"The most useful measure of a bipartite entanglement is the von Neumann
entropy of either of the reduced density matrices. For a particular class of
continuous-variable states, the Gaussian states, the entropy of entanglement
can be expressed rather elegantly in terms of the symplectic eigenvalues,
elements that characterize a Gaussian state and depend on the correlations of
the canonical variables. We give a pedagogical step-by-step derivation of this
result and provide some insights that can be useful in practical calculations.",1209.2748v1
2015-05-31,Defect induced negative magnetoresistance and surface state immunity in topological insulator BiSbTeSe2,"Absence of backscattering and occurrence of weak anti-localization are two
characteristic features of topological insulators. We find that the
introduction of defects results in the appearance of a negative contribution to
magnetoresistance in the topological insulator BiSbTeSe2, at temperatures below
50 K. Our analysis shows that the negative magnetoresistance originates from an
increase in the density of defect states created by introduction of disorder,
which leaves the surface states unaffected. We find a decrease in the magnitude
of the negative magnetoresistance contribution with increasing temperature and
a robustness of the topological surface states to external disorder.",1506.00208v1
2020-10-27,Classical simulation of Gaussian quantum circuits with non-Gaussian input states,"We consider Gaussian quantum circuits supplemented with non-Gaussian input
states and derive sufficient conditions for efficient classical strong
simulation of these circuits. In particular, we generalise the stellar
representation of continuous-variable quantum states to the multimode setting
and relate the stellar rank of the input non-Gaussian states, a recently
introduced measure of non-Gaussianity, to the cost of evaluating classically
the output probability densities of these circuits. Our results have
consequences for the strong simulability of a large class of near-term
continuous-variable quantum circuits.",2010.14363v2
2001-08-06,Skyrmion $\leftrightarrow$ pseudoSkyrmion Transition in Bilayer Quantum Hall States at $ν=1$,"Bilayer quantum Hall states at $\nu =1$ have been demonstrated to possess a
distinguished state with interlayer phase coherence. The state has both
excitations of Skyrmion with spin and pseudoSkyrmion with pseudospin. We show
that Skyrmion $\leftrightarrow$ pseudoSkyrmion transition arises in the state
by changing imbalance between electron densities in both layers; PseudoSkyrmion
is realized at balance point, while Skyrmion is realized at large imbalance.
The transition can be seen by observing the dependence of activation energies
on magnetic field parallel to the layers.",0108096v1
2006-06-16,Theory of Four-dimensional Fractional Quantum Hall States,"We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized
fractional quantum Hall states to be the exact and unique ground states.
Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the
generalized fractional quantum Hall states are extended objects. They are
vortex-like excitations with fractional charges $+(-)1/m^3$ in the total
configuration space CP$^3$. The density correlation function of the Zhang-Hu
states indicates that they are incompressible liquid.",0606434v3
2007-01-03,Entropy and Entanglement in Quantum Ground States,"We consider the relationship between correlations and entanglement in gapped
quantum systems, with application to matrix product state representations. We
prove that there exist gapped one-dimensional local Hamiltonians such that the
entropy is exponentially large in the correlation length, and we present strong
evidence supporting a conjecture that there exist such systems with arbitrarily
large entropy. However, we then show that, under an assumption on the density
of states which is believed to be satisfied by many physical systems such as
the fractional quantum Hall effect, that an efficient matrix product state
representation of the ground state exists in any dimension. Finally, we comment
on the implications for numerical simulation.",0701055v1
2004-02-05,Weak Measurements with Arbitrary Pointer States,"The exact conditions on valid pointer states for weak measurements are
derived. It is demonstrated that weak measurements can be performed with any
pointer state with vanishing probability current density. This condition is
found both for weak measurements of noncommuting observables and for $c$-number
observables. In addition, the interaction between pointer and object must be
sufficiently weak. There is no restriction on the purity of the pointer state.
For example, a thermal pointer state is fully valid.",0402050v1
2007-12-14,Confined Ge-Pt states in self-organized Pt nanowire arrays on Ge(001),"By means of band structure calculations within the density functional theory
and the generalized gradient approximation, we investigate the electronic
structure of self-organized Pt nanowires on the Ge(001) surface. In particular,
we deal with a novel one-dimensional surface state confined in the nanowire
array and clarify its origin. Due to large Pt contributions, the novel state is
rather a mixed Ge-Pt hybrid state than a confined Ge surface state. Moreover,
we compare our results to data from scanning tunneling microscopy.",0712.2325v1
2011-10-09,Pure Fulde-Ferrell-Larkin-Ovchinnikov state in optical lattices,"We study the phase diagram of a one-dimensional, two-component attractive
fermions on optical lattices in an off-diagonal confinement. We identify in
this system a pure Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with spatially
modulated superfluidity and polarization in a large parameter window, which
provides an easier playground to detect the FFLO state experimentally. The
clear signature of FFLO state is analyzed in the ground state properties, the
pair correlation functions, and the magnetic structure factor, using the
density-matrix renormalization group method.",1110.1799v2
2012-08-03,Metal-insulator transition in Sr2-xLaxCoO4 driven by spin-state transition,"We sought the origin of the metal-insulator transition in Sr2-xLaxCoO4, using
electron-correlation corrected density functional calculations. Our results
show that Sr2CoO4 is in an intermediate-spin (IS) state and a strong Co4+ 3d-O
2p hybridization is responsible for its ferromagnetic metallicity. Upon La
doping, however, a spin-state transition occurs in Sr1.5La0.5CoO4: IS-Co4+ x 2
+ 1e --> LS-Co4+ + HS-Co3+ (LS: low spin; HS: high spin). Then the spin-state
transition suppresses an electron hopping via a spin-blockade and gives rise to
the insulating behavior of Sr1.5La0.5CoO4. A corresponding superexchange
accounts for its ferromagnetism. Thus, spin state could provide a way to tune
materials properties.",1208.0637v1
2013-01-22,Two-pion excited state contribution to pseudo-scalar correlators,"We study multi-particle state contributions to the QCD two-point functions of
pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently
small quark masses one expects three-meson states with two additional pions at
rest to have the lowest total energy after the ground state. Using chiral
perturbation theory, we find the amplitude of this state to be too small to be
seen in present-day lattice simulations. We speculate that curvature in the
effective mass plot extracted from the pseudo-scalar density two-point function
instead corresponds to a genuine resonance, the \pi(1300).",1301.5151v1
2015-04-16,Quantum state tomography for qutrits subject to laser cooling,"In this article we propose a dynamic quantum state tomography model for
qutrits subject to laser cooling. We prove that one can reduce the number of
distinct measurement setups required for state reconstruction by employing the
stroboscopic approach. The results are in line with current advances in quantum
tomography where there is a strong tendency to investigate the optimal criteria
for state reconstruction. We believe that the stroboscopic approach can be
considered an efficient tool for density matrix identification since it allows
to determine the minimal number of distinct observables needed for quantum
state tomography.",1504.04385v2
2023-07-25,"Decoherence, Branching, and the Born Rule in a Mixed-State Everettian Multiverse","In Everettian quantum mechanics, justifications for the Born rule appeal to
self-locating uncertainty or decision theory. Such justifications have focused
exclusively on a pure-state Everettian multiverse, represented by a wave
function. Recent works in quantum foundations suggest that it is viable to
consider a mixed-state Everettian multiverse, represented by a (mixed-state)
density matrix. Here, we develop the conceptual foundations for decoherence and
branching in a mixed-state multiverse, and extend the standard Everettian
justifications for the Born rule to this setting. This extended framework
provides a unification of 'classical' and 'quantum' probabilities, and
additional theoretical benefits, for the Everettian picture.",2307.13218v1
1997-03-03,Low density ferromagnetism in Extended Hubbard ( t-t'-U ) Model,"We study the existence of ferromagnetism in one dimensional Hubbard Model
with on site interaction and nearest and next nearest neighbor hopping. Using
the Hubbard I approximation, a self consistent equation for $<n_\sigma>$, the
particle density with spin $\sigma$ is obtained. We find that ferromagnetism
exists over a wide range of values of the next nearest neighbor hopping element
t' when on-site interaction U is large. The phase diagram as a function of t'/t
and the electron density $<n>$ has been obtained by numerically solving the
self consistent equation. It is found that the maximum density at which
ferromagnetism can occur, peaks around $t'/t \approx -0.53$. We show that this
phenomenon is a result of the peculiar way in which the t' term modifies the
density of states.",9703022v1
2005-08-17,Local Spectral Density and Vacuum Energy near a Quantum Graph Vertex,"The delta interaction at a vertex generalizes the Robin (generalized Neumann)
boundary condition on an interval. Study of a single vertex with N infinite
leads suffices to determine the localized effects of such a vertex on densities
of states, etc. For all the standard initial-value problems, such as that for
the wave equation, the pertinent integral kernel (Green function) on the graph
can be easily constructed from the corresponding elementary Green function on
the real line. From the results one obtains the spectral-projection kernel,
local spectral density, and local energy density. The energy density, which
refers to an interpretation of the graph as the domain of a quantized scalar
field, is a coefficient in the asymptotic expansion of the Green function for
an elliptic problem involving the graph Hamiltonian; that expansion contains
spectral/geometrical information beyond that in the much-studied heat-kernel
expansion.",0508335v1
2011-02-15,Dynamics of the quantum vacuum: Cosmology as relaxation to the equilibrium state,"The behavior of the gravitating vacuum energy density in an expanding
universe is discussed. A scenario is presented with a step-wise relaxation of
the vacuum energy density. The vacuum energy density moves from plateau to
plateau and follows, on average, the steadily decreasing matter energy density.
The current plateau with a small positive value of the vacuum energy density
(effective cosmological constant) may result from a still not equilibrated
contribution of the light massive neutrinos to the quantum vacuum.",1102.3152v4
2013-03-26,Fragment-based Time-dependent Density-functional Theory,"Using the Runge-Gross theorem that establishes the foundation of
Time-dependent Density Functional Theory (TDDFT) we prove that for a given
electronic Hamiltonian, choice of initial state, and choice of fragmentation,
there is a unique single-particle potential (dubbed time-dependent partition
potential) which, when added to each of the pre-selected fragment potentials,
forces the fragment densities to evolve in such a way that their sum equals the
exact molecular density at all times. This uniqueness theorem suggests new ways
of computing time-dependent properties of electronic systems via fragment-TDDFT
calculations. We derive a formally exact relationship between the partition
potential and the total density, and illustrate our approach on a simple model
system for binary fragmentation in a laser field.",1303.6362v1
2013-11-06,A Density Difference Based Analysis of Orbital--Dependent Exchange--Correlation Functionals,"We present a density difference based analysis for a range of
orbital--dependent Kohn--Sham functionals. Results for atoms, some members of
the neon isoelectronic series and small molecules are reported and compared
with ab initio wave-function calculations. Particular attention is paid to the
quality of approximations to the exchange--only optimized effective potential
(OEP) approach: we consider both the Localized Hartree Fock as well as the
Krieger-Li-Iafrate methods. Analysis of density differences at the
exchange--only level reveals the impact the approximations have on the
resulting electronic densities. These differences are further quantified in
terms of the ground state energies, frontier orbital energy differences and
highest occupied orbital energies obtained. At the correlated level an OEP
approach based on a perturbative second--order correlation energy expression is
shown to deliver results comparable with those from traditional wave function
approaches, making it suitable for use as a benchmark against which to compare
standard density--functional approximations.",1311.1299v1
2013-12-09,Bounded weak solutions to matrix drift-diffusion model for spin-coherent electron transport in semiconductors,"The global-in-time existence and uniqueness of bounded weak solutions to a
spinorial matrix drift-diffusion model for semiconductors is proved. Developing
the electron density matrix in the Pauli basis, the coefficients (charge
density and spin-vector density) satisfy a parabolic $4\times 4$
cross-diffusion system. The key idea of the existence proof is to work with
different variables: the spin-up and spin-down densities as well as the
parallel and perpendicular components of the spin-vector density with respect
to the magnetization. In these variables, the diffusion matrix becomes
diagonal. The proofs of the $L^\infty$ estimates are based on Stampacchia
truncation as well as Moser- and Alikakos-type iteration arguments. The
monotonicity of the entropy (or free energy) is also proved. Numerical
experiments in one space dimension using a finite-volume discretization
indicate that the entropy decays exponentially fast to the equilibrium state.",1312.2461v1
2019-08-02,Accurate optical spectra of solids from pure time-dependent density-functional theory,"We present accurate optical spectra of semiconductors and insulators within a
pure Kohn-Sham time-dependent density-functional approach. In particular, we
show that the onset of the absorption is well reproduced when comparing to
experiment. No empirical information nor a theory beyond Kohn-Sham
density-functional theory, such as $GW$, is invoked to correct the Kohn-Sham
gap. Our approach relies on the link between the exchange-correlation kernel of
time-dependent density functional theory and the derivative discontinuity of
ground-state density-functional theory. We show explicitly how to relate these
two quantities. We illustrate the accuracy and simplicity of our approach by
applying it to various semiconductors (Si, GaP, GaAs) and wide-gap insulators
(C, LiF, Ar).",1908.00808v3
2020-07-22,The different flavors of extragalactic jets: the role of relativistic flow deceleration,"We perform three-dimensional numerical simulations of relativistic (with a
Lorentz factor of 10), non magnetized jets propagating in a uniform density
environment, in order to study the effect of the entrainment and the consequent
deceleration. Our simulations investigate the jet propagation inside the galaxy
core, where, most likely, the deceleration occurs more efficiently. We compare
cases with different density and pressure ratios with respect to the ambient
medium finding that low density jets are efficiently decelerated and reach a
quasi steady state in which, over a length of 600 jet radii, slow down from
highly to sub-relativistic velocities. At the opposite, denser jets keep highly
relativistic velocity over the same length. We discuss these results in
relation to the Faranoff Riley (FR) radio-sources classification. We infer that
lower density jets can give rise to FR 0 and FR I radio-sources, while higher
density jets may be connected to FR II radio-sources.",2007.11423v1
2017-09-04,Global analysis of Skyrme forces with higher-order density dependence,"The density dependent term in Skyrme forces is essential, which simulates
three-body and many-body correlations beyond the low-momentum two-body
interaction. We speculate that a single density term may be insufficient and a
higher-order density dependent term is added. The present work investigates the
influences of higher-order density dependencies based on extended UNEDF0 and
SkM* forces. The global descriptions of nuclear masses and charge radii have
been presented. Consequently the extended UNEDF0 force gives a global rms error
on binding energies of 1.29 MeV. The influences on fission barriers and
equation of state have also been investigated. The perspectives to improve
Skyrme forces have also been discussed, including global center-of-mass
corrections and Lipkin-Nogami pairing corrections.",1709.00802v2
2019-07-08,Damping of density oscillations in neutrino-transparent nuclear matter,"We calculate the bulk-viscous dissipation time for adiabatic density
oscillations in nuclear matter at densities of 1-7 times nuclear saturation
density and at temperatures ranging from 1 MeV, where corrections to previous
low-temperature calculations become important, up to 10 MeV, where the
assumption of neutrino transparency is no longer valid. Under these conditions,
which are expected to occur in neutron star mergers, damping of density
oscillations arises from beta equilibration via weak interactions. We find that
for 1 kHz oscillations the shortest dissipation times are in the 5 to 20 ms
range, depending on the equation of state, which means that bulk viscous
damping could affect the dynamics of a neutron star merger. For higher
frequencies the dissipation time can be even shorter.",1907.03795v2
2021-12-06,Density dependence of the excitation gaps in an undoped Si/SiGe double-quantum-well heterostructure,"We report low-temperature magneto-transport measurements of an undoped
Si/SiGe asymmetric double quantum well heterostructure. The density in both
layers is tuned independently utilizing a top and a bottom gate, allowing the
investigation of quantum wells at both imbalanced and matched densities.
Integer quantum Hall states at total filling factor $\nu_{\text{T}} = 1$ and
$\nu_{\text{T}} = 2$ are observed in both density regimes, and the evolution of
their excitation gaps is reported as a function of density. The $\nu_{\text{T}}
= 1$ gap evolution departs from the behavior generally observed for valley
splitting in the single layer regime. Furthermore, by comparing the
$\nu_{\text{T}} = 2$ gap to the single particle tunneling energy,
$\Delta_{\text{SAS}}$, obtained from Schr\""{o}dinger-Poisson (SP) simulations,
evidence for the onset of spontaneous inter-layer coherence (SIC) is observed
for a relative filling fraction imbalance smaller than ${\sim}50\%$",2112.03138v1
1994-07-07,Heavy resonance production in high energy nuclear collisions,"We estimate freezeout conditions for $s$, $c$, and $b$ quarks in high energy
nuclear collisions. Freezeout is due either to loss of thermal contact, or to
particles ``wandering'' out of the region of hot matter. We then develop a
thermal recombination model in which both single-particle (quark and antiquark)
and two-particle (quark-antiquark) densities are conserved. Conservation of
two-particle densities is necessary because quarks and antiquarks are always
produced in coincidence, so that the local two-particle density can be much
larger than the product of the single-particle densities. We use the freezeout
conditions and recombination model to discuss heavy resonance production at
zero baryon density in high energy nuclear collisions.",9407014v1
2008-04-01,Condensation and Extreme Value Statistics,"We study the factorised steady state of a general class of mass transport
models in which mass, a conserved quantity, is transferred stochastically
between sites. Condensation in such models is exhibited when above a critical
mass density the marginal distribution for the mass at a single site develops a
bump, $p_{\rm cond}(m)$, at large mass $m$. This bump corresponds to a
condensate site carrying a finite fraction of the mass in the system. Here, we
study the condensation transition from a different aspect, that of extreme
value statistics. We consider the cumulative distribution of the largest mass
in the system and compute its asymptotic behaviour. We show 3 distinct
behaviours: at subcritical densities the distribution is Gumbel; at the
critical density the distribution is Fr\'echet, and above the critical density
a different distribution emerges. We relate $p_{\rm cond}(m)$ to the
probability density of the largest mass in the system.",0804.0197v1
2010-01-04,Arrested phase separation in reproducing bacteria: a generic route to pattern formation?,"We present a generic mechanism by which reproducing microorganisms, with a
diffusivity that depends on the local population density, can form stable
patterns. It is known that a decrease of swimming speed with density can
promote separation into bulk phases of two coexisting densities; this is
opposed by the logistic law for birth and death which allows only a single
uniform density to be stable. The result of this contest is an arrested
nonequilibrium phase separation in which dense droplets or rings become
separated by less dense regions, with a characteristic steady-state length
scale. Cell division mainly occurs in the dilute regions and cell death in the
dense ones, with a continuous flux between these sustained by the diffusivity
gradient. We formulate a mathematical model of this in a case involving
run-and-tumble bacteria, and make connections with a wider class of mechanisms
for density-dependent motility. No chemotaxis is assumed in the model, yet it
predicts the formation of patterns strikingly similar to those believed to
result from chemotactic behavior.",1001.0057v1
2010-06-14,Long-range correlations and ensemble inequivalence in a generalized ABC model,"A generalization of the ABC model, a one-dimensional model of a driven system
of three particle species with local dynamics, is introduced, in which the
model evolves under either (i) density-conserving or (ii) nonconserving
dynamics. For equal average densities of the three species, both dynamical
models are demonstrated to exhibit detailed balance with respect to a
Hamiltonian with long-range interactions. The model is found to exhibit two
distinct phase diagrams, corresponding to the canonical (density-conserving)
and grand canonical (density nonconserving) ensembles, as expected in
long-range interacting systems. The implication of this result to
nonequilibrium steady states, such as those of the ABC model with unequal
average densities, are briefly discussed.",1006.2715v2
2011-07-29,Nuclear energy density functional from chiral two- and three-nucleon interactions,"An improved density-matrix expansion is used to calculate the nuclear energy
density functional from chiral two- and three-nucleon interactions. The
two-body interaction comprises long-range one- and two-pion exchange
contributions and a set of contact terms contributing up to fourth power in
momenta. In addition we employ the leading order chiral three-nucleon
interaction with its parameters $c_E, c_D$ and $c_{1,3,4}$ fixed in
calculations of nuclear few-body systems. With this input the nuclear energy
density functional is derived to first order in the two- and three-nucleon
interaction. We find that the strength functions $F_\nabla(\rho)$ and
$F_{so}(\rho)$ of the surface and spin-orbit terms compare in the relevant
density range reasonably with results of phenomenological Skyrme forces.
However, an improved description requires (at least) the treatment of the
two-body interaction to second order. This observation is in line with the
deficiencies in the nuclear matter equation of state $\bar E(\rho)$ that remain
in the Hartree-Fock approximation with low-momentum two- and three-nucleon
interactions.",1107.5966v1
2012-06-30,Implicit Density Estimation by Local Moment Matching to Sample from Auto-Encoders,"Recent work suggests that some auto-encoder variants do a good job of
capturing the local manifold structure of the unknown data generating density.
This paper contributes to the mathematical understanding of this phenomenon and
helps define better justified sampling algorithms for deep learning based on
auto-encoder variants. We consider an MCMC where each step samples from a
Gaussian whose mean and covariance matrix depend on the previous state, defines
through its asymptotic distribution a target density. First, we show that good
choices (in the sense of consistency) for these mean and covariance functions
are the local expected value and local covariance under that target density.
Then we show that an auto-encoder with a contractive penalty captures
estimators of these local moments in its reconstruction function and its
Jacobian. A contribution of this work is thus a novel alternative to
maximum-likelihood density estimation, which we call local moment matching. It
also justifies a recently proposed sampling algorithm for the Contractive
Auto-Encoder and extends it to the Denoising Auto-Encoder.",1207.0057v1
2013-02-12,Molecular Density Functional Theory of Water,"Three dimensional implementations of liquid state theories offer an efficient
alternative to computer simulations for the atomic-level description of aqueous
solutions in complex environments. In this context, we present a (classical)
molecular density functional theory (MDFT) of water that is derived from first
principles and is based on two classical density fields, a scalar one, the
particle density, and a vectorial one, the multipolar polarization density. Its
implementation requires as input the partial charge distribution of a water
molecule and three measurable bulk properties, namely the structure factor and
the k-dependent longitudinal and transverse dielectric constants. It has to be
complemented by a solute-solvent three-body term that reinforces tetrahedral
order at short range. The approach is shown to provide the correct
three-dimensional microscopic solvation profile around various molecular
solutes, possibly possessing H-bonding sites, at a computer cost two-three
orders of magnitude lower than with explicit simulations.",1302.2848v1
2014-01-09,The equation of state and symmetry energy of low density nuclear matter,"The symmetry energy of nuclear matter is a fundamental ingredient in the
investigation of exotic nuclei, heavy-ion collisions and astrophysical
phenomena. A recently developed quantum statistical (QS) approach that takes
the formation of clusters into account predicts low density symmetry energies
far above the usually quoted mean field limits. A consistent description of the
symmetry energy has been developed that joins the correct low-density limit
with values calculated from quasi-particle approaches valid near the saturation
density. The results are confronted with experimental values for free symmetry
energies and internal symmetry energies, determined at sub-saturation densities
and temperatures below 10 MeV using data from heavy-ion collisions. There is
very good agreement between the experimental symmetry energy values and those
calculated in the QS approach",1401.2074v1
2015-03-18,Exploring competing density order in the ionic Hubbard model with ultracold fermions,"We realize and study the ionic Hubbard model using an interacting
two-component gas of fermionic atoms loaded into an optical lattice. The
bipartite lattice has honeycomb geometry with a staggered energy-offset that
explicitly breaks the inversion symmetry. Distinct density-ordered phases are
identified using noise correlation measurements of the atomic momentum
distribution. For weak interactions the geometry induces a charge density wave.
For strong repulsive interactions we detect a strong suppression of doubly
occupied sites, as expected for a Mott insulating state, and the externally
broken inversion symmetry is not visible anymore in the density distribution.
The local density distributions in different configurations are characterized
by measuring the number of doubly occupied lattice sites as a function of
interaction and energy-offset. We further probe the excitations of the system
using direction dependent modulation spectroscopy and discover a complex
spectrum, which we compare with a theoretical model.",1503.05549v2
2018-11-17,Proposal to measure the pair field correlator of a fluctuating pair density wave,"I propose a method to directly measure the space and time dependence of the
pair field correlator of a pair density wave. The method is based on two
separate ideas. First, we adopt the solenoid insertion method of Kapon et al
(2017) to provide the momentum in a tunnel junction. Second, we suggest the use
of optimal or over-doped Bi-2201 films as a tunneling electrode with a known
charge ordering wave-vector which can match the expected pair density wave
wave-vectors we wish to study. The method is applicable to both fluctuating and
ordered states. Potential applications are to the proposed stripe pair density
wave order in LBCO and the possible pair density wave fluctuations at finite
temperature or in high magnetic field in underdoped YBCO as well as other
members of the Cuprate family.",1811.07089v1
2018-11-29,Anisotropic charge density wave in electron-hole double monolayers: Applied to phosphorene,"The possibility of an inhomogeneous charge density wave phase is investigated
in a system of two coupled electron and hole monolayers separated by a
hexagonal boron nitride insulating layer. The charge density wave state is
induced through the assumption of negative compressibility of electron/hole
gases in a Coulomb drag configuration between the electron and hole sheets.
Under equilibrium conditions, we derive analytical expressions for the density
oscillation along the zigzag and armchair directions. We find that the density
modulation not only depends on the sign of the compressibility but also on the
anisotropy of the low energy bands. Our results are applicable to any two
dimensional system with anisotropic parabolic bands, characterized by different
effective masses. For equal effective masses, i.e., isotropic energy bands, our
results agree with Hrolak et al.[1]. Our numerical results are applied to
phosphorene.",1811.12268v1
2010-05-17,Numerical Renormalization Group Study of Probability Distributions for Local Fluctuations in the Anderson-Holstein and Holstein-Hubbard Models,"We show that information on the probability density of local fluctuations can
be obtained from a numerical renormalisation group calculation of a reduced
density matrix. We apply this approach to the Anderson-Holstein impurity model
to calculate the ground state probability density $\rho(x)$ for the
displacement $x$ of the local oscillator. From this density we can deduce an
effective local potential for the oscillator and compare its form with that
obtained from a semiclassical approximation as a function of the coupling
strength. The method is extended to infinite dimensional Holstein-Hubbard model
using dynamical mean field theory. We use this approach to compare the
probability densities for the displacement of the local oscillator in the
normal, antiferromagnetic and charge ordered phases.",1005.2852v1
2013-08-01,Cooperative Enhancement of Energy Transfer in a High-Density Thermal Vapor,"We present an experimental study of energy transfer in a thermal vapor of
atomic rubidium. We measure the fluorescence spectrum in the visible and near
infra-red as a function of atomic density using confocal microscopy. At low
density we observe energy transfer consistent with the well-known energy
pooling process. In contrast, above a critical density we observe a dramatic
enhancement of the fluorescence from high-lying states that is not to be
expected from kinetic theory. We show that the density threshold for excitation
on the D1 and D2 resonance line corresponds to the value at which the
dipole-dipole interactions begins to dominate, thereby indicate the key role of
these interactions in the enhanced emission.",1308.0129v1
2018-08-17,Large Baryon Densities Achievable in High Energy Heavy Ion Collisions Outside the Central Rapidity Region,"Nuclei are nearly transparent to each other when they collide at high energy,
but the collisions do produce high energy density matter in the central
rapidity region where most experimental measurements are made. What happens to
the receding nuclear fireballs? We calculate the energy loss of the nuclei
using the color glass condensate model. We then use a simple space-time picture
of the collision to calculate the baryon and energy densities of the receding
fireballs. For central collisions of large nuclei at the BNL Relativistic Heavy
Ion Collider and the CERN Large Hadron Collider we find baryon densities more
than ten times that of normal nuclear matter. These results provide initial
conditions for subsequent hydrodynamic evolution and could test the equation of
state at very high baryon densities.",1808.05751v2
2018-08-27,Density-gradient-free variable in exchange-correlation functionals for detecting inhomogeneities in the electron density,"An alternative type of approximation for the exchange and correlation
functional in density functional theory is proposed. This approximation depends
on a variable $u$ that is able to detect inhomogeneities in the electron
density $\rho$ without using derivatives of $\rho$. Instead, $u$ depends on the
orbital energies which can also be used to measure how a system differs from
the homogeneous electron gas. Starting from the functional of Perdew, Burke,
and Ernzerhof (PBE) [Phys. Rev. Lett. 77, 3865 (1996)], a functional depending
on $u$ is constructed. Tests on the lattice constant, bulk modulus, and
cohesive energy of solids show that this $u$-dependent PBE-like functional is
on average as accurate as the original PBE or its solid-state version PBEsol.
Since $u$ carries more nonlocality than the reduced density gradient $s$ used
in functionals of the generalized gradient approximation (GGA) like PBE and
$\alpha$ used in meta-GGAs, it will be certainly useful for the future
development of more accurate exchange-correlation functionals.",1808.08887v2
2008-07-14,Exact results of two-component Fermi gas in a hard wall trap,"We investigate the ground state properties of a one-dimensional two-component
ultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solution
is used to calculate the many-body wave function of the system. Then we
evaluate the single-particle reduced density matrix and two-particle density
density correlations of the system for different interaction strengths. We find
that the momentum density distributions of the strongly interacting
two-component Fermi gas is distinct from that of free spinless Fermi gas
although their position density distributions are similar. This interacting
system may be experimentally accessible using ultra-cold atoms.",0807.2154v1
2017-07-02,Asymptotics of fast rotating density-dependent incompressible fluids in two space dimensions,"In the present paper we study the fast rotation limit for viscous
incompressible fluids with variable density, whose motion is influenced by the
Coriolis force. We restrict our analysis to two dimensional flows. In the case
when the initial density is a small perturbation of a constant state, we
recover in the limit the convergence to the homogeneous incompressible
Navier-Stokes equations (up to an additional term, due to density
fluctuations). For general non-homogeneous fluids, the limit equations are
instead linear, and the limit dynamics is described in terms of the vorticity
and the density oscillation function: we lack enough regularity on the latter
to prove convergence on the momentum equation itself. The proof of both results
relies on a compensated compactness argument, which enables one to treat also
the possible presence of vacuum.",1707.00321v1
2019-06-07,Properties of isospin asymmetric matter derived from chiral effective field theory,"We present and discuss properties of isospin asymmetric matter whose equation
of state is derived from recent high-quality chiral nucleon-nucleon potentials
and chiral effective three-nucleon forces. After a brief review of the chiral
few-nucleon forces which we adopt, we concentrate on the symmetry energy and
its density derivatives. We also explore the correlation between the symmetry
energy at saturation density and its slope parameter, L. We estimate the
truncation error across three orders of the chiral expansion for both the
symmetry energy as a function of density and the slope parameter. Through an
energy-density functional inspired by the liquid drop model, we establish a
simple connection to finite nuclei. Specifically, we address the symmetry
energy coefficient, the so-called reference (or equivalent) density, as well as
the neutron skin thickness for 208Pb and 48Ca.",1906.02905v1
2020-11-07,Deeply-Supervised Density Regression for Automatic Cell Counting in Microscopy Images,"Accurately counting the number of cells in microscopy images is required in
many medical diagnosis and biological studies. This task is tedious,
time-consuming, and prone to subjective errors. However, designing automatic
counting methods remains challenging due to low image contrast, complex
background, large variance in cell shapes and counts, and significant cell
occlusions in two-dimensional microscopy images. In this study, we proposed a
new density regression-based method for automatically counting cells in
microscopy images. The proposed method processes two innovations compared to
other state-of-the-art density regression-based methods. First, the density
regression model (DRM) is designed as a concatenated fully convolutional
regression network (C-FCRN) to employ multi-scale image features for the
estimation of cell density maps from given images. Second, auxiliary
convolutional neural networks (AuxCNNs) are employed to assist in the training
of intermediate layers of the designed C-FCRN to improve the DRM performance on
unseen datasets. Experimental studies evaluated on four datasets demonstrate
the superior performance of the proposed method.",2011.03683v2
2021-09-27,Freeze-in from Preheating,"We consider the production of dark matter during the process of reheating
after inflation. The relic density of dark matter from freeze-in depends on
both the energy density and energy distribution of the inflaton scattering or
decay products composing the radiation bath. We compare the perturbative and
non-perturbative calculations of the energy density in radiation. We also
consider the (likely) possibility that the final state scalar products are
unstable. Assuming either thermal or non-thermal energy distribution functions,
we compare the resulting relic density based on these different approaches. We
show that the present-day cold dark matter density can be obtained through
freeze-in from preheating for a large range of dark matter masses.",2109.13280v1
2021-10-06,Relative Entropy Gradient Sampler for Unnormalized Distributions,"We propose a relative entropy gradient sampler (REGS) for sampling from
unnormalized distributions. REGS is a particle method that seeks a sequence of
simple nonlinear transforms iteratively pushing the initial samples from a
reference distribution into the samples from an unnormalized target
distribution. To determine the nonlinear transforms at each iteration, we
consider the Wasserstein gradient flow of relative entropy. This gradient flow
determines a path of probability distributions that interpolates the reference
distribution and the target distribution. It is characterized by an ODE system
with velocity fields depending on the density ratios of the density of evolving
particles and the unnormalized target density. To sample with REGS, we need to
estimate the density ratios and simulate the ODE system with particle
evolution. We propose a novel nonparametric approach to estimating the
logarithmic density ratio using neural networks. Extensive simulation studies
on challenging multimodal 1D and 2D mixture distributions and Bayesian logistic
regression on real datasets demonstrate that the REGS outperforms the
state-of-the-art sampling methods included in the comparison.",2110.02787v1
2023-12-15,Quantum to classical parton evolution in the QGP,"We study the time evolution of the density matrix of a high energy quark in
the presence of a dense QCD background that is modeled as a stochastic Gaussian
color field. At late times, we find that only the color singlet component of
the quark's reduced density matrix survives the in-medium evolution and that
the density matrix becomes asymptotically diagonal in both transverse position
and momentum spaces. In addition, we observe an accelerated entropy growth due
to the larger phase space being explored by the quark and that the quantum and
classical quark entropies converge at late times. We further observe that the
quark state loses all memory of the initial condition. Combined with the fact
that the reduced density matrix satisfies Boltzmann-diffusion transport, we
conclude that the quark reduced density matrix can be interpreted as a
classical phase space distribution.",2312.10236v1
2016-10-19,Density of states and dynamical crossover in a dense fluid revealed by exponential mode analysis of the velocity autocorrelation function,"Extending a previous study of the velocity autocorrelation function (VAF) in
a simulated Lennard-Jones fluid to cover higher-density and lower-temperature
states, we show that the recently demonstrated multiexponential expansion
allows for a full account and understanding of the dynamical processes
encompassed by a fundamental quantity as the VAF. In particular, besides
obtaining evidence of a persisting long-time tail, we assign specific and
unambiguous physical meanings to groups of exponential modes related to the
longitudinal and transverse collective dynamics, respectively. We have made
this possible by consistently introducing the interpretation of the VAF
frequency spectrum as a global density of states in fluids, generalizing a
solid-state concept, and by giving to specific spectral components, obtained
via the VAF exponential expansion, the corresponding meaning of partial
densities of states relative to specific dynamical processes. The clear
identification of a high-frequency oscillation of the VAF with the near-top
excitation frequency in the dispersion curve of acoustic waves is a neat
example of the power of the method. As for the transverse mode contribution,
its analysis turns out to be particularly important, because the
multiexponential expansion reveals a transition marking the onset of
propagating excitations when the density is increased above a threshold value.
While this finding agrees with recent literature debating the issue of
dynamical crossover boundaries, such as the one identified with the Frenkel
line, we can add detailed information on the modes involved in this specific
process in the domains of both time and frequency. This will help obtain a
still missing full account of transverse dynamics, in its nonpropagating and
propagating aspects which are linked by dynamical transitions depending on both
the thermodynamic states and the excitation wavevectors.",1610.06146v1
1998-02-23,Theory of Local Density of States of d-Wave Superconducting State Near the Surfaces of the t-J Model,"Spatial dependencies of the pair potential and the local density of states
near the surfaces of $d_{x^{2}-y^{2}}$-wave superconductors are studied
theoretically. The calculation is based on the t-J model within a mean-field
theory with Gutzwiller approximation. Various types of surface geometries are
considered. Similar to our result in the extended Hubbard model, it is found
that the formation of zero-energy states strongly depends on the surface
geometry. In addition to this feature, the zero-energy states give peak
splitting for the (110) surfaces when the super-exchange interaction $J$ is
large. This is due to the induced s-wave component near the surface. The
present result explains the microscopic origin of the spontaneous time-
reversal symmetry breaking at the surfaces of high-$T_{c}$ superconductors.",9802243v1
2010-10-18,Generating random density matrices,"We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.",1010.3570v2
2012-08-08,Quantum decoherence of spin states in an electric-field controllable single molecular magnet,"The time evolution of low energy spin states of a single molecular magnet in
a local electric field is investigated. The decoherence of the driven single
molecular magnet weakly coupled to a thermal bosonic environment is analyzed by
the second-order time-convolutionless non-Markovian master equation. If the
characteristic time of the system is much smaller than the correlation time of
the environment, the analytical expression of the reduced density matrix of the
system is obtained. The non-Markovian dynamics of the spin states at low
temperatures is induced by the memory effects in the decay rates. The
non-Markovian oscillation of the Bloch vector is presented. The quantum
decoherence can be effectively restrained with the help of the reasonable
manipulation of the environment spectral density function and local electric
field. The influence of the dissipation on the pointer states are investigated
by the von Neumann entropy. The pointer states can be selected by the
environment.",1208.1549v1
2015-06-19,Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard,"We calculate the joint distribution $P(S,Q)$ of the scattering matrix $S$ and
time-delay matrix $Q=-i\hbar S^\dagger dS/dE$ of a chaotic quantum dot coupled
by point contacts to metal electrodes. While $S$ and $Q$ are statistically
independent for ballistic coupling, they become correlated for tunnel coupling.
We relate the ensemble averages of $Q$ and $S$ and thereby obtain the average
density of states at the Fermi level. We apply this to a calculation of the
effect of a tunnel barrier on the Majorana resonance in a topological
superconductor. We find that the presence of a Majorana bound state is hidden
in the density of states and in the thermal conductance if even a single
scattering channel has unit tunnel probability. The electrical conductance
remains sensitive to the appearance of a Majorana bound state, and we calculate
the variation of the average conductance through a topological phase
transition.",1506.05995v1
2014-06-05,Power-law approach to steady state in open lattices of non-interacting electrons,"We address the question of how a non-equilibrium steady state (NESS) is
reached in the Linbdladian dynamics of an open quantum system. We develop an
expansion of the density matrix in terms of the NESS-excitations, each of which
has its own (exponential) decay rate. However, when the decay rates tend to
zero for many NESS-excitations (the spectral gap of the Liouvillian is closed
in the thermodynamic limit), the long-time dynamics of the system can exhibit a
power-law behaviour. This relaxation to NESS expectation values is determined
by the density of states close to zero spectral gap and the value of the
operator in these states. We illustrate this main idea on the example of the
lattice of non-interacting fermions coupled to Markovian leads at infinite bias
voltage. The current comes towards its NESS value starting from a typical
initial state as $\tau^{-3/2}$. This behaviour is universal and independent of
the space dimension.",1406.1408v1
2016-08-23,Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension,"We compute exactly the von Neumann entanglement entropy of the eta-pairing
states - a large set of exact excited eigenstates of the Hubbard Hamiltonian.
For the singlet eta-pairing states the entropy scales with the logarithm of the
spatial dimension of the (smaller) partition. For the eta-pairing states with
finite spin magnetization density, the leading term can scale as the volume or
as the area-times-log, depending on the momentum space occupation of the
Fermions with flipped spins. We also compute the corrections to the leading
scaling. In order to study the eigenstate thermalization hypothesis (ETH), we
also compute the entanglement Renyi entropies of such states and compare them
with the corresponding entropies of thermal density matrix in various
ensembles. Such states, which we find violate strong ETH, may provide a useful
platform for a detailed study of the time-dependence of the onset of
thermalization due to perturbations which violate the total pseudospin
conservation.",1608.06639v3
2017-07-21,A histogram-free multicanonical Monte Carlo algorithm for the basis expansion of density of states,"We report a new multicanonical Monte Carlo (MC) algorithm to obtain the
density of states (DOS) for physical systems with continuous state variables in
statistical mechanics. Our algorithm is able to obtain an analytical form for
the DOS expressed in a chosen basis set, instead of a numerical array of finite
resolution as in previous variants of this class of MC methods such as the
multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled
by storing the visited states directly in a data set and avoiding the explicit
collection of a histogram. This practice also has the advantage of avoiding
undesirable artificial errors caused by the discretization and binning of
continuous state variables. Our results show that this scheme is capable of
obtaining converged results with a much reduced number of Monte Carlo steps,
leading to a significant speedup over existing algorithms.",1707.07049v1
2019-03-27,Switching of magnetism via modifying phase shift of quantum-well states by tailoring the interface electronic structure,"We demonstrate control of the magnetism of Pd(100) ultrathin films, which
show d-electron quantum-well induced ferromagnetism, via modulation of the
interface electronic state using density functional calculation. From an
analysis based on the phase model, forming the Au/Pd(100) interface induces
hybridization of the wave function of d-electron quantum-well states, and
modulates the term of the scattering phase shift as a function of the
reciprocal lattice point. In contrast, forming the Al interface, which has only
s-electrons at the Fermi energy, cannot modify the scattering phase shift. Our
finding indicates the possibility of modifying the phase shift by tailoring the
interface electronic states using hybridization of the wave function, and this
efficiently changes the density of states near the Fermi energy of Pd films,
and the switching between paramagnetism and ferromagnetism occurs based on the
condition for ferromagnetism (Stoner criterion).",1903.11404v3
2020-01-15,Neural network representation of the probability density function of diffusion processes,"Physics-informed neural networks are developed to characterize the state of
dynamical systems in a random environment. The neural network approximates the
probability density function (pdf) or the characteristic function (chf) of the
state of these systems which satisfy the Fokker-Planck equation or an
integro-differential equation under Gaussian and/or Poisson white noises. We
examine analytically and numerically the advantages and disadvantages of
solving each type of differential equation to characterize the state. It is
also demonstrated how prior information of the dynamical system can be
exploited to design and simplify the neural network architecture. Numerical
examples show that: 1) the neural network solution can approximate the target
solution even for partial integro-differential equations and system of PDEs
describing the time evolution of the pdf/chf, 2) solving either the
Fokker-Planck equation or the chf differential equation using neural networks
yields similar pdfs of the state, and 3) the solution to these differential
equations can be used to study the behavior of the state for different types of
random forcings.",2001.05437v2
2021-07-13,Representing individual electronic states for machine learning GW band structures of 2D materials,"Choosing optimal representation methods of atomic and electronic structures
is essential when machine learning properties of materials. We address the
problem of representing quantum states of electrons in a solid for the purpose
of machine leaning state-specific electronic properties. Specifically, we
construct a fingerprint based on energy decomposed operator matrix elements
(ENDOME) and radially decomposed projected density of states (RAD-PDOS), which
are both obtainable from a standard density functional theory (DFT)
calculation. Using such fingerprints we train a gradient boosting model on a
set of 46k G$_0$W$_0$ quasiparticle energies. The resulting model predicts the
self-energy correction of states in materials not seen by the model with a mean
absolute error of 0.14 eV. By including the material's calculated dielectric
constant in the fingerprint the error can be further reduced by 30%, which we
find is due to an enhanced ability to learn the correlation/screening part of
the self-energy. Our work paves the way for accurate estimates of quasiparticle
band structures at the cost of a standard DFT calculation.",2107.06029v3
2022-04-29,Local density of states and particle entanglement in topological quantum fluids,"The understanding of particle entanglement is an important goal in the
studies of correlated quantum matter. The widely-used method of scanning
tunneling spectroscopy -- which measures the local density of states (LDOS) of
a many-body system by injecting or removing an electron from it -- is expected
to be sensitive to particle entanglement. In this paper, we systematically
investigate the relation between the particle entanglement spectrum (PES) and
the LDOS of fractional quantum Hall (FQH) states, the paradigmatic
strongly-correlated phases of electrons with topological order. Using exact
diagonalization, we show that the counting of levels in both the LDOS and PES
in the Jain sequence of FQH states can be predicted from the composite fermion
theory. We point out the differences between LDOS and PES characterization of
the bulk quasihole excitations, and we discuss the conditions under which the
LDOS counting can be mapped to that of PES. Our results affirm that tunneling
spectroscopy is a sensitive tool for identifying the nature of FQH states.",2205.00024v2
1993-12-06,Weak Disorder Expansion for the Anderson Model on a Tree,"We show how certain properties of the Anderson model on a tree are related to
the solutions of a non-linear integral equation. Whether the wave function is
extended or localized, for example, corresponds to whether or not the equation
has a complex solution. We show how the equation can be solved in a weak
disorder expansion. We find that, for small disorder strength $\lambda$, there
is an energy $E_c(\lambda )$ above which the density of states and the
conducting properties vanish to all orders in perturbation theory. We compute
perturbatively the position of the line $E_c(\lambda )$ which begins, in the
limit of zero disorder, at the band edge of the pure system. Inside the band of
the pure system the density of states and conducting properties can be computed
perturbatively. This expansion breaks down near $E_c(\lambda )$ because of
small denominators. We show how it can be resummed by choosing the appropriate
scaling of the energy. For energies greater than $E_c(\lambda )$ we show that
non-perturbative effects contribute to the density of states but have been
unable tell whether they also contribute to the conducting properties.",9312023v1
1997-12-31,Disorder-Induced Broadening of the Density of States for 2D Electrons with Strong Spin-Orbit Coupling,"We study theoretically the disorder-induced smearing of the density of states
in a two-dimensional electron system taking into account a spin-orbit term in
the Hamiltonian of a free electron. We show that the characteristic energy
scale for the smearing increases with increasing the spin-orbit coupling. We
also demonstrate that in the limit of a strong spin-orbit coupling the diagrams
with self-intersections give a parametrically small contribution to the
self-energy. As a result, the coherent potential approximation becomes
asymptotically exact in this limit. The tail of the density of states has the
energy scale which is much smaller than the magnitude of the smearing. We find
the shape of the tail using the instanton approach.",9712328v1
1998-11-27,The importance of self-consistency in determining interface properties of S-I-N and D-I-N structures,"We develop a method to solve the Bogoliubov de Gennes equation for
superconductors self-consistently, using the recursion method. The method
allows the pairing interaction to be either local or non-local corresponding to
$s$ and $d$--wave superconductivity, respectively. Using this method we examine
the properties of various $S-I-N$ and $D-I-N$ interfaces. In particular we
self-consistently calculate the spatially varying density of states and the
superconducting order parameter. We see that changing the strength of the
insulating barrier, at the interface, does not, in the case of an $s$--wave
superconductor, dramatically, change the low energy local density of states, in
the superconducting region near the interface. This is in stark contrast to
what we see in the case of a $D-I-N$ interface where the local particle density
of states is changed dramatically. Hence we deduce that in calculating such
properties as the conductance of $S-I-N$ and $D-I-N$ structures it is far more
important to carry out a self-consistent calculations in the $d$--wave case.",9811389v1
2001-02-15,Diffusion-Limited Reaction in One Dimension: Paired and Unpaired Nucleation,"We consider the dynamics of diffusing particles in one space dimension with
annihilation on collision and nucleation (creation of particles) with constant
probability per unit time and length. The cases of nucleation of single
particles and nucleation in pairs are considered. A new method of analysis
permits exact calculation of the steady state density and its time evolution in
terms of the three parameters describing the microscopic dynamics: the
nucleation rate, the initial separation of nucleated pairs and the diffusivity
of a particle. For paired nucleation at sufficiently small initial separation
the nucleation rate is proportional to the square of the steady state density.
For unpaired nucleation, and for paired nucleation at sufficiently large
initial separation, the nucleation rate is proportional to the cube of the
steady state density.",0102270v2
2001-10-02,Zero-bias anomaly in two-dimensional electron layers and multiwall nanotubes,"The zero-bias anomaly in the dependence of the tunneling density of states
$\nu (\epsilon)$ on the energy $\epsilon$ of the tunneling particle for two-
and one-dimensional multilayered structures is studied. We show that for a
ballistic two-dimensional (2D) system the first order interaction correction to
DOS due to the plasmon excitations studied by Khveshchenko and Reizer is partly
compensated by the contribution of electron-hole pairs which is twice as small
and has the opposite sign. For multilayered systems the total correction to the
density of states near the Fermi energy has the form $\delta \nu/\nu_0 = {max}
(| \epsilon |, \epsilon^*)/4\epsilon_F$, where $\epsilon^*$ is the plasmon
energy gap of the multilayered 2D system. In the case of one-dimensional
conductors we study multiwall nanotubes with the elastic mean free path
exceeding the radius of the nanotube. The dependence of the tunneling density
of states energy, temperature and on the number of shells is found.",0110065v2
2006-02-07,A first-principles comparison of the electronic properties of MgC_{y}Ni_{3} and ZnC_{y}Ni_{3} alloys,"First-principles, density-functional-based electronic structure calculations
are employed to study the changes in the electronic properties of ZnC_{y}Ni_{3}
and MgC_{y}Ni_{3} using the Korringa-Kohn-Rostoker coherent-potential
approximation method in the atomic sphere approximation (KKR-ASA CPA). As a
function of decreasing C at%, we find a steady decrease in the lattice constant
and bulk modulus in either alloys. However, the pressure derivative of the bulk
modulus displays an opposite trend. Following the Debye model, which relates
the pressure derivative of the bulk modulus with the average phonon frequency
of the crystal, it can thus be argued that ZnCNi_{3} and its disordered alloys
posses a different phonon spectra in comparison to its MgCNi_{3} counterparts.
This is further justified by the marked similarity we find in the electronic
structure properties such as the variation in the density of states and the
Hopfield parameters calculated for these alloys. The effects on the equation of
state parameters and the density of states at the Fermi energy, for partial
replacement of Mg by Zn are also discussed.",0602181v1
2005-11-11,On the Equation of State for Diquark Systems and their importance in Astrophysics and Cosmology,"With a view to studying diquark formation in QCD phase transition and its
consequences in high energy density physics, the energy per quark for the
extended scalar diquarks (ESD) as a function of density is calculated, within
the framework of an effective phi four theory, for several values of the
effective interaction parameter (lamda). Various equations of state for the ESD
systems corresponding to the different values of lamda are obtained. The
importance of the equations of state for such matter under extreme conditions
of density and/or temperature is discussed and the role of the astrophysical
diquarks in astrophysics and cosmological diquarks in cosmological conditions
is also highlighted.",0511140v2
2007-06-19,Tunneling into low-dimensional and strongly correlated conductors,"A general nonperturbative theory of the low-energy electron propagator is
developed and used to calculate the single-particle density of states in a
variety of systems. This method involves the decoupling of the
electron-electron interaction through a Hubbard-Stratonovich transformation,
followed by a saddle-point approximation of the remaining functional integral.
The final expression is found to be the tunneling analog of the infrared
catastrophe that occurs in the x-ray edge problem; here, the host system
responds to the potential produced by the abrupt addition of an electron during
a tunneling event. This response can lead to a suppression in the tunneling
density of states near the Fermi energy. This method is adaptable to lattice or
continuum models of any dimensionality, with or without translational
invariance. When applied, the exact density of states is obtained for the
Tomonaga-Luttinger model, and the pseudogap of a fractional quantum Hall fluid
is recovered.",0706.2774v2
2008-12-16,Pattern Speeds and Galaxy Morphology,"The morphology of a disk galaxy is closely linked to its kinematic state.
This is because density wave features are likely made of spontaneously-formed
modes which are allowed to arise in the galactic resonant cavity of a
particular basic disk state. The pattern speed of a density wave is an
important parameter that characterizes the wave and its associated resonances.
Numerical simulations by various authors have enabled us to interpret some
galaxies in terms of high or low pattern speeds. The potential-density
phase-shift method for locating corotation radii is an effective new tool for
utilizing galaxy morphology to determine the kinematic properties of galaxies.
The dynamical mechanism underlying this association is also responsible for the
secular evolution of galaxies. We describe recent results from the application
of this new method to more than 150 galaxies in the Ohio State University
Bright Galaxy Survey and other datasets.",0812.2959v1
2010-09-14,Thermodynamics of itinerant metamagnetic transitions,"Theoretical studies of the metamagnetism and anomalous phase of Sr3Ru2O7 have
focused on the role of van Hove singularities, although much experimental
evidence points towards quantum criticality having a large effect. We
investigate the magnetic and thermodynamic properties of systems where magnetic
field tunes through such a peak in the electronic density of states. We study
the generic case of a van Hove singularity in 2D. We see that in combination
with the requirement of number conservation and interaction effects the peak in
the density of states produces several interesting phenomena including raising
the critical field of the transition above naive estimates, altering the
relationship between temperature and field scales and creating a distinctive
double-peak structure in the electronic specific heat. We show that this
apparent non-Fermi liquid behaviour can be caused at mean-field level by a peak
in the density of states.",1009.2777v1
2010-09-20,Random Block Operators,"We study fundamental spectral properties of random block operators that are
common in the physical modelling of mesoscopic disordered systems such as dirty
superconductors. Our results include ergodic properties, the location of the
spectrum, existence and regularity of the integrated density of states, as well
as Lifshits tails. Special attention is paid to the peculiarities arising from
the block structure such as the occurrence of a robust gap in the middle of the
spectrum. Without randomness in the off-diagonal blocks the density of states
typically exhibits an inverse square-root singularity at the edges of the gap.
In the presence of randomness we establish a Wegner estimate that is valid at
all energies. It implies that the singularities are smeared out by randomness,
and the density of states is bounded. We also show Lifshits tails at these band
edges. Technically, one has to cope with a non-monotone dependence on the
random couplings.",1009.3795v1
2011-02-16,Thermodynamics of Trapped Imbalanced Fermi Gases at Unitarity,"We present a theory for the low-temperature properties of a resonantly
interacting Fermi mixture in a trap, that goes beyond the local-density
approximation. The theory corresponds essentially to a Landau-Ginzburg-like
approach that includes self-energy effects to account for the strong
interactions at unitarity. We show diagrammatically how these self-energy
effects arise from fluctuations in the superfluid order parameter. Gradient
terms of the order parameter are included to account for inhomogeneities. This
approach incorporates the state-of-the-art knowledge of the homogeneous mixture
with a population imbalance exactly and gives good agreement with the
experimental density profiles of Shin et al. [Nature 451, 689 (2008)]. This
allows us to calculate the universal surface tension of the interface between
the equal-density superfluid and the partially polarized normal state of the
mixture. We also discuss the possibility of a metastable state to explain the
deformation of the superfluid core that is seen in the experiment of Partridge
et al. [Science 311, 503 (2006)].",1102.3320v1
2011-10-06,Density of states of continuous and discrete spin models: a case study,"A relation between O(n) lattice spin models and Ising models defined on the
same lattice was recently put forward [L. Casetti, C. Nardini, and R.
Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by
an energy landscape analysis, implies that the density of states of an O(n)
spin model on a lattice can be effectively approximated, at least close to the
phase transition, in terms of the density of states of an Ising model defined
on the same lattice and with the same interactions. In the present paper we
show that such a relation exactly holds, albeit in a slightly modified form, in
the special cases of the mean-field XY model and of the one-dimensional XY
model. We also discuss the possible consequences of this result for the general
case.",1110.1276v2
2013-04-10,Lattice dynamics of coesite,"The lattice dynamics of coesite has been studied by a combination of diffuse
x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics
calculation. The combined technique gives access to the full lattice dynamics
in harmonic description and thus eventually provides detailed information on
the elastic properties, the stability and metastability of crystalline systems.
The experimentally validated calculation was used for the investigation of
eigenvectors, mode character and their influence on the density of vibrational
states. High symmetry sections of the reciprocal space distribution of diffuse
scattering and inelastic x-ray scattering spectra as well as the density of
vibrational states and the dispersion relation are reported and compared to the
calculation. A critical point at the zone boundary is found to contribute
strongly to the main peak of the low energy part in the density of vibrational
states. Comparison with the most abundant SiO2 polymorph - alpha-quartz -
reveals similarities and distinct differences in the low-energy vibrational
properties.",1304.3046v2
2013-05-17,Effect of weak impurities on electronic properties of graphene: functional renormalization-group analysis,"We consider an effect of weak impurities on electronic properties of graphene
within the functional renormalization-group approach. The energy dependences of
the electronic self-energy and density of states near the neutrality point are
discussed. Depending on the symmetry of the impurities, the electronic damping
$\Gamma$ and density of states $\rho$ can deviate substantially from those
given by the self-consistent Born approximation. We investigate the crossover
from the results of the self-consistent Born approximation, which are valid far
from the neutrality point to the strong-coupling (diffusive) regime near the
neutrality point. For impurities, which are diagonal in both, valley and
sublattice indices, we obtain finite density of states at the Fermi level with
the values, which are much bigger than the results of the self-consistent Born
approximation.",1305.4127v3
2015-09-30,The origin of anisotropy and high density of states in the electronic structure of Cr$_2$GeC by means of polarized soft X-ray spectroscopy and ab initio calculations,"The anisotropy in the electronic structure of the inherently nanolaminated
ternary phase Cr$_{2}$GeC is investigated by bulk-sensitive and element
selective soft x-ray absorption/emission spectroscopy. The angle-resolved
absorption/emission measurements reveal differences between the in-plane and
out-of-plane bonding at the (0001) interfaces of Cr$_{2}$GeC. The Cr $L_{2,3}$,
C $K$, and Ge $M_{1}$, $M_{2,3}$ emission spectra are interpreted with
first-principles density-functional theory (DFT) including core-to-valence
dipole transition matrix elements. For the Ge $4s$ states, the x-ray emission
measurements reveal two orders of magnitude higher intensity at the Fermi level
than DFT within the General Gradient Approximation (GGA) predicts. We provide
direct evidence of anisotropy in the electronic structure and the orbital
occupation that should affect the thermal expansion coefficient and transport
properties. As shown in this work, hybridization and redistribution of
intensity from the shallow $3d$ core levels to the $4s$ valence band explain
the large Ge density of states at the Fermi level.",1509.09190v1
2017-03-29,3$d$ - 4$d$ hybridization anomaly in Ni$_x$Pd$_{1-x}$ alloys at quantum critical point,"$First-principles$ density functional theory computations of electronic
structure and local magnetic properties of the non-fluctuating ground state of
Ni$_x$Pd$_{1-x}$ alloy system around its quantum critical point $x_c = 0.026$
have been performed. The density of states at the Fermi energy and certain
other parameters characterizing the Ni 3$d$ - Pd 4$d$ hybridization apparently
follow power-laws with $x$ similar to that obeyed by the reported ferromagnetic
to paramagnetic transition temperature. The width of Pd $4d$ density of states
(DOS) and centroid of Ni 3$d$ DOS show peak-like anomalies in the neighbourhood
of $x_c$, and so indicate a possible scenario of the existence of a definite
relation between the orbital hybridization and the emergence of quantum
fluctuations in the system.",1703.09967v1
2018-04-06,Dependence of the density of states on the probability distribution for discrete random Schrödinger operators,"We prove that the the density of states measure (DOSm) for random
Schr\""odinger operators on $\mathbb{Z}^d$ is weak-$^*$ H\""older-continuous in
the probability measure. The framework we develop is general enough to extend
to a wide range of discrete, random operators, including the Anderson model on
the Bethe lattice, as well as random Schr\""odinger operators on the strip. An
immediate application of our main result provides quantitive continuity
estimates for the disorder dependence of the DOSm and the integrated density of
states (IDS) in the weak disorder regime. These results hold for a general
compactly supported single-site probability measure, without any further
assumptions. The few previously available results for the disorder dependence
of the IDS valid for dimensions $d \geq 2$ assumed absolute continuity of the
single-site measure and thus excluded the Bernoulli-Anderson model. As a
further application of our main result, we establish quantitative continuity
results for the Lyapunov exponent of random Schr\""odinger operators for $d=1$
in the probability measure with respect to the weak-$^*$ topology.",1804.02444v2
2020-07-21,Density of States Analysis of Electrostatic Confinement in Gapped Graphene,"We investigate the electrostatic confinement of charge carriers in a gapped
graphene quantum dot in the presence of a magnetic flux. The circular quantum
dot is defined by an electrostatic gate potential delimited in an infinite
graphene sheet which is then connected to a two terminal setup. Considering
different regions composing our system, we explicitly determine the solutions
of the energy spectrum in terms of Hankel functions. Using the scattering
matrix together with the asymptotic behavior of the Hankel functions for large
arguments, we calculate the density of states and show that it has an
oscillatory behavior with the appearance of resonant peaks. It is found that
the energy gap can controls the amplitude and width of these resonances and
affect their location in the density of states profile.",2007.10655v1
2016-05-02,Resistance oscillations of two-dimensional electrons in crossed electric and tilted magnetic fields,"Effect of dc electric field on transport of highly mobile 2D electrons is
studied in wide GaAs single quantum wells placed in titled magnetic fields. The
study shows that in perpendicular magnetic field resistance oscillates due to
electric field induced Landau-Zener transitions between quantum levels that
corresponds to geometric resonances between cyclotron orbits and periodic
modulation of electron density of states. Magnetic field tilt inverts these
oscillations. Surprisingly the strongest inverted oscillations are observed at
a tilt corresponding to nearly absent modulation of the electron density of
states in regime of magnetic breakdown of semiclassical electron orbits. This
phenomenon establishes an example of quantum resistance oscillations due to
Landau quantization, which occur in electron systems with a constant density of
states.",1605.00675v1
2016-12-19,Spontaneous Distortion and Ferromagnetism Induced by Quantum-well States in Pd(100) Ultrathin Films,"We study the crystal structure of Pd(100) ultrathin films, which show
ferromagnetism induced by the quantum confinement effect, using in-situ X-ray
crystal truncation rod measurement and density functional calculation. The
energy gain due to the appearance of ferromagnetism in Pd results in flatter
and uniform film growth of ferromagnetic Pd films compared with paramagnetic
Pd. In addition, ferromagnetic Pd films expand the lattice constant in order to
suppress the increase in kinetic energy of electrons accompanied by the
occurrence of exchange splitting. Although the traditional theory of magnetism
in metals indicates that the increase in density of states that induces
ferromagnetism (Stoner criterion), our present finding reveals a mechanism of
modulation in the density of states via the appearance of ferromagnetism, i.e.,
the inverse mechanism of Stoner's theory.",1612.06216v1
2017-06-10,"Energy structure, density of states and transmission properties of the periodic 1D Tight-Binding lattice with a generic unit cell of $u$ sites","We report on the electronic structure, density of states and transmission
properties of the periodic one-dimensional Tight-Binding (TB) lattice with a
single orbital per site and nearest-neighbor interactions, with a generic unit
cell of $u$ sites. The determination of the eigenvalues is equivalent to the
diagonalization of a real tridiagonal symmetric $u$-Toeplitz matrix with
(cyclic boundaries) or without (fixed boundaries) perturbed upper right and
lower left corners. We solve the TB equations via the Transfer Matrix Method,
producing, analytical solutions and recursive relations for its eigenvalues,
closely related to the Chebyshev polynomials. We examine the density of states
and provide relevant analytical relations. We attach semi-infinite leads,
determine and discuss the transmission coefficient at zero bias and investigate
the peaks number and position, and the effect of the coupling strength and
asymmetry as well as of the lead properties on the transmission profiles. We
introduce a generic optimal coupling condition and demonstrate its physical
meaning.",1706.03250v1
2018-09-21,The Equation of State of Dark Matter Superfluids,"We derive the finite-temperature equation of state of dark matter superfluids
with 2-body and 3-body contact interactions. The latter case is relevant to a
recently proposed model of dark matter superfluidity that unifies the
collisionless aspects of dark matter with the empirical success of MOdified
Newtonian Dynamics at fitting galactic rotation curves. The calculation uses a
self-consistent mean-field approximation. It relies on the
Hartree-Fock-Bogoliubov approximation and follows the Yukalov-Yukalova proposal
to circumvent the well-known Hohenberg-Martin dilemma. The resulting equation
of state is consistent with a gapless spectrum, and simultaneously satisfies
the equation of motion for the condensate wavefunction. As an application, we
derive the finite-temperature density profile for dark matter superfluids,
assuming spherical symmetry and uniform temperature. The density profiles
consist of a nearly homogeneous superfluid core, surrounded by an isothermal
""atmosphere"" of normal particles, with the transition taking place at the
critical density.",1809.08286v1
2018-10-08,Local Density of States induced near Impurities in Mott Insulators,"The local density of states near dopants or impurities has recently been
probed by scanning tunneling microscopy in both the parent and very lightly
doped compounds of the high-$T_c$ cuprate superconductors. Our calculations
based on a slave-rotor description account for all the following key features
of the observed local density of states: i) positions and amplitudes of the
in-gap spectral weights of a single impurity; ii) the spectral weight transfer
from the upper Hubbard band to the lower Hubbard band; iii) the difference
between the cases of single and multiple impurities. For multiple impurities,
our study explains the complete suppression of spectral weight observed at
precisely the Fermi energy and links this property to zeros of the underlying
bulk Green's function of the Mott insulating phase.",1810.03309v1
2020-06-13,Spaces of Random Plane Triangulations and the Density of States,"Tiling spaces are constructed using a metric in which two tilings of
$\mathbb{R}^n$ are close if and only if, after a small translation, they agree
on a large ball around the origin. We construct analogous spaces to study
random triangulations of the plane. We construct a continuous space which is a
foliated space equipped with a transverse measure, and a discrete space which
is a transversal of that space. Measures on these triangulations can be
constructed as limits of measures on spheres.
  We consider von Neumann algebras associated with these spaces. Under certain
conditions, we show that the von Neumann algebra associated with the discrete
space is a hyperfinite type $II_1$ factor. We also show that the density of
states of certain operators is well-behaved with respect to the convergence of
measures, and in particular can be computed by approximating it on spheres,
where eigenvalues can be directly computed. Additionally, we prove a connection
between jumps of the integrated density of states and compactly supported
eigenfunctions analogous to arXiv:0709.2836.",2006.07582v3
2020-12-18,New equation of state involving Bose-Einstein condensate of antikaon for supernova and neutron star merger simulations,"We compute a new equation of state table including Bose-Einstein condensate
of $K^{-}$ mesons for core collapse supernova and neutron star merger
simulations. Nuclei and interacting nucleons in non-uniform matter is described
in an extended version of the nuclear statistical equilibrium model including
excluded volume effects whereas the uniform matter at higher densities is
treated in the relativistic hadron field theory with density dependent
couplings. The equation of state table is generated for a wide range of density
($10^{-12}$ to $\sim 1$ fm$^{-3}$), positive charge fraction (0.01 to 0.60) and
temperature (0.1 to 158.48 MeV). The impact of antikaon condensate is
investigated on different thermodynamic quantities for example free energy per
baryon, entropy per baryon, pressure as well as compositions of matter.
Furthermore, critical temperatures of antikaon condensation and the phase
diagram of matter are also studied in this article.",2012.10127v1
2022-04-03,Convergence of the Planewave Approximations for Quantum Incommensurate Systems,"Incommensurate structures arise from stacking single layers of
low-dimensional materials on top of one another with misalignment such as an
in-plane twist in orientation. While these structures are of significant
physical interest, they pose many theoretical challenges due to the loss of
periodicity. In this paper, we characterize the density of states of
Schr\""{o}dinger operators in the weak sense for the incommensurate system and
develop novel numerical methods to approximate them. In particular, we (i)
justify the thermodynamic limit of the density of states in the real space
formulation; and (ii) propose efficient numerical schemes to evaluate the
density of states based on planewave approximations and reciprocal space
sampling. We present both rigorous analysis and numerical simulations to
support the reliability and efficiency of our numerical algorithms.",2204.00994v3
2010-04-22,The high-density regime of kinetic-dominated loop quantum cosmology,"We study the dynamics of states perturbatively expanded about a harmonic
system of loop quantum cosmology, exhibiting a bounce. In particular, the
evolution equations for the first and second order moments of the system are
analyzed. These moments back-react on the trajectories of the expectation
values of the state and hence alter the energy density at the bounce. This
analysis is performed for isotropic loop quantum cosmology coupled to a scalar
field with a small but non-zero constant potential, hence in a regime in which
the kinetic energy of matter dominates. Analytic restrictions on the existence
of dynamical coherent states and the meaning of semi-classicality within these
systems are discussed. A numerical investigation of the trajectories of states
that remain semi-classical across the bounce demonstrates that, at least for
such states, the bounce persists and that its properties are similar to the
standard case, in which the moments of the states are entirely neglected.
However the bounce density does change, implying that a quantum bounce may not
be guaranteed to happen when the potential is no longer negligible.",1004.3979v2
2014-08-21,A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry,"We extend the spin-adapted density matrix renormalization group (DMRG)
algorithm of McCulloch and Gulacsi [Europhys. Lett.57, 852 (2002)] to quantum
chemical Hamiltonians. This involves two key modifications to the
non-spin-adapted DMRG algorithm: the use of a quasi-density matrix to ensure
that the renormalised DMRG states are eigenvalues of $S^2$ , and the use of the
Wigner-Eckart theorem to greatly reduce the overall storage and computational
cost. We argue that the advantages of the spin-adapted DMRG algorithm are
greatest for low spin states. Consequently, we also implement the
singlet-embedding strategy of Nishino et al [Phys. Rev. E61, 3199 (2000)] which
allows us to target high spin states as a component of a mixed system which is
overall held in a singlet state. We evaluate our algorithm on benchmark
calculations on the Fe$_2$S$_2$ and Cr$_2$ transition metal systems. By
calculating the full spin ladder of Fe$_2$S$_2$ , we show that the spin-adapted
DMRG algorithm can target very closely spaced spin states. In addition, our
calculations of Cr$_2$ demonstrate that the spin-adapted algorithm requires
only roughly half the number of renormalised DMRG states as the
non-spin-adapted algorithm to obtain the same accuracy in the energy, thus
yielding up to an order of magnitude increase in computational efficiency.",1408.5039v1
2014-05-07,"Comment on Consensus formation on a simplicial complex of opinions (arXiv:1212.1940, Physica A, Vol. 397 (1), pp. 111-120, 2014)","In the commented paper, the authors declare an analogy with the quantum
mechanical pure states established through the application of the
high-dimensional combinatorial Laplacian considering that the simplicial
complex is in the pure state when it is formed by collection of the pure
states. In their work, besides giving a completely erroneous analogy for the
pure quantum mechanical state, which contradicts to very basic postulates of
quantum mechanic, the authors clearly fail to provide and explain mathematical
formalism behind their claims. Their intention is to rigorously prove that the
existence of opinion space in all considered cases consists of the pure quantum
states using incorrect normalization constant which does not produce trace
equal to one. In this comment we prove out that their claims are erroneous. In
order to show incorrectness of Maletic & Rajkovic model and conclusions we
calculated and examined connections between different combinatorial structures
of q- dimensional simplicial complexes and their Laplacian spectra and analyzed
resulting symmetric and positive semidefinite matrices in the context of the
density matrix of a quantum mechanical system. Importance of presented research
is to further develop accurate quantitative topological-based characterization
method for convertibility and distillation of density matrix.",1405.1700v3
2020-11-26,Covariant density functional theory input for r-process simulations in actinides and superheavy nuclei: the ground state and fission properties,"The systematic investigation of the ground state and fission properties of
even-even actinides and superheavy nuclei with $Z=90-120$ from the two-proton
up to two-neutron drip lines with proper assessment of systematic theoretical
uncertainties has been performed for the first time in the framework of
covariant density functional theory (CDFT). These results provide a necessary
theoretical input for the r-process modeling in heavy nuclei and, in
particular, for the study of fission recycling. Four state-of-the-art globally
tested covariant energy density functionals (CEDFs), namely, DD-PC1, DD-ME2,
NL3* and PC-PK1, representing the major classes of the CDFT models are employed
in the present study. Ground state deformations, binding energies, two neutron
separation energies, $\alpha$-decay $Q_{\alpha}$ values and half-lives and the
heights of fission barriers have been calculated for all these nuclei.
Theoretical uncertainties in these physical observables and their evolution as
a function of proton and neutron numbers have been quantified and their major
sources have been identified. Spherical shell closures at $Z=120$, $N=184$ and
$N=258$ and the structure of the single-particle (especially, high-$j$) states
in their vicinities as well as nuclear matter properties of employed CEDFs are
two major factors contributing into theoretical uncertainties. However,
different physical observables are affected in a different way by these two
factors. For example, theoretical uncertainties in calculated ground state
deformations are affected mostly by former factor, while theoretical
uncertainties in fission barriers depend on both of these factors.",2011.13368v1
1998-07-24,Relativistic Trace Formula for Bound States in Terms of Classical Periodic Orbits,"We set up a trace formula for the relativistic density of states in terms of
a topological sum of classical periodic orbits. The result is applicable to any
relativistic integrable system.",9807068v1
1999-10-29,Exactly Solvable Model of Quantum Spin Interacting with Spin Environment,"An exactly solvable model of a quantum spin interacting with a spin
environment is considered. The interaction is chosen to be such that the state
of the environment is conserved. The reduced density matrix of the spin is
calculated for arbitrary coupling strength and arbitrary time. The stationary
state of the spin is obtained explicitely in the $t \to \infty$ limit.",9910119v1
2001-07-04,Correlations in quantum systems and branch points in the complex plane,"Branch points in the complex plane are responsible for avoided level
crossings in closed and open quantum systems. They create not only an exchange
of the wave functions but also a mixing of the states of a quantum system at
high level density. The influence of branch points in the complex plane on the
low-lying states of the system is small.",0107018v1
2008-04-22,Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on $\T$,"We prove that if a Borel probability measure (\mu) on (\T) is invariant under
the action of a ""large"" multiplicative semigroup (lower logarithmic density is
positive) and the action of the whole semigroup is ergodic then (\mu) is either
Lebesgue or has finite support.",0804.3586v2
2009-06-20,Energy States of Universe and New Phantom Energy,"Energy states of the universe is obtained when the scale factor is defined as
a=At^n, and n varies as -1<=n<=1,with the aid of the wavefunction which was
constructed in, Mahgoub Salih, A Canonical Quantization formalism of curvature
squared action. we found new properties of early Phantom energy, which it`s
energy density increases with time while w=-1/3 .",0906.3830v1
2010-12-21,Optimal verification of entanglement in a photonic cluster state experiment,"We report on the quantification of entanglement by means of entanglement
measures on a four- and a six- qubit cluster state realized by using photons
entangled both in polarization and linear momentum. This paper also addresss
the question of the scaling of entanglement bounds from incomplete tomographic
information on the density matrix under realistic experimental conditions.",1012.4637v1
2011-04-02,Witness to detect quantum correlation of bipartite states in arbitrary dimension,"In this work we introduce a nonlinear witness that is a sufficient condition
for detecting the vanishment of quantum correlation of bipartite states. Our
result directly generalizes the result of [J. Maziero, R. M. Serra,
arXiv:1012.3075] to arbitrary dimension based on the Bloch representation of
density matrices.",1104.0299v1
2014-07-25,Uncertainty relations based on mutually unbiased measurements,"We derive uncertainty relation inequalities according to the mutually
unbiased measurements. Based on the calculation of the index of coincidence of
probability distribution given by $d+1$ MUMs on any density operator $\rho$ in
$\mathbb{C}^{d}$, both state-dependent and state-independent forms of lower
entropic bounds are given. Furthermore, we formulate uncertainty relations for
MUMs in terms of R\'{e}nyi and Tsallis entropies.",1407.6816v1
2015-12-19,A Complete Equation of State for Astrophysical Simulations,"We construct a complete equation of state (EOS) covering a wide range of
temperature, proton fraction, and baryon density for the use of astrophysical
simulations. We employ the relativistic mean-field (RMF) theory to describe
nuclear interactions and adopt the Thomas-Fermi approximation to describe the
nonuniform nuclear matter. The uniform matter and nonuniform matter are studied
consistently using the same RMF theory.",1512.06196v1
2022-02-24,Improved Spectral Representations of Neutron-Star Equations of State,"Spectral representations have been shown to provide an efficient way to
represent the poorly understood high-density portion of the neutron-star
equation of state. This paper shows how the efficiency and accuracy of those
representations can be improved by a very simple change.",2202.12285v1
2008-04-03,Analytical Approach to the One-Dimensional Disordered Exclusion Process with Open Boundaries and Random Sequential Dynamics,"A one dimensional disordered particle hopping rate asymmetric exclusion
process (ASEP) with open boundaries and a random sequential dynamics is studied
analytically. Combining the exact results of the steady states in the pure case
with a perturbative mean field-like approach the broken particle-hole symmetry
is highlighted and the phase diagram is studied in the parameter space
$(\alpha,\beta)$, where $\alpha$ and $\beta$ represent respectively the
injection rate and the extraction rate of particles. The model displays, as in
the pure case, high-density, low-density and maximum-current phases. All
critical lines are determined analytically showing that the high-density
low-density first order phase transition occurs at $\alpha \neq \beta$. We show
that the maximum-current phase extends its stability region as the disorder is
increased and the usual $1/\sqrt{\ell}$-decay of the density profile in this
phase is universal. Assuming that some exact results for the disordered model
on a ring hold for a system with open boundaries, we derive some analytical
results for platoon phase transition within the low-density phase and we give
an analytical expression of its corresponding critical injection rate
$\alpha^*$. As it was observed numerically$^{(19)}$, we show that the quenched
disorder induces a cusp in the current-density relation at maximum flow in a
certain region of parameter space and determine the analytical expression of
its slope. The results of numerical simulations we develop agree with the
analytical ones.",0804.0519v1
2022-08-03,KiDS-1000 Cosmology: Constraints from density split statistics,"Context. Weak lensing and clustering statistics beyond two-point functions
can capture non-Gaussian information about the matter density field, thereby
improving the constraints on cosmological parameters relative to the mainstream
methods based on correlation functions and power spectra. Aims. This paper
presents a cosmological analysis of the fourth data release of the Kilo Degree
Survey based on the density split statistics, which measures the mean shear
profiles around regions classified according to foreground densities. The
latter is constructed from a bright galaxy sample, which we further split into
red and blue samples, allowing us to probe their respective connection to the
underlying dark matter density. Methods. We use the state-of-the-art model of
the density splitting statistics and validate its robustness against mock data
infused with known systematic effects such as intrinsic galaxy alignment and
baryonic feedback. Results. After marginalising over the photometric redshift
uncertainty and the residual shear calibration bias, we measure for the full
KiDS-bright sample a structure growth parameter of $S_8 = \sigma_8
\sqrt{\Omega_\mathrm{m}/0.3} = 0.74^{+0.03}_{-0.02}$ that is competitive to and
consistent with two-point cosmic shear results, a matter density of
$\Omega_\mathrm{m} = 0.28 \pm 0.02$, and a constant galaxy bias of $b =
1.32^{+0.12}_{-0.10}$.",2208.02171v2
2024-03-03,Towards Provable Log Density Policy Gradient,"Policy gradient methods are a vital ingredient behind the success of modern
reinforcement learning. Modern policy gradient methods, although successful,
introduce a residual error in gradient estimation. In this work, we argue that
this residual term is significant and correcting for it could potentially
improve sample-complexity of reinforcement learning methods. To that end, we
propose log density gradient to estimate the policy gradient, which corrects
for this residual error term. Log density gradient method computes policy
gradient by utilising the state-action discounted distributional formulation.
We first present the equations needed to exactly find the log density gradient
for a tabular Markov Decision Processes (MDPs). For more complex environments,
we propose a temporal difference (TD) method that approximates log density
gradient by utilizing backward on-policy samples. Since backward sampling from
a Markov chain is highly restrictive we also propose a min-max optimization
that can approximate log density gradient using just on-policy samples. We also
prove uniqueness, and convergence under linear function approximation, for this
min-max optimization. Finally, we show that the sample complexity of our
min-max optimization to be of the order of $m^{-1/2}$, where $m$ is the number
of on-policy samples. We also demonstrate a proof-of-concept for our log
density gradient method on gridworld environment, and observe that our method
is able to improve upon the classical policy gradient method by a clear margin,
thus indicating a promising novel direction to develop reinforcement learning
algorithms that require fewer samples.",2403.01605v1
2024-03-20,Longitudinal changes in deep learning-estimated breast density and their impact on the risk of screen-detected breast cancer: The DeepJoint Algorithm,"Mammography-based screening programs play a crucial role in reducing breast
cancer mortality through early detection. Their efficacy is influenced by
breast density, a dynamic factor that evolves over time, modifying breast
cancer risk. Women with high breast density face increased breast cancer risk,
coupled with reduced mammographic sensitivity. In this work, we present the
DeepJoint algorithm, a pipeline for quantitative breast density assessment,
investigating its association with breast cancer risk. First, we develop a
lightweight deep-learning segmentation model that uses processed mammography
images acquired from multiple manufacturers to assess quantitative breast
density metrics such as dense area and percent density. Then, we fit a joint
model to evaluate the association of these metrics with the time-to-breast
cancer occurrence using an extensive database of 77,298 women participating in
breast cancer screening in the United States. We demonstrate the impact of the
current value and slope of the biomarker on breast cancer risk. We also derive
individual and dynamic breast cancer risk predictions to describe how the
individual longitudinal evolution of dense area and percent density impacts the
risk of breast cancer. This innovative approach aligns with the growing
interest in personalized risk monitoring during screening, offering valuable
insights for improving breast cancer prevention strategies.",2403.13488v1
2015-10-04,Disentangling the role of structure and friction in shear jamming,"Amorphous packings of spheres have been intensely investigated in order to
understand the mechanical and flow behaviour of dense granular matter, and to
explore universal aspects of the transition from fluid to structurally arrested
or jammed states. Considerable attention has recently been focussed on
anisotropic packings of frictional grains generated by shear deformation
leading to shear jamming, which occurs below the jamming density for isotropic
packings of frictionless grains. With the aim of disentangling the role of
shear deformation induced structures and friction in generating shear jamming,
we study sheared assemblies of frictionless spheres computationally, over a
wide range of densities, extending far below the isotropic jamming point. We
demonstrate the emergence of a variety of geometric features characteristic of
jammed packings with the increase of shear strain. The average contact number
and the distributions of contact forces suggest the presence of a threshold
density, well below the isotropic jamming point, above which a qualitative
change occurs in the jamming behaviour of sheared configurations. We show that
above this threshold density, friction stabilizes the sheared configurations we
generate. Our results thus reveal the emergence of geometric features
characteristic of jammed states as a result of shear deformation alone, while
friction is instrumental in stabilising packings over a range of densities
below the isotropic jamming point.",1510.00962v1
2015-08-28,$p$-orbital density wave with $d$ symmetry in high-$T_c$ cuprate superconductors predicted by the renormalization-group + constrained RPA theory,"The discovery of the charge-density-wave formation in the high-$T_c$ cuprate
superconductors has activated intensive theoretical studies for the pseudogap
states. However, the microscopic origin of the charge-density-wave state has
been unknown so far since the many-body effects beyond the mean-field-level
approximations, called the vertex corrections, are essential. Toward solving
this problem, we employ the recently developed functional renormalization-group
method, by which we can calculate the higher-order vertex corrections in a
systematic and unbiased way with high numerical accuracy. We discover the
critical development of the $p$-orbital-density-wave ($p$-ODW) instability in
the strong-spin-fluctuation region. The obtained $p$-ODW state possesses the
key characteristics of the charge ordering pattern in Bi- and Y-based
superconductors, such as the wave vector parallel to the nearest Cu-Cu
direction, and the $d$-symmetry form factor with the antiphase correlation
between $p_x$ and $p_y$ orbitals in the same unit cell. In addition, from the
observation of the beautiful scaling relation between the spin susceptibility
and the $p$-ODW susceptibility, we conclude that the main driving force of the
density wave is the Aslamazov-Larkin vertex correction that becomes very
singular near the magnetic quantum-critical point.",1508.07218v3
1996-12-26,Equation of State of the Photoionized Intergalactic Medium,"We develop an efficient method to study the effects of reionization history
on the temperature-density relation of the intergalactic medium in the low
density limit (overdensity less than 5). It is applied to the study of
photo-reionization models in which the amplitude, spectrum and onset epoch of
the ionizing flux, as well as the cosmology, are systematically varied. We find
that the mean temperature-density relation at z=2-4 is well approximated by a
power-law equation of state for uniform reionization models. We derive
analytical expressions for its evolution and exhibit its asymptotic behavior:
it is found that for sufficiently early reionization, imprints of reionization
history prior to z=10 on the temperature-density relation are washed out. In
this limit the temperature at cosmic mean density is proportional to (\Omega_b
h/\sqrt\Omega_0)^{1/1.7}. While the amplitude of the radiation flux at the
ionizing frequency of HI is found to have a negligible effect on the
temperature-density relation as long as the universe reionizes before z=5, the
spectrum can change the overall temperature by about 20%, through variations in
the abundances of helium species. However the slope of the mean equation of
state is found to lie within a narrow range for all reionization models we
study, where reionization takes place before z=5. We discuss the implications
of these findings for the observational properties of the Lyman-alpha forest.
In particular, uncertainties in the temperature of the intergalactic medium,
due to the uncertain reionization history of our universe, introduces a 30%
scaling in the amplitude of the column density distribution while the the slope
of the distribution is only affected by about 5%. Finally, we discuss how a
fluctuating ionizing field affects the above results. We argue that under",9612232v1
2008-06-18,"A Survey of Metal Lines at High-redshift (II) : SDSS Absorption Line Studies - OVI line density, space density and gas metallicity at z_abs ~ 3.0","We have analysed a large data set of OVI absorber candidates found in the
spectra of 3702 SDSS quasars, focusing on a subsample of 387 AGN sightlines
with an average S/N>5.0, allowing for detection of absorbers above rest-frame
equivalents widths W_r>0.19 A for the OVI 1032 A component. Accounting for
random interlopers mimicking an OVI doublet, we derive for the first time a
secure lower limit for the redshift number density $\Delta N / \Delta z$ for
redshifts z_abs>2.8. With extensive Monte Carlo simulations we quantify the
losses of absorbers due to blending with the ubiquitous Lyman forest lines, and
estimate the success rate of retrieving each individual candidate as a function
of its redshift, the emission redshift of the quasar, the strength of the
absorber and the measured S/N of the spectrum by modelling typical Ly forest
spectra. These correction factors allow us to derive the 'incompleteness and
S/N corrected' redshift number densities of OVI absorbers :$\Delta N _{OVI, c}
/ \Delta z_{c} (2.8 < z < 3.2) = 4.6+-0.3, at 3.2 < z < 3.6 = 6.7+-0.8,and at
3.6 < z < 4.0 = 8.4+-2.9. We can place a secure lower limit for the
contribution of OVI to the closure mass density at the redshifts probed here:
$\Omega _{OVI} (2.8 < z < 3.2) >1.9x10^{-8} h^-1. We show that the strong lines
we probe account for over 65\% of the mass in the OVI absorbers; the weak
absorbers, while dominant in line number density, do not contribute
significantly to the mass density. Making a conservative assumption about the
ionisation fraction, and adopting the Anders (1989) solar abundance values, we
derive the mean metallicty of the gas probed in our search : $\zeta (2.8 < z <
3.2) > 3.6 x 10^-4 h, in good agreement with other studies. These results
demonstrate that large spectroscopic datasets such as SDSS can play an
important role in QSO absorption line studies, in spite of the relatively low
resolution.",0806.3071v2
2020-02-18,Identity of the JET M-mode and the ASDEX Upgrade I-phase phenomena,"An H-mode plasma state free of edge-localized mode (ELM), close to the L-H
transition with clear density and temperature pedestal has been observed both
at the Joint European Torus (JET) and at the ASDEX Upgrade (AUG) tokamaks
usually identified by a low frequency (LFO, 1-2 kHz), m=1, n=0 oscillation of
the magnetics and the modulation of pedestal profiles. The regime at JET is
referred to as M-mode while at AUG as intermediate phase or I-phase. This
contribution aims at a comparative analysis of these phenomena in terms of the
density and temperature pedestal properties, the magnetic oscillations and
symmetries. Lithium beam emission spectroscopy (Li-BES) and reflectometer
measurements at JET and AUG show that the M-mode and the I-phase modulates the
plasma edge density. A high frequency oscillation of the magnetics and the
density at the pedestal is also associated with both the M-mode and the
I-phase, and its power is modulated with the LFO frequency. The power
modulation happens simultaneously in every Mirnov coil signal where it can be
detected. The bursts of the magnetic signals and the density at the pedestal
region are followed by the flattening of the density profile, and by a radially
outward propagating density pulse in the scrape-off layer (SOL). The analysis
of the helium line ratio spectroscopy (He-BES) signals at AUG revealed that the
electron temperature is modulated in phase with the density, thus the I-phase
modulates the pressure profile gradient. This analysis gave opportunity to
compare Li-BES and He-BES density profiles at different locations suggesting a
toroidal and poloidal symmetry of the density modulation. The presented results
indicate that the regimes, the AUG I-phase and the JET M-mode, exhibit similar
characteristics, which leads to the conclusion that the regimes are likely the
same.",2002.07502v1
2000-10-05,Phase separation frustrated by the long range Coulomb interaction I: Theory,"We analyze the combined effect of the long range Coulomb (LRC) interaction
and of surface energy on first order density-driven phase transitions in the
presence of a compensating rigid background. We study mixed states formed by
regions of one phase surrounded by the other in the case in which the scale of
the inhomogeneities is much larger than the interparticle distance. Two
geometries are studied in detail: spherical drops of one phase into the other
and a layered structure of one phase alternating with the other. We find the
optimum density profile in an approximation in which the free energy is a
functional of the local density (LDA). It is shown that an approximation in
which the density is assumed to be uniform (UDA) within each phase region gives
results very similar to those of the more involved LDA approach. Within the UDA
we derive the general equations for the chemical potential and the pressures of
each phase which generalize the Maxwell construction to this situation. The
equations are valid for a rather arbitrary geometry. We find that the
transition to the mixed state is quite abrupt i.e. inhomogeneities of the first
phase appear with a finite value of the radius and of the phase volume
fraction. The maximum size of the inhomogeneities is found to be on the scale
of a few electric field screening lengths. Contrary to the ordinary Maxwell
construction, the inverse specific volume of each phase depends here on the
global density in the coexistence region and can decrease as the global density
increases. The range of densities in which coexistence is observed shrinks as
the LRC interaction increases until it reduces to a singular point. We argue
that close to this singular point the system undergoes a lattice instability as
long as the inverse lattice compressibility is finite.",0010092v2
1999-09-01,Pointer states via Decoherence in a Quantum Measurement,"We consider the interaction of a quantum system (spin-1/2) with a macroscopic
quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of
harmonic oscillators. Exact solutions of the Markovian Master equation show
that the reduced density matrix of the system-apparatus combine decoheres to a
statistical mixture where up and down spins eventually correlate with pointer
states of the apparatus. For the zero temperature bath these pointer states
turn out to be coherent states of the harmonic oscillator for arbitrary initial
states of the apparatus. For a high temperature bath pointer states are
Gaussian distributions (generalized coherent states). For both cases, the
off-diagonal elements in spin-space decohere over a time scale which goes
inversely as the square of the ""separation"" between the ""pointers"". Our exact
results also demonstrate in an unambiguous way that the pointer states in this
measurement model emerge independent of the initial state of the apparatus.",9909005v1
2007-04-30,Separability Criterion for multipartite quantum states based on the Bloch representation of density matrices,"We give a new separability criterion, a necessary condition for separability
of $N$-partite quantum states. The criterion is based on the Bloch
representation of a $N$-partite quantum state and makes use of multilinear
algebra, in particular, the matrization of tensors. Our criterion applies to
{\it arbitrary} $N$-partite quantum states in
$\mathcal{H}=\mathcal{H}^{d_1}\otimes \mathcal{H}^{d_2} \otimes ... \otimes
\mathcal{H}^{d_N}.$ The criterion can test whether a $N$-partite state is
entangled and can be applied to different partitions of the $N$-partite system.
We provide examples that show the ability of this criterion to detect
entanglement. We show that this criterion can detect bound entangled states. We
prove a sufficiency condition for separability of a 3-partite state,
straightforwardly generalizable to the case $N > 3,$ under certain condition.
We also give a necessary and sufficient condition for separability of a class
of $N$-qubit states which includes $N$-qubit PPT states.",0704.3942v5
2016-06-20,Approximating local observables on projected entangled pair states,"Tensor network states are for good reasons believed to capture ground states
of gapped local Hamiltonians arising in the condensed matter context, states
which are in turn expected to satisfy an entanglement area law. However, the
computational hardness of contracting projected entangled pair states in two
and higher dimensional systems is often seen as a significant obstacle when
devising higher-dimensional variants of the density-matrix renormalisation
group method. In this work, we show that for those projected entangled pair
states that are expected to provide good approximations of such ground states
of local Hamiltonians, one can compute local expectation values in
quasi-polynomial time. We therefore provide a complexity-theoretic
justification of why state-of-the-art numerical tools work so well in practice.
We comment on how the transfer operators of such projected entangled pair
states have a gap and discuss notions of local topological quantum order. We
finally turn to the computation of local expectation values on quantum
computers, providing a meaningful application for a small-scale quantum
computer.",1606.06301v2
2023-04-23,Toy model for the correlation of qudit bipartite states with maximally mixed marginals,"In this paper, we consider the local unitary classification of the class of
qudit bipartite mixed states for which no information can be obtained locally.
These states are represented by symmetrical density matrices in which both
tracial states are maximally mixed. Interestingly, this symmetry facilitates
the local unitary classification of two-qubit states. However, the same
formalism fails in the case of systems of higher dimensions. We consider a
broader set of states by introducing a family of qudit bipartite mixed states
with maximally mixed marginals. For this family of states, we determine several
constants which are in variant under local unitary transformations so can be
used for entanglement classification. Finally, we consider the two-qutrit case
and in particular, a two-parameter family of states for which the local unitary
classification is complete. We relate this classification to known entanglement
measures such as purity and negativity.",2304.11637v1
2023-10-31,Ordering dynamics of nonlinear voter models,"We study the ordering dynamics of nonlinear voter models with multiple
states, also providing a discussion of the two-state model. The rate with which
an individual adopts an opinion scales as the $q$-th power of the number of the
individual's neighbours in that state. For $q>1$ the dynamics favor the opinion
held by the most agents. The ordering to consensus is driven by deterministic
drift, and noise only plays a minor role. For $q<1$ the dynamics favors
minority opinions, and for multistate models the ordering proceeds through a
noise-driven succession of metastable states. Unlike linear multi-state
systems, the nonlinear model cannot be reduced to an effective two-state model.
We find that the average density of active interfaces in the model with
multiple opinion states does not show a single exponential decay in time for
$q<1$, again at variance with the linear model. This highlights the special
character of the conventional (linear) voter model, in which deterministic
drift is absent. As part of our analysis, we develop a pair approximation for
the multi-state model on graphs, valid for any positive real value of $q$,
improving on previous approximations for nonlinear two-state voter models.",2310.20548v1
1996-03-05,Superfluid-Insulator Transition of Interacting Multi-Component Bosons,"Various types of superfluid-insulator transitions are investigated for
two-component lattice boson systems in two dimensions with on-site hard-core
repulsion and the component-dependent intersite interaction. The mean-field
phase diagram is obtained by the Gutzwiller-type variational technique in the
plane of filling and interaction parameters. Various ground-state properties
are also studied by the quantum Monte Carlo method. Our model exhibits two
types of diagonal long-range orders; the density order around the density
$n=1/2$ and the Ising-type component order near $n=1$. The quantum Monte Carlo
results for the transitions from the superfluid state to these two ordered
states show marked contrast with the Gutzwiller results. Namely, although they
are both accompanied by phase separation into commensurate ($n=1/2$ or $n=1$)
and incommensurate density phases, these transitions are both continuous. The
continuous growth of the component correlation severely suppresses the
superfluidity as well as the inverse of the effective mass in the critical
region of the component order transition in contrast to the persistence of the
superfluidity in the density-ordered state. We propose a mechanism of the mass
enhancement observed even far from the Mott insulating filling $n=1$, when the
Ising-type component order persists into $n \neq 1$. Possible relevance of this
type of mass enhancement in other systems is also discussed.",9603028v1
2008-11-13,State diagrams for harmonically trapped bosons in optical lattices,"We use quantum Monte Carlo simulations to obtain zero-temperature state
diagrams for strongly correlated lattice bosons in one and two dimensions under
the influence of a harmonic confining potential. Since harmonic traps generate
a coexistence of superfluid and Mott insulating domains, we use local
quantities such as the quantum fluctuations of the density and a local
compressibility to identify the phases present in the inhomogeneous density
profiles. We emphasize the use of the ""characteristic density"" to produce a
state diagram that is relevant to experimental optical lattice systems,
regardless of the number of bosons or trap curvature and of the validity of the
local-density approximation. We show that the critical value of U/t at which
Mott insulating domains appear in the trap depends on the filling in the
system, and it is in general greater than the value in the homogeneous system.
Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402
(2008)] are analyzed in the context of our two-dimensional state diagram, and
shown to exhibit a value for the critical point in good agreement with
simulations. We also study the effects of finite, but low (T<t/2),
temperatures. We find that in two dimensions they have little influence on our
zero-temperature results, while their effect is more pronounced in one
dimension.",0811.2219v2
2009-02-06,Superfluid density of the $\pm$s-wave state for the iron-based superconductors,"We study the superfluid density of the $\pm$s-wave state of the minimal two
band model for the Fe-based superconductors and its evolution with impurity
concentration. We show that the impurity scattering of the strong coupling
limit induces the selfenergy of a generic form $Im \Sigma_{imp} (\omega)
\approx i \gamma + i \beta \omega$ beyond a critical impurity concentration
$\Gamma_{imp} > \Gamma_{crit}$. This form of $Im \Sigma_{imp} (\omega)$ causes
the temperature dependence of the superfluid density $[\rho_{s}(T) -
\rho_{s}(0)] \approx - \gamma T^2 -\beta T^3$. Combining with the full gap
behavior of $\rho_{s}(T)$ for lower impurity concentration $\Gamma_{imp} <
\Gamma_{crit}$, the $\pm$s-wave state produces a continuous evolution of
$\Delta \lambda(T)$: exponentially flat $\to T^3 \to T^2$ with increasing
impurity concentration that is consistent with the measurements of the Fe
pnictide superconductors such as $M$-1111 ($M$=La,Nd,Sm,Pr) and Ba-122 with
various dopings, except LaFePO which shows $\Delta \lambda(T) \propto T^{1.2}$
at low temperatures by recent experiment. Our results also demonstrate that the
density of states (DOS) measured by thermodynamic properties and the DOS
measured by transport properties can in general be different.",0902.1020v3
2019-05-22,Transport and spectral signatures of transient fluctuating superfluids in the absence of long-range order,"Results are presented for the quench dynamics of a clean and interacting
electron system, where the quench involves varying the strength of the
attractive interaction along arbitrary quench trajectories. The initial state
before the quench is assumed to be a normal electron gas, and the dynamics is
studied in a regime where long-range order is absent, but nonequilibrium
superconducting fluctuations need to be accounted for. A quantum kinetic
equation using a two-particle irreducible formalism is derived. Conservation of
energy, particle-number, and momentum emerge naturally, with the conserved
currents depending on both the electron Green's functions and the Green's
functions for the superconducting fluctuations. The quantum kinetic equation is
employed to derive a kinetic equation for the current, and the transient
optical conductivity relevant to pump-probe spectroscopy is studied. The
general structure of the kinetic equation for the current is also justified by
a phenomenological approach that assumes model-F in the Halperin-Hohenberg
classification, corresponding to a non-conserved order-parameter coupled to a
conserved density. Linear response conductivity and the diffusion coefficients
in thermal equilibrium are also derived, and connections with Aslamazov-Larkin
fluctuation corrections are highlighted. Results are also presented for the
time-evolution of the local density of states. It is shown that Andreev
scattering processes result in an enhanced density of states at low
frequencies. For a quench trajectory corresponding to a sudden quench to the
critical point, the density of states is shown to grow in a manner where the
time after the quench plays the role of the inverse detuning from the critical
point.",1905.08906v2
2017-11-30,Biredox ionic liquids with solid-like redox density in the liquid state for high-energy supercapacitors,"Kinetics of electrochemical reactions are several orders of magnitude slower
in solids than in liquids as a result of the much lower ion diffusivity. Yet,
the solid state maximizes the density of redox species, which is at least two
orders of magnitude lower in liquids because of solubility limitations. With
regard to electrochemical energy storage devices, this leads to high-energy
batteries with limited power and high-power supercapacitors with a well-known
energy deficiency. For such devices the ideal system should endow the liquid
state with a density of redox species close to the solid state. Here we report
an approach based on biredox ionic liquids to achieve bulk-like redox density
at liquid like fast kinetics. The cation and anion of these biredox ILs bear
moieties that undergo very fast reversible redox reactions. As a first
demonstration of their potential for high-capacity / high-rate charge storage,
we used them in redox supercapacitors. These ionic liquids are able to decouple
charge storage from ion accessible electrode surface, by storing significant
charge in the pores of the electrodes, to minimize self-discharge and leakage
current as a result of retaining the redox species in the pores, and to raise
working voltage due to their wide electrochemical window.",1711.11518v1
2019-06-30,Evaluating Superconductors through Current Induced Depairing,"The phenomenon of superconductivity occurs in the phase space of three
principal parameters: temperature T, magnetic field B, and current density Jd .
The critical temperature Tc is one of the first parameters that is measured and
in a certain way defines the superconductor. From the practical applications
point of view, of equal importance is the upper critical magnetic field Bc2 and
conventional critical current density Jc (above which the system begins to show
resistance without entering the normal state). However, a seldom-measured
parameter, the depairing current density Jd , holds the same fundamental
importance as Tc and Bc2, in that it defines a boundary between the
superconducting and normal states. A study of Jd sheds unique light on other
important characteristics of the superconducting state such as the superfluid
density and the nature of the normal state below Tc, information that can play
a key role in better understanding newly-discovered superconducting materials.
From a measurement perspective, the extremely high values of Jd make it
difficult to measure, which is the reason why it is seldom measured. Here, we
will review the fundamentals of current-induced depairing and the fast-pulsed
current technique that facilitates its measurement and discuss the results of
its application to the topological-insulator/chalcogenide interfacial
superconducting system.
  Keywords: pairbreaking, pair-breaking, vortex, vortices, theory, tutorial,
RTS, room-temperature supeconductivity",1907.00427v1
2020-06-16,Density of States Estimation for Out-of-Distribution Detection,"Perhaps surprisingly, recent studies have shown probabilistic model
likelihoods have poor specificity for out-of-distribution (OOD) detection and
often assign higher likelihoods to OOD data than in-distribution data. To
ameliorate this issue we propose DoSE, the density of states estimator. Drawing
on the statistical physics notion of ``density of states,'' the DoSE decision
rule avoids direct comparison of model probabilities, and instead utilizes the
``probability of the model probability,'' or indeed the frequency of any
reasonable statistic. The frequency is calculated using nonparametric density
estimators (e.g., KDE and one-class SVM) which measure the typicality of
various model statistics given the training data and from which we can flag
test points with low typicality as anomalous. Unlike many other methods, DoSE
requires neither labeled data nor OOD examples. DoSE is modular and can be
trivially applied to any existing, trained model. We demonstrate DoSE's
state-of-the-art performance against other unsupervised OOD detectors on
previously established ``hard'' benchmarks.",2006.09273v2
2022-03-08,Is the dark energy equation of state parameter singular?,"A dark energy with a negative energy density in the past can simultaneously
address various cosmological tensions, and if it is to be positive today to
drive the observed acceleration of the universe, we show that it should have a
pole in its equation of state parameter. More precisely, in a spatially uniform
universe, a perfect fluid (submitting to the usual continuity equation of local
energy conservation) whose energy density $\rho(z)$ vanishes at an isolated
zero $z=z_p$, necessarily has a pole in its equation of state parameter $w(z)$
at $z_p$, and, $w(z)$ diverges to positive infinity in the limit $z\to z_p^+$
and it diverges to negative infinity in the limit $z\to z_p^-$ -- we assume
that $z_p$ is not an accumulation point for poles of $w(z)$.
  However, the converse statement that this kind of a pole of $w(z)$
corresponds to a vanishing energy density at that point is not true as we show
by a counterexample. An immediate implication of this result is that one should
be hesitant to observationally reconstruct the equation of state parameter of
the dark energy directly, and rather infer it from a directly reconstructed
dark energy density.",2203.04167v2
2022-07-05,Partial wave analysis of two-body decay with helicity formalism,"In this paper, We find that the angular distribution of two-body decay and
scattering process that can be studied by introducing the helicity method.It
has been argued that the angular distribution only depends on magnitude of the
decaying amplitude which final particle momentum is along the $Z$ axis.
Therefore, when calculating the angular distribution,we only need to know the
helicity amplitude in the $Z$ direction. At the same time, we also discuss the
symmetry of physical processes, such as parity and time inversion
transformation and so on. The effects of these symmetric transformations on the
helicity state and the canonical states are studied in this paper. When it is
applied to two body decay process, the symmetry of the amplitude can be
obtained by helicity method. In addition, we also introduce the density matrix
to study the polarization of the final state particles, and discuss some
inherent symmetries of the density matrix. When we study the polarization and
angular distribution of final state particles, we can use these properties to
simplify density matrix without knowing all the elements of the density
matrix.Then we find that there is a close relationship between the partial
wave\cite{2003Tree}coupling constants and the angular distribution parameters,
indicating that these coupling constants can be obtained by experimental
fitting to data.In a word, the properties of two body decay and two body
cascade decay process can be analyzed by helicity method, which has a very good
application .",2207.02020v1
2006-12-04,Specific Heat and Superfluid Density for Possible Two Different Superconducting States in NaxCoO2.yH2O,"Several thermodynamic measurements for the cobaltate superconductor,
NaxCoO2.yH2O, have so far provided results inconsistent with each other. In
order to solve the discrepancies, we microscopically calculate the temperature
dependences of specific heat and superfluid density for this superconductor. We
show that two distinct specific-heat data from Oeschler et al. and Jin et al.
are reproduced, respectively, for the extended s-wave state and the p-wave
state. Two different superfluid-density data are also reproduced for each case.
These support our recent proposal of possible two different pairing states in
this material. In addition, we discuss the experimentally proposed large
residual Sommerfeld coefficient and extremely huge effective carrier mass.",0612071v2
2009-10-06,Effect of dimensionality on the charge-density-wave in few-layers 2H-NbSe$_2$,"We investigate the charge density wave (CDW) instability in single and double
layers, as well as in the bulk 2H-NbSe$_{2}$. We demonstrate that the density
functional theory correctly describes the metallic CDW state in the bulk
2H-NbSe$_{2}$. We predict that both mono- and bilayer NbSe$_{2}$ undergo a CDW
instability. However, while in the bulk the instability occurs at a momentum
$\mathbf{q}_{CDW}\approx{2/3}\mathbf{\Gamma M}$, in free-standing layers it
occurs at $\mathbf{q}_{CDW}\approx{1/2}\mathbf{\Gamma M}$. Furthermore, while
in the bulk the CDW leads to a metallic state, in a monolayer the ground state
becomes semimetallic, in agreement with recent experimental data. We elucidate
the key role that an enhancement of the electron-phonon matrix element at
$\mathbf{q}\approx\mathbf{q}_{CDW}$ plays in forming the CDW ground state.",0910.0956v1
2004-11-11,Impurity-induced states in conventional and unconventional superconductors,"We review recent developments in our understanding of how impurities
influence the electronic states in the bulk of superconductors. Our focus is on
the quasi-localized states in the vicinity of impurity sites in conventional
and unconventional superconductors and our goal is to provide a unified
framework for their description. The non-magnetic impurity resonances in
unconventional superconductors are directly related to the Yu-Shiba-Rusinov
states around magnetic impurities in conventional s-wave systems. We review the
physics behind these states, including quantum phase transition between
screened and unscreened impurity, and emphasize recent work on d-wave
superconductors. The bound states are most spectacularly seen in scanning
tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe
in detail. We also discuss very recent progress on the states coupled to
impurity sites which have their own dynamics, and impurity resonances in the
presence of an order competing with superconductivity. Last part of the review
is devoted to influence of local deviations of the impurity concentration from
its average value on the density of states in s-wave superconductors. We review
how these fluctuations affect the density of states and show that s-wave
superconductors are, strictly speaking, gapless in the presence of an
arbitrarily small concentration of magnetic impurities.",0411318v1
2019-06-28,"Iso-entangled mutually unbiased bases, symmetric quantum measurements and mixed-state designs","Discrete structures in Hilbert space play a crucial role in finding optimal
schemes for quantum measurements. We solve the problem whether a complete set
of five iso-entangled mutually unbiased bases exists in dimension four,
providing an explicit analytical construction. The reduced density matrices of
these $20$ pure states forming this generalized quantum measurement form a
regular dodecahedron inscribed in a sphere of radius $\sqrt{3/20}$ located
inside the Bloch ball of radius $1/2$. Such a set forms a mixed-state
$2$-design --- a discrete set of quantum states with the property that the mean
value of any quadratic function of density matrices is equal to the integral
over the entire set of mixed states with respect to the flat Hilbert-Schmidt
measure. We establish necessary and sufficient conditions mixed-state designs
need to satisfy and present general methods to construct them. Furthermore, it
is shown that partial traces of a projective design in a composite Hilbert
space form a mixed-state design, while decoherence of elements of a projective
design yields a design in the classical probability simplex. We identify a
distinguished two-qubit orthogonal basis such that four reduced states are
evenly distributed inside the Bloch ball and form a mixed-state $2$-design.",1906.12291v2
1998-08-11,Re-entrant insulator-metal-insulator transition at B=0 in a two dimensional hole gas,"We report the observation of a re-entrant insulator--metal--insulator
transition at B=0 in a two dimensional (2D) hole gas in GaAs at temperatures
down to 30mK. At the lowest carrier densities the holes are strongly localised.
As the carrier density is increased a metallic phase forms, with a clear
transition at \sigma = ~5e^2/h. Further increasing the density weakens the
metallic behaviour, and eventually leads to the formation of a second
insulating state for \sigma > ~50e^2/h. In the limit of high carrier densities,
where k_F.l is large and r_s is small, we thus recover the results of previous
work on weakly interacting systems showing the absence of a metallic state in
2D.",9808108v1
2001-01-23,Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz,"We present a new algorithm to calculate the thermodynamic quantities of
three-dimensional (3D) classical statistical systems, based on the ideas of the
tensor product state and the density matrix renormalization group. We represent
the maximum-eigenvalue eigenstate of the transfer matrix as the product of
local tensors which are iteratively optimized by the use of the ``vertical
density matrix'' formed by cutting the system along the transfer direction.
This algorithm, which we call vertical density matrix algorithm (VDMA), is
successfully applied to the 3D Ising model. Using the Suzuki-Trotter
transformation, we can also apply the VDMA to two-dimensional (2D) quantum
systems, which we demonstrate for the 2D transverse field Ising model.",0101360v2
2002-09-16,Measuring the condensate fraction of rapidly rotating trapped boson systems: off-diagonal order from the density,"We demonstrate a direct connection between the density profile of a system of
ultra-cold trapped bosonic particles in the rapid-rotation limit and its
condensate fraction. This connection can be used to probe the crossover from
condensed vortex-lattice states to uncondensed quantum fluid states that occurs
in rapidly rotating boson systems as the particle density decreases or the
rotation frequency increases. We illustrate our proposal with a series of
examples, including ones based on models of realistic finite trap systems, and
comment on its application to freely expanding boson density profile
measurements.",0209374v2
2005-01-17,Ground-state densities and pair correlation functions in parabolic quantum dots,"We present an extensive comparative study of ground-state densities and pair
distribution functions for electrons confined in two-dimensional parabolic
quantum dots over a broad range of coupling strength and electron number. We
first use spin-density-functional theory to determine spin densities that are
compared with Diffusion Monte Carlo (DMC) data. This accurate knowledge of
one-body properties is then used to construct and test a local approximation
for the electron-pair correlations. We find very satisfactory agreement between
this local scheme and the available DMC data, and provide a detailed picture of
two-body correlations in a coupling-strength regime preceding the formation of
Wigner-like electron ordering.",0501375v1
2005-08-12,Order via Nonlinearity in Randomly Confined Bose Gases,"A Hartree-Fock mean-field theory of a weakly interacting Bose-gas in a
quenched white noise disorder potential is presented. A direct continuous
transition from the normal gas to a localized Bose-glass phase is found which
has localized short-lived excitations with a gapless density of states and
vanishing superfluid density. The critical temperature of this transition is as
for an ideal gas undergoing Bose-Einstein condensation. Increasing the
particle-number density a first-order transition from the localized state to a
superfluid phase perturbed by disorder is found. At intermediate number
densities both phases can coexist.",0508306v2
2006-10-02,Superfluid Suppression in d-Wave Superconductors due to Disordered Magnetism,"The influence of static magnetic correlations on the temperature-dependent
superfluid density \rho_s(T) is calculated for d-wave superconductors. In
self-consistent calculations, itinerant holes form incommensurate spin density
waves (SDW) which coexist with superconductivity. In the clean limit, the
density of states is gapped, and \rho_s(T << T_c) is exponentially activated.
In inhomogeneously-doped cases, the SDW are disordered and both the density of
states and \rho_s(T) obtain forms indistinguishable from those in dirty but
pure d-wave superconductors, in accordance with experiments. We conclude that
the observed collapse of \rho_s at x\approx 0.35 in underdoped YBCO may
plausibly be attributed to the coexistence of SDW and superconductivity.",0610041v2
2006-11-27,Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases,"The ground state and structure of a one-dimensional Bose gas with dipolar
repulsions is investigated at zero temperature by a combined Reptation Quantum
Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid
behavior emerges in a wide range of intermediate densities, evolving into a
Tonks-Girardeau gas at low density and into a classical quasi-ordered state at
high density. The density dependence of the Luttinger exponent is extracted
from the numerical data, providing analytical predictions for observable
quantities, such as the structure factor and the momentum distribution. We
discuss the accessibility of such predictions in current experiments with
ultracold atomic and molecular gases.",0611667v1
1996-10-25,Collective transition densities in neutron-rich nuclei,"Quadrupole transition densities in neutron-rich nuclei in the vicinity of the
neutron drip-line are calculated in the framework of the Random Phase
Approximation. The continuum is treated by expansion in oscillator functions.
We focus on the states which contribute to the usual Giant Quadrupole
Resonance, and not on the low-lying strength which is also expected in such
nuclei and whose collective character is still under debate. We find that, due
to the large neutron skin in these nuclei, the isoscalar and isovector modes
are in general strongly mixed. We further show that the transition densities
corresponding to the GQR states can be reasonably well described by the
collective model in terms of in phase and out of phase oscillations of neutron
and proton densities which have different radii.",9610039v1
2007-08-27,One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap,"We investigate the ground state of the one-dimensional fermionic system
enclosed in a hard-wall trap with attractive contact p-wave interactions. Based
on the Bethe ansatz method, the explicit wave function is derived by
numerically solving the Bethe ansatz equations for the full physical regimes
($-\infty \leq c_F\leq 0$). With the exact wave function some quantities which
are important in many-body physics are obtained, including the one-body density
matrix and the momentum distribution of the ground state for finite system. It
is shown that the shell structure of the density profiles disappears with the
increase of the interaction and in the fermionic Tonks-Girardeau (FTG) limit
the density distribution shows the same behavior as that of an ideal Bose gas.
However the one-body density matrix and the momentum distribution exhibit
completely different structures compared with their bosonic counterparts.",0708.3548v2
2010-03-08,Orbital-transverse density-wave instabilities in iron-based superconductors,"Besides the conventional spin-density-wave (SDW) state, a new kind of
orbital-transverse density-wave (OTDW) state is shown to exist generally in
multi-orbital systems. We demonstrate that the orbital character of Fermi
surface nesting plays an important role in density responses. The relationship
between antiferromagnetism and structural phase transition in LaFeAsO (1111)
and BaFe$_2$As$_2$ (122) compounds of iron-based superconductors may be
understood in terms of the interplay between the SDW and OTDW with a
five-orbital Hamiltonian. We propose that the essential difference between 1111
and 122 compounds is crucially determined by the presence of the
two-dimensional $d_{xy}$-like Fermi surface around (0,0) being only in 1111
parent compounds.",1003.1660v2
2011-07-24,Is reduced-density-matrix functional theory a suitable vehicle to import explicit correlations into density-functional calculations?,"A variational formulation for the calculation of interacting fermion systems
based on the density-matrix functional theory is presented. Our formalism
provides for a natural integration of explicit many-particle effects into
standard density-functional-theory based calculations and it avoids ambiguities
of double-counting terms inherent to other approaches. Like the dynamical
mean-field theory, we employ a local approximation for explicit correlations.
Aiming at the ground state only, trade some of the complexity of Green's
function based many-particle methods against efficiency. Using short Hubbard
chains as test systems we demonstrate that the method captures ground state
properties, such as left-right-correlation, beyond those accessible by
mean-field theories.",1107.4780v1
2012-09-18,Stability and structure of an anisotropically trapped dipolar Bose-Einstein condensate: angular and linear rotons,"We study theoretically Bose-Einstein condensates with polarized dipolar
interactions in anisotropic traps. We map the parameter space by varying the
trap frequencies and dipolar interaction strengths and find an irregular-shaped
region of parameter space in which density-oscillating condensate states occur,
with maximum density away from the trap center. These density-oscillating
states may be biconcave (red-blood-cell-shaped), or have two or four peaks. For
all trap frequencies, the condensate becomes unstable to collapse for
sufficiently large dipole interaction strength. The collapse coincides with the
softening of an elementary excitation. When the condensate mode is
density-oscillating, the character of the softening excitation is related to
the structure of the condensate. We classify these excitations by linear and
angular characteristics. We also find excited solutions to the Gross-Pitaevskii
equation, which are always unstable.",1209.3839v2
2013-12-17,Superconducting pairing in the spin-density-wave phase of iron pnictides,"Some of the iron pnictides show coexisting superconductivity and
spin-density-wave order. We study the superconducting pairing instability in
the spin-density-wave phase. Assuming that the pairing interaction is due to
spin fluctuations, we calculate the effective pairing interactions in the
singlet and triplet channels by summing the bubble and ladder diagrams taking
the reconstructed band structure into account. The leading pairing
instabilities and the corresponding superconducting gap structures are then
obtained from the superconducting gap equation. We illustrate this approach for
a minimal two-band model of the pnictides. Analytical and numerical results
show that the existence of propagating magnons in the spin-density-wave phase
strongly enhances the pairing in both the singlet and the spin s_z=0 triplet
channel. Over a limited parameter range, a spin s_z=0 triplet p_x-wave state is
the dominant instability. It competes with various singlet states, which have
mostly s^\pm-type structures. We analyze the effect of various symmetry-allowed
interactions on the pairing in some detail.",1312.4720v2
2016-02-24,GPView: a program for wave function analysis and visualization,"In this manuscript, we will introduce a recently developed program GPView,
which can be used for wave function analysis and visualization. The wave
function analysis module can calculate and generate 3D cubes for various types
of molecular orbitals and electron density of electronic excited states, such
as natural orbitals, natural transition orbitals, natural difference orbitals,
hole-particle density, detachment-attachment density and transition density.
The visualization module of GPView can display molecular and electronic
(iso-surfaces) structures. It is also able to animate single trajectories of
molecular dynamics and non-adiabatic excited state molecular dynamics using the
data stored in existing files. There are also other utilities to extract and
process the output of quantum chemistry calculations. The GPView provides full
graphic user interface (GUI), so it very easy to use. It is available from
website \href{http://life-tp.com/gpview}{http://life-tp.com/gpview}.",1602.07302v3
2016-10-27,Phase Separation Transition in a Nonconserved Two Species Model,"A one dimensional stochastic exclusion process with two species of particles,
$+$ and $-$, is studied where density of each species can fluctuate but the
total particle density is conserved. From the exact stationary state weights we
show that, in the limiting case where density of negative particles vanishes,
the system undergoes a phase separation transition where a macroscopic domain
of vacancies form in front of a single surviving negative particle. We also
show that the phase separated state is associated with a diverging correlation
length for any density and the critical exponents characterizing the behaviour
in this region are different from those at the transition line. The static and
the dynamical critical exponents are obtained from the exact solution and
numerical simulations, respectively.",1610.08898v2
2017-02-16,Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe$_2$,"We report a study of the quantum Hall states (QHSs) sequence of holes in
mono- and bilayer WSe$_2$. The QHSs sequence transitions between predominantly
even and predominantly odd filling factors as the hole density is tuned in the
range $1.6 - 12\times10^{12}$ cm$^{-2}$. The QHSs sequence is insensitive to
the transverse electric field, and tilted magnetic field measurements reveal an
insensitivity of the QHSs sequence to the in-plane magnetic field, evincing
that the hole spin is locked perpendicular to the WSe$_2$ plane. These
observations imply that the QHSs sequence is controlled by the
Zeeman-to-cyclotron energy ratio, which remains constant as a function of
perpendicular magnetic field at a fixed carrier density, but changes as a
function of density due to strong electron-electron interaction.",1702.05166v1
2018-12-09,Quantum phase transitions in the dimerized extended Bose-Hubbard model,"We present an unbiased numerical density-matrix renormalization group study
of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor
Coulomb interaction and bond dimerization. It places the emphasis on the
determination of the ground-state phase diagram and shows that, besides
dimerized Mott and density-wave insulating phases, an intermediate
symmetry-protected topological Haldane insulator emerges at weak Coulomb
interactions for filling factor one, which disappears, however, when the
dimerization becomes too large. Analyzing the critical behavior of the model,
we prove that the phase boundaries of the Haldane phase to Mott insulator and
density-wave states belong to the Gaussian and Ising universality classes with
central charges $c=1$ and $c=1/2$, respectively, and merge in a tricritical
point. Interestingly we can demonstrate a direct Ising quantum phase transition
between the dimerized Mott and density-wave phases above the tricritical point.
The corresponding transition line terminates at a critical end point that
belongs to the universality class of the dilute Ising model with $c=7/10$. At
even stronger Coulomb interactions the transition becomes first order.",1812.03489v2
2011-11-18,"Structural and electronic properties of ScnOm (n=1~3, m=1~2n) clusters: Theoretical study using screened hybrid density functional theory","The structural and electronic properties of small scandium oxide clusters
ScnOm (n = 1 - 3, m = 1 - 2n) are systematically studied within the screened
hybrid density functional theory. It is found that the ground states of these
scandium oxide clusters can be obtained by the sequential oxidation of small
""core"" scandium clusters. The fragmentation analysis demonstrates that the ScO,
Sc2O2, Sc2O3, Sc3O3, and Sc3O4 clusters are especially stable. Strong
hybridizations between O-2p and Sc-3d orbitals are found to be the most
significant character around the Fermi level. In comparison with standard
density functional theory calculations, we find that the screened hybrid
density functional theory can correct the wrong symmetries and yield more
precise description for the localized 3d electronic states of scandium.",1111.4294v1
2011-11-28,Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder,"We compute the multifractal spectra associated to local density of states
(LDOS) fluctuations due to weak quenched disorder, for a single Dirac fermion
in two spatial dimensions. Our results are relevant to the surfaces of Z_2
topological insulators such as Bi_2Se_3 and Bi_2Te_3, where LDOS modulations
can be directly probed via scanning tunneling microscopy. We find a qualitative
difference in spectra obtained for magnetic versus non-magnetic disorder.
Randomly polarized magnetic impurities induce quadratic multifractality at
first order in the impurity density; by contrast, no operator exhibits
multifractal scaling at this order for a non-magnetic impurity profile. For the
time-reversal invariant case, we compute the first non-trivial multifractal
correction, which appears at two loops (impurity density squared). We discuss
spectral enhancement approaching the Dirac point due to renormalization, and we
survey known results for the opposite limit of strong disorder.",1111.6639v2
2016-12-02,Anyonic Haldane insulator in one dimension,"We demonstrate numerically the existence of a nontrivial topological Haldane
phase for the one-dimensional extended ($U$-$V$) Hubbard model with a mean
density of one particle per site, not only for bosons but also for anyons,
despite a broken reflection parity symmetry. The Haldane insulator, surrounded
by superfluid, Mott insulator and density-wave phases in the $V$-$U$ parameter
plane, is protected by combined (modified) spatial-inversion and time-reversal
symmetries, which is verified within our matrix-product-state based infinite
density-matrix renormalization group scheme by analyzing generalized transfer
matrices. With regard to an experimental verification of the anyonic Haldane
insulator state the calculated asymmetry of the dynamical density structure
factor should be of particular importance.",1612.00605v2
2018-10-02,Momentum maps for mixed states in quantum and classical mechanics,"This paper presents the momentum map structures which emerge in the dynamics
of mixed states. Both quantum and classical mechanics are shown to possess
analogous momentum map pairs. In the quantum setting, the right leg of the pair
identifies the Berry curvature, while its left leg is shown to lead to more
general realizations of the density operator which have recently appeared in
quantum molecular dynamics. Finally, the paper shows how alternative
representations of both the density matrix and the classical density are
equivariant momentum maps generating new Clebsch representations for both
quantum and classical dynamics. Uhlmann's density matrix and Koopman-von
Neumann wavefunctions are shown to be special cases of this construction.",1810.01332v2
2019-06-04,Modeling the pseudogap metallic state in cuprates: quantum disordered pair density wave,"We present a way to quantum-disorder a pair density wave, and propose it to
be a candidate of the effective low-energy description of the pseudogap metal
which may reveal itself in a sufficiently high magnetic field that suppresses
the d-wave pairing. The ground state we construct is a small-pocket Fermi
liquid with a bosonic Mott insulator in the density-wave-enlarged unit cell. At
low energy, the charge density is mainly carried by charge 2e bosons, which
develop a small insulating gap. As an intermediate step, we discuss the quantum
disordering of a fully gapped superconductor and its excitation spectrum. In
order to illustrate the concepts we introduce, we introduce a simplified 1D
model which we solve numerically. We discuss a number of experimental
consequences. The interplay between the electron and the small-gap boson
results in a step function background in the electron spectral function which
may be consistent with existing ARPES data. Optical excitation across the boson
gap can explain the onset and the magnitude of the mid-infra-red absorption
reported long ago.",1906.01656v2
2019-09-05,Efficient unitary method for simulation of driven quantum dot systems,"Density matrices evolved according the von Neumann equation are commonly used
to simulate the dynamics of driven quantum systems. However, computational
methods using density matrices are often too slow to explore the large
parameter spaces of solid state quantum systems. Here we develop a unitary
computation method to quickly perform simulations for closed quantum systems,
where dissipation to the environment can be ignored. We use three techniques to
optimize simulations, apply them to six time-dependent pulses for a
semiconductor quantum dot qubit system, and predict the dynamic evolutions. We
compare computational times between our unitary method and the density matrix
method for a variety of image sizes. As an example, we implement our unitary
method for a realistic four-state system [Z. Shi, et al., Nat. Commun. 5, 3020
(2014)], and find that it is over two orders of magnitude faster than the
corresponding density matrix method implemented in the popular quantum
simulation software QuTiP.",1909.02532v2
2020-03-31,"Topological term, QCD anomaly, and the eta' chiral soliton lattice in rotating baryonic matter","We study the ground states of low-density hadronic matter and high-density
color-flavor locked color superconducting phase in three-flavor QCD at finite
baryon chemical potential under rotation. We find that, in both cases under
sufficiently fast rotation, the combination of the rotation-induced topological
term for the eta' meson and the QCD anomaly leads to an inhomogeneous
condensate of the eta' meson, known as the chiral soliton lattice (CSL). We
find that, when baryon chemical potential is much larger than isospin chemical
potential, the critical angular velocity for the realization of the eta' CSL is
much smaller than that for the pi_0 CSL found previously. We also argue that
the eta' CSL states in flavor-symmetric QCD at low density and high density
should be continuously connected, extending the quark-hadron continuity
conjecture in the presence of the rotation.",2003.13945v2
2023-01-31,Preserving local densities in low-dimensional embeddings,"Low-dimensional embeddings and visualizations are an indispensable tool for
analysis of high-dimensional data. State-of-the-art methods, such as tSNE and
UMAP, excel in unveiling local structures hidden in high-dimensional data and
are therefore routinely applied in standard analysis pipelines in biology. We
show, however, that these methods fail to reconstruct local properties, such as
relative differences in densities (Fig. 1) and that apparent differences in
cluster size can arise from computational artifact caused by differing sample
sizes (Fig. 2). Providing a theoretical analysis of this issue, we then suggest
dtSNE, which approximately conserves local densities. In an extensive study on
synthetic benchmark and real world data comparing against five state-of-the-art
methods, we empirically show that dtSNE provides similar global reconstruction,
but yields much more accurate depictions of local distances and relative
densities.",2301.13732v1
2023-04-16,An Artificial Neural Network-based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes,"During the past decades, approximate Kohn-Sham density-functional theory
schemes garnered many successes in computational chemistry and physics; yet the
performance in the prediction of spin state energetics is often unsatisfactory.
By means of a machine-learning approach, an enhanced exchange and correlation
functional is developed to describe adiabatic energy differences in transition
metal complexes. The functional is based on the computationally efficient
revision of the regularized strongly constrained and appropriately normed
(R2SCAN) functional and improved by an artificial neural-network correction
trained over a small dataset of electronic densities, atomization energies
and/or spin state energetics. The training process, performed using a
bio-inspired non gradient-based approach adapted for this work from Particle
Swarm Optimization, is discussed in detail. The meta-GGA functional is finally
shown to outperform most known density functionals in the prediction of
adiabatic energy differences for both the validation test and the generality
test.",2304.07899v2
2003-07-16,"Wigner rotations, Bell states, and Lorentz invariance of entanglement and von Neumann entropy","We compute, for massive particles, the explicit Wigner rotations of
one-particle states for arbitrary Lorentz transformations; and the explicit
Hermitian generators of the infinite-dimensional unitary representation. For a
pair of spin 1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and
their behaviour under the Lorentz group are analysed in the context of quantum
field theory. Group theoretical considerations suggest a convenient definition
of the Bell states which is slightly different from the conventional
assignment. The behaviour of Bell states under arbitrary Lorentz
transformations can then be described succinctly. Reduced density matrices
applicable to identical particles are defined through Yang's prescription. The
von Neumann entropy of each of the reduced density matrix is Lorentz invariant;
and its relevance as a measure of entanglement is discussed, and illustrated
with an explicit example. A regularization of the entropy in terms of
generalized zeta functions is also suggested.",0307107v4
2010-10-29,Doping driven magnetic instabilities and quantum criticality of NbFe$_{2}$,"Using density functional theory we investigate the evolution of the magnetic
ground state of NbFe$_{2}$ due to doping by Nb-excess and Fe-excess. We find
that non-rigid-band effects, due to the contribution of Fe-\textit{d} states to
the density of states at the Fermi level are crucial to the evolution of the
magnetic phase diagram. Furthermore, the influence of disorder is important to
the development of ferromagnetism upon Nb doping. These findings give a
framework in which to understand the evolution of the magnetic ground state in
the temperature-doping phase diagram. We investigate the magnetic instabilities
in NbFe$_{2}$. We find that explicit calculation of the Lindhard function,
$\chi_{0}(\mathbf{q})$, indicates that the primary instability is to finite
$\mathbf{q}$ antiferromagnetism driven by Fermi surface nesting. Total energy
calculations indicate that $\mathbf{q}=0$ antiferromagnetism is the ground
state. We discuss the influence of competing $\mathbf{q}=0$ and finite
$\mathbf{q}$ instabilities on the presence of the non-Fermi liquid behavior in
this material.",1010.6199v1
2013-07-09,Electronic states of disordered grain boundaries in graphene prepared by chemical vapor deposition,"Perturbations of the two dimensional carbon lattice of graphene, such as
grain boundaries, have significant influence on the charge transport and
mechanical properties of this material. Scanning tunneling microscopy
measurements presented here show that localized states near the Dirac point
dominate the local density of states of grain boundaries in graphene grown by
chemical vapor deposition. Such low energy states are not reproduced by
theoretical models which treat the grain boundaries as periodic
dislocation-cores composed of pentagonal-heptagonal carbon rings. Using ab
initio calculations, we have extended this model to include disorder, by
introducing vacancies into a grain boundary consisting of periodic
dislocation-cores. Within the framework of this model we were able to reproduce
the measured density of states features. We present evidence that grain
boundaries in graphene grown on copper incorporate a significant amount of
disorder in the form of two-coordinated carbon atoms.",1307.2373v1
2014-07-07,Lower threshold ground state energy and testability of minimal balanced cut density,"Lov\'asz and his coauthors defined the notion of microcanonical ground state
energy $\hat{\mathcal{E}}_\mathbb{a} (G,J)$ -- borrowed from the statistical
physics -- for weighted graphs $G$, where $\mathbb{a}$ is a probability
distribution on $\{1,...,q\}$ and $J$ is a symmetric $q \times q$ matrix with
real entries. We define a new version of the ground state energy,
$\hat{\mathcal{E}}^c (G,J)=\inf_{\mathbb{a}\in A_c}\hat{\mathcal{E}}_\mathbb{a}
(G,J)$, called lower threshold ground state energy, where $A_c = \{\mathbb{a}
:\, a_i\ge c,\,i=1,\dots, q \}$. Both types of energies can be extended for
graphons $W$, the limit objects of convergent sequences of simple graphs. In
the main result of the paper it is stated that if $0\leq c_1<c_2 \leq 1$, then
the convergence of the sequences $(\hat{\mathcal{E}}^{c_2/q} (G_n,J))$ for each
$J$ implies convergence of the sequences $(\hat{\mathcal{E}}^{c_1/q} (G_n,J))$
for each $J$. As a byproduct one can derive in a natural way the testability of
minimum balanced multiway cut densities, that is one of the fundamental
problems of cluster analysis.",1407.1662v1
2014-10-24,Multipartite Quantum States and their Marginals,"Subsystems of composite quantum systems are described by reduced density
matrices, or quantum marginals. Important physical properties often do not
depend on the whole wave function but rather only on the marginals. Not every
collection of reduced density matrices can arise as the marginals of a quantum
state. Instead, there are profound compatibility conditions -- such as Pauli's
exclusion principle or the monogamy of quantum entanglement -- which
fundamentally influence the physics of many-body quantum systems and the
structure of quantum information. The aim of this thesis is a systematic and
rigorous study of the general relation between multipartite quantum states,
i.e., states of quantum systems that are composed of several subsystems, and
their marginals. In the first part, we focus on the one-body marginals of
multipartite quantum states; in the second part, we study general quantum
marginals from the perspective of entropy.",1410.6820v1
2018-03-07,Neutron star tidal deformabilities constrained by nuclear theory and experiment,"We confront observational data from gravitational wave event GW170817 with
microscopic modeling of the cold neutron star equation of state. We develop and
employ a Bayesian statistical framework that enables us to implement
constraints on the equation of state from laboratory measurements of nuclei and
state-of-the-art chiral effective field theory methods. The energy density
functionals constructed from the posterior probability distributions are then
used to compute consistently the neutron star equation of state from the outer
crust to the inner core, assuming a composition consisting of protons,
neutrons, electrons, and muons. In contrast to previous studies, we find that
the 95% credibility range of predicted neutron star tidal deformabilities ($136
< \Lambda < 519$) for a 1.4 solar-mass neutron star is already consistent with
the upper bound deduced from observations of the GW170817 event. However, we
find that lower bounds on the neutron star tidal deformability will very
strongly constrain microscopic models of the dense matter equation of state. We
also demonstrate a strong correlation between the neutron star tidal
deformability and the pressure of beta-equilibrated matter at twice saturation
density.",1803.02803v2
2020-02-04,Topology and the one-dimensional Kondo-Heisenberg model,"The Kondo-Heinsberg chain is an interesting model of a strongly correlated
system which has a broad superconducting state with pair-density wave (PDW)
order. Some of us have recently proposed that this PDW state is a
symmetry-protected topological (SPT) state, and the gapped spin sector of the
model supports Majorana zero modes. In this work, we reexamine this problem
using a combination of numeric and analytic methods. In extensive density
matrix renormalization group calculations, we find no evidence of a topological
ground state degeneracy or the previously proposed Majorana zero modes in the
PDW phase of this model. This result motivated us to reexamine the original
arguments for the existence of the Majorana zero modes. A careful analysis of
the effective continuum field theory of the model shows that the Hilbert space
of the spin sector of the theory does not contain any single Majorana fermion
excitations. This analysis shows that the PDW state of the doped 1D
Kondo-Heisenberg model is not an SPT with Majorana zero modes.",2002.01483v1
2024-01-12,Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles,"We analyze a general bipartite-like representation of arbitrary pure states
of $N$-indistinguishable particles, valid for both bosons and fermions, based
on $M$- and $(N-M)$-particle states. It leads to exact $(M,N-M)$ Schmidt-like
expansions of the state for any $M<N$ and is directly related to the
isospectral reduced $M$- and $(N-M)$-body density matrices $\rho^{(M)}$ and
$\rho^{(N-M)}$. The formalism also allows for reduced yet still exact
Schmidt-like decompositions associated with blocks of these densities, in
systems having a fixed fraction of the particles in some single particle
subspace. Monotonicity of the ensuing $M$-body entanglement under a certain set
of quantum operations is also discussed. Illustrative examples in fermionic and
bosonic systems with pairing correlations are provided, which show that in the
presence of dominant eigenvalues in $\rho^{(M)}$, approximations based on a few
terms of the pertinent Schmidt expansion can provide a reliable description of
the state. The associated one- and two-body entanglement spectrum and entropies
are also analyzed.",2401.06917v1
2022-04-25,Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory,"Background: The transverse densities $\rho_{1, 2}(b)$ describe the
distributions of electric charge and magnetic moment at fixed light-front time
and connect the nucleon's elastic form factors with its partonic structure. The
dispersive representation of the form factors $F_{1, 2}(t)$ expresses the
densities in terms of exchanges of hadronic states in the $t$-channel and
permits their analysis using hadronic physics methods.
  Purpose: Compute the densities at peripheral distances $b =
\mathcal{O}(M_\pi^{-1})$, where they are generated predominantly by the
two-pion states in the dispersive representation. Quantify the uncertainties.
  Methods: Dispersively improved chiral effective field theory (DI$\chi$EFT) is
used to calculate the isovector spectral functions $\textrm{Im}\, F_{1, 2}(t)$
on the two-pion cut. The method includes $\pi\pi$ interactions ($\rho$
resonance) through elastic unitarity and provides realistic spectral functions
up to $t \approx$ 1 GeV$^2$. Higher-mass states are parametrized by effective
poles and constrained by sum rules (charges, radii, superconvergence
relations). The densities $\rho_{1, 2}(b)$ are obtained from their dispersive
representation. Uncertainties are quantified by varying the spectral functions.
The method respects analyticity and ensures the correct $b \rightarrow \infty$
asymptotic behavior of the densities.
  Results: Accurate densities are obtained at all distances $b \gtrsim 0.5$ fm,
with correct behavior down to $b \rightarrow 0$. The region of distances is
quantified where transverse nucleon structure is governed by the two-pion
state. The light-front current distributions in the polarized nucleon are
computed and discussed.
  Conclusions: Peripheral nucleon structure can be computed from first
principles using DI$\chi$EFT. The method can be extended to generalized parton
distributions and other nucleon form factors.",2204.11863v1
2020-06-29,Singular mean-field states: A brief review of recent results,"This article provides a focused review of recent findings which demonstrate,
in some cases quite counter-intuitively, the existence of bound states with a
singularity of the density pattern at the center, while the states are
physically meaningful because their total norm converges. One model of this
type is based on the 2D Gross-Pitaevskii equation (GPE) which combines the
attractive potential ~ 1/r^2 and the quartic self-repulsive nonlinearity,
induced by the Lee-Huang-Yang effect (quantum fluctuations around the
mean-field state). The GPE demonstrates suppression of the 2D quantum collapse,
driven by the attractive potential, and emergence of a stable ground state
(GS), whose density features an integrable singularity ~1/r^{4/3} at r --> 0.
Modes with embedded angular momentum exist too, and they have their stability
regions. A counter-intuitive peculiarity of the model is that the GS exists
even if the sign of the potential is reversed from attraction to repulsion,
provided that its strength is small enough. This peculiarity finds a relevant
explanation. The other model outlined in the review includes 1D, 2D, and 3D
GPEs, with the septimal (seventh-order), quintic, and cubic self-repulsive
terms, respectively. These equations give rise to stable singular solitons,
which represent the GS for each dimension D, with the density singularity
~1/r^{2/(4-D). Such states may be considered as a result of screening of a
""bare"" delta-functional attractive potential by the respective nonlinearity.",2007.02320v1
2019-09-05,Time-dependent spectral properties of photoexcited one-dimensional ionic Hubbard model: an exact diagonalization study,"Motivated by the recent progress in time-resolved nonequilibrium spectroscopy
in condensed matter, we study an optically excited one-dimensional ionic
Hubbard model by exact diagonalization. The model is relevant to organic
crystals, transition metal oxides, or ultracold atoms in optical lattices. We
implement numerical pump-probe measurements to calculate time-dependent
conductivity and single-particle spectral functions. In general, short optical
excitation induces a metallic behavior imprinted as a Drude peak in
conductivity or an in-gap density of states. In a Mott insulator, we find that
the induced Drude peak oscillates at the pump frequency and its second
harmonic. The former comes from the oscillation of currents, and the latter
from the interference of single- and three-photon excited states. In a band
insulator, the Drude peak oscillates only at the pump frequency, and quantities
such as the double occupancy do not oscillate. The absence of the second
harmonic oscillation is due to the degeneracy of multi-photon excited states.
The in-gap density of states in both insulators correlates with the Drude
weight and the energy absorption for weak pumping. Strong pumping leads to
saturation of the in-gap density of states and to suppression of the Drude
weight in the Mott regime. We have also checked that the above features are
robust for insulators in the intermediate parameter range. Our study
demonstrates the distinct natures of the multi-photon excited states in two
different insulators.",1909.02471v2
1997-09-12,Entanglement of Formation of an Arbitrary State of Two Qubits,"The entanglement of a pure state of a pair of quantum systems is defined as
the entropy of either member of the pair. The entanglement of formation of a
mixed state is defined as the minimum average entanglement of an ensemble of
pure states that represents the given mixed state. An earlier paper [Phys. Rev.
Lett. 78, 5022 (1997)] conjectured an explicit formula for the entanglement of
formation of a pair of binary quantum objects (qubits) as a function of their
density matrix, and proved the formula to be true for a special class of mixed
states. The present paper extends the proof to arbitrary states of this system
and shows how to construct entanglement-minimizing pure-state decompositions.",9709029v2
2000-07-27,Neutron Stars and Quantum Billiards,"Homogeneous neutron matter at subnuclear densities becomes unstable towards
the formation of inhomogeneities. Depending on the average value of the neutron
density one can observe the appearance of either bubbles, rods, tubes or plates
embeded in a neutron gas. We estimate the quantum corrections to the ground
state energy (which could be termed either shell correction or Casimir energy)
of such phases of neutron matter. The calculations are performed by evaluating
the contribution of the shortest periodic orbits in the Gutzwiller trace
formula for the density of states. The magnitude of the quantum corrections to
the ground state energy of neutron matter are of the same order as the energy
differences between various phases.",0007423v2
1999-04-21,Magnetic field effects on the density of states of orthorhombic superconductors,"The quasiparticle density of states in a two-dimensional d-wave
superconductor depends on the orientation of the in-plane external magnetic
field H. This is because. in the region of the gap nodes, the Doppler shift due
to the circulating supercurrents around a vortex depend on the direction of H.
For a tetragonal system the induced pattern is four-fold symmetric and, at zero
energy, the density of states exhibits minima along the node directions. But
YBa_2C_3O_{6.95} is orthorhombic because of the chains and the pattern becomes
two-fold symmetric with the position of the minima occuring when H is oriented
along the Fermi velocity at a node on the Fermi surface. The effect of impurity
scattering in the Born and unitary limit is discussed.",9904305v1
2002-06-24,"On the Wang-Landau Method for Off-Lattice Simulations in the ""Uniform"" Ensemble","We present a rigorous derivation for off-lattice implementations of the
so-called ""random-walk"" algorithm recently introduced by Wang and Landau [PRL
86, 2050 (2001)]. Originally developed for discrete systems, the algorithm
samples configurations according to their inverse density of states using
Monte-Carlo moves; the estimate for the density of states is refined at each
simulation step and is ultimately used to calculate thermodynamic properties.
We present an implementation for atomic systems based on a rigorous separation
of kinetic and configurational contributions to the density of states. By
constructing a ""uniform"" ensemble for configurational degrees of freedom--in
which all potential energies, volumes, and numbers of particles are equally
probable--we establish a framework for the correct implementation of simulation
acceptance criteria and calculation of thermodynamic averages in the continuum
case. To demonstrate the generality of our approach, we perform sample
calculations for the Lennard-Jones fluid using two implementation variants and
in both cases find good agreement with established literature values for the
vapor-liquid coexistence locus.",0206461v2
2003-11-07,Nonequilibrium stationary states and equilibrium models with long range interactions,"It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.",0311149v1
2005-03-03,Transport properties of diluted magnetic semiconductors: Dynamical mean field theory and Boltzmann theory,"The transport properties of diluted magnetic semiconductors (DMS) are
calculated using dynamical mean field theory (DMFT) and Boltzmann transport
theory. Within DMFT we study the density of states and the dc-resistivity,
which are strongly parameter dependent such as temperature, doping, density of
the carriers, and the strength of the carrier-local impurity spin exchange
coupling. Characteristic qualitative features are found distinguishing weak,
intermediate, and strong carrier-spin coupling and allowing quantitative
determination of important parameters defining the underlying ferromagnetic
mechanism. We find that spin-disorder scattering, formation of bound state, and
the population of the minority spin band are all operational in DMFT in
different parameter range. We also develop a complementary Boltzmann transport
theory for scattering by screened ionized impurities. The difference in the
screening properties between paramagnetic ($T>T_c$) and ferromagnetic ($T<T_c$)
states gives rise to the temperature dependence (increase or decrease) of
resistivity, depending on the carrier density, as the system goes from the
paramagnetic phase to the ferromagnetic phase. The metallic behavior below
$T_c$ for optimally doped DMS samples can be explained in the Boltzmann theory
by temperature dependent screening and thermal change of carrier spin
polarization.",0503077v1
2002-12-31,Local Spectral Density for a Periodically Driven System of Coupled Quantum States with Strong Imperfection in Unperturbed Energies,"A random matrix theory approach is applied in order to analyze the
localization properties of local spectral density for a generic system of
coupled quantum states with strong static imperfection in the unperturbed
energy levels. The system is excited by an external periodic field, the
temporal profile of which is close to monochromatic one. The shape of local
spectral density is shown to be well described by the contour obtained from a
relevant model of periodically driven two-states system with irreversible
losses to an external thermal bath. The shape width and the inverse
participation ratio are determined as functions both of the Rabi frequency and
of parameters specifying the localization effect for our system in the absence
of external field.",0212160v1
2007-06-18,Mott-Hubbard Transition and Anderson Localization: Generalized Dynamical Mean-Field Theory Approach,"Density of states, dynamic (optical) conductivity and phase diagram of
strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model
are analyzed within the generalized dynamical mean field theory (DMFT+\Sigma
approximation). Strong correlations are accounted by DMFT, while disorder is
taken into account via the appropriate generalization of self-consistent theory
of localization. The DMFT effective single impurity problem is solved by
numerical renormalization group (NRG) and we consider the three-dimensional
system with semi-elliptic density of states. Correlated metal, Mott insulator
and correlated Anderson insulator phases are identified via the evolution of
density of states and dynamic conductivity, demonstrating both Mott-Hubbard and
Anderson metal-insulator transition and allowing the construction of complete
zero-temperature phase diagram of Anderson-Hubbard model. Rather unusual is the
possibility of disorder induced Mott insulator to metal transition.",0706.2618v1
2007-10-26,Multi-gluon field approach of QCD,"The decay of 2-gluon colour singlets in quarks: 2g --> q-qbar +2q-2qbar has
been simulated with the Monte-Carlo method, taking into account an effective
1-gluon exchange interaction between the emitted quarks, which was folded with
a 2-gluon density determined self-consistently. 2-gluon densities were found
with different radii, which correspond to 0^{++} glueballs of the size of light
q-qbar, s-sbar, c-cbar, b-bbar, and heavier q-qbar systems. Binding potentials
between the two gluons have been deduced, which are consistent with the
confinement potential from lattice results. However, self-consistency for the
deduction of 2-gluon densities requires massless (or very light) quarks for all
flavours. The masses are given by the binding energies of quarks and gluons,
yielding excitation spectra of 0^{++} glueballs and Phi, J/Psi, and Upsilon
states consistent with observation. The sum of q-q potentials yields a strong
coupling alpha_s consistent with the available data up to large momenta. The
nucleon is described by a gluonium state coupled to 3 valence quarks, yielding
ground state and radial excitations consistent with experiment. Finally, we
discuss the compressibility of the nucleon and relate it to that of nuclear
matter.",0710.5107v1
2007-11-25,Hölder continuity of the IDS for matrix-valued Anderson models,"We study a class of continuous matrix-valued Anderson models acting on
$L^{2}(\R^{d})\otimes \C^{N}$. We prove the existence of their Integrated
Density of States for any $d\geq 1$ and $N\geq 1$. Then for $d=1$ and for
arbitrary $N$, we prove the H\""older continuity of the Integrated Density of
States under some assumption on the group $G_{\mu_{E}}$ generated by the
transfer matrices associated to our models. This regularity result is based
upon the analoguous regularity of the Lyapounov exponents associated to our
model, and a new Thouless formula which relates the sum of the positive
Lyapounov exponents to the Integrated Density of States. In the final section,
we present an example of matrix-valued Anderson model for which we have already
proved, in a previous article, that the assumption on the group $G_{\mu_{E}}$
is verified. Therefore the general results developed here can be applied to
this model.",0711.3889v2
2008-08-19,Separability bounds on multiqubit moments due to positivity under partial transpose,"Positivity of the density operator reflects itself in terms of sequences of
inequalities on observable moments. Uncertainty relations for non-commuting
observables form a subset of these inequalities. In addition, criterion of
positivity under partial transposition (PPT) imposes distinct bounds on
moments, violations of which signal entanglement. We present bounds on some
novel sets of composite moments, consequent to positive partial transposition
of the density operator and report their violation by entangled multiqubit
states. In particular, we derive separability bounds on a multiqubit moment
matrix (based on PPT constraints on bipartite divisions of the density matrix)
and show that three qubit pure states with non-zero tangle violate these PPT
moment constraints. Further, we recover necessary and sufficient condition of
separability in a multiqubit Werner state through PPT bounds on moments.",0808.2581v2
2008-10-15,Magnetic Exchange Couplings from Noncollinear Spin Density Functional Perturbation Theory,"We propose a method for the evaluation of magnetic exchange couplings based
on noncollinear spin-density functional calculations. The method employs the
second derivative of the total Kohn-Sham energy of a single reference state, in
contrast to approximations based on Kohn-Sham total energy differences. The
advantage of our approach is twofold: It provides a physically motivated
picture of the transition from a low-spin to a high-spin state, and it utilizes
a perturbation scheme for the evaluation of magnetic exchange couplings. The
latter simplifies the way these parameters are predicted using
first-principles: It avoids the non-trivial search for different spin-states
that needs to be carried out in energy difference methods and it opens the
possibility of ""black-boxifying"" the extraction of exchange couplings from
density functional theory calculations. We present proof of concept
calculations of magnetic exchange couplings in the H--He--H model system and in
an oxovanadium bimetallic complex where the results can be intuitively
rationalized.",0810.2699v1
2009-03-11,Some notes about the density of states for a negative pressure matter,"The main goal of this paper is deriving Density of states $g(\epsilon)$
(degeneracy function) per volume for an equation of state (EOS) $p=-\rho$ (we
called it dark energy(DE)).We have concluded that thermodynamic quantities such
as pressure and energy density are simple functions of temperature, fugacity,
curvature and mass of Bosons. Our work has been expressed the origin of some
claims about the negativity of the entropy for the scalar fields models of DE.",0903.2020v7
2009-03-25,The Complete Jamming Landscape of Confined Hard Discs,"An exact description of the complete jamming landscape is developed for a
system of hard discs of diameter $\sigma$, confined between two lines separated
by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local
packing arrangements, the generalized ensemble partition function of jammed
states is obtained using the transfer matrix method, which allows us to
calculate the configurational entropy and the equation of state for the
packings. Exploring the relationship between structural order and packing
density, we find that the geometric frustration between local packing
environments plays an important role in determining the density distribution of
jammed states and that structural ""randomness"" is a non-monotonic function of
packing density. Molecular dynamics simulations show that the properties of the
equilibrium liquid are closely related to those of the landscape.",0903.4380v1
2010-08-03,Density of states in an optical speckle potential,"We study the single particle density of states of a one-dimensional speckle
potential, which is correlated and non-Gaussian. We consider both the repulsive
and the attractive cases. The system is controlled by a single dimensionless
parameter determined by the mass of the particle, the correlation length and
the average intensity of the field. Depending on the value of this parameter,
the system exhibits different regimes, characterized by the localization
properties of the eigenfunctions. We calculate the corresponding density of
states using the statistical properties of the speckle potential. We find good
agreement with the results of numerical simulations.",1008.0589v2
2011-10-12,Theory of Bulk Recombination in a Medium with Energetic Disorder under Continuous Irradiation with Excitation Light,"We study bulk recombination in a medium with energetic disorder by using the
multiple trapping (MT) model under continuous irradiation with excitation
light. Charge densities are shown to obey power law as a function of the
intensity of excitation light and the exponent is related to the dispersion
parameter $\alpha$ of the MT model. The theory is applied to analyze charge
densities in bulk heterojunction photovoltaic cells measured by light-induced
electron spin resonance (LESR). The values of the exponent are consistent with
those obtained from the transient decay of charge densities after pulsed
excitations.We show that the value of the exponent is robust against addition
of Gaussian trapping energy distribution due to shallow trap states. We also
show that open-circuit voltage ($V_{\rm OC}$) depends linearly on logarithm of
the light intensity and the slope is equal to $k_B T/e$ when only shallow trap
states are present. The same linear relation holds with a slope larger than
$k_B T/e$ in the presence of an exponential trapping energy distribution due to
deep trap states.",1110.2566v4
2012-05-24,Electronic Structure of New Multiple Band Pt-Pnictide Superconductors APt3P,"We report LDA calculated band structure, densities of states and Fermi
surfaces for recently discovered Pt-pnictide superconductors APt3P
(A=Ca,Sr,La), confirming their multiple band nature. Electronic structure is
essentially three dimensional, in contrast to Fe pnictides and chalcogenides.
LDA calculated Sommerfeld coefficient agrees rather well with experimental
data, leaving little space for very strong coupling superconductivity,
suggested by experimental data on specific heat of SrPt3P. Elementary estimates
show, that the values of critical temperature can be explained by rather weak
or moderately strong coupling, while the decrease of superconducting transition
temperature Tc from Sr to La compound can be explained by corresponding
decrease of total density of states at the Fermi level N(E_F). The shape of the
density of states near the Fermi level suggests that in SrPt3P electron doping
(such as replacement Sr by La) decreases N(E_F) and Tc, while hole doping (e.g.
partial replacement of Sr with K, Rb or Cs, if possible) would increase N(E_F)
and possibly Tc.",1205.5387v2
2013-04-16,Semilocal and Hybrid Density Embedding Calculations of Ground-State Charge-Transfer Complexes,"We apply the frozen density embedding method, using a full relaxation of
embedded densities through a freeze-and-thaw procedure, to study the electronic
structure of several benchmark ground-state charge-transfer complexes, in order
to assess the merits and limitations of the approach for this class of systems.
The calculations are performed using both semilocal and hybrid
exchange-correlation (XC) functionals. The results show that embedding
calculations using semilocal XC functionals yield rather large deviations with
respect to the corresponding supermolecular calculations. Due to a large error
cancellation effect, however, they can often provide a relatively good
description of the electronic structure of charge-transfer complexes, in
contrast to supermolecular calculations performed at the same level of theory.
On the contrary, when hybrid XC functionals are employed, both embedding and
supermolecular calculations agree very well with each other and with the
reference benchmark results.
  In conclusion, for the study of ground-state charge-transfer complexes via
embedding calculations hybrid XC functionals are the method of choice due to
their higher reliability and superior performance.",1304.4417v1
2013-04-30,Exterior integrability: Yang-Baxter form of nonequilibrium steady state density operator,"A new type of quantum transfer matrix, arising as a Cholesky factor for the
steady state density matrix of a dissipative Markovian process associated with
the boundary-driven Lindblad equation for the isotropic spin-1/2 Heisenberg
(XXX) chain, is presented. The transfer matrix forms a commuting family of
non-Hermitian operators depending on the spectral parameter which is
essentially the strength of dissipative coupling at the boundaries. The
intertwining of the corresponding Lax and monodromy matrices is performed by an
infinitely dimensional Yang-Baxter R-matrix which we construct explicitly and
which is essentially different from the standard XXX R-matrix. We also discuss
a possibility to construct Bethe Ansatz for the spectrum and eigenstates of the
non-equilibrium steady state density operator. Furthermore, we indicate the
existence of a deformed R-matrix in the infinitely-dimensional auxiliary space
for the anisotropic XXZ spin-1/2 chain which in general provides a sequence of
new, possibly quasi-local, conserved quantities of the bulk XXZ dynamics.",1304.7944v1
2013-05-02,Density of states of disordered topological superconductor-semiconductor hybrid nanowires,"Using Bogoliubov-de Gennes (BdG) equations we numerically calculate the
disorder averaged density of states of disordered semiconductor nanowires
driven into a putative topological p-wave superconducting phase by spin-orbit
coupling, Zeeman spin splitting and s-wave superconducting proximity effect
induced by a nearby superconductor. Comparing with the corresponding
theoretical self-consistent Born approximation (SCBA) results treating disorder
effects, we comment on the topological phase diagram of the system in the
presence of increasing disorder. Although disorder strongly suppresses the
zero-bias peak (ZBP) associated with the Majorana zero mode, we find some clear
remnant of a ZBP even when the topological gap has essentially vanished in the
SCBA theory because of disorder. We explicitly compare effects of disorder on
the numerical density of states in the topological and trivial phases.",1305.0554v1
2015-06-23,Negative partial density of states in mesoscopic systems,"Since the experimental observation of quantum mechanical scattering phase
shift in mesoscopic systems, several aspects of it has not yet been understood.
The experimental observations has also accentuated many theoretical problems
related to Friedel sum rule and negativity of partial density of states. We
address these problems using the concepts of Argand diagram and Burgers
circuit. We can prove the possibility of negative partial density of states in
mesoscopic systems. Such a conclusive and general evidence cannot be given in
one, two or three dimensions. We can show a general connection between phase
drops and exactness of semi classical Friedel sum rule. We also show Argand
diagram for a scattering matrix element can be of few classes based on their
topology and all observations can be classified accordingly.",1506.06954v2
2016-02-29,The local density of optical states of a metasurface,"While metamaterials are often desirable for near-field functions, such as
perfect lensing, or cloaking, they are often quantified by their response to
plane waves from the far field. Here, we present a theoretical analysis of the
local density of states near lattices of discrete magnetic scatterers, i.e.,
the response to near field excitation by a point source. Based on a
point-dipole theory using Ewald summation and an array scanning method, we can
swiftly and semi-analytically evaluate the local density of states (LDOS) for
magnetoelectric point sources in front of an infinite two-dimensional (2D)
lattice composed of arbitrary magnetoelectric dipole scatterers. The method
takes into account radiation damping as well as all retarded electrodynamic
interactions in a self-consistent manner. We show that a lattice of magnetic
scatterers evidences characteristic Drexhage oscillations. However, the
oscillations are phase shifted relative to the electrically scattering lattice
consistent with the difference expected for reflection off homogeneous magnetic
respectively electric mirrors. Furthermore, we identify in which source-surface
separation regimes the metasurface may be treated as a homogeneous interface,
and in which homogenization fails. A strong frequency and in-plane position
dependence of the LDOS close to the lattice reveals coupling to guided modes
supported by the lattice.",1602.08862v1
2016-06-03,Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization,"Interacting fermions on the half-filled honeycomb lattice with short-range
repulsions have been suggested to host a variety of interesting many-body
ground states, e.g., a topological Mott insulator. A number of recent studies
of the spinless case in terms of exact diagonalization, the infinite density
matrix renormalization group and the functional renormalization group, however,
indicate a suppression of the topological Mott insulating phase in the whole
range of interaction parameters. Here, we complement the previous studies by
investigating the quantum many-body instabilities of the physically relevant
case of spin-1/2 fermions with onsite, nearest-neighbor and
second-nearest-neighbor repulsion. To this end, we employ the multi-patch
functional renormalization group for correlated fermions with refined momentum
resolution observing the emergence of an antiferromagnetic spin-density wave
and a charge-density wave for dominating onsite and nearest-neighbor
repulsions, respectively. For dominating second-nearest neighbor interaction
our results favor an ordering tendency towards a charge-modulated ground state
over the topological Mott insulating state. The latter evades a stabilization
as the leading instability by the additional onsite interaction.",1606.01125v1
2016-07-07,Metal hydrogen sulfide critical temperature at the pressure 225 gpa,"\'Eliashberg theory, being generalized to the electron-phonon (EP) systems
with not constant density of electronic states, as well as to the frequency
behavior of the renormalization of both the electron mass and the chemical
potential, is used to study hydrogen sulphide phase under pressure. The phonon
contribution to the anomalous electron Green's function (GF) is considered. The
pairing is considered within the overall width of the electron band, and not
only in a narrow layer at the Fermi surface. The frequency and the temperature
dependences of the electron mass renormalization ReZ , the density of
electronic states , renormalized by the EP interaction , the spectral function
of the electron-phonon interaction, obtained by calculation are used to
calculate the electronic abnormal GF. The \'Eliashberg generalized equations
with the variable density of electronic states are resolved. The dependence of
both the real and the imaginary part of the order parameter on the frequency in
the phase is obtained. The value in the hydrogen sulfide phase at the pressure
P = 225 GPa has been defined.",1607.02162v1
2019-05-29,Bayesian Dynamic Fused LASSO,"The new class of Markov processes is proposed to realize the flexible
shrinkage effects for the dynamic models. The transition density of the new
process consists of two penalty functions, similarly to Bayesian fused LASSO in
its functional form, that shrink the current state variable to its previous
value and zero. The normalizing constant of the density, which is not ignorable
in the posterior computation, is shown to be essentially the log-geometric
mixture of double-exponential densities. This process comprises the state
equation of the dynamic regression models, which is shown to be conditionally
Gaussian and linear in state variables and utilize the forward filtering and
backward sampling in posterior computation by Gibbs sampler. The problem of
overshrinkage that is inherent in lasso is moderated by considering the
hierarchical extension, which can even realize the shrinkage of horseshoe
priors marginally. The new prior is compared with the standard
double-exponential prior in the estimation of and prediction by the dynamic
linear models for illustration. It is also applied to the time-varying vector
autoregressive models for the US macroeconomic data, where we examine the
(dis)similarity of the additional shrinkage effect to dynamic variable
selection or, specifically, the latent threshold models.",1905.12275v2
2011-11-20,Confined p-band Bose-Einstein condensates,"We study bosonic atoms on the p-band of a two dimensional optical square
lattice in the presence of a confining trapping potential. Using a mean-field
approach, we show how the anisotropic tunneling for p-band particles affects
the cloud of condensed atoms by characterizing the ground state density and the
coherence properties of the atomic states both between sites and atomic
flavors. In contrast to the usual results based on the local density
approximation, the atomic density can become anisotropic. This anisotropic
effect is especially pronounced in the limit of weak atom-atom interactions and
of weak lattice amplitudes, i.e. when the properties of the ground state are
mainly driven by the kinetic energies. We also investigate how the trap
influences known properties of the non-trapped case. In particular, we focus on
the behavior of the anti-ferromagnetic vortex-antivortex order, which for the
confined system, is shown to disappear at the edges of the condensed cloud.",1111.4633v2
2019-06-14,Generalization of the Wall Theorem to Out-of-equilibrium Conditions,"The well-known Wall theorem states a simple and precise relation among
temperature, pressure and density of a fluid at contact with a confining hard
wall in thermodynamic equilibrium. In this Letter we develop an extension of
the Wall theorem to out-of-equilibrium conditions, providing an exact relation
between pressure, density and temperaure at the wall, valid for strong
non-equilibrium situations. We derive analytically this Non-equilibrium Wall
theorem for stationary states and validate it with non-equilibrium event-driven
molecular-dynamics simulations. We compare the analytical expression with
simulations by direct evaluation of temperature, density and pressure on the
wall in linear regime, medium and very strong out-of-equilibrium conditions of
a nanoconfined liquid under flow in stationary state, presenting viscous
heating and heat transport. The agreement between theory and simulation is
excellent, allowing for a conclusive validation. In addition, we explore the
degree of accuracy of using the equilibrium Wall theorem and different
expressions for the local temperature, employed in non-equilibrium
molecular-dynamics simulations.",1906.06264v1
2021-08-27,Quantum fluctuation in an inhomogeneous background and its influence on the phase transition in a finite volume system,"We have studied the grand potential and phase transitions of an inhomogeneous
finite volume spherical quark system. First the finite volume effects are
considered by applying the multiple reflection expansion method which is an
approximation for the density of states of the momentum in the grand potential
of the finite size system. Then, the density of states of momentum is further
modified by the thermal fluctuations in the thermal system with the
inhomogeneous field background. The modification of the density of states is
calculated by the scattering phase shift from the Dirac equation of quarks in
the inhomogeneous field background. By the numerical calculation we show how
the phase transition is changed by varying the configuration of the
inhomogeneous field background and find that the strong first order phase
transition could be weakened or even changed to a crossover as a result.",2108.12325v2
2022-12-18,Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density,"We update results on the QCD equation of state in (2+1)-flavor QCD with
non-zero conserved charge chemical potentials obtained from an eighth-order
Taylor series. We present results for basic bulk thermodynamic observables of
strangeness-neutral strong-interaction matter, i.e. pressure, number densities,
energy and entropy density, and resum Taylor series results using Pad\'e
approximants. Furthermore, we calculate the speed of sound as well as the
adiabatic compression factor of strangeness-neutral matter on lines of constant
entropy per net baryon number. We show that the equation of state ($P(n_B),
\epsilon (n_B)$) is already well described by the $4^{\rm th}$-order Taylor
series in almost the entire range of temperatures accessible with the beam
energy scan in collider mode at the Relativistic Heavy Ion Collider.",2212.09043v2
2023-12-22,Toward Initial Conditions of Conserved Charges,"At top collider energies where baryon stopping is negligible, the initial
state of heavy ion collisions is overall charge neutral and predominantly
composed of gluons. Nevertheless, there can also be significant local
fluctuations of the baryon number, strangeness, and electric charge densities
about zero, perturbatively corresponding to the production of quark/antiquark
pairs. These previously ignored local charge fluctuations can permit the study
of charge diffusion in the quark-gluon plasma (QGP), even at top collider
energies. In this paper we present a new model denoted \code{iccing} (Initial
Conserved Charges in Nuclear Geometry) which can reconstruct the initial
conditions of conserved charges in the QGP by sampling a ($g \rightarrow
q\bar{q}$) splitting probability over the initial energy density. We find that
the new charge distributions generally differ from the bulk energy density; in
particular, the strangeness distribution is significantly more eccentric than
standard bulk observables and appears to be associated with the geometry of hot
spots in the initial state. The new information provided by these conserved
charges opens the door to studying a wealth of new charge- and flavor-dependent
correlations in the initial state and ultimately the charge transport
parameters of the QGP.",2312.15008v1
2016-11-28,A Simple Hubbard Model for the Excited States of Dibenzoterrylene,"We use a simple Hubbard model to characterize the electronic excited states
of the dibenzoterrylene (DBT) molecule; we compute the excited state transition
energies and oscillator strengths from the ground state to several singlet
excited states. We consider the lowest singlet and triplet states of the
molecule, examine their wavefunctions, and compute the density correlation
functions that describe these states. We find that the DBT ground state is
mostly a closed shell singlet with very slight radical character. We predict a
relatively small singlet-triplet splitting of 0.75 eV, which is less than the
mid-sized -acenes but larger than literature predictions for this state; this
is because the Hubbard interaction makes a very small correction to the singlet
and triplet states.",1611.09286v1
2000-06-03,Edge electron states for quasi-one-dimensional organic conductors in the magnetic-field-induced spin-density-wave phases,"We develop a microscopic picture of the electron states localized at the
edges perpendicular to the chains in the Bechgaard salts in the quantum Hall
regime. In a magnetic-field-induced spin-density-wave state (FISDW)
characterized by an integer N, there exist N branches of chiral gapless edge
excitations. Localization length is much longer and velocity much lower for
these states than for the edge states parallel to the chains. We calculate the
contribution of these states to the specific heat and propose a time-of-flight
experiment to probe the propagating edge modes directly.",0006050v2
2006-12-14,Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot,"We reexamine basic aspects of a nonequilibrium steady state in the Kondo
problem for a quantum dot under a bias voltage using a reduced density matrix,
which is obtained in the Fock space by integrating out one of the two
conduction channels. The integration has been carried out by discretizing the
conduction channels preserving the two-fold degeneracy due to the left-going
and right-going scattering states. The remaining subspace is described by a
single-channel Anderson model, and the statistical weight is determined by the
reduced density matrix. In the noninteracting case, it can be constructed as
the mixed states that show a close similarity to the high-temperature
distribution in equilibrium. Specifically, if the system has an inversion
symmetry, the one-particle states in an energy window between the two chemical
potentials \mu_R and \mu_L are occupied, or unoccupied, completely at random
with an equal weight. The Coulomb interaction preserves these aspects, and the
correlation functions can be expressed in a Lehmann-representation form using
the mixed-state statistical weight.",0612359v1
2013-05-21,Understanding quantum entanglement by thermo field dynamics,"We propose a new method to understand quantum entanglement using the thermo
field dynamics (TFD) described by a double Hilbert space. The entanglement
states show a quantum-mechanically complicated behavior. Our new method using
TFD makes it easy to understand the entanglement states, because the states in
the tilde space in TFD play a role of tracer of the initial states. For our new
treatment, we define an extended density matrix on the double Hilbert space.
From this study, we make a general formulation of this extended density matrix
and examine some simple cases using this formulation. Consequently, we have
found that we can distinguish intrinsic quantum entanglement from the thermal
fluctuations included in the definition of the ordinary quantum entanglement at
finite temperatures. Through the above examination, our method using TFD can be
applied not only to equilibrium states but also to non-equilibrium states. This
is shown using some simple finite systems in the present paper.",1305.4679v1
2022-03-26,A construction of exotic metallic states,"We discuss examples of two dimensional metallic states with charge
fractionalization, and we will demonstrate that the mechanism of charge
fractionalization leads to exotic metallic behaviors at low and intermediate
temperature. The simplest example of such state is constructed by fermionic
partons at finite density coupled to a $Z_N$ gauge field, whose properties can
be studied through rudimentary methods. This simple state has the following
exotic features: (1) at low temperature this state is a ""bad metal"" whose
resistivity can exceed the Mott-Ioffe-Regel limit; (2) while increasing
temperature $T$ the resistivity $\rho(T)$ is a nonmonotonic function, and it
crosses over from a bad metal at low $T$ to a good metal at relatively high
$T$; (3) the optical conductivity $\sigma(\omega)$ has a small Drude weight at
low $T$, and a larger Drude weight at intermediate $T$; (4) at low temperature
the metallic state has a large Lorenz number, which strongly violates the
Wiedemann-Franz law. A more complex example with fermionic partons at finite
density coupled to a SU(N) gauge field will also be constructed.",2203.14168v1
2022-05-11,Fabrication of Nanostructured GaAs/AlGaAs Waveguide for Low-Density Polariton Condensation from a Bound State in the Continuum,"Exciton-polaritons are hybrid light-matter states that arise from strong
coupling between an exciton resonance and a photonic cavity mode. As bosonic
excitations, they can undergo a phase transition to a condensed state that can
emit coherent light without a population inversion. This aspect makes them good
candidates for thresholdless lasers, yet short exciton-polariton lifetime has
made it difficult to achieve condensation at very low power densities. In this
sense, long-lived symmetry-protected states are excellent candidates to
overcome the limitations that arise from the finite mirror reflectivity of
monolithic microcavities. In this work we use a photonic symmetry protected
bound state in the continuum coupled to an excitonic resonance to achieve
state-of-the-art polariton condensation threshold in GaAs/AlGaAs waveguide.
Most important, we show the influence of fabrication control and how surface
passivation via atomic layer deposition provides a way to reduce exciton
quenching at the grating sidewalls.",2205.05722v1
1999-04-16,Phase Transitions in Neutron Stars and Maximum Masses,"Using the most recent realistic effective interactions for nuclear matter
with a smooth extrapolation to high densities including causality, we constrain
the equation of state and calculate maximum masses of rotating neutron stars.
First and second order phase transitions to, e.g., quark matter at high
densities are included. If neutron star masses of $\sim 2.3M_\odot$ from
quasi-periodic oscillations in low mass X-ray binaries are confirmed, a soft
equation of state as well as strong phase transitions can be excluded in
neutron star cores.",9904214v2
1994-01-25,Variational Calculations for $^3$He Impurities on $^4$He Droplets,"Variational Monte Carlo method is used to calculate ground state properties
of $^4$He droplets, containing 70, 112, 168, 240, 330, and 728 particles. The
resulting particle and kinetic energy densities are used as an input in the
Feynman-Lekner theory for $^3$He impurities. The kinetic energy density of
$^4$He atoms and the energy of the $^3$He surface states are compared with the
results of previous phenomenological calculations.",9401054v1
1994-09-26,Universal Correlations in the random matrices and 1D particles with long range interactions in a confinement potential,"We study the correlations between eigenvalues of the large random matrices by
a renormalization group approach. The results strongly support the universality
of the correlations proposed by Br\'ezin and Zee. Then we apply the results to
the ground state of the 1D particles with long range interactions in a
confinement potential. We obtain the exact ground state. We also show the
existence of a transition similar to a phase separation. Before and after the
transition, we obtain the density-density correlation explicitly. The
correlation shows nontrivial universal behavior.",9409110v2
1996-10-07,Exact density of states of a two-dimensional electron gas in a strong magnetic field and a long-range correlated random potential,"We derive an exact result for the averaged Feynman propagator and the
corresponding density of states of an electron in two dimensions in a
perpendicular homogeneous magnetic field and a Gaussian random potential with
long-range spatial correlations described by a quadratic correlation function.",9610043v1
1996-10-09,Singularity of the Vortex Density of States in d-wave Superconductors,"In d-wave superconductors, the electronic density of states (DOS) induced by
a vortex exhibits 1/|E| divergency at low energies. It is the result of gap
nodes in the excitations spectrum outside the vortex core. The heat capacity in
two regimes, (T/T_c)^2 >> B/B_{c2} and (T/T_c)^2 << B/B_{c2}, is discussed.",9610077v1
1997-04-28,Ferromagnetism in the Hubbard Model on fcc-type lattices,"The Hubbard model on fcc-type lattices is studied in the dynamical mean-field
theory of infinite spatial dimensions. At intermediate interaction strength
finite temperature Quantum Monte Carlo calculations yield a second order phase
transition to a highly polarized, metallic ferromagnetic state. The Curie
temperatures are calculated as a function of electronic density and interaction
strength. A necessary condition for ferromagnetism is a density of state with
large spectral weight near one of the band edges.",9704229v2
1997-09-05,``Bare'' Effective Mass in Finite Sized $ν= 1/2$ Systems,"In this note, we discuss the effective mass of quasiparticles in finite sized
$\nu = 1/2$ systems in the lowest Landau level, given a natural notion we have
of the Fermi surface in these finite sized systems. The effective mass is
related to the difference between instantaneous density-density response
functions of the ground state and excited states of the system; we do a finite
size calculation for this difference for $\nu = 1/2$ systems with 7, 8 and 9
fermions, and conjecture how the difference must look in the thermodynamic
limit.",9709081v1
1998-01-29,Negative superfluid densities in superconducting films in a parallel magnetic field,"In this paper we develop a theory of mesoscopic fluctuations in disordered
thin superconducting films in a parallel magnetic field. At zero temperature
and sufficiently strong magnetic field the system undergoes a phase transition
into a state characterized by a superfluid density, which is random in sign.
Consequently, in this region, random supercurrents are spontaneously created in
the ground state of the system, and it belongs to the same universality class
as the two dimensional XY spin glass with a random sign of the exchange
interaction.",9801315v1
1998-10-08,Density Matrix Renormalization Group of Gapless Systems,"We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as $\xi \sim m^{1.3}$, where $m$ is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry $E(k)=E(\pi -k)$ for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.",9810093v1
2001-02-21,Inverse proximity effect in superconductors near ferromagnetic material,"We study the electronic density of states in a mesoscopic superconductor near
a transparent interface with a ferromagnetic metal. In our tunnel spectroscopy
experiment, a substantial density of states is observed at sub-gap energies
close to a ferromagnet. We compare our data with detailed calculations based on
the Usadel equation, where the effect of the ferromagnet is treated as an
effective boundary condition. We achieve an excellent agreement with theory
when non-ideal quality of the interface is taken into account.",0102367v2
2001-02-23,Order parameter of quasi-one-dimensional superconductors: symmetry features in quasiparticle density of states and spin susceptibility,"Recent experiments indicate that the Bechgaard salts (TMTSF)$_2$ ClO$_4$ and
(TMTSF)$_2$ PF$_6$ may be unconventional triplet superconductors. The
quasiparticle density of states and the uniform spin susceptibility tensor are
computed at low temperatures for order parameter symmetries, as an attempt to
narrow the number of possibilities based on experimental evidence.",0102439v1
2001-03-23,Ferromagnetic instabilities in atomically-thin lithium and sodium wires,"Using density functional theory the ground state structural, electronic, and
magnetic properties of monatomic lithium and sodium chains with low average
density are investigated. A metallic, zigzag ground state structure is
predicted but, most interestingly, stable equilibria for chains under tension
are predicted to be {\it ferromagnetic}, which can be traced to exchange
effects arising from occupation of the second subband as a function of the
interatomic distance.",0103499v2
2001-05-16,Transport in nanostructures: A comparison between nonequilibrium Green functions and density matrices,"Stationary electric transport in semiconductor nanostructures is studied by
the method of nonequilibrium Green functions. In the case of sequential
tunneling the results are compared with density matrix theory, providing almost
identical results. Nevertheless, the method of Green functions is easier to
handle due to the availability of an absolute energy scale. It is demonstrated,
that the transport in complicated structures, like quantum cascade lasers, can
be described in reasonable agreement with experiment.",0105312v1
2001-08-22,Quantum Phase Transition in a Multi-Level Dot,"We discuss electronic transport through a lateral quantum dot close to the
singlet-triplet degeneracy in the case of a single conduction channel per lead.
By applying the Numerical Renormalization Group, we obtain rigorous results for
the linear conductance and the density of states. A new quantum phase
transition of the Kosterlitz-Thouless type is found, with an exponentially
small energy scale $T^*$ close to the degeneracy point. Below $T^*$, the
conductance is strongly suppressed, corresponding to a universal dip in the
density of states. This explains recent transport measurements.",0108359v2
2001-09-24,Generalized Einstein relation for disordered semiconductors - implications for device performance,"The ratio between mobility and diffusion parameters is derived for a
Gaussian-like density of states. This steady-state analysis is expected to be
applicable to a wide range of organic materials (polymers or small molecules)
as it relies on the existence of quasi-equilibrium only. Our analysis shows
that there is an inherent dependence of the transport in trap-free disordered
organic-materials on the charge density. The implications for the contact
phenomena and exciton generation rate in light emitting diodes as well as
channel-width in field-effect transistors is discussed.",0109432v2
2002-08-03,Third Order Perturbation Analysis of Pairing Symmetry in Two-Dimensional Hubbard Model,"We study the superconducting instabilities of singlet and triplet pairing in
a two-dimensional Hubbard model on the basis of the third-order perturbation
theory (TOPT). We investigate the effect of the vertex correction that is given
by TOPT, comparing with the study with only the second-order effective
interaction. In our results, a stable p-wave pairing state spreads from low to
intermediate electron density. A dx2-y2-wave pairing is dominant for the high
density near a half-filling. It is shown that the vertex correction plays an
essential role in making the p-wave pairing state dominant.",0208057v2
2002-10-17,Charge Modulations in the Superconducting State of the Cuprates,"Motivated by the recent scanning tunneling microscopy (STM) and neutron
scattering experiments, we investigate various charge density wave orders
coexisting with superconductivity in the cuprate superconductors. The explicit
expressions of the local density of states and its Fourier component at the
ordering wavevector for the weak charge modulations are derived. It is shown
that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained by
a site- or bond-centered charge modulation alone, but agree well with the
presence of the dimerization hopping and transverse pairing modulations. We
also calculate the spectral function for the charged stripes, which is measured
by the ARPES experiments.",0210386v1
2002-12-14,Charge and Phase Fluctuations in Attractive Hubbard Model,"Using the negative U Hubbard model we analyze normal state properties of a
superconductor. In this model there exists a characteristic pairing temperature
T_P above a superconducting critical temperature. Below T_P electrons start to
form incoherent pairs. The fluctuations in charge and phase are precursors of
charge density wave and superconductivity phases depending on band filling.
They lead naturally to pseudogap opening in the density of states.",0212337v1
2003-12-30,The anisotropic conductivity of two-dimensional electrons on a half-filled high Landau level,"We study the conductivity of two-dimensional interacting electrons on the
half-filled $N$th Landau level with $N \gg 1$ in the presence of the quenched
disorder. The existence of the unidirectional charge-density wave state at
temperature $T<T_c$, where $T_c$ is the transition temperature, leads to the
anisotropic conductivity tensor. We find that the leading anisotropic
corrections are proportional to $(T_c-T)/T_c$ just below the transition in
accordance with the experimental findings. Above $T_c$ the correlations
corresponding to the unidirectional charge-density wave state below $T_c$
result in the corrections to the conductivity proportional to
$\sqrt{T_c/(T-T_c)}$.",0312693v1
2004-04-13,Electronic band structure and chemical bonding in the novel antiperovskite ZnCNi3 as compared with 8-K superconductor MgCNi3,"Energy band structure of the discovered ternary perovskite-like compound
ZnCNi3 reported by Park et al (2004) as a non-superconducting paramagnetic
metal was investigated using the FLMTO-GGA method. The electronic bands,
density of states, Fermi surface, charge density and electron localization
function distributions for ZnCNi3 are obtained and analyzed in comparison with
the isoelectronic and isostructural 8K superconductor MgCNi3. The effect of
external pressure on the electronic states of ZnCNi3 and MgCNi3 is studied.",0404283v1
2004-05-10,The Hall conductivity in unconventional charge density wave systems,"Charge density waves with unconventional order parameters, for instance, with
d-wave symmetry (DDW), may be relevant in the underdoped regime of high-T_c
cuprates or other quasi-one or two dimensional metals. A DDW state is
characterized by two branches of low-lying electronic excitations. The
resulting quantum mechanical current has an inter-branch component which leads
to an additional mass term in the expression for the Hall conductivity. This
extra mass term is parametrically enhanced near the ``hot spots'' of fermionic
dispersion and is non-neglegible as is shown by numerical calculations of the
Hall number in the DDW state.",0405194v1
2005-11-12,Constructing thermodynamically consistent models with a non-ideal equation of state,"A recently introduced particle-based model for fluid dynamics with continuous
velocities is generalized to model fluids with excluded volume effects. This is
achieved through the use of biased stochastic multi-particle collisions which
depend on local velocities and densities and conserve momentum and kinetic
energy. The equation of state is derived and criteria for the correct choice of
collision probabilities are discussed. In particular, it is shown how a naive
implementation can lead to inconsistent density fluctuations.",0511312v1
2006-01-24,Anomalous electronic correlations in ground state momentum density of Al$_{97}$Li$_3$,"We report high resolution Compton scattering measurements on an
Al$_{97}$Li$_3$ disordered alloy single crystal for momentum transfer along the
[100], [110] and [111] symmetry directions. The results are interpreted via
corresponding KKR-CPA (Korringa-Kohn-Rostoker coherent potential approximation)
first principles computations. By comparing spectra for Al$_{97}$Li$_3$ and Al,
we show that the momentum density in the alloy differs significantly from the
predictions of the conventional Fermi liquid picture and that the ground state
of Al is modified anomalously by the addition of Li.",0601530v1
2006-02-05,Half-metallic ferromagnetism induced by dynamic electron correlations in VAs,"The electronic structure of the VAs compound in the zinc-blende structure is
investigated using a combined density-functional and dynamical mean-field
theory approach. Contrary to predictions of a ferromagnetic semiconducting
ground state obtained by density-functional calculations, dynamical
correlations induce a closing of the gap and produce a half-metallic
ferromagnetic state. These results emphasize the importance of dynamic
correlations in materials suitable for spintronics.",0602112v2
2006-07-25,Tunnelling density of states at Coulomb blockade peaks,"We calculate the tunnelling density of states (TDoS) for a quantum dot in the
Coulomb blockade regime, using a functional integral representation with
allowing correctly for the charge quantisation. We show that in addition to the
well-known gap in the TDoS in the Coulomb-blockade valleys, there is a
suppression of the TDoS at the peaks. We show that such a suppression is
necessary in order to get the correct result for the peak of the differential
conductance through an almost close quantum dot.",0607649v1
2006-10-02,Interplay between different states in heavy fermion physics,"Calorimetry experiments under high pressure were used to clarify the
interplay between different states such as superconductivity and
antiferromagnetism in CeRhIn5, spin density wave and large moment
antiferromagnetism in URu2Si2. Evidences are given on the re-entrance of
antiferromagnetism under magnetic field in the superconducting phase of CeRhIn5
up to pc = 2.5 GPa where the Neel temperature will collapse in the absence of
superconductivity. For URu2Si2 measurements up to 10 GPa support strongly the
coexistence of spin density wave and large moment antiferromagnetism at high
pressures.",0610042v1
2007-01-19,Excited states of quantum many-body interacting systems: A variational coupled-cluster description,"We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin $\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.",0701482v1
2007-03-05,The Mixed State of Charge-Density-Wave in a Ring-Shaped Single Crystals,"Charge-density-wave (CDW) phase transition in a ring-shaped crystals,
recently synthesized by Tanda et al. [Nature, 417, 397 (2002)], is studied
based on a mean-field-approximation of Ginzburg-Landau free energy. It is shown
that in a ring-shaped crystals CDW undergoes frustration due to the curvature
(bending) of the ring (geometrical frustration) and, thus, forms a mixed state
analogous to what a type-II superconductor forms under a magnetic field. We
discuss the nature of the phase transition in the ring-CDW in relation to
recent experiments.",0703107v1
2000-10-30,Thermal and electromagnetic properties of 166-Er and 167-Er,"The primary gamma-ray spectra of 166-Er and 167-Er are deduced from the
(3-He,alpha gamma) and (3-He,3-He' gamma) reaction, respectively, enabling a
simultaneous extraction of the level density and the gamma-ray strength
function. Entropy, temperature and heat capacity are deduced from the level
density within the micro-canonical and the canonical ensemble, displaying
signals of a phase-like transition from the pair-correlated ground state to an
uncorrelated state at Tc=0.5 MeV. The gamma-ray strength function displays a
bump around E-gamma=3 MeV, interpreted as the pygmy resonance.",0010019v1
2004-05-13,Alpha-Particle Condensate in Nuclear Matter at Normal Density and Statistics of Composite Bosons,"It is proved that alpha-particle states are well described by the Elliott
SU(3) model. This result is used to analyze the alpha-particle condensation
effect. It is shown that these states possess the basic attributes of the
alpha-condensate and, also, the normal nuclear density on frequent occasions.
The statistics of alpha-particles (and of arbitrary composite bosons) turns out
to be something other than the Bose-Einstein, Fermi-Dirac statistics, and
parastatistics.",0405038v1
2004-11-17,Fluctuations in the level density of a Fermi gas,"We present a theory that accurately describes the counting of excited states
of a noninteracting fermionic gas. At high excitation energies the results
reproduce Bethe's theory. At low energies oscillatory corrections to the
many--body density of states, related to shell effects, are obtained. The
fluctuations depend non-trivially on energy and particle number. Universality
and connections with Poisson statistics and random matrix theory are
established for regular and chaotic single--particle motion.",0411068v1
2006-10-10,The Nuclear Equation of State at high densities,"Ab inito calculations for the nuclear many-body problem make predictions for
the density and isospin dependence of the nuclear equation-of-state (EOS) far
away from the saturation point of nuclear matter. I compare predictions from
microscopic and phenomenological approaches. Constraints on the EOS derived
from heavy ion reactions, in particular from subthreshold kaon production, as
well as constraints from neutron stars are discussed.",0610038v1
2004-03-29,Off-diagonal quantum holonomy along density operators,"Uhlmann's concept of quantum holonomy for paths of density operators is
generalised to the off-diagonal case providing insight into the geometry of
state space when the Uhlmann holonomy is undefined. Comparison with previous
off-diagonal geometric phase definitions is carried out and an example
comprising the transport of a Bell-state mixture is given.",0403204v2
2007-05-07,Fermionic stabilization and density-wave ground state of a polar condensate,"We examine the stability of a trapped dipolar condensate mixed with a
single-component fermion gas at T=0. Whereas pure dipolar condensates with
small s-wave interaction are unstable even for small dipole-dipole interaction
strength, we find that the admixture of fermions can significantly stabilize
them, depending on the strength of the boson-fermion interaction. Within the
stable regime we find a region where a ground state is characterized by a
density wave along the soft trap direction.",0705.0972v2
2007-06-21,Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System,"We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat
eigenvalue problem corresponding to the attractive non-linear Schroedinger
equation with a Gaussian random pulse as initial value function. Using an
extension of the Thouless formula to non-Hermitian random operators, we
calculate the corresponding average density of states. We analyze two cases,
one with circularly symmetric complex Gaussian pulses and the other with real
Gaussian pulses. We discuss the implications in the context of the information
transmission through non-linear optical fibers.",0706.3129v2
2007-10-18,Inefficient quantum walks on networks: the role of the density of states,"We show by general arguments that networks whose density of states contains
few highly degenerate eigenvalues result in inefficient performances of
continuous-time quantum walks (CTQW) over these networks, while systems whose
eigenvalues all have the same degeneracy lead to very efficient transport. We
exemplify our results by considering CTQW and, for comparison, its classical
counterpart, continuous-time random walks, over simple structures, whose
eigenvalues and eigenstates can be calculated analytically. Extensions to more
complicated, hyper-branched networks are discussed.",0710.3453v1
2007-10-29,Probing the photonic local density of states with electron energy loss spectroscopy,"Electron energy-loss spectroscopy (EELS) performed in transmission electron
microscopes is shown to directly render the photonic local density of states
(LDOS) with unprecedented spatial resolution, currently below the nanometer.
Two special cases are discussed in detail: (i) 2D photonic structures with the
electrons moving along the translational axis of symmetry and (ii) quasi-planar
plasmonic structures under normal incidence. Nanophotonics in general and
plasmonics in particular should benefit from these results connecting the
unmatched spatial resolution of EELS with its ability to probe basic optical
properties like the photonic LDOS.",0710.5553v1
2008-10-23,Supercurrents in color-superconducting quark matter,"We review the basic properties of the currCFL-K^0 phase in dense quark
matter. At asymptotically large densities, three-flavor quark matter is in the
color-flavor locked (CFL) state. The currCFL-K^0 state is a way to respond to
``stress'' on the quark Cooper pairing, imposed at more moderate densities by
the strange quark mass and the conditions of electric and color neutrality. We
show how a kaon supercurrent is incorporated in a purely fermionic formalism,
and show that the net current vanishes due to cancellation of fermion and
charge-conjugate fermion contributions.",0810.4243v1
2009-01-21,Holographic modified gravity,"In this paper we study cosmological application of holographic dark energy
density in the modified gravity framework. We employ the holographic model of
dark energy to obtain the equation of state for the holographic energy density
in spatially flat universe. Our calculation show, taking
$\Omega_{\Lambda}=0.73$ for the present time, it is possible to have $w_{\rm
\Lambda}$ crossing -1. This implies that one can generate phantom-like equation
of state from a holographic dark energy model in flat universe in the modified
gravity cosmology framework. Also we develop a reconstruction scheme for the
modified gravity with $f(R)$ action.",0901.3252v1
2009-02-02,Evolution of the local superconducting density of states in ErRh$_4$B$_{4}$ close to the ferromagnetic transition,"We present local tunneling spectroscopy experiments in the superconducting
and ferromagnetic phases of the reentrant superconductor ErRh$_4$B$_{4}$. The
tunneling conductance curves jump from showing normal to superconducting
features within a few mK close to the ferromagnetic transition temperature,
with a clear hysteretic behavior. Within the ferromagnetic phase, we do not
detect any superconducting correlations. Within the superconducting phase we
find a peculiar V-shaped density of states at low energies, which is produced
by the magnetically modulated phase that coexists with superconductivity just
before ferromagnetism sets in.",0902.0308v1
2009-07-15,Spin-density functional study of the organic polymer dimethylaminopyrrole: A realization of the organic periodic Anderson model,"While the periodic Anderson model (PAM) has been recognized as a good model
for various heavy f-electron systems, here we design a purely organic polymer
whose low-energy physics can be captured by PAM. By means of the spin density
functional calculation, we show that polymer of dimethylaminopyrrole is a
candidate, where its ground state can indeed be magnetic depending on the
doping. We discuss the factors favoring ferromagnetic ground state.",0907.2477v2
2009-08-03,New Agegraphic Dark Energy in $f(R)$ Gravity,"In this paper we study cosmological application of new agegraphic dark energy
density in the $f(R)$ gravity framework. We employ the new agegraphic model of
dark energy to obtain the equation of state for the new agegraphic energy
density in spatially flat universe. Our calculation show, taking $n<0$, it is
possible to have $w_{\rm \Lambda}$ crossing -1. This implies that one can
generate phantom-like equation of state from a new agegraphic dark energy model
in flat universe in the modified gravity cosmology framework. Also we develop a
reconstruction scheme for the modified gravity with $f(R)$ action.",0908.0196v1
2009-08-31,Aharonov-Bohm oscillations in the local density of states,"The scattering of electrons with inhomogeneities produces modulations in the
local density of states of a metal. We show that electron interference
contributions to these modulations are affected by the magnetic field via the
Aharonov-Bohm effect. This can be exploited in a simple STM setup that serves
as an Aharonov-Bohm interferometer at the nanometer scale.",0909.0019v2
2009-09-28,Nonlinearity and constrained quantum motion,"The dynamical equation satisfied by the density matrix, when a quantum system
is subjected to one or more constraints arising from conserved quantities, is
derived. The resulting nonlinear motion of the density matrix has the property
that the evolution is independent of the specific composition of the pure-state
mixture generating the initial state of the system.",0909.5164v1
2009-11-19,Optical properties of UO2 and PuO2,"We perform first-principles calculations of electronic structure and optical
properties for UO2 and PuO2 based on the density functional theory using the
generalized gradient approximation (GGA)+\emph{U} scheme. The main features in
orbital-resolved partial density of states for occupied \emph{f} and \emph{p}
orbitals, unoccupied \emph{d} orbitals, and related gaps are well reproduced
compared to experimental observations. Based on the satisfactory ground-state
electronic structure calculations, the dynamical dielectric function and
related optical spectra, i.e., the reflectivity, adsorption coefficient,
energy-loss, and refractive index spectrum, are obtained. These results are
consistent well with the attainable experiments.",0911.3733v1
2010-02-05,Optimizing Hartree-Fock orbitals by the density-matrix renormalization group,"We have proposed a density-matrix renormalization group (DMRG) scheme to
optimize the one-electron basis states of molecules. It improves significantly
the accuracy and efficiency of the DMRG in the study of quantum chemistry or
other many-fermion system with nonlocal interactions. For a water molecule, we
find that the ground state energy obtained by the DMRG with only 61 optimized
orbitals already reaches the accuracy of best quantum Monte Carlo calculation
with 92 orbitals.",1002.1287v2
2010-02-10,Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid,"We have used the variational and diffusion quantum Monte Carlo methods to
calculate the energy, pair correlation function, static structure factor, and
momentum density of the ground state of the two-dimensional homogeneous
electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave
functions and twist averaging to reduce finite-size effects where applicable.
We compare our results with others in the literature and construct a
local-density-approximation exchange-correlation functional for 2D systems.",1002.2122v1
2010-03-07,An example of a violation of the quantum inequalities for a massless scalar field in 1-1 dimensional space-time,"It is well known that the energy density of a quantum state can be negative.
It has been shown that there are limits on this negative energy density which
are called the quantum inequalities. In this paper we will demonstrate an
example of a quantum state which violates the quantum inequalities.",1003.1526v6
2010-03-15,Inferring the transport properties of edge-states formed at quantum Hall based Aharonov-Bohm interferometers theoretically,"Here, we report on our results where self-consistent calculations are
performed to investigate the interference conditions, numerically. We employ
the successful 4$^{th}$ order grid technique to obtain the actual electrostatic
quantities of the samples used at the quantum Hall based Aharonov-Bohm
interferometers. By knowing the electron density distribution we calculate the
spatial distribution of the edge-states, which are considered as mono-energetic
current channels. Our results are in accord with the experimental findings
concerning the electron density distribution. Finally, we also comment on the
""optimized"" sample design in which highest visibility oscillations can be
measured.",1003.3008v1
2010-09-15,Quantum phase transitions of two-species bosons in square lattice,"We investigate various quantum phase transitions of attractive two-species
bosons in a square lattice. Using the algorithm based on the tensor product
states, the phase boundaries of the pair superfluid states with nonzero pair
condensate density \emph{and} vanishing atomic condensate density are
determined. Various quantum phase transitions across the phase boundaries are
characterized. Our work thus provides guides to the experimental search of the
pair superfluid phase in lattice boson systems.",1009.2841v1
2011-02-18,Tunneling conductance and local density of states in tight-binding junctions,"We study the relationship between the differential conductance and the local
density of states in tight-binding tunnel junctions where the junction'
geometry can be varied between the point-contact and the planar-contact limits.
The conductances are found to differ significantly in these two limiting cases.
We also examine how the matrix element influences the tunneling characteristics
and produces contrast in a simple model of scanning tunneling microscope (STM).
Some implications regarding the interpretation of STM spectroscopic data in the
cuprates are discussed. The calculations are carried out within the real-space
Keldysh formalism.",1102.3895v2
2011-05-03,A correction method for the pair density to get close to the ground state one,"We present a correction method for the pair density (PD) to get close to the
ground state one. The PD is corrected to be a variationally-best PD within the
search region that is extended by adding the uniformly-scaled PDs to its
elements. The corrected PD is kept N-representable and satisfies the virial
relation rigorously. The validity of the present method is confirmed by
numerical calculations of neon atom. It is shown that the root-mean-square
error of the electron-electron interaction and external potential energies,
which is a good benchmark for the error of the PD, is reduced by 69.7% without
additional heavy calculations.",1105.0461v1
2011-08-29,Proximity-induced density-of-states oscillations in a superconductor/strong-ferromagnet system,"We have measured the evolution of the tunneling density of states (DOS) in
superconductor/ferromagnet (S/F) bilayers with increasing F-layer thickness,
where F in our experiment is the strong ferromagnet Ni. As a function of
increasing Ni thickness, we detect multiple oscillations in the DOS at the
Fermi energy from differential conductance measurements. The features in the
DOS associated with the proximity effect change from normal to inverted twice
as the Ni thickness increases from 1 to 5 nm.",1108.5613v1
2011-09-02,Imaging of quantum Hall states in ultracold atomic gases,"We examine off-resonant light scattering from ultracold atoms in the quantum
Hall regime. When the light scattering is spin dependent, we show that images
formed in the far field can be used to distinguish states of the system. The
spatial dependence of the far-field images is determined by the two-particle
spin-correlation functions, which the images are related to by a
transformation. Quasiholes in the system appear in images of the density formed
by collecting the scattered light with a microscope, where the quasihole
statistics are revealed by the reduction in density at the quasihole position.",1109.0493v2
2012-03-06,Signatures of orbital loop currents in the spatially resolved local density of states,"Polarized neutron scattering measurements have suggested that intra-unit cell
antiferromagnetism may be associated with the pseudogap phase. Assuming that
loop current order is responsible for the observed magnetism, we calculate some
signatures of such circulating currents in the local density of states around a
single non-magnetic impurity in a coexistence phase with superconductivity. We
find a distinct C4 symmetry breaking near the disorder which is also detectable
in the resulting quasi-particle interference patterns.",1203.1181v1
2012-06-13,Fluid phases of argon,"A phase diagram of argon based upon percolation transition loci determined
from literature experimental density-pressure isotherms, and simulation values
using a Lennard-Jones model shows three fluid phases. The liquid phase spans
all temperatures, from a metastable amorphous ground state at 0K, to ultra-high
T. There is a supercritical mesophase bounded by two 2nd-order percolation
transition loci, and a gas phase. Intersection of two percolation loci in the
p-T plane thermodynamically defines an equilibrium line of critical density
states.",1206.2638v1
2012-10-04,The two-state Bose-Hubbard model in the hard-core boson limit: Non-ergodicity and the Bose-Einstein condensation,"The Bose-Einstein condensation in the hard-core boson limit (HCB) of the
Bose-Hubbard model with two local states and the particle hopping in the
excited band only is investigated. For the purpose of considering the
non-ergodicity, a single-particle spectral density is calculated in the random
phase approximation by means of the temperature boson Green functions. The
non-ergodic contribution to the momentum distribution function of particles
(connected with the static density fluctuations) increases significantly and
becomes comparable with the ergodic contribution in the superfluid phase near
the tricritical point.",1210.1424v1
2012-10-30,Fifth-order nonlinear optical response of excitonic states in an InAs quantum dot ensemble measured with 2D spectroscopy,"Exciton, trion and biexciton dephasing rates are measured within the
inhomogeneous distribution of an InAs quantum dot (QD) ensemble using
two-dimensional Fourier-transform spectroscopy. The dephasing rate of each
excitonic state is similar for all QDs in the ensemble and the rates are
independent of excitation density. An additional spectral feature -- too weak
to be observed in the time-integrated four-wave mixing signal -- appears at
high excitation density and is attributed to the $\chi^{\textrm{(5)}}$
biexcitonic nonlinear response.",1210.8096v1
2012-12-12,Mixing of Edge States at a Bipolar Graphene Junction,"An Atomic Force Microscope is used to locally manipulate a single layer
graphene sheet. Transport measurements in this region as well as in the
unmanipulated part reveal different charge carrier densities while mobilities
stay in the order of 10000 cm^2/(Vs). With a global backgate, the system is
tuned from a unipolar n-n' or p-p' junction with different densities to a
bipolar p-n junction. Magnetotransport across this junction verifies its
nature, showing the expected quantized resistance values as well as the
switching with the polarity of the magnetic field. The mixing of edge states at
the p-n junction is shown to be supressed at high magnetic fields.",1212.2824v1
2013-02-26,"""Polar"" and ""antiferromagnetic"" order in f=1 many-boson systems","In a system of interacting f=1 bosons (in the subspace where the total spin
in the z-direction is vanishing), we prove inequalities for the ground state
expectation value of the density of spin-0 bosons. The inequalities imply that
the ground state possesses ""polar"" or ""antiferromagnetic"" order when the
quadratic Zeeman term q is large enough. In the low density limit, the
inequalities establish the existence of a sharp transition at q=0 when q is
varied.",1302.6349v2
2013-07-01,Representability Conditions by Grassmann Integration,"Representability conditions on the one- and two-particle density matrix for
fermion systems are formulated by means of Grassmann integrals. A positivity
condition for a certain kind of Grassmann integral is established which, in
turn, induces the well-known G-, P- and Q-Conditions of quantum chemistry by an
appropriate choice of the integrand. Similarly, the T1- and T2-Conditions are
derived. Furthermore, quasifree Grassmann states are introduced and it is shown
that every so-called generalized one-particle density matrix which is bounded
between 0 and 1 corresponds to a unique quasifree Grassmann state.",1307.0465v1
2013-11-01,"Long-Lived Complexes, Ergodicity and Chaos in Ultracold Molecular Collisions","Estimates for the lifetime of collision complexes formed during ultracold
molecular collisions based on density-of-states arguments are shown to be
consistent with similar estimate based on classical trajectory calculations. In
the classical version, these collisions are shown to exhibit chaos, and their
fractal dimensions are calculated versus collision energy. From these results,
a picture emerges that ultracold collisions are classically ergodic, justifying
the density-of-states estimates for lifetimes. These results point the way
toward using the techniques of classical and quantum chaos to interpret
molecular collisions in the ultracold regime.",1311.0294v2
2014-07-11,Pseudogap phenomena in a two-dimensional ultracold Fermi gas near the Berezinskii-Kosterlitz-Thouless transition,"We investigate single-particle excitations and strong-coupling effects in a
two-dimensional Fermi gas. Including pairing fluctuations within a Gaussian
fluctuation theory, we calculate the density of states $\rho(\omega)$ near the
Berezinskii-Kosterlitz-Thouless (BKT) transition temperature $T_{\rm BKT}$.
Near $T_{\rm BKT}$, we show that superfluid fluctuations induce a pseudogap in
$\rho(\omega)$. The pseudogap structure is very similar to the BCS superfluid
density of states, although the superfluid order parameter is absent in the
present two-dimensional case. Since a two-dimensional $^{40}$K Fermi gas has
recently been realized, our results would contribute to the understanding of
single-particle properties near the BKT instability.",1407.3076v1
2015-10-27,Vortex line in the unitary Fermi gas,"We report diffusion Monte Carlo results for the ground state of unpolarized
spin-1/2 fermions in a cylindrical container and properties of the system with
a vortex-line excitation. The density profile of the system with a vortex line
presents a non-zero density at the core. We calculate the ground-state energy
per particle, the superfluid pairing gap, and the excitation energy per
particle. These simulations can be extended to calculate the properties of
vortex excitations in other strongly interacting systems, such as superfluid
neutron matter using realistic nuclear Hamiltonians.",1510.07952v2
2016-06-30,Density of States for Random Band Matrices in two dimensions,"We consider a two dimensional random band matrix ensemble, in the limit of
infinite volume and fixed but large band width $W$. For this model we
rigorously prove smoothness of the averaged density of states. We also prove
that the resulting expression coincides with Wigner's semicircle law with a
precision $W^{-2+\delta },$ where $\delta\to 0$ when $W\to \infty.$ The proof
uses the supersymmetric approach and extends results by Disertori, Pinson and
Spencer from three to two dimensions.",1606.09387v2
2017-05-23,On the density of states of graphene in the nearest-neighbor approximation,"We propose an alternative analytical expression for the density of states of
a clean graphene in the nearest-neighbor approximation. In contrast to the
previously known expression, it can be written as a single formula valid for
the whole energy range. The correspondence with the previously known expression
is shown and the limiting cases are analyzed.",1705.08120v3
2017-08-21,URu$_2$Si$_2$ under intense magnetic fields: from hidden order to spin-density wave,"A review of recent state-of-the-art pulsed field experiments performed on
URu$_2$Si$_2$ under a magnetic field applied along its easy magnetic axis
$\mathbf{c}$ is given. Resistivity, magnetization, magnetic susceptibility,
Shubnikov-de Haas, and neutron diffraction experiments are presented,
permitting to emphasize the relationship between Fermi surface reconstructions,
the destruction of the hidden-order and the appearance of a spin-density wave
state in a high magnetic field.",1708.06122v1
2016-11-30,Chiral optical Local Density of States in spiral plasmonic cavity,"We introduce a new paradigm: the chiral electromagnetic local density of
states (LDOS) in a spiral plasmonic nanostructure. In both classical and
quantum regimes, we reveal using scanning near-field optical microscopy (NSOM)
in combination with spin analysis that a spiral cavity possesses spin-dependent
local optical modes. We expect this work to lead to promising directions for
future quantum plasmonic device development, highlighting the potentials of
chirality in quantum information processing.",1611.10137v1
2020-09-08,Qubit dynamics with classical noise,"We study the evolution of a qubit evolving according to the Schr\""odinger
equation with a Hamiltonian containing noise terms, modeled by random diagonal
and off-diagonal matrix elements. We show that the noise-averaged qubit density
matrix converges to a final state, in the limit of large times $t.$ The
convergence speed is polynomial in $1/t$, with a power depending on the
regularity of the noise probability density and its low frequency behaviour. We
evaluate the final state explicitly. We show that in the regimes of weak and
strong off-diagonal noise, the process implements the dephasing channel in the
energy- (localized) and the delocalized basis, respectively.",2009.03517v1
2009-12-07,Thermoelectric spin diffusion in a ferromagnetic metal,"We present a semiclassical theory of spin-diffusion in a ferromagnetic metal
subject to a temperature gradient. Spin-flip scattering can generate pure
thermal spin currents by short-circuiting spin channels while suppressing spin
accumulations. A thermally induced spin density is locally generated when the
energy dependence of the density of states is spin polarized.",0912.1213v1
2016-08-05,Electronic Density of States for Incommensurate Layers,"We prove that the electronic density of states (DOS) for 2D incommensurate
layered structures, where Bloch theory does not apply, is well-defined as the
thermodynamic limit of finite clusters. In addition, we obtain an explicit
representation formula for the DOS as an integral over local configurations.
Next, based on this representation formula, we propose a novel algorithm for
computing electronic structure properties in incommensurate heterostructures,
which overcomes limitations of the common approach to artificially strain a
large supercell and then apply Bloch theory.",1608.01968v1
2018-09-18,"Mutually disjoint, maximally commuting set of physical observables for optimum state determination","We consider the state determination problem using Mutually Unbiased
Bases(MUBs). For spin-1, spin-3/2 and spin-2 systems, analogous to Pauli
operators of spin-1/2 system, which are experimentally implementable and
correspond to the optimum measurement in characterizing the density matrix, we
describe a procedure to construct an orthonormal set of operators from MUBs.
The constructed operators are maximally commuting, can be physically realized,
and correspond to physical observables. The method of construction is general
enough to allow for extensions to higher-dimensional spin systems and arbitrary
density matrices in finite dimensions for which MUBs are known to exist.",1809.06762v2
2020-04-09,Toward equilibrium ground state of charge density waves in rare-earth tritellurides,"We show that the charge density wave (CDW) ground state below the Peierls
transition temperature, $T_{CDW}$, of rare-earth tritellurides is not at its
equilibrium value, but depends on the time where the system was kept at a fixed
temperature below $T_{CDW}$. This ergodicity breaking is revealed by the
increase of the threshold electric field for CDW sliding which depends
exponentially on time. We tentatively explain this behavior by the
reorganization of the oligomeric (Te$_x$)$^{2-}$ sequence forming the CDW
modulation.",2004.04503v1
2020-10-30,Regularity of the density of states for random Dirac operators,"We consider the random Dirac operators for which we have proved Anderson
localization in arXiv:1812.01868. We use the Wegner estimate we have got in
that paper to prove Lipschitz regularity of the density of states. Since usual
methods for Schr\""odinger operators do not work in this case, we give a new one
based on the Helffer-Sj\""ostrand formula.",2010.16377v2
2021-03-15,Efficient bit encoding of neural networks for Fock states,"We present a bit encoding scheme for a highly efficient and scalable
representation of bosonic Fock number states in the restricted Boltzmann
machine neural network architecture. In contrast to common density matrix
implementations, the complexity of the neural network scales only with the
number of bit-encoded neurons rather than the maximum boson number. Crucially,
in the high occupation regime its information compression efficiency is shown
to surpass even maximally optimized density matrix implementations, where a
projector method is used to access the sparsest Hilbert space representation
available.",2103.08285v2
2022-03-05,Accurate Estimate of the Joint Density of States via Flat Scan Sampling,"A Monte Carlo method to estimate the Joint Density of States g(E,M) of the
Ising and Ising-like models is presented. The method is applied to the
well-known 2D Ising model, and is shown to be accurate, efficient, and
embarrassingly parallel. The method presented offers major improvements over
existing approaches. Furthermore, we obtain g(E,M) estimates for the spin S
Ising model, with the spin number S = {1/2, 1, 3/2, 2}, thus showing that the
algorithm can handle larger and more complex (E, M) phase spaces.",2203.02718v1
2023-03-15,The Quantum Density Matrix and its many uses: From quantum structure to quantum chaos and noisy simulators,"The quantum density matrix generalises the classical concept of probability
distribution to quantum theory. It gives the complete description of a quantum
state as well as the observable quantities that can be extracted from it. Its
mathematical structure is described, with applications to understanding quantum
correlations, illustrating quantum chaos and its unravelling, and developing
software simulators for noisy quantum systems with efficient quantum state
tomography.",2303.08738v2
2023-07-25,Local density of states above a disk -- geometrical vs. thermal boundary conditions,"We analytically calculate the contribution to the local density of states due
to thermal sources in a disk-like patch within the framework of fluctuational
electrodynamics. We further introduce a wavevector cutoff method to approximate
this contribution. We compare the results obtained with the source and cutoff
method with the numerical exact LDOS above a metal disk attained by SCUFF-EM
calculations. By this comparison we highlight the difference and resemblance of
thermal and geometrical boundary conditions which are both relevant for
near-field scanning microscope measurements. Finally, we give an outlook to
general lateral temperature profiles and compare it with surface profiles.",2307.13438v1
2023-10-13,Periodic skyrmionic textures via conformal cartographic projections,"We find periodic skyrmionic textures via conformal cartographic projections
that map either an entire spherical parameter space or a hemisphere onto every
regular polygon that provides regular tessellations of the plane. These maps
preserve the sign of the Skyrme density throughout the entire space. We
implement these textures in the polarization state of a laser beam, and
demonstrate that paraxial fields where a periodic texture preserving the sign
of the Skyrme density is implemented in the polarization state distribution
unavoidably exhibit zeros.",2310.08964v1
2024-03-20,"Tripartite entanglement in $H \to ZZ,WW$ decays","The decays of the Higgs boson produce a state in which the spins of the decay
products and the orbital angular momentum ($L$) are highly entangled. We obtain
the tripartite density operator, as well as reduced operators, for the decay
into two weak bosons. For $H \to ZZ$ in the four-lepton final state we also
estimate the statistical sensitivity at the Large Hadron Collider and future
upgrades, using a binned method to reconstruct the density operators from
distributions. With the expected Run 3 data, establishing genuine tripartite
entanglement would be possible beyond the $5\sigma$ level. The violation of
Bell inequalities involving the spins of the two weak bosons could also be
established beyond the $5\sigma$ level.",2403.13942v1
2008-11-03,Internal One-Particle Density Matrix for Bose-Einstein Condensates with Finite Number of Particles in a Harmonic Potential,"Investigations on the internal one-particle density matrix in the case of
Bose-Einstein condensates with a finite number ($N$) of particles in a harmonic
potential are performed. We solve the eigenvalue problem of the
Pethick-Pitaevskii-type internal density matrix and find a fragmented
condensate. On the contrary the condensate Jacobi-type internal density matrix
gives complete condensation into a single state. The internal one-particle
density matrix is, therefore, shown to be different in general for different
choices of the internal coordinate system. We propose two physically motivated
criteria for the choice of the adequate coordinate systems which give us a
unique answer for the internal one-particle density matrix. One criterion is
that in the infinite particle number limit ($N=\infty$) the internal
one-particle density matrix should have the same eigenvalues and eigenfunctions
as those of the corresponding ideal Bose-Einstein condensate in the laboratory
frame. The other criterion is that the coordinate of the internal one-particle
density matrix should be orthogonal to the remaining $(N - 2)$ internal
coordinates. This second criterion is shown to imply the first criterion. It is
shown that the internal Jacobi coordinate system satisfies these two criteria
while the internal coordinate system adopted by Pethick and Pitaevskii for the
construction of the internal one-particle density matrix does not. It is
demonstrated that these two criteria uniquely determine the internal
one-particle density matrix which is identical to that calculated with the
Jacobi coordinates. The relevance of this work concerning $\alpha$-particle
condensates in nuclei, as well as bosonic atoms in traps, is pointed out.",0811.0288v2
2024-01-13,In-plane Density Gradation of Shoe Midsoles for Optimized Cushioning Performance,"Midsoles are important components in footwear as they provide shock
absorption and stability, thereby improving comfort and effectively preventing
certain foot and ankle injuries. A rationally tailored midsole can potentially
mitigate plantar pressure, improving performance and comfort levels. Despite
the importance of midsole design, the potential of using in-plane density
gradation in midsole has been rarely explored in earlier studies. The present
work investigates the effectiveness of in-plane density gradation in shoe
midsoles using a new class of polyurea foams as the material candidate. Their
excellent cushioning properties justify the use of polyurea foams. Different
polyurea foam densities, ranging from 95 to 350 kg/m3 are examined and tested
to construct density-dependent correlative mathematical relations required for
the optimization process. An optimization framework is then created to allocate
foam densities at certain plantar zones based on the required cushioning
performance constrained by the local pressures. The interior-point algorithm
was used to solve the constrained optimization problem. The optimization
algorithm introduces a novel approach, utilizing the maximum specific energy
absorption as the objective function. The optimization process identifies
specific foam densities at various plantar regions for maximum biomechanical
energy dissipation without incurring additional weight penalties. Our results
suggest midsole design can benefit from horizontal (in-plane) density
gradation, leading to potential weight reduction and localized cushioning
improvements. With local plantar peak pressure data analysis, the optimization
results indicate low-density polyurea foams (140 kg/m3) for central and lateral
phalanges, whereas stiffer foams (185-230 kg/m3) are identified as suitable
candidates for metatarsal and arch regions in an in-plane density graded
midsole design.",2401.06940v1
2000-02-25,The Polytropic Equation of State of Interstellar Gas Clouds,"Models are presented for the polytropic equation of state of
self-gravitating, quiescent interstellar gas clouds. A detailed analysis,
including chemistry, thermal balance, and radiative transfer, is performed for
the physical state of the gas as a function of density, metallicity, velocity
field, and background radiation field. It is found that the stiffness of the
equation of state strongly depends on all these physical parameters, and the
adiabatic index varies between 0.2-1.4. The implications for star formation, in
particular at high redshift and in starburst galaxies, and the initial stellar
mass function are discussed.",0002483v1
2004-09-25,Neutron Stars With A Quark Core. I. Equations Of State,"An extensive set of realistic equations of state for superdense matter with a
quark phase transition is derived on the basis of the three equations of state
for neutron matter and the eight variants of strange quark-gluon plasmas in the
MIT quark bag model. The characteristics of the phase transitions are described
and the calculated equations of state with a density jump are studied in
detail.",0409602v1
2003-01-24,Maximum-entropy theory of steady-state quantum transport,"We develop a new theoretical framework for describing steady-state quantum
transport phenomena, based on the general maximum-entropy principle of
non-equilibrium statistical mechanics. The general form of the many-body
density matrix is derived, which contains the invariant part of the current
operator that guarantees the non-equilibrium and steady-state character of the
ensemble. Several examples of the theory are given, demonstrating the
relationship of the present treatment to the widely-used scattering-states
occupation schemes at the level of the self-consistent single-particle
approximation.",0301485v3
2004-11-25,Localization and hybridization of electronic states in thin films of Ag on V(100),"We have studied the electronic states in 1-5 layers thick Ag films on V(100),
by means of ab initio density functional calculations. Due to the mismatch of
the electronic structure of Ag and V, quantum well states of both sp and d
character localized on Ag films are formed. We find that the hybridization of
the Ag quantum well states with the V orbitals is nevertheless important, and
must be taken into account in order to fully understand the observed
properties, in particular the energies and the dispersion of the photoemission
peaks in ARPES experiments.",0411646v1
2003-05-08,Evidence for parallel confinement in resonant charge transfer of negative hydrogen ion near metal surfaces,"Using a wave packet propagation approach, we find that the resonant charge
transfer process of H^- near a Cu(111) surface is strongly influenced by
transient hybrid states. These states originate from an ion-induced confinement
parallel to the surface together with the surface-localization character of the
metal potential along the surface normal. The lowest members of these states
have lifetimes of the order of interaction times in typical particle-surface
scattering experiments. The propagation of the electron probability density
provides clear evidence for this effect in visualizing the evolution and the
decay of these transient states.",0305031v1
1999-01-15,Broadband detection of squeezed vacuum: A spectrum of quantum states,"We demonstrate the simultaneous quantum state reconstruction of the spectral
modes of the light field emitted by a continuous wave degenerate optical
parametric amplifier. The scheme is based on broadband measurement of the
quantum fluctuations of the electric field quadratures and subsequent Fourier
decomposition into spectral intervals. Applying the standard reconstruction
algorithms to each bandwidth-limited quantum trajectory, a ""spectrum"" of
density matrices and Wigner functions is obtained. The recorded states show a
smooth transition from the squeezed vacuum to a vacuum state. In the time
domain we evaluated the first order correlation function of the squeezed output
field, showing good agreement with the theory.",9901044v1
2001-04-16,Space of State Vectors in PT Symmetrical Quantum Mechanics,"Space of states of PT symmetrical quantum mechanics is examined. Requirement
that eigenstates with different eigenvalues must be orthogonal leads to the
conclusion that eigenfunctions belong to the space with an indefinite metric.
The self consistent expressions for the probability amplitude and average value
of operator are suggested. Further specification of space of state vectors
yield the superselection rule, redefining notion of the superposition
principle. The expression for the probability current density, satisfying
equation of continuity and vanishing for the bound state, is proposed.",0104077v2
2005-04-29,Distance-based degrees of polarization for a quantum field,"It is well established that unpolarized light is invariant with respect to
any SU(2) polarization transformation. This requirement fully characterizes the
set of density matrices representing unpolarized states. We introduce the
degree of polarization of a quantum state as its distance to the set of
unpolarized states. We use two different candidates of distance, namely the
Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally
different degrees of polarization. We apply these notions to relevant field
states and we demonstrate that they avoid some of the problems arising with the
classical definition.",0504226v1
2005-09-01,Partial scaling transform of multiqubit states as a criterion of separability,"The partial scaling transform of the density matrix for multiqubit states is
introduced to detect entanglement of quantum states. The transform contains
partial transposition as a special case. The scaling transform corresponds to
partial time scaling of subsystem (or partial Planck's constant scaling) which
was used to formulate recently separability criterion for continous variables.A
measure of entanglement which is a generalization of negativity measure is
introduced being based on tomographic probability description of spin states.",0509006v1
2007-05-15,Separability of entangled qutrits in noisy channels,"We present an analysis of noisy atomic channels involving qutrits. We choose
a three-level atom with V-configuration to be the qutrit state. Gell-Mann
matrices and a generalized Bloch vector (8-dimensional) are used to describe
the qutrit density operator. We introduce quantum quasi-distributions for
qutrits that provide a simple description of entanglement. Studying the
time-evolution for the atomic variables we find the Kraus representation of
spontaneous emission quantum channel (SE channel). Furthermore, we consider a
generalized Werner state of two qutrits and investigate the separability
condition in the presence of spontaneous emission noise. The influence of
spontaneous emission on the separability of Werner states for qutrit and qubit
states is compared.",0705.2162v2
2007-08-07,Characteristic Energy of the Coulomb Interactions and the Pileup of States,"Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm
Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the
density of states. Importantly, the data and analysis at high energy, E, show a
pileup of states: most of the states removed from near the Fermi level are
found between ~40 and 130 meV, from which we infer the possibility of universal
behavior. The agreement of our tunneling data with recent photoemission results
further confirms our analysis.",0708.0950v1
2007-10-05,Numerical study of metastable states in the T=0 RFIM,"We study numerically the number of single-spin-flip stable states in the T=0
Random Field Ising Model (RFIM) on random regular graphs of connectivity $z=2$
and $z=4$ and on the cubic lattice. The annealed and quenched complexities
(i.e. the entropy densities) of the metastable states with given magnetization
are calculated as a function of the external magnetic field. The results show
that the appearance of a (disorder-induced) out-of-equilibrium phase transition
in the magnetization hysteresis loop at low disorder can be ascribed to a
change in the distribution of the metastable states in the field-magnetization
plane.",0710.1170v1
2007-11-26,Quantum reflection and dwell times of metastable states,"The concept of phase and dwell times used in tunneling is extended to quantum
collisions to derive a relation between the phase and dwell time delays in
scattering. This relation can be used to remove the near threshold s-wave
singularities in the Wigner-Eisenbud delay times and amounts to an extension of
the concept of quantum reflection to strong interactions. Dwell time delay
emerges as the quantity which gives the correct behaviour of the density of
states of a metastable state at all energies. This fact is demonstrated by
investigating some recently found metastable states of mesic-nuclei.",0711.4066v1
2008-01-06,Localized charged states and phase separation near second order phase transition,"Localized charged states and phase segregation are described in the framework
of the phenomenological Ginzburg-Landau theory of phase transitions. The
Coulomb interactions determines the charge distribution and the characteristic
length of the phase separated states. The phase separation with charge
segregation becomes possible because of the large dielectric constant and the
small density of extra charge in the range of charge localization. The phase
diagram is calculated and the energy gain of the phase separated state is
estimated. The role of the Coulomb interaction is elucidated.",0801.0854v1
2009-11-14,The checkerboard family of entangled states of two qutrits,"By modifying the method of Bruss and Peres, we construct two new families of
entangled two qutrit states. For all density matrices in these families the
(i,j)th entry is 0 for i+j odd. The first family depends on 27 independent real
parameters and includes both PPT and NPT states. The second family consists of
PPT entangled states. The number of independent real parameters of this family
is at least 11.",0911.2797v3
2010-11-12,Effect of weak magnetic field on quantum spin correlation in an s-wave superconductor,"We study the effect of a weak magnetic field on the state of the spins of a
pair of electrons forming a Cooper pair in an s-wave superconductor. By
perturbatively solving time-dependent Bogoliubov equations up to first order,
we obtain the two-particle Green function, and whence the two-electron
spin-space density matrix. It appears that up to first order approximation, the
spin state of a Cooper pair retains the form of a Werner state. This state is
then examined in the sense of quantum correlations, i.e., quantum discord.",1011.3011v1
2012-09-17,Ground state properties of multi-polaron systems,"We summarize our recent results on the ground state energy of multi-polaron
systems. In particular, we discuss stability and existence of the thermodynamic
limit, and we discuss the absence of binding in the case of large Coulomb
repulsion and the corresponding binding-unbinding transition. We also consider
the Pekar-Tomasevich approximation to the ground state energy and we study
radial symmetry of the ground state density.",1209.3717v1
2014-04-21,Fluctuation energies in quantum cosmology,"Quantum fluctuations or other moments of a state contribute to energy
expectation values and can imply interesting physical effects. In quantum
cosmology, they turn out to be important for a discussion of density bounds and
instabilities of initial-value problems in the presence of signature change in
loop-quantized models. This article provides an effective description of these
issues, accompanied by a comparison with existing numerical results and an
extension to squeezed states. The comparison confirms that canonical effective
methods are well-suited for computations of properties of physical states. As a
side product, an example is found for a simple state in which quantum
fluctuations can cancel holonomy modifications of loop quantum cosmology.",1404.5284v1
2015-02-12,Anomalies in the electronic structure of Bi(2)Se(3),"We studied the electronic structure Bi(2)Se(3) employing density functional
theory. The calculations show that the Dirac states primarily consists of the
states at the interface of surface and sub-surface quintuple layers and the
emergence of the Dirac states depends on the surface terminations in sharp
contrast to their surface character expected for such systems. This manifests
the complexity of real materials and the realization of topological order in
real materials as an outstanding problem. We discover that the surface
character of the Dirac states can be achieved by adsorption of oxygen on
Bi-terminated surface due to the change in covalency by the relatively more
electronegative oxygens.",1502.03631v1
2015-11-01,Experimental demonstration of quantum contextuality on an NMR qutrit,"We experimentally test quantum contextuality of a single qutrit using NMR.
The contextuality inequalities based on nine observables developed by Kurzynski
et. al. are first reformulated in terms of traceless observables which can be
measured in an NMR experiment. These inequalities reveal the contextuality of
almost all single-qutrit states. We demonstrate the violation of the inequality
on four different initial states of a spin-1 deuterium nucleus oriented in a
liquid crystal matrix, and follow the violation as the states evolve in time.
We also describe and experimentally perform a single-shot test of contextuality
for a subclass of qutrit states whose density matrix is diagonal in the energy
basis.",1511.00241v1
2016-02-10,The weak side of strong topological insulators,"Strong topological insulators may have nonzero weak indices. The nonzero weak
indices allow for the existence of topologically protected helical states along
line defects of the lattice. If the lattice admits line defects that connect
opposite surfaces of a slab of such a ""weak-and-strong"" topological insulator,
these states effectively connect the surface states at opposite surfaces.
Depending on the phases accumulated along the dislocation lines, this
connection results in a suppression of in-plane transport and the opening of a
spectral gap or in an enhanced density of states and an increased conductivity.",1602.03443v1
2017-05-11,All coherent field states entangle equally,"We analyze the interactions of particle detectors with coherent states of a
free scalar field. We find that the eigenvalues of the post-interaction density
matrices of i) a single detector, ii) two detectors, and iii) the partial
transpose of the latter, are all independent of which coherent state the field
was in. A consequence of these results is that a detector pair can harvest the
same amount of entanglement from any coherent field state as from the vacuum.",1705.04341v2
2018-03-11,Quench Dynamics of the Gaudin-Yang Model,"We study the quench dynamics of one dimensional bosons or fermion quantum
gases with either attractive or repulsive contact interactions. Such systems
are well described by the Gaudin-Yang model which turns out to be quantum
integrable. We use a contour integral approach, the Yudson approach, to expand
initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making
use of the contour, we obtain a complete set of eigenstates, including both
free states and bound states. These states constitute a larger Hilbert space
than described by the standard String hypothesis. We calculate the density and
noise correlations of several quenched systems such as a static or kinetic
impurity evolving in an array of particles.",1803.04846v1
2020-06-23,Entanglement of pseudo-Hermitian random states,"In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density
matrix of non-Hermitian Hamiltonians has been used to investigate the
entanglement of states of a PT-symmetric bosonic system. They found that von
Neumann entropy can show a different behavior in the broken and unbroken
regime. We show that their results can be recast in terms of an abstract model
of pseudo-Hermitian random matrices. It is found however that, although the
formalism is practically the same, the entanglement is not of Fock states but
of Bell states.",2006.13151v1
2021-05-06,On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model,"We study the dynamics of perturbations around an inhomogeneous stationary
state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized
stability criterion (Penrose criterion). We consider solutions of the
linearized equation around the steady state, and prove the algebraic decay in
time of the Fourier modes of their density. We prove moreover that these
solutions exhibit a scattering behavior to a modified state, implying a linear
Landau damping effect with an algebraic rate of damping.",2105.02484v1
2000-05-03,Spin Properties of Low Density One-Dimensional Wires,"We report conductance measurements of a ballistic one-dimensional (1D) wire
defined in the lower two-dimensional electron gas of a GaAs/AlGaAs double
quantum well. At low temperatures there is an additional structure at
$0.7(2e^2/h)$ in the conductance, which tends to $e^2/h$ as the electron
density is decreased. We find evidence for complete spin polarization in a
weakly disorderd 1D wire at zero magnetic field through the observation of a
conductance plateau at $e^2/h$, which strengthens in an in-plane magnetic field
and disappears with increasing electron density. In all cases studied, with
increasing temperature structure occurs at $0.6(2e^2/h)$. We suggest that the
0.7 structure is a many-body spin state excited out of, either the
spin-polarized electron gas at low densities, or the spin-degenerate electron
gas at high densities.",0005075v1
2001-09-26,Correlation energy and spin polarization in the 2D electron gas,"The ground state energy of the two--dimensional uniform electron gas has been
calculated with fixed--node diffusion Monte Carlo, including backflow
correlations, for a wide range of electron densities as a function of spin
polarization. We give a simple analytic representation of the correlation
energy which fits the density and polarization dependence of the simulation
data and includes several known high- and low-density limits. This
parametrization provides a reliable local spin density energy functional for
two-dimensional systems and an estimate for the spin susceptibility. Within the
proposed model for the correlation energy, a weakly first--order polarization
transition occurs shortly before Wigner crystallization as the density is
lowered.",0109492v4
2001-11-17,Friedel Oscillations and Charge Density Waves in Chains and Ladders,"The density matrix renormalization group method for ladders works much more
efficiently with open boundary conditions. One consequence of these boundary
conditions is groundstate charge density oscillations that often appear to be
nearly constant in magnitude or to decay only slightly away from the
boundaries. We analyse these using bosonization techniques, relating their
detailed form to the correlation exponent and distinguishing boundary induced
generalized Friedel oscillations from true charge density waves. We also
discuss a different approach to extracting the correlation exponent from the
finite size spectrum which uses exclusively open boundary conditions and can
therefore take advantage of data for much larger system sizes. A general
discussion of the Friedel oscillation wave-vectors is given, and a convenient
Fourier transform technique is used to determine it. DMRG results are analysed
on Hubbard and t-J chains and 2 leg t-J ladders. We present evidence for the
existence of a long-ranged charge density wave state in the t-J ladder at a
filling of n=0.75 and near J/t \approx 0.25.",0111320v1
2002-05-13,Multiperiodic magnetic structures in Hubbard superlattices,"We consider fermions in one-dimensional superlattices (SL's), modeled by
site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive
(i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG)
diagonalization of finite systems is used to calculate the local moment and the
magnetic structure factor in the ground state. We have found four regimes for
magnetic behavior: uniform local moments forming a spin-density wave (SDW),
`floppy' local moments with short-ranged correlations, local moments on
repulsive sites forming long-period SDW's superimposed with short-ranged
correlations, and local moments on repulsive sites solely with long-period
SDW's; the boundaries between these regimes depend on the range of electronic
densities, rho, and on the SL aspect ratio. Above a critical electronic
density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and
with the spacer thickness. The former oscillation allows one to reproduce all
SDW wave vectors within a small range of electronic densities, unlike the
homogeneous system. The latter oscillation is related to the exchange
oscillation observed in magnetic multilayers. A crossover between regimes of
`thin' to `thick' layers has also been observed.",0205266v1
2004-12-10,Gapped optical excitations from gapless phases: imperfect nesting in unconventional density waves,"We consider the effect of imperfect nesting in quasi-one-dimensional
unconventional density waves in the case, when the imperfect nesting and the
gap depends on the same wavevector component.
  The phase diagram is very similar to that in a conventional density wave. The
density of states is highly asymmetric with respect to the Fermi energy.
  The optical conductivity at T=0 remains unchanged for small deviations from
perfect nesting. For higher imperfect nesting parameter, an optical gap opens,
and considerable amount of spectral weight is transferred to higher
frequencies. This makes the optical response of our system very similar to that
of a conventional density wave. Qualitatively similar results are expected in
d-density waves.",0412274v1
2005-07-22,Tomonaga-Luttinger parameters for doped Mott insulators,"The Tomonaga--Luttinger parameter $K_{\rho}$ determines the critical behavior
in quasi one-dimensional correlated electron systems, e.g., the exponent
$\alpha$ for the density of states near the Fermi energy. We use the numerical
density-matrix renormalization group method to calculate $K_{\rho}$ from the
slope of the density-density correlation function in momentum space at zero
wave vector. We check the accuracy of our new approach against exact results
for the Hubbard and XXZ Heisenberg models. We determine $K_{\rho}$ in the phase
diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and
confirm the bosonization results $K_{\rho}=n_{\rm c}^2=1/4$ on the critical
line and $K_{\rho}^{\rm CDW}=n_{\rm c}^2/2=1/8$ at infinitesimal doping of the
charge-density-wave (CDW) insulator for all interaction strengths. The doped
CDW insulator exhibits exponents $\alpha>1$ only for small doping and strong
correlations.",0507508v1
2003-12-02,Study of QCD thermodynamics at finite density by Taylor expansion,"We discuss the phase structure and the equation of state for QCD at non-zero
temperature and density. Derivatives of $\ln Z$ with respect to quark chemical
potential $\mu_q$ up to fourth order are calculated for 2-flavor QCD, enabling
estimates of the pressure, quark number density and associated susceptibilities
as functions of $\mu_q$ via a Taylor series expansion. Also, the phase
transition line for 2 and 3-flavor QCD and the critical endpoint in the $(T,
\mu_q)$ plane are investigated in the low density regime.",0312006v2
2007-07-03,Low densities in asymmetric nuclear matter,"Asymmetric nuclear matter is investigated in the low density region below the
nuclear saturation density. Microscopic calculations based on the Dirac
Brueckner Hartree-Fock (DBHF) approach with realistic nucleon-nucleon
potentials are used to adjust a low density functional. This functional is
constructed on a density expansion of the relativistic mean field theory which
allows a clear interpretation of the role of the mesons to the equation of
state. It is shown that a correction term should be added to the functional in
order to take into account the effects beyond the mean field. Two functionals
with different corrections are obtained. Those functionals converge to predict
a reduction of the spinodal zone in asymmetric nuclear matter by about 15-20%
and an isoscalar unstable mode closer to the constant Z/A direction than the
functional without correction.",0707.0354v2
2007-09-04,Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations,"We describe a procedure for mapping a self-consistent mean-field theory (also
known as density functional theory) into a shell model Hamiltonian that
includes quadrupole-quadrupole and monopole pairing interactions in a truncated
space. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 and
Ar-36, starting from the Hartree-Fock plus BCS approximation of the USD shell
model interaction. A similar procedure is then followed using the SLy4 Skyrme
energy density functional in the particle-hole channel plus a zero-range
density-dependent force in the pairing channel. Using the ground-state solution
of this density functional theory at the Hartree-Fock plus BCS level, an
effective shell model Hamiltonian is constructed. We use this mapped
Hamiltonian to extract quadrupolar and pairing correlation energies beyond the
mean field approximation. The rescaling of the mass quadrupole operator in the
truncated shell model space is found to be almost independent of the coupling
strength used in the pairing channel of the underlying mean-field theory.",0709.0508v1
2012-07-17,Friedel oscillations and horizon charge in 1D holographic liquids,"In many-body fermionic systems at finite density correlation functions of the
density operator exhibit Friedel oscillations at a wavevector that is twice the
Fermi momentum. We demonstrate the existence of such Friedel oscillations in a
3d gravity dual to a compressible finite-density state in a (1+1) dimensional
field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and
all the charge is behind a bulk horizon. The bulk gauge theory is compact and
so there exist magnetic monopole tunneling events. We compute the effect of
these monopoles on holographic density-density correlation functions and
demonstrate that they cause Friedel oscillations at a wavevector that directly
counts the charge behind the bulk horizon. If the magnetic monopoles are taken
to saturate the bulk Dirac quantization condition then the observed Fermi
momentum exactly agrees with that predicted by Luttinger's theorem, suggesting
some Fermi surface structure associated with the charged horizon. The mechanism
is generic and will apply to any charged horizon in three dimensions. Along the
way we clarify some aspects of the holographic interpretation of Maxwell
electromagnetism in three bulk dimensions and show that perturbations about the
charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.",1207.4208v1
2012-08-28,Alternative route to charge density wave formation in multiband systems,"Charge and spin density waves, periodic modulations of the electron and
magnetization densities, respectively, are among the most abundant and
non-trivial low-temperature ordered phases in condensed matter. The ordering
direction is widely believed to result from the Fermi surface topology.
However, several recent studies indicate that this common view needs to be
supplemented. Here, we show how an enhanced electron-lattice interaction can
contribute to or even determine the selection of the ordering vector in the
model charge density wave system ErTe3. Our joint experimental and theoretical
study allows us to establish a relation between the selection rules of the
electronic light scattering spectra and the enhanced electron-phonon coupling
in the vicinity of band degeneracy points. This alternative proposal for charge
density wave formation may be of general relevance for driving phase
transitions into other broken-symmetry ground states, particularly in multiband
systems such as the iron based superconductors.",1208.5701v2
2013-10-20,"Conventional BCS, Unconventional BCS, and Non-BCS Hidden Dineutron Phases in Neutron Matter","The nature of pairing correlations in neutron matter is re-examined. Working
within the conventional approximation in which the $nn$ pairing interaction is
provided by a realistic bare $nn$ potential fitted to scattering data, it is
demonstrated that the standard BCS theory fails in regions of neutron number
density where the pairing constant $\lambda$, depending crucially on density,
has a non-BCS negative sign. We are led to propose a non-BCS scenario for
pairing phenomena in neutron matter that involves the formation of a hidden
dineutron state. In low-density neutron matter where the pairing constant has
the standard BCS sign, two phases organized by pairing correlations are
possible and compete energetically: a conventional BCS phase and a dineutron
phase. In dense neutron matter, where $\lambda$ changes sign, only the
dineutron phase survives and exists until the critical density for termination
of pairing correlations is reached at approximately twice the neutron density
in heavy atomic nuclei.",1310.5342v1
2016-07-12,Volume and surface contributions to the nuclear symmetry energy within the coherent density fluctuation model,"The volume and surface components of the nuclear symmetry energy (NSE) and
their ratio are calculated within the coherent density fluctuation model
(CDFM). The estimations use the results of the model for the NSE in finite
nuclei based on the Brueckner energy-density functional for nuclear matter. In
addition, we present results for the NSE and its volume and surface
contributions obtained by using the Skyrme energy-density functional. The CDFM
weight function is obtained using the proton and neutron densities from the
self-consistent HF+BCS method with Skyrme interactions. We present and discuss
the values of the volume and surface contributions to the NSE and their ratio
obtained for the Ni, Sn, and Pb isotopic chains studying their isotopic
sensitivity. The results are compared with estimations of other approaches
which have used available experimental data on binding energies, neutron-skin
thicknesses, excitation energies to isobaric analog states (IAS) and also with
results of other theoretical methods.",1607.03325v2
2016-10-27,Partition-DFT on the Water Dimer,"As is well known, the ground-state symmetry group of the water dimer switches
from its equilibrium $C_{s}$-character to $C_{2h}$-character as the distance
between the two oxygen atoms of the dimer decreases below $R_{\rm O-O}\sim 2.5$
\AA{}. For a range of $R_{\rm O-O}$ between 1 and 5 \AA{}, and for both
symmetries, we apply Partition Density Functional Theory (PDFT) to find the
unique monomer densities that sum to the correct dimer densities while
minimizing the sum of the monomer energies. We calculate the work involved in
deforming the isolated monomer densities and find that it is slightly larger
for the $C_s$ geometry for all $R_{\rm O-O}$. We discuss how the PDFT densities
and the corresponding partition potentials support the orbital-interaction
picture of hydrogen-bond formation.",1610.08787v1
2018-06-21,Discommensuration-enhanced superconductivity in the charge density wave phases of transition-metal dichalcogenides,"We introduce a McMillan-Ginzburg-Landau theory to describe the cooperative
coexistence of charge-density and superconducting order in two-dimensional
crystals. With a free-energy that explicitly accounts for the competition
between commensurate and incommensurate ground states, we are able to map the
transition between these phases and monitor the development of
discommensurations in the near-commensurate regime. Attributing the enhancement
of superconducting order to density-wave fluctuations, we propose a coupling
scheme that yields a phase diagram in qualitative agreement with experiments in
conducting transition metal dichalcogenides. The model predicts the development
of non-uniform superconductivity similar to that arising from a pair-density
wave, with a spatial texture driven by the underlying charge-density wave
fluctuations.",1806.08064v2
2020-07-18,Tracking-by-Counting: Using Network Flows on Crowd Density Maps for Tracking Multiple Targets,"State-of-the-art multi-object tracking~(MOT) methods follow the
tracking-by-detection paradigm, where object trajectories are obtained by
associating per-frame outputs of object detectors. In crowded scenes, however,
detectors often fail to obtain accurate detections due to heavy occlusions and
high crowd density. In this paper, we propose a new MOT paradigm,
tracking-by-counting, tailored for crowded scenes. Using crowd density maps, we
jointly model detection, counting, and tracking of multiple targets as a
network flow program, which simultaneously finds the global optimal detections
and trajectories of multiple targets over the whole video. This is in contrast
to prior MOT methods that either ignore the crowd density and thus are prone to
errors in crowded scenes, or rely on a suboptimal two-step process using
heuristic density-aware point-tracks for matching targets.Our approach yields
promising results on public benchmarks of various domains including people
tracking, cell tracking, and fish tracking.",2007.09509v1
2018-08-03,Stochastic Expansions Including Random Inputs on the Unit Circle,"Stochastic expansion-based methods of uncertainty quantification, such as
polynomial chaos and separated representations, require basis functions
orthogonal with respect to the density of random inputs. Many modern
engineering problems employ stochastic circular quantities, which are defined
on the unit circle in the complex plane and characterized by probability
density functions on this periodic domain. Hence, stochastic expansions with
circular data require corresponding orthogonal polynomials on the unit circle
to allow for their use in uncertainty quantification. Rogers-Szego polynomials
enable uncertainty quantification for random inputs described by the wrapped
normal density. For the general case, this paper presents a framework for
numerically generating orthogonal polynomials as a function of the
distribution's characteristic function and demonstrates their use with the von
Mises density. The resulting stochastic expansions allow for estimating
statistics describing the posterior density using the expansion coefficients.
Results demonstrate the exponential convergence of these stochastic expansions
and apply the proposed methods to propagating orbit-state uncertainty with
equinoctial elements. The astrodynamics application of the theory improves
robustness and accuracy when compared to approximating angular quantities as
variables on the real line.",1808.01052v1
2016-08-21,Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in CuxTiSe2,"X-ray diffraction was employed to study the evolution of the charge density
wave (CDW) in CuxTiSe2 as a function of copper intercalation in order to
clarify the relationship between the CDW and superconductivity. The results
show a CDW incommensuration arising at an intercalation value coincident with
the onset of superconductivity at around x=0.055(5). Additionally, it was found
that the charge density wave persists to higher intercalant concentrations than
previously assumed, demonstrating that the CDW does not terminate inside the
superconducting dome. A charge density wave peak was observed in samples up to
x=0.091(6), the highest copper concentration examined in this study. The phase
diagram established in this work suggests that charge density wave
incommensuration may play a role in the formation of the superconducting state.",1608.05957v2
2019-03-05,Crowd Counting Using Scale-Aware Attention Networks,"In this paper, we consider the problem of crowd counting in images. Given an
image of a crowded scene, our goal is to estimate the density map of this
image, where each pixel value in the density map corresponds to the crowd
density at the corresponding location in the image. Given the estimated density
map, the final crowd count can be obtained by summing over all values in the
density map. One challenge of crowd counting is the scale variation in images.
In this work, we propose a novel scale-aware attention network to address this
challenge. Using the attention mechanism popular in recent deep learning
architectures, our model can automatically focus on certain global and local
scales appropriate for the image. By combining these global and local scale
attention, our model outperforms other state-of-the-art methods for crowd
counting on several benchmark datasets.",1903.02025v1
2019-03-25,CODA: Counting Objects via Scale-aware Adversarial Density Adaption,"Recent advances in crowd counting have achieved promising results with
increasingly complex convolutional neural network designs. However, due to the
unpredictable domain shift, generalizing trained model to unseen scenarios is
often suboptimal. Inspired by the observation that density maps of different
scenarios share similar local structures, we propose a novel adversarial
learning approach in this paper, i.e., CODA (\emph{Counting Objects via
scale-aware adversarial Density Adaption}). To deal with different object
scales and density distributions, we perform adversarial training with pyramid
patches of multi-scales from both source- and target-domain. Along with a
ranking constraint across levels of the pyramid input, consistent object counts
can be produced for different scales. Extensive experiments demonstrate that
our network produces much better results on unseen datasets compared with
existing counting adaption models. Notably, the performance of our CODA is
comparable with the state-of-the-art fully-supervised models that are trained
on the target dataset. Further analysis indicates that our density adaption
framework can effortlessly extend to scenarios with different objects.
\emph{The code is available at https://github.com/Willy0919/CODA.}",1903.10442v1
2019-04-11,Autoregressive Energy Machines,"Neural density estimators are flexible families of parametric models which
have seen widespread use in unsupervised machine learning in recent years.
Maximum-likelihood training typically dictates that these models be constrained
to specify an explicit density. However, this limitation can be overcome by
instead using a neural network to specify an energy function, or unnormalized
density, which can subsequently be normalized to obtain a valid distribution.
The challenge with this approach lies in accurately estimating the normalizing
constant of the high-dimensional energy function. We propose the Autoregressive
Energy Machine, an energy-based model which simultaneously learns an
unnormalized density and computes an importance-sampling estimate of the
normalizing constant for each conditional in an autoregressive decomposition.
The Autoregressive Energy Machine achieves state-of-the-art performance on a
suite of density-estimation tasks.",1904.05626v1
2019-06-17,Content-aware Density Map for Crowd Counting and Density Estimation,"Precise knowledge about the size of a crowd, its density and flow can provide
valuable information for safety and security applications, event planning,
architectural design and to analyze consumer behavior. Creating a powerful
machine learning model, to employ for such applications requires a large and
highly accurate and reliable dataset. Unfortunately the existing crowd counting
and density estimation benchmark datasets are not only limited in terms of
their size, but also lack annotation, in general too time consuming to
implement. This paper attempts to address this very issue through a content
aware technique, uses combinations of Chan-Vese segmentation algorithm,
two-dimensional Gaussian filter and brute-force nearest neighbor search. The
results shows that by simply replacing the commonly used density map generators
with the proposed method, higher level of accuracy can be achieved using the
existing state of the art models.",1906.07258v1
2020-06-22,Telescoping Density-Ratio Estimation,"Density-ratio estimation via classification is a cornerstone of unsupervised
learning. It has provided the foundation for state-of-the-art methods in
representation learning and generative modelling, with the number of use-cases
continuing to proliferate. However, it suffers from a critical limitation: it
fails to accurately estimate ratios p/q for which the two densities differ
significantly. Empirically, we find this occurs whenever the KL divergence
between p and q exceeds tens of nats. To resolve this limitation, we introduce
a new framework, telescoping density-ratio estimation (TRE), that enables the
estimation of ratios between highly dissimilar densities in high-dimensional
spaces. Our experiments demonstrate that TRE can yield substantial improvements
over existing single-ratio methods for mutual information estimation,
representation learning and energy-based modelling.",2006.12204v2
2020-11-07,Coarse- and Fine-grained Attention Network with Background-aware Loss for Crowd Density Map Estimation,"In this paper, we present a novel method Coarse- and Fine-grained Attention
Network (CFANet) for generating high-quality crowd density maps and people
count estimation by incorporating attention maps to better focus on the crowd
area. We devise a from-coarse-to-fine progressive attention mechanism by
integrating Crowd Region Recognizer (CRR) and Density Level Estimator (DLE)
branch, which can suppress the influence of irrelevant background and assign
attention weights according to the crowd density levels, because generating
accurate fine-grained attention maps directly is normally difficult. We also
employ a multi-level supervision mechanism to assist the backpropagation of
gradient and reduce overfitting. Besides, we propose a Background-aware
Structural Loss (BSL) to reduce the false recognition ratio while improving the
structural similarity to groundtruth. Extensive experiments on commonly used
datasets show that our method can not only outperform previous state-of-the-art
methods in terms of count accuracy but also improve the image quality of
density maps as well as reduce the false recognition ratio.",2011.03721v1
2021-04-21,Global Classical Solutions to the 3D Density-Dependent Viscosity Compressible Navier-Stokes Equations with Navier-Slip Boundary Condition in a Simply Connected Bounded Domain,"This paper concerns the global existence for classical solutions problem to
the 3D Density-Dependent Viscosity barotropic compressible Navier-Stokes in
$\Omega$ with slip boundary condition, where $\Omega$ is a simply connected
bounded $C^{\infty}$ domain in $\mathbb{R}^3$ and its boundary only has a
finite number of 2-dimensional connected components. By a series of a priori
estimates, we show that the classical solution to the system exists globally in
time under the assumption that the initial energy is suitably small. The
initial density of such a classical solution is allowed to have large
oscillations and contain vacuum states. We also adopt some new techniques and
methods to obtain necessary a priori estimates, especially the boundary
integral terms estimates. This is the first result concerning the global
existence of classical solutions to the compressible Navier-Stokes equations
with density containing vacuum initially and viscosity coefficients depending
on density for general 3D bounded smooth domains.",2104.10606v1
2021-06-10,Density matrix formulation of dynamical systems,"Physical systems that dissipate, mix and develop turbulence also irreversibly
transport statistical density. In statistical physics, laws for these processes
have a mathematical form and tractability that depends on whether the
description is classical or quantum mechanical. Here, we establish a theory for
density transport in any classical dynamical system that is analogous to the
density matrix formulation of quantum mechanics. Defining states in terms of a
classical density matrix leads to generalizations of Liouville's theorem and
Liouville's equation, establishing an alternative computationally-tractable
basis for nonequilibrium statistical mechanics. The formalism is complete with
classical commutators and anti-commutators that embed measures of local
instability and chaos and are directly related to Poisson brackets when the
dynamics are Hamiltonian. It also recovers the traditional Liouville equation
and the Liouville theorem by imposing trace preservation or Hamiltonian
dynamics. Applying to systems that are driven, transient, dissipative, regular,
and chaotic, this formalism has the potential for broad applications.",2106.05911v3
2022-11-15,LEAN-DMKDE: Quantum Latent Density Estimation for Anomaly Detection,"This paper presents an anomaly detection model that combines the strong
statistical foundation of density-estimation-based anomaly detection methods
with the representation-learning ability of deep-learning models. The method
combines an autoencoder, for learning a low-dimensional representation of the
data, with a density-estimation model based on random Fourier features and
density matrices in an end-to-end architecture that can be trained using
gradient-based optimization techniques. The method predicts a degree of
normality for new samples based on the estimated density. A systematic
experimental evaluation was performed on different benchmark datasets. The
experimental results show that the method performs on par with or outperforms
other state-of-the-art methods.",2211.08525v1
2023-04-11,Superadiabatic dynamical density functional study of Brownian hard-spheres in time-dependent external potentials,"Superadiabatic dynamical density functional theory (superadiabatic-DDFT), a
first-principles approach based on the inhomogeneous two-body correlation
functions, is employed to investigate the response of interacting Brownian
particles to time-dependent external driving. Predictions for the
superadiabatic dynamics of the one-body density are made directly from the
underlying interparticle interactions, without need for either adjustable fit
parameters or simulation input. The external potentials we investigate have
been chosen to probe distinct aspects of structural relaxation in dense,
strongly interacting liquid states. Nonequilibrium density profiles predicted
by the superadiabatic theory are compared with those obtained from both
adiabatic DDFT and event-driven Brownian dynamics simulation. Our findings show
that superadiabatic-DDFT accurately predicts the time-evolution of the one-body
density.",2304.05248v2
2023-04-20,"Atoms, dimers, and nanoparticles from orbital-free density-potential functional theory","Density-potential functional theory (DPFT) is an alternative formulation of
orbital-free density functional theory that may be suitable for modeling the
electronic structure of large systems. To date, DPFT has been applied mainly to
quantum gases in one- and two dimensional settings. In this work, we study the
performance of DPFT when applied to real-life systems: atoms, dimers, and
nanoparticles. We build on systematic Suzuki-Trotter factorizations of the
quantum-mechanical propagator and on the Wigner function formalism,
respectively, to derive nonlocal as well as semilocal functional approximations
in complete analogy to their well-established lower-dimensional versions --
without resorting to system-specific approximations or ad-hoc measures of any
kind. The cost for computing the associated semiclassical ground-state
single-particle density scales (quasi-)linearly with particle number. We
illustrate that the developed density formulae become relatively more accurate
for larger particle numbers, can be improved systematically, are quite
universally applicable, and, hence, may offer alternatives to existing
orbital-free methods for mesoscopic quantum systems.",2304.10059v1
2023-10-28,Ultralong-term high-density data storage with atomic defects in SiC,"There is an urgent need to increase the global data storage capacity, as
current approaches lag behind the exponential growth of data generation driven
by the Internet, social media and cloud technologies. In addition to increasing
storage density, new solutions should provide long-term data archiving that
goes far beyond traditional magnetic memory, optical disks and solid-state
drives. Here, we propose a concept of energy-efficient, ultralong, high-density
data archiving based on optically active atomic-size defects in a radiation
resistance material, silicon carbide (SiC). The information is written in these
defects by focused ion beams and read using photoluminescence or
cathodoluminescence. The temperature-dependent deactivation of these defects
suggests a retention time minimum over a few generations under ambient
conditions. With near-infrared laser excitation, grayscale encoding and
multi-layer data storage, the areal density corresponds to that of Blu-ray
discs. Furthermore, we demonstrate that the areal density limitation of
conventional optical data storage media due to the light diffraction can be
overcome by focused electron-beam excitation.",2310.18843v1
2024-01-04,Effective Single Particle Theory for Active System,"A collection of active self-propelled particles exhibits motility-induced
phase separation at a packing density much lower than the corresponding
equilibrium counterpart. Unlike the equilibrium counterpart, the steady state
in a system of active particles is characterized by the continuous association
and dissociation of clusters. In this work, we propose an effective
single-particle model in which the effect of neighboring particles is replaced
by a time-dependent local density around the particle, having a unique
auto-correlation function. Such that the local density around the particles has
a memory with a finite correlation time. The correlation time increases with
packing density. Further, by using the same local density and its correlation
function, we solve the system of many particles and compare the results with
numerical simulations. Our proposed analytical theory matches well with the
numerical study.",2401.02247v1
2024-02-05,Fluidization and anomalous density fluctuations in epithelial tissues with pulsating activity,"Cells not only can have self-motility by crawling, but also are capable of
other types of active motions like periodic contraction or pulsation. In this
work, by using the Voronoi cell model, we show how this non-motility activity
affects the structure, dynamic and density fluctuations of cellular monolayers.
We found that random cell pulsation can fluidize solid epithelial tissues,
resulting in a \emph{hyperuniform} fluid state, while pulsation synchronization
inhibits the fluidity, causes a reversed solidification. We prove this
solidification is BKT-type transition, characterized by strong density/dynamic
heterogeneity arising from the creation of topological defects in the pulsating
phase space. The magnitude and length scale of density heterogeneity diverge as
the pulsating period increases, resulting in an opposite \emph{giant} density
fluctuation. Our findings accord with recent experimental observations and can
be quantitatively explained by a proposed fluctuating hydrodynamic theory.",2402.02981v1
2024-03-29,Impact of solar wind disappearance event on Martian nightside ionospheric species: First results,"For the first time, we report the impact of a rarest solar wind phenomenon,
i.e., disappearing solar wind (DSW) event on the Martian nightside ionosphere
using MAVEN spacecraft datasets. During an extremely low solar wind density
event, the nightside ionospheric densities particularly above 200 km, including
electrons and ions (NO+, O2+, CO2+, C+, N+, O+, and OH+) experience significant
enhancement at a fixed altitude. The electron and ion densities increase by a
factor of ~2.5 and 10-67, respectively, compared to average quiet time. The
increased plasma density, during DSW, suggests the expansion of the Martian
ionosphere under extremely low solar wind dynamic pressure (~1.4 $\times
10^{-11}$ Pa) contrasting with nightside ionospheric thermal pressure
(>$10^{-10}$ Pa). Further, the day-to-night plasma transport through
cross-terminator magnetic topology may also be a contributing factor, causing
the increased nightside ionospheric density. Therefore, this study sheds light
on an unusual extreme state of the Mars-solar wind interaction.",2403.20003v1
2015-05-19,The Dense Matter Equation of State from Neutron Star Radius and Mass Measurements,"We present a comprehensive study of spectroscopic radius measurements of
twelve neutron stars obtained during thermonuclear bursts or in quiescence. We
incorporate, for the first time, a large number of systematic uncertainties in
the measurement of the apparent angular sizes, Eddington fluxes, and distances,
in the composition of the interstellar medium, and in the flux calibration of
X-ray detectors. We also take into account the results of recent theoretical
calculations of rotational effects on neutron star radii, of atmospheric
effects on surface spectra, and of relativistic corrections to the Eddington
critical flux. We employ Bayesian statistical frameworks to obtain neutron star
radii from the spectroscopic measurements as well as to infer the equation of
state from the radius measurements. Combining these with the results of
experiments in the vicinity of nuclear saturation density and the observations
of ~2 Msun neutron stars, we place strong and quantitative constraints on the
properties of the equation of state between approximately 2-8 times the nuclear
saturation density. We find that around M=1.5 Msun, the preferred equation of
state predicts radii between 10.1 - 11.1 km. When interpreting the pressure
constraints in the context of high density equations of state based on
interacting nucleons, our results suggest a relatively weak contribution of the
three-body interaction potential.",1505.05155v2
2015-02-06,Stochastic Newton Sampler: R Package sns,"The R package sns implements Stochastic Newton Sampler (SNS), a
Metropolis-Hastings Monte Carlo Markov Chain algorithm where the proposal
density function is a multivariate Gaussian based on a local, second-order
Taylor series expansion of log-density. The mean of the proposal function is
the full Newton step in Newton-Raphson optimization algorithm. Taking advantage
of the local, multivariate geometry captured in log-density Hessian allows SNS
to be more efficient than univariate samplers, approaching independent sampling
as the density function increasingly resembles a multivariate Gaussian. SNS
requires the log-density Hessian to be negative-definite everywhere in order to
construct a valid proposal function. This property holds, or can be easily
checked, for many GLM-like models. When initial point is far from density peak,
running SNS in non-stochastic mode by taking the Newton step, augmented with
with line search, allows the MCMC chain to converge to high-density areas
faster. For high-dimensional problems, partitioning of state space into
lower-dimensional subsets, and applying SNS to the subsets within a Gibbs
sampling framework can significantly improve the mixing of SNS chains. In
addition to the above strategies for improving convergence and mixing, sns
offers diagnostics and visualization capabilities, as well as a function for
sample-based calculation of Bayesian predictive posterior distributions.",1502.02008v1
2022-02-10,Introducing screening in one-body density matrix functionals: impact on the Extended Koopmans' Theorem's charged excitations of model systems,"In this work we get insight into the impact of reduced density matrix
functionals on the quality of removal/addition energies obtained using the
Extended Koopmans' Theorem (EKT). Within reduced density matrix functional
theory (RDMFT) the EKT approach reduces to a matrix diagonalization, whose
ingredients are the one- and two-body reduced density matrices. A striking
feature of the EKT within RDMFT is that it opens a band gap, although too
large, in strongly correlated materials, which are a challenge for
state-of-the-art methods such as GW . Using the one-dimensional Hubbard model
and the homogeneous electron gas as test cases, we find that: i) with exact or
very accurate density matrices the EKT systematically overestimates the band
gap in the Hubbard model and the bandwidth in the homogeneous electron gas; ii)
with approximate density matrices, instead, the EKT can benefit from error
cancellation. In particular we test a new approximation which combines RPA
screening with the Power functional (PF) approximation to the two-body reduced
density matrix introduced by Sharma et al. [Phys. Rev. B 78, 201103(R) (2008)].
An important feature of this approximation is that it reduces the EKT band gap
in the studied models; it can hence be a promising approximation for correcting
the EKT band-gap overestimation in strongly correlated materials.",2202.04946v1
2023-04-27,Sound velocity peak and conformality in isospin QCD,"We study zero temperature equations of state (EOS) in isospin QCD within a
quark-meson model which is renormalizable and hence eliminates high density
artifacts in models with the ultraviolet cutoff (e.g., NJL models). The model
exhibits a crossover transition of pion condensations from the
Bose-Einstein-Condensation regime at low density to the
Bardeen-Cooper-Schrieffer regime at high density. The EOS stiffens quickly and
approaches the quark matter regime at density significantly less than the
density for pions to spatially overlap. The sound velocity develops a peak in
the crossover region, and then gradually relaxes to the conformal value $1/3$
from above, in contrast to the perturbative QCD results which predicts the
approach from below. In the context of QCD computations, this opposite trend is
in part due to the lack of gluon exchanges in our model, and also due to the
non-perturbative power corrections arising from the condensates. We argue that
with large power corrections the trace anomaly can be negative. In quantitative
level, our EOS is consistent with the lattice results in the BEC regime but
begins to get stiffer at higher density. The sound velocity peak also appears
at higher density. The BCS gap in our model is $\Delta \simeq 300$ MeV in the
quark matter domain, and naive application of the BCS relation for the critical
temperature $T_c \simeq 0.57\Delta$ yields the estimate $T_c \simeq 170$ MeV,
in good agreement with the lattice data.",2304.13920v4
2024-03-29,MCNet: A crowd denstity estimation network based on integrating multiscale attention module,"Aiming at the metro video surveillance system has not been able to
effectively solve the metro crowd density estimation problem, a Metro Crowd
density estimation Network (called MCNet) is proposed to automatically classify
crowd density level of passengers. Firstly, an Integrating Multi-scale
Attention (IMA) module is proposed to enhance the ability of the plain
classifiers to extract semantic crowd texture features to accommodate to the
characteristics of the crowd texture feature. The innovation of the IMA module
is to fuse the dilation convolution, multiscale feature extraction and
attention mechanism to obtain multi-scale crowd feature activation from a
larger receptive field with lower computational cost, and to strengthen the
crowds activation state of convolutional features in top layers. Secondly, a
novel lightweight crowd texture feature extraction network is proposed, which
can directly process video frames and automatically extract texture features
for crowd density estimation, while its faster image processing speed and fewer
network parameters make it flexible to be deployed on embedded platforms with
limited hardware resources. Finally, this paper integrates IMA module and the
lightweight crowd texture feature extraction network to construct the MCNet,
and validate the feasibility of this network on image classification dataset:
Cifar10 and four crowd density datasets: PETS2009, Mall, QUT and SH_METRO to
validate the MCNet whether can be a suitable solution for crowd density
estimation in metro video surveillance where there are image processing
challenges such as high density, high occlusion, perspective distortion and
limited hardware resources.",2403.20173v1
2023-03-13,Quark pair angular correlations in the proton: entropy versus entanglement negativity,"Two-particle correlations in the proton on the light-front are described by a
mixed density matrix obtained by tracing over all other, unobserved, degrees of
freedom. We quantify genuinely quantum quark azimuthal correlations in terms of
the entanglement negativity measure of Quantum Information Theory. While the
two-quark state in color space is one of high entropy and weak quantum
correlation, we find that a standard three-quark model wave function from the
literature predicts an azimuthally correlated state of low entropy and high
entanglement negativity. Low entropy is consistent with expectations for many
colors (at fixed 't Hooft coupling $g^2 N_c$) but high negativity indicates
substantial two-particle quantum correlations at $N_c=3$. Suppressing quantum
correlations associated with entanglement negativity strongly modifies quark
pair azimuthal moments $\langle \zeta^n \rangle$, $\zeta = \exp(i
(\phi_1-\phi_2))$, intrinsic to the proton state.
  We also describe how to account for the leading ${\cal O}(g^2)$ correction to
the density matrix from light-cone perturbation theory which is due to the
presence (or exchange) of a gluon in the proton. This correction increases the
entropy and reduces the negativity of the density matrix for quark pair
azimuthal correlations. Hence, the entanglement negativity measure may provide
novel insight into the structure of the proton state of QCD.",2303.07408v2
2015-02-27,Invertibility of retarded response functions for Laplace transformable potentials: application to one-body reduced density matrix functional theory,"A theorem for the invertibility of arbitrary response functions is presented
under the following conditions: the time-dependence of the potentials should be
Laplace transformable and the initial state should be a ground state, though it
might be degenerate. This theorem provides a rigorous foundation for all
density-functional-like theories in the time-dependent linear response regime.
Especially for time-dependent one-body reduced density matrix (1RDM) functional
theory this is an important step forward, since a solid foundation has
currently been lacking. The theorem is equally valid for static response
functions in the non-degenerate case, so can be used to characterize the
uniqueness of the potential in the ground state version of the corresponding
density-functional-like theory. Such a classification of the uniqueness of the
non-local potential in ground state 1RDM functional theory has been lacking for
decades. With the aid of presented invertibility theorem presented here, a
complete classification of the non-uniqueness of the non-local potential in
1RDM functional theory can be given for the first time.",1502.07914v5
2022-02-25,Modelling Magnetic Multipolar Phases in Density Functional Theory,"Multipolar magnetic phases in correlated insulators represent a great
challenge for Density Functional Theory (DFT) due to the coexistence of
intermingled interactions, typically spin-orbit coupling, crystal field and
complex non-collinear and high-rank inter-site exchange, creating a complected
configurational space with multiple minima. Though the +U correction to DFT
allows, in principle, the modelling of such magnetic ground states, its results
strongly depend on the initially symmetry breaking, constraining the nature of
order parameter in the converged DFT+U solution. As a rule, DFT+U calculations
starting from a set of initial on-site magnetic moments result in a
conventional dipolar order. A more sophisticated approach is clearly needed in
the case of magnetic multipolar ordering, which is revealed by a null integral
of the magnetization density over spheres centered on magnetic atoms, but with
non-zero local contributions. Here we show how such phases can be efficiently
captured using an educated constrained initialisation of the onsite density
matrix, which is derived from the multipolar-ordered ground state of an ab
initio effective Hamiltonian. Various properties of such exotic ground states,
like their one-electron spectra, become therefore accessible by all-electron
DFT+U methods. We assess the reliability of this procedure on the
Ferro-Octupolar ground state recently predicted in Ba$_2$MOsO$_6$ (M = Ca, Mg,
Zn) [Phys. Rev. Lett. 127, 237201 (2021)]",2202.12920v1
2023-06-01,A sparse approximation of the Lieb functional with moment constraints,"The aim of this paper is to present new sparsity results about the so-called
Lieb functional, which is a key quantity in Density Functional Theory for
electronic structure calculations for molecules. The Lieb functional was
actually shown by Lieb to be a convexification of the so-called L\'evy-Lieb
functional. Given an electronic density for a system of $N$ electrons, which
may be seen as a probability density on $\mathbb{R}^3$, the value of the Lieb
functional for this density is defined as the solution of a quantum
multi-marginal optimal transport problem, which reads as a minimization problem
defined on the set of trace-class operators acting on the space of electronic
wave-functions that are anti-symmetric $L^2$ functions of $\mathbb{R}^{3N}$,
with partial trace equal to the prescribed electronic density. We introduce a
relaxation of this quantum optimal transport problem where the full partial
trace constraint is replaced by a finite number of moment constraints on the
partial trace of the set of operators. We show that, under mild assumptions on
the electronic density, there exist sparse minimizers to the resulting moment
constrained approximation of the Lieb (MCAL) functional that read as operators
with rank at most equal to the number of moment constraints. We also prove
under appropriate assumptions on the set of moment functions that the value of
the MCAL functional converges to the value of the exact Lieb functional as the
number of moments go to infinity. We also prove some rates of convergence on
the associated approximation of the ground state energy. We finally study the
mathematical properties of the associated dual problem.",2306.00806v2
2006-01-04,$\bar K$ nuclear bound states in a dynamical model,"A comprehensive data base of K- atom level shifts and widths is re-analyzed
in order to study the density dependence of the Kbar-nuclear optical potential.
Significant departure from a t*rho form is found only for nuclear densities
about and less than 20% of nuclear-matter density, and extrapolation to
nuclear-matter density yields an attractive potential, about 170 MeV deep.
Partial restoration of chiral symmetry compatible with pionic atoms and
low-energy pion-nuclear data plays no role at the relevant low-density regime,
but this effect is not ruled out at high densities. Kbar-nuclear bound states
are generated across the periodic table self consistently, using a relativistic
mean-field model Lagrangian which couples the Kbar to the scalar and vector
meson fields mediating the nuclear interactions. The reduced phase space
available for Kbar absorption from these bound states is taken into account by
adding an energy-dependent imaginary term which underlies the corresponding
Kbar-nuclear level widths, with a strength required by fits to the atomic data.
Substantial polarization of the core nucleus is found for light nuclei, and the
binding energies and widths calculated in this dynamical model differ
appreciably from those calculated for a static nucleus. A wide range of binding
energies is spanned by varying the Kbar couplings to the meson fields. Our
calculations provide a lower limit of Gamma(Kbar) = 50 +/- 10 MeV on the width
of nuclear bound states for Kbar binding energy in the range B(Kbar) = 100 -
200 MeV. Comments are made on the interpretation of the FINUDA experiment at
DAFNE, Frascati, which claimed evidence for deeply bound (K- pp) states in
light nuclei.",0601009v2
2013-11-19,Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum,"We study the spontaneous parity breaking and generating of Hall viscosity and
angular momentum in holographic p+ip model, which can describe strongly-coupled
chiral superfluid states in many quantum systems. The dual gravity theory, an
SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant
but allows a black hole solution with vector hair corresponding to a
parity-broken superfluid state. We show that this state possesses a
non-vanishing parity-odd transport coefficient -- Hall viscosity -- and an
angular momentum density. We first develop an analytic method to solve this
model near the critical regime and to take back-reactions into account. Then we
solve the equation for the tensor mode fluctuations and obtain the expression
for Hall viscosity via Kubo formula. We also show that a non-vanishing angular
momentum density can be obtained through the vector mode fluctuations and the
corresponding boundary action. We give analytic results of both Hall viscosity
and angular momentum density near the critical regime in terms of physical
parameters. The near-critical behavior of Hall viscosity is different from that
obtained from a gravitational Chern-Simons model. We find that the magnitude of
Hall viscosity to angular momentum density ratio is numerically consistent with
being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in
agreement with previous results obtained for various quantum fluid systems and
from effective theory approaches. In addition, we find the shear viscosity to
entropy density ratio remains above the universal bound.",1311.4882v2
2016-03-17,Ghost interaction correction in ensemble density-functional theory for excited states with and without range separation,"Ensemble density-functional theory (eDFT) suffers from the so-called ""ghost
interaction"" error when approximate exchange-correlation functionals are used.
In this work, we present a rigorous ghost interaction correction (GIC) scheme
in the context of range-separated eDFT. The method relies on an exact
decomposition of the ensemble short-range exchange-correlation energy into a
multideterminantal exact exchange term, which involves the long-range
interacting ensemble density matrix instead of the Kohn--Sham (KS) one, and a
complementary density-functional correlation energy. A generalized adiabatic
connection formula is derived for the latter. In order to perform practical
calculations, the complementary correlation functional has been simply modeled
by its ground-state local density approximation (LDA) while long-range
interacting ground- and excited-state wavefunctions have been obtained
self-consistently by combining a long-range configuration interaction
calculation with a short-range LDA potential. We show that GIC reduces the
curvature of approximate range-separated ensemble energies drastically while
providing considerably more accurate excitation energies, even for
charge-transfer and double excitations. Interestingly, the method performs well
also in the context of standard KS-eDFT, which is recovered when the
range-separation parameter is set to zero.",1603.05385v2
2023-03-19,High-density reflection spectroscopy of black hole X-ray binaries in the hard state,"We present a high-density relativistic reflection analysis of 21 spectra of
six black hole X-ray binaries in the hard state with data from \textit{NuSTAR}
and \textit{Swift}. We find that 76\% of the observations in our sample require
a disk density higher than the 10$^{15}$~cm$^{-3}$ assumed in the previous
reflection analysis. Compared with the measurements from active galactic
nuclei, stellar mass black holes have higher disk densities. Our fits indicate
that the inner disk radius is close to the innermost stable circular orbit in
the hard state. The coronal temperatures are significantly lower than the
prediction of a purely thermal plasma, which can be explained with a hybrid
plasma model. If the disk density is fixed at 10$^{15}$~cm$^{-3}$, the disk
ionization parameter would be overestimated while the inner disk radius is
unaffected.",2303.10593v2
2007-07-14,Dineutron structure in $^{8}$He,"The ground and excited states of $^{8}$He were investigated with a method of
antisymmetrized molecular dynamics(AMD). We adopted effective nuclear
interactions which systematically reproduce the binding energies of $^4$He,
$^6$He and $^8$He. The ground state of $^8$He has both the $j$-$j$ coupling
feature($p_{3/2}$ closure) and the $L$-$S$ coupling feature($^4$He$+2n+2n$)
with a slight tail of dineutron at the long distance region. The theoretical
results give an indication of the $0^+_2$ state with dineutron gas-like
structure. The dineutron structure, $^4$He+$2n$+$2n$, of this state is similar
to the $3\alpha$-cluster structure of the $^{12}$C($0^+_2$) state which has
been interpreted as an $\alpha$ condensate state. Since the $^8$He($0^+_2$)
state has a significant overlap with the dineutron condensate wave function
where two dineutrons are moving in $S$ wave around the $\alpha$ core with a
dilute density, we suggest that this theoretically predicted $0^+_2$ state is a
candidate of the dineutron condensate state.",0707.2120v1
2010-01-19,Ground-state phase diagram of the two-dimensional t-J model,"The ground-state phase diagram of the two-dimensional t-J model is
investigated in the context of the tensor network algorithm in terms of the
graded Projected Entangled-Pair State representation of the ground-state wave
functions. There is a line of phase separation between the Heisenberg
anti-ferromagnetic state without hole and a hole-rich state. For both J=0.4t
and J=0.8t, a systematic computation is performed to identify all the competing
ground states for various dopings. It is found that, besides a possible
Nagaoka's ferromagnetic state, the homogeneous regime consists of four
different phases: one phase with charge and spin density wave order coexisting
with a p_x (p_y)-wave superconducting state, one phase with the symmetry mixing
of d+s-wave superconductivity in the spin-singlet channel and p_x (p_y)-wave
superconductivity in the spin-triplet channel in the presence of an
anti-ferromagnetic background, one superconducting phase with extended s-wave
symmetry, and one superconducting phase with p_x (p_y)-wave symmetry in a
ferromagnetic background.",1001.3343v1
2010-07-18,Realization of Quantum State Privacy Amplification in a Nuclear Magnetic Resonance Quantum System,"Quantum state privacy amplification (QSPA) is the quantum analogue of
classical privacy amplification. If the state information of a series of single
particle states has some leakage, QSPA reduces this leakage by condensing the
state information of two particles into the state of one particle. Recursive
applications of the operations will eliminate the quantum state information
leakage to a required minimum level. In this paper, we report the experimental
implementation of a quantum state privacy amplification protocol in a nuclear
magnetic resonance system. The density matrices of the states are constructed
in the experiment, and the experimental results agree with theory well.",1007.2975v1
2016-01-12,Exact results for Schrödinger cats in driven-dissipative systems and their feedback control,"In quantum optics, photonic Schr\""odinger cats are superpositions of two
coherent states with opposite phases and with a significant number of photons.
Recently, these states have been observed in the transient dynamics of
driven-dissipative resonators subject to engineered two-photon processes. Here
we present an exact analytical solution of the steady-state density matrix for
this class of systems, including one-photon losses, which are considered
detrimental for the achievement of cat states. We demonstrate that the unique
steady state is a statistical mixture of two cat-like states with opposite
parity, in spite of significant one-photon losses. The transient dynamics to
the steady state depends dramatically on the initial state and can pass through
a metastable regime lasting orders of magnitudes longer than the photon
lifetime. By considering individual quantum trajectories in photon-counting
configuration, we find that the system intermittently jumps between two cats.
Finally, we propose and study a feedback protocol based on this behaviour to
generate a pure cat-like steady state.",1601.02861v2
2020-01-10,Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator: The Majorana bound state,"By analytically solving the Bogoliubov-de Gennes equations we study the
fermion bound states at the center of the core of a vortex in a two-dimensional
superconductor. We consider three kinds of 2D superconducting models: (a) a
standard type II superconductor in the mixed state with low density of vortex
lines, (b) a superconductor with strong spin-orbit coupling locking the spin
parallel to the momentum and (c) a superconductor with strong spin-orbit
coupling locking the spin perpendicular to the momentum. The 2D superconducting
states are induced via proximity effect between an $s$-wave superconductor and
the surface states of a strong topological insulator. In case (a) the energy
gap for the excitations is of order $\Delta_{\infty}^2/(2E_F)$, while for cases
(b) and (c) a zero-energy Majorana state arises together with an equally spaced
($\Delta^2_{\infty}/E_F$) sequence of fermion excitations. The spin-momentum
locking is key to the formation of the Majorana state. We present analytical
expressions for the energy spectrum and the wave functions.",2001.03666v2
2022-03-10,Dynamical steady-states of active colloids interacting via chemical fields,"We study the dynamical steady-states of a monolayer of chemically active
self-phoretic colloids as a function of packing fraction and self-propulsion
speed by means of Brownian dynamics simulations. We focus on the case that a
chemical field induces competing attractive positional and repulsive
orientational interactions. Analyzing the distribution of cluster size and
local density as well as the hexatic order parameter, we distinguish four
distinct dynamical states which include collapsed, active gas, dynamical
clustering, and motility-induced phase-separated states. The long-range
chemical field-induced interactions shift the onset of motility-induced phase
separation (MIPS) to very low packing fractions at intermediate self-propulsion
speeds. We also find that the fraction of particles in the largest clusters is
a suitable order parameter characterizing the dynamical phase transitions from
an active gas or dynamical clustering steady-state to a phase-separated state
upon increase of the packing fraction. The order parameter changes
discontinuously when going from an active gas to a MIPS-like state at
intermediate self-propulsion speeds, whereas it changes continuously at larger
activities where the system undergoes a transition from a dynamical clustering
state to MIPS-like state.",2203.05213v1
2024-02-14,Replica topological order in quantum mixed states and quantum error correction,"Topological phases of matter offer a promising platform for quantum
computation and quantum error correction. Nevertheless, unlike its counterpart
in pure states, descriptions of topological order in mixed states remain
relatively under-explored. Our work give two definitions for replica
topological order in mixed states, which involve $n$ copies of density matrices
of the mixed state. Our framework categorizes topological orders in mixed
states as either quantum, classical, or trivial, depending on the type of
information that can be encoded. For the case of the toric code model in the
presence of decoherence, we associate for each phase a quantum channel and
describes the structure of the code space. We show that in the
quantum-topological phase, there exists a postselection-based error correction
protocol that recovers the quantum information, while in the
classical-topological phase, the quantum information has decohere and cannot be
fully recovered. We accomplish this by describing the mixed state as a
projected entangled pairs state (PEPS) and identifying the symmetry-protected
topological order of its boundary state to the bulk topology. We discuss the
extent that our findings can be extrapolated to $n \to 1$ limit.",2402.09516v1
2019-10-24,The theoretical direct-band-gap optical gain of Germanium nanowires,"We calculate the electronic structures of Germanium nanowires by taking the
effective-mass theory. The electron and hole states at the G-valley are studied
via the eight-band k.p theory. For the [111] L-valley, we expand the envelope
wave function using Bessel functions to calculate the energies of the electron
states for the first time. The results show that the energy dispersion curves
of electron states at the L-valley are almost parabolic irrespective of the
radius of Germanium nanowires. Based on the electronic structures, the density
of states of Germanium nanowires are also obtained, and we find that the
conduction band density of states mostly come from the electron states at the
L-valley because of the eight equivalent degenerate L points in Germanium.
Furthermore, the optical gain spectra of Germanium nanowires are investigated.
The calculations show that there are no optical gain along z direction even
though the injected carrier density is 4x1019 cm-3 when the doping
concentration is zero, and a remarkable optical gain can be obtained when the
injected carrier density is close to 1x1020 cm-3, since a large amount of
electrons will prefer to occupy the low-energy L-valley. In this case, the
negative optical gain will be encountered considering free-carrier absorption
loss as the increase of the diameter. We also investigate the optical gain
along z direction as functions of the doping concentration and injected carrier
density for the doped Germanium nanowires. When taking into account
free-carrier absorption loss, the calculated results show that a positive net
peak gain is most likely to occur in the heavily doped nanowires with smaller
diameters. Our theoretical studies are valuable in providing a guidance for the
applications of Germanium nanowires in the field of microelectronics and
optoelectronics.",1910.10957v1
2008-09-05,Reconstruction of non-classical cavity field states with snapshots of their decoherence,"The state of a microscopic system encodes its complete quantum description,
from which the probabilities of all measurement outcomes are inferred. Being a
statistical concept, the state cannot be obtained from a single system
realization. It can be reconstructed from an ensemble of copies, by performing
measurements on different realizations. Reconstructing the state of a set of
trapped particles shielded from their environment is an important step for the
investigation of the quantum to classical boundary. While trapped atom state
reconstructions have been achieved, it is challenging to perform similar
experiments with trapped photons which require cavities storing light for very
long times. Here, we report the complete reconstruction and pictorial
representation of a variety of radiation states trapped in a cavity in which
several photons survive long enough to be repeatedly measured. Information is
extracted from the field by atoms crossing the cavity one by one. We exhibit a
gallery of pictures featuring coherent states, Fock states with a definite
photon number and Schrodinger cat states which are superpositions of coherent
states with different phases. These states are equivalently represented by
their density matrices in the photon-number basis or by their Wigner functions,
which are distributions of the field complex amplitude. Quasi-classical
coherent states have a Gaussian-shaped Wigner function while Fock and
Schrodinger cat Wigner functions show oscillations and negativities revealing
quantum interferences. Cavity damping induces decoherence which quickly washes
out the Wigner functions oscillations. We observe this process and realize
movies of decoherence by reconstructing snapshots of Schrodinger cat states at
successive times.",0809.1064v1
2015-05-26,Quantum state of the black hole interior,"If a black hole (BH) is initially in an approximately pure state and it
evaporates by a unitary process, then the emitted radiation will be in a highly
quantum state. As the purifier of this radiation, the state of the BH interior
must also be in some highly quantum state. So that, within the interior region,
the mean-field approximation cannot be valid and the state of the BH cannot be
described by some semiclassical metric. On this basis, we model the state of
the BH interior as a collection of a large number of excitations that are
packed into closely spaced but single-occupancy energy levels; a sort-of ""Fermi
sea"" of all light-enough particles. This highly quantum state is surrounded by
a semiclassical region that lies close to the horizon and has a non-vanishing
energy density. It is shown that such a state looks like a BH from the outside
and decays via gravitational pair production in the near-horizon region at a
rate that agrees with the Hawking rate. We also consider the fate of a
classical object that has passed through to the BH interior and show that, once
it has crossed over the near-horizon threshold, the object meets its demise
extremely fast. This result cannot be attributed to a ""firewall"", as the trauma
to the in-falling object only begins after it has passed through the
near-horizon region and enters a region where semiclassical spacetime ends but
the energy density is still parametrically smaller than Planckian.",1505.07131v1
2019-06-11,Phase Crystals,"Superconductivity owes its properties to the phase of the electron pair
condensate that breaks the $U(1)$ symmetry. In the most traditional ground
state, the phase is uniform and rigid. The normal state can be unstable towards
special inhomogeneous superconducting states: the Abrikosov vortex state, and
the Fulde-Ferrell-Larkin-Ovchinnikov state. Here we show that the phase-uniform
superconducting state can go into a fundamentally different and more ordered
non-uniform ground state, that we denote as a phase crystal. The new state
breaks translational invariance through formation of a spatially periodic
modulation of the phase, manifested by unusual superflow patterns and
circulating currents, that also break time-reversal symmetry. We list the
general conditions needed for realization of phase crystals. Using microscopic
theory we then derive an analytic expression for the superfluid density tensor
for the case of a non-uniform environment in a semi-infinite superconductor. We
demonstrate how the surface quasiparticle states enter the superfluid density
and identify phase crystallization as the main player in several previous
numerical observations in unconventional superconductors, and predict existence
of a similar phenomenon in superconductor-ferromagnetic structures. This
analytic approach provides a new unifying aspect for the exploration of
boundary-induced quasiparticles and collective excitations in superconductors.
More generally, we trace the origin of phase crystallization to non-local
properties of the gradient energy, which implies existence of similar
pattern-forming instabilities in many other contexts.",1906.04793v2
2021-06-12,"Quantum coherence, correlations and nonclassical states in the two-qubit Rabi model with parametric oscillator","Quantum coherence and quantum correlations are studied in the strongly
interacting system composed of two qubits and an oscillator with the presence
of a parametric medium. To analytically solve the system, we employ the
adiabatic approximation approach. It assumes each qubit's characteristic
frequency is substantially lower than the oscillator frequency. To validate our
approximation, a good agreement between the calculated energy spectrum of the
Hamiltonian with its numerical result is presented. The time evolution of the
reduced density matrices of the two-qubit and the oscillator subsystems are
computed from the tripartite initial state. Starting with a factorized
two-qubit initial state, the quasi-periodicity in the revival and collapse
phenomenon that occurs in the two-qubit population inversion is studied. Based
on the measure of relative entropy of coherence, we investigate the quantum
coherence and its explicit dependence on the parametric term both for the
two-qubit and the individual qubit subsystems by adopting different choices of
the initial states. Similarly, the existence of quantum correlations is
demonstrated by studying the geometric discord and concurrence. Besides, by
numerically minimizing the Hilbert-Schmidt distance, the dynamically produced
near maximally entangled states are reconstructed. The reconstructed states are
observed to be nearly pure generalized Bell states. Furthermore, utilizing the
oscillator density matrix, the quadrature variance and phase-space distribution
of the associated Husimi $Q$-function are computed in the minimum entropy
regime and conclude that the obtained nearly pure evolved state is a squeezed
coherent state.",2106.06746v1
1998-05-22,On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities,"The dynamical behavior of a harmonic chain in a spatially periodic potential
(Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of
an external force and a velocity proportional damping is investigated. We do
this at zero temperature for long chains in a regime where inertia and damping
as well as the nearest-neighbor interaction and the potential are of the same
order. There are two types of regular sliding states: Uniform sliding states,
which are periodic solutions where all particles perform the same motion
shifted in time, and nonuniform sliding states, which are quasi-periodic
solutions where the system forms patterns of domains of different uniform
sliding states. We discuss the properties of this kind of pattern formation and
derive equations of motion for the slowly varying average particle density and
velocity. To observe these dynamical domains we suggest experiments with a
discrete ring of at least fifty Josephson junctions.",9805287v1
2001-10-08,Reduction in the electron density-of-states in superconducting MgB$_2$ disordered by $n^1$-irradiation: the $^{11}$B and $^{25}$Mg NMR estimates,"NMR line shift and nuclear spin-lattice relaxation rate T_1^{-1} of 11B and
25Mg were measured in superconducting MgB_2 (T_c^{ons}=38K) structurally
disordered by nuclear reactor neutrons up to the fluence of thermal neutrons
$\Phi=1 10^{19} cm^{-2}. The temperature of superconducting transition was
shifted down to T_{c,irrad}^{ons}=7K under irradiation. The change due
irradiation in the partial electron density of states (DOS) at the Fermi energy
of boron and magnesium were traced by taking into account that T_1^{-1} of 11B
and 25Mg are determined by hyperfine magnetic interactions with carriers. It
was revealed that electronic states near E_F of Mg are influenced negligibly by
irradiation whereas partial DOS of the B 2p_{x,y} states reduces greatly in
irradiated MgB_2. The NMR estimates for DOS using the McMillan formula show
that critical temperature decreases in irradiated MgB_2 mainly due to reduction
in the partial DOS of p states of boron.",0110158v2
2005-12-07,Surface effects on the statistics of the local density of states in metallic nanoparticles: manifestation on the NMR spectra,"In metallic nanoparticles, shifts in the ionization energy of surface atoms
with respect to bulk atoms can lead to surface bands. Within a simple Tight
Binding model we find that the projection of the electronic density of states
on these sites presents two overlapping structures. One of them is
characterized by the level spacing coming from bulk states and the other arises
from the surface states. In very small particles, this contributes to an
over-broadening of the NMR absorption spectra, determined by the Knight shift
distribution of magnetic nuclei. We compare our calculated Knight shifts with
experiments on aluminum nanoparticles, and show that the deviation of the
scaling law as a function of temperature and particle size can be explained in
terms of surface states.",0512160v1
2006-09-04,Quantum Field Theoretical Description of Unstable Behavior of Trapped Bose-Einstein Condensates with Complex Eigenvalues of Bogoliubov-de Gennes Equations,"The Bogoliubov-de Gennes equations are used for a number of theoretical works
on the trapped Bose-Einstein condensates. These equations are known to give the
energies of the quasi-particles when all the eigenvalues are real. We consider
the case in which these equations have complex eigenvalues. We give the
complete set including those modes whose eigenvalues are complex. The quantum
fields which represent neutral atoms are expanded in terms of the complete set.
It is shown that the state space is an indefinite metric one and that the free
Hamiltonian is not diagonalizable in the conventional bosonic representation.
We introduce a criterion to select quantum states describing the metastablity
of the condensate, called the physical state conditions. In order to study the
instability, we formulate the linear response of the density against the
time-dependent external perturbation within the regime of Kubo's linear
response theory. Some states, satisfying all the physical state conditions,
give the blow-up and damping behavior of the density distributions
corresponding to the complex eigenmodes. It is qualitatively consistent with
the result of the recent analyses using the time-dependent Gross-Pitaevskii
equation.",0609052v2
2009-04-20,Complexity of D-dimensional hydrogenic systems in position and momentum spaces,"The internal disorder of a D-dimensional hydrogenic system, which is strongly
associated to the non-uniformity of the quantum-mechanical density of its
physical states, is investigated by means of the shape complexity in the two
reciprocal spaces. This quantity, which is the product of the disequilibrium or
averaging density and the Shannon entropic power, is mathematically expressed
for both ground and excited stationary states in terms of certain entropic
functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We
emphasize the ground and circular states, where the complexity is explicitly
calculated and discussed by means of the quantum numbers and dimensionality.
Finally, the position and momentum shape complexities are numerically discussed
for various physical states and dimensionalities, and the dimensional and
Rydberg energy limits as well as their associated uncertainty products are
explicitly given. As a byproduct, it is shown that the shape complexity of the
system in a stationary state does not depend on the strength of the Coulomb
potential involved.",0904.3001v2
2010-01-26,Inverse spin-s portrait and representation of qudit states by single probability vectors,"Using the tomographic probability representation of qudit states and the
inverse spin-portrait method, we suggest a bijective map of the qudit density
operator onto a single probability distribution. Within the framework of the
approach proposed, any quantum spin-j state is associated with the
(2j+1)(4j+1)-dimensional probability vector whose components are labeled by
spin projections and points on the sphere. Such a vector has a clear physical
meaning and can be relatively easily measured. Quantum states form a convex
subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits
(j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and
(2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s
portraits. We also address an auxiliary problem of the optimum reconstruction
of qudit states, where the optimality implies a minimum relative error of the
density matrix due to the errors in measured probabilities.",1001.4813v2
2017-09-30,Theoretical Investigation of the Magnetoelectric Properties of Bi2NiTiO6,"We report the first principle investigations on the structural, electronic,
magnetic and ferroelectric properties of a Pb free double perovskite
multiferroic Bi2NiTiO6 using density functional theory within the general
gradient approximation (GGA) and GGA+U method. Our results show that Bi2NiTiO6
will be an insulator with G-type magnetic ordering in its ground state with
Ni2+ in a high spin state and a spin moment of 1.74\mu_B. The paraelectric
phase stabilizes in nonmagnetic state with Ni2+ in low spin configuration
showing that spin state transition plays an important role in strong
magnetoelectric coupling in Bi2NiTiO6. The bonding characteristics of the
constituents are analyzed with the help of partial density of states and Born
effective charges. The presence of Ti ions at Ni sites suppresses the
disproportionation observed in case of BiNiO3 and results in a
noncentrosymmetric crystal structure. The coexistence of Bi 6s lone pair and
Ti4+ d0 ions which brings covalency produces a polarization of 32 \muCcm-2.",1710.00155v1
2000-07-31,Gauge Invariant Bosonization of Quantum Hall Systems and Skyrmions : Kinematics,"We develop a systematic semiclassical approximation scheme for quantum Hall
skyrmions near filling factors $\nu = {1 \over 2n+1}$, which is exact in the
long wavelength limit. We construct a coherent state basis for the Hilbert
space of Chern-Simons gauge fields and composite bosons with spin. These states
are projected to the physical gauge invariant subspace and their wavefunctions
explicitly evaluated. The lowest Landau level (LLL) condition is shown to be
equivalent to an analyticity condition on the parameters.
  The matrix elements of physical observables between these states are shown to
be calculable in the limit of small amplitude long wavelength density
fluctuations. The electric charge density is shown to be proportional to the
toplological charge density if and only if the LLL condition is satisfied.
  We then show that these states themselves form a generalised coherent state
basis, parameterised by the values of physical observables. The theory can
therefore be written in terms of these gauge invariant bosonic fields in the
long wavelength regime. The off diagonal matrix elements of observables in
these coherent states are computed and shown to vanish in the long wavelength
limit. Thus we are able to prove that the classical description of the skyrmion
is exact in the limit of large skyrmions.",0007498v1
2018-01-09,"Investigating the electronic structure of MSi (M = Cr, Mn, Fe $\&$ Co) and calculating $\textit{$U_{eff}$}$ $\&$ $\textit{J}$ by using cDFT","We have investigated electronic energy band structures and partial density of
states of intermetallic compounds $\textit{viz.}$ CrSi, MnSi, FeSi and CoSi, by
using density functional theory (DFT). CrSi \& MnSi, FeSi and CoSi have
metallic, indirect band gap semiconducting (band gap $ \sim$ 90 meV) and
semi-metallic ground state, respectively. On studying the band structures while
going across the series Cr-Co, the occupied bands around the Fermi level are
getting narrower while the unoccupied bands are getting wider. Similarly, band
edge in partial density of states is shifting away from the Fermi level due to
increased hybridizations. The effective mass of holes for FeSi is found to be
much larger than that of electrons, giving rise to positive Seebeck coefficient
and negative Hall coefficient, which is consistent with experimental results.
For different ionic states of 3\textit{d}-metal, the values of
$\textit{$U_{eff}$}$ and $\textit{J}$ are evaluated by using constrained DFT
method. $\textit{$U_{eff}$}$ ($\textit{J}$) for $2^{+} $ ionic state across the
series are $\sim $ 3.3 eV ($\sim $0.65 eV), $\sim $ 3.7 eV ($\sim $0.72 eV),
$\sim $ 4.4 eV ($\sim $ 0.82 eV) and $\sim $ 4.5 eV ($\sim $ 0.87 eV).
$\lambda$ and $\textit{J}$ are also calculated by considering Yukawa form of
Coulomb interaction. $\lambda $ values for $2^{+} $ ionic state along the
series are $\sim $ 1.97 a.$u^{-1}$, $\sim $ 2.07 a.$u^{-1}$, $\sim $ 2.07
a.$u^{-1}$ and $\sim $ 2.34 a.$u^{-1}$. 4$\textit{s}$ electrons are found to be
contributing more in screening the 3$\textit{d}$ electrons as compared to
4$\textit{p}$ electrons of 3$\textit{d}$ metals.",1801.03496v1
2021-12-07,In-gap band in the one-dimensional two-orbital Kanamori-Hubbard model with inter-orbital Coulomb interaction,"We study the electronic spectral properties at zero temperature of the
one-dimensional (1D) version of the degenerate two-orbital Kanamori Hubbard
model (KHM), one of the well established frameworks to study transition metal
compounds, using state-of-the-art numerical techniques based on the Density
Matrix Renormalization Group. While the system is Mott insulating for the
half-filled case, as expected for an interacting 1D system, we find interesting
and rich structures in the single-particle density of states (DOS) for the
hole-doped system. In particular, we find the existence of in-gap states which
are pulled down to lower energies from the upper Hubbard band (UHB) with
increasing the inter-orbital Coulomb interaction $V$. We analyze the
composition of the DOS by projecting it onto different local excitations and we
observe that for large dopings these in-gap excitations are formed mainly by
inter-orbital holon-doublon (HD) states and their energies follow approximately
the HD states in the atomic limit. We observe that the Hund interaction $J$
increases the width of the in-gap band, as expected from the two-particle
fluctuations in the Hamiltonian. The observation of a finite density of states
within the gap between the Hubbard bands for this extended 1D model indicates
that these systems present a rich excitation spectra which could help us
understand the microscopic physics behind multi-orbital compounds.",2112.03794v2
2023-04-06,On separable states in relativistic quantum field theory,"We initiate an investigation into separable, but physically reasonable,
states in relativistic quantum field theory. In particular we will consider the
minimum amount of energy density needed to ensure the existence of separable
states between given spacelike separated regions. This is a first step towards
improving our understanding of the balance between entanglement entropy and
energy (density), which is of great physical interest in its own right and also
in the context of black hole thermodynamics. We will focus concretely on a
linear scalar quantum field in a topologically trivial, four-dimensional
globally hyperbolic spacetime. For rather general spacelike separated regions
$A$ and $B$ we prove the existence of a separable quasi-free Hadamard state. In
Minkowski spacetime we provide a tighter construction for massive free scalar
fields: given any $R>0$ we construct a quasi-free Hadamard state which is
stationary, homogeneous, spatially isotropic and separable between any two
regions in an inertial time slice $t=\mathrm{const.}$ all of whose points have
a distance $>R$. We also show that the normal ordered energy density of these
states can be made $\le 10^{31}\frac{m^4}{(mR)^8}e^{-\frac14mR}$ (in Planck
units). To achieve these results we use a rather explicit construction of
test-functions $f$ of positive type for which we can get sufficient control on
lower bounds on $\hat{f}$.",2304.03120v2
2016-09-13,Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes,"A Bayesian model to infer edge electron density profiles is developed for the
JET lithium beam emission spectroscopy system, measuring Li I line radiation
using 26 channels with ~1 cm spatial resolution and 10~20 ms temporal
resolution. The density profile is modelled using a Gaussian process prior, and
the uncertainty of the density profile is calculated by a Markov Chain Monte
Carlo (MCMC) scheme. From the spectra measured by the transmission grating
spectrometer, the Li line intensities are extracted, and modelled as a function
of the plasma density by a multi-state model which describes the relevant
processes between neutral lithium beam atoms and plasma particles. The spectral
model fully takes into account interference filter and instrument effects, that
are separately estimated, again using Gaussian processes. The line intensities
are inferred based on a spectral model consistent with the measured spectra
within their uncertainties, which includes photon statistics and electronic
noise. Our newly developed method to infer JET edge electron density profiles
has the following advantages in comparison to the conventional method: i)
providing full posterior distributions of edge density profiles, including
their associated uncertainties, ii) the available radial range for density
profiles is increased to the full observation range (~26 cm), iii) an
assumption of monotonic electron density profile is not necessary, iv) the
absolute calibration factor of the diagnostic system is automatically estimated
overcoming the limitation of the conventional technique and allowing us to
infer the electron density profiles for all pulses without preprocessing the
data or an additional boundary condition, and v) since the full spectrum is
modelled, the procedure of modulating the beam to measure the background signal
is only necessary for the case of overlapping of the Li line with impurity
lines.",1609.03787v1
2004-03-24,Reduction of multipartite qubit density matrixes to bipartite qubit density matrixes and criteria of partial separability of multipartite qubit density matrixes,"The partial separability of multipartite qubit density matrixes is strictly
defined. We give a reduction way from N-partite qubit density matrixes to
bipartite qubit density matrixes, and prove a necessary condition that a
N-partite qubit density matrix to be partially separable is its reduced density
matrix to satisfy PPT condition.",0403173v2
2003-03-04,S-wave superconductivity near a surface,"We study the superconducting order parameter near a surface with the
Bogoliubov-de Gennes formalism. For definiteness we use the attractive Hubbard
model. Near a surface, the order parameter and the density distribution exhibit
``Friedel-like'' oscillations. Although the local density of states is quite
different from that in the bulk, the energy gap in the spectrum on a surface is
almost the same as the bulk value. In the low-density limit, however, the
energy gap tends to vanish on a surface.",0303069v1
1994-10-10,The Spectral Function for Finite Nuclei in the Local Density Approximation,"The spectral function for finite nuclei is computed within the framework of
the Local Density Approximation, starting from nuclear matter spectral
functions obtained with a realistic nucleon-nucleon interaction. The spectral
function is decomposed into a single-particle part and a ''correlated'' part;
the latter is treated in the local density approximation.
  As an application momentum distributions, quasi-particle strengths and
overlap functions for valence hole states, and the light-cone momentum
distribution in finite nuclei are computed.",9410019v1
2007-04-20,Time-dependent Density Functional calculation of e-H scattering,"Phase shifts for single-channel elastic electron-atom scattering are derived
from time-dependent density functional theory. The H$^-$ ion is placed in a
spherical box, its discrete spectrum found, and phase shifts deduced.
Exact-exchange yields an excellent approximation to the ground-state Kohn-Sham
potential, while the adiabatic local density approximation yields good singlet
and triplet phase shifts.",0704.2790v2
2012-03-13,Working out density fluctuation spectra from shear spectra,"Forthcoming experiments will enable us to determine high precision
tomographic shear spectra. Matter density fluctuation spectra, at various $z$,
should then be worked out of them, in order to constrain the model and
determine the DE state equation. Available analytical expressions, however, do
the opposite, enabling us to derive shear spectra from fluctuation spectra.
Here we find the inverse expression, yielding density fluctuation spectra from
observational tomographic shear spectra. The procedure involves SVD techniques
for matrix inversion. We show in detail how the approach works and provide a
few examples.",1203.2777v3
2012-05-22,Exact time-dependent density functional theory for impurity models,"We employ the density matrix renormalization group to construct the exact
time-dependent exchange correlation potential for an impurity model with an
applied transport voltage. Even for short-ranged interaction we find an
infinitely long-ranged exchange correlation potential which is built up
{instantly} after switching on the voltage. Our result demonstrates the
fundamental difficulties of transport calculations based on time-dependent
density functional theory. While formally the approach works, important
information can be missing in the ground-state functionals and may be hidden in
the usually unknown non-equilibrium functionals.",1205.4854v1
2012-12-04,Anion-radical oxygen centers in small (AgO)n clusters: density functional theory predictions,"Anion-radical form of the oxygen centers O(-) is predicted at the DFT level
for small silver oxide particles having the AgO stoichiometry. Model clusters
(AgO)n appear to be ferromagnetic with appreciable spin density at the oxygen
centers. In contrast to these clusters, the Ag2O model cluster have no unpaired
electrons in the ground state. The increased O/Ag ratio in the oxide particles
is proved to be responsible for the spin density at oxygen centers.",1212.0712v1
2013-12-12,Improved Performance of Tunneling FET Based on Hetero Graphene Nanoribbons,"A heterojunction tunneling field effect transistor based on armchair graphene
nanoribbons is proposed and studied using ballistic quantum transport
simulation based on 3D real space nonequilibrium Green's function formalism. By
using low band gap nanoribbons as the source/drain material, the hetero-
structure shows better performance including higher on current, lower off
current, and improved steep subthreshold swings compared with homostructure. It
is also found the device performance greatly depends on the source/drain
dopping density. High doping density leads to fewer density states in the
source and degrades the device performance.",1312.3391v1
2014-09-29,The generalized t-V model in one dimension,"We develop a systematic strong coupling approach for studying an extended t-V
model with interactions of a finite range. Our technique is not based on the
Bethe ansatz and is applicable to both integrable and non-integrable models. We
illustrate our technique by presenting analytic results for the ground state
energy (up to order 7 in t/V), the current density and density-density
correlations for integrable and non-integrable models with commensurate filling
factors. We further present preliminary numerical results for incommensurate
non-integrable models.",1409.8344v1
2014-03-02,Asymmetric exclusion processes on a closed network with bottlenecks,"We study the generic non-equilibrium steady states in asymmetric exclusion
processes on a closed network with bottlenecks. To this end we proposes and
study closed simple networks with multiply-connected non-identical junctions.
Depending upon the parameters that define the network junctions and the
particle number density, the models display phase transitions with both static
and moving density inhomogeneities. The currents in the models can be tuned by
the junction parameters. Our models highlight how extended and point defects
may affect the density profiles in a closed directed network. Phenomenological
implications of our results are discussed.",1403.0206v2
2020-08-11,"Reply to the Comment on ""Surface Pair-Density-Wave Superconducting and Superfluid States""","The recent Comment by Vorontsov [arXiv:2007.13696] claims that surface
pair-density-wave superconductivity with critical temperature higher than the
bulk FFLO critical temperature is not supported by microscopic theory. The
conclusion is reached by using an approximate semi-microscopic quasiclassical
approach. Here we show that a fully microscopic approach unambiguously
demonstrates the existence of surface pair-density-wave superconductivity.",2008.04740v2
2023-07-01,Exact Conditions for Ensemble Density Functional Theory,"Ensemble density functional theory (EDFT) is a promising alternative to
time-dependent density functional theory for computing electronic excitation
energies. Using coordinate scaling, we prove several fundamental exact
conditions in EDFT and illustrate them on the exact singlet bi-ensemble of the
Hubbard dimer. Several approximations violate these conditions, and some
ground-state conditions from quantum chemistry do not generalize to EDFT. The
strong-correlation limit is derived for the dimer, revealing weight-dependent
derivative discontinuities in EDFT.",2307.00187v1
2004-11-11,Phase Transitions In Compact Stars,"We report on a three--month research project for undergraduate students about
the mass-radius relation of compact stars. The equation of state used is
constrained at low densities by well-established equations of state of the
nuclear phase (the solid crust) and then extended to higher densities with a
phenomenological, parametric approach. A first order phase transition from
hadronic matter to a phase of higher density, assumed to be quark matter is
studied in addition. The mass-radius relation is obtained by solving
numerically the Tolman-Oppenheimer-Volkoff equation. We derive some conditions
for the existence of a third family of compact stars on the form of the
equation of state and its different global properties.",0411295v2
1999-04-22,Semiclassical Non-Trace Type Formulas for Matrix Element Fluctuations and Weighted Densities of States,"Densities of states weighted with the diagonal matrix elements of two
operators A and B, i.e., rho^(A,B)(E) = sum_n <n|A|n><n|B|n> delta(E-E_n)
cannot, in general, be written as a trace formula, and therefore no simple
extension of semiclassical trace formulas is known for this case. However, from
the high resolution analysis of quantum spectra in the semiclassical regime we
find strong evidence that weighting the delta-functions in the quantum
mechanical density of states with the product of diagonal matrix elements,
<n|A|n><n|B|n>, is equivalent to weighting the periodic orbit contributions in
the semiclassical periodic orbit sum with the product of the periodic orbit
means, <A>_p<B>_p, of the classical observables A and B. Results are presented
for the hydrogen atom in a magnetic field for both the chaotic and
near-integrable regime, and for the circle billiard.",9904040v1
1997-03-05,Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions,"We consider a disordered d--wave superconductor in two dimensions. Recently,
we have shown in an exact calculation that for a lattice model with a
Lorentzian distributed random chemical potential the quasiparticle density of
states at the Fermi level is nonzero. As the exact result holds only for the
special choice of the Lorentzian, we employ different methods to show that for
a large class of distributions, including the Gaussian distribution, one can
establish a nonzero lower bound for the Fermi level density of states. The fact
that the tails of the distributions are unimportant in deriving the lower bound
shows that the exact result obtained before is generic.",9703047v1
1997-11-27,Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes,"We study the effect of quenched spatial disorder on the steady states of
driven systems of interacting particles. Two sorts of models are studied:
disordered drop-push processes and their generalizations, and the disordered
asymmetric simple exclusion process. We write down the exact steady-state
measure, and consequently a number of physical quantities explicitly, for the
drop-push dynamics in any dimensions for arbitrary disorder. We find that three
qualitatively different regimes of behaviour are possible in 1-$d$ disordered
driven systems. In the Vanishing-Current regime, the steady-state current
approaches zero in the thermodynamic limit. A system with a non-zero current
can either be in the Homogeneous regime, chracterized by a single macroscopic
density, or the Segregated-Density regime, with macroscopic regions of
different densities. We comment on certain important constraints to be taken
care of in any field theory of disordered systems.",9711302v1
1999-06-16,Lyapounov exponent and density of states of a one-dimensional non-Hermitian Schroedinger equation,"We calculate, using numerical methods, the Lyapounov exponent gamma(E) and
the density of states rho(E) at energy E of a one-dimensional non-Hermitian
Schroedinger equation with off-diagonal disorder. For the particular case we
consider, both gamma(E) and rho(E) depend only on the modulus of E. We find a
pronounced maximum of rho(|E|) at energy E=2/sqrt(3), which seems to be linked
to the fixed point structure of an associated random map. We show how the
density of states rho(E) can be expanded in powers of E. We find rho(|E|) =
1/pi^2 + 4/(3 pi^3) |E|^2 + ... This expansion, which seems to be asymptotic,
can be carried out to an arbitrarily high order.",9906235v1
2000-06-23,Photoinduced absorption from localized intra-gap states,"A model is developed for photoinduced absorption from localized states
observed in femtosecond pump-probe experiments in high-Tc superconductors and
other materials. The dynamics of localized carriers are described in terms of
phenomenological approach similar to that originaly proposed by Rothwarf and
Taylor. Expanding the relaxation rate in powers of the order parameter we have
shown that density of localized carriers is sensitive to Tc. From the analysis
of the experimental data on YBa2Cu3O(7-x) and K0.3MoO3 we conclude that
significant intra-gap density of localized states exists in these materials.
Temperature dependence of the density of photoexcited localized carriers in
underdoped YBa2Cu3O(7-x) and in K0.3MoO3 is consistent with the observation of
the pseudogap above Tc.",0006357v1
2004-06-22,Electronic structure properties and BCS superconductivity in beta-pyrochlore oxides: KOs_2O_6,"We report a first-principles density-functional calculation of the electronic
structure and properties of the recently discovered superconducting
beta-pyrochlore oxide KOs_2O_6. We find that the electronic structure near the
Fermi energy E_F is dominated by strongly hybridized Os-5d and O-2p states. A
van Hove singularity very close to E_F leads to a relatively large density of
states at E_F, and the Fermi surface exhibits strong nesting along several
directions. These features could provide the scattering processes leading to
the observed anomalous temperature dependence of the resistivity and to the
rather large specific heat mass enhancement we obtain from the calculated
density of states and the observed specific heat coefficient. An estimate of
T_c within the framework of the BCS theory of superconductivity taking into
account the possible effects of spin fluctuations arising from nesting yields
the experimental value.",0406538v1
2005-03-16,Elegance of disordered granular packings: a validation of Edwards' hypothesis,"We have found a way to analyze Edwards' density of states for static granular
packings in the special case of round, rigid, frictionless grains assuming
constant coordination number. It obtains the most entropic density of single
grain states, which predicts several observables including the distribution of
contact forces. We compare these results against empirical data obtained in
dynamic simulations of granular packings. The agreement is quite good, helping
validate the use of statistical mechanics methods in granular physics. The
differences between theory and empirics are mainly related to the coordination
number, and when the empirical data are sorted by that number we obtain several
insights that suggest an underlying elegance in the density of states.",0503416v2
2006-05-22,Magnetic interactions in transition metal doped ZnO : An abinitio study,"We calculate the nature of magnetic interactions in transition-metal doped
ZnO using the local spin density approximation and LSDA+\textit{U} method of
density functional theory. We investigate the following four cases: (i) single
transition metal ion types (Cr, Mn, Fe, Co, Ni and Cu) substituted at Zn sites,
(ii) substitutional magnetic transition metal ions combined with additional Cu
and Li dopants, (iii) substitutional magnetic transition metal ions combined
with oxygen vacancies and (iv) pairs of magnetic ion types (Co and Fe, Co and
Mn, etc.). Extensive convergence tests indicate that the calculated magnetic
ground state is unusually sensitive to the k-point mesh and energy cut-off, the
details of the geometry optimizations and the choice of the
exchange-correlation functional. We find that ferromagnetic coupling is
sometimes favorable for single type substitutional transition metal ions within
the local spin density approximation. However, the nature of magnetic
interactions changes when correlations on the transition-metal ion are treated
within the more realistic LSDA + \textit{U} method, often disfavoring the
ferromagnetic state. The magnetic configuration is sensitive to the detailed
arrangement of the ions and the amount of lattice relaxation, except in the
case of oxygen vacancies when an antiferromagnetic state is always favored.",0605543v1
2006-07-05,Appearance of New Energy Gap and Periodic Local Density-of-States Modulation in $Bi_2 Sr_{1.6} La_{0.4} CuO_{6+δ}$,"The spatial variation of the local density of states in optimally doped
Bi$_{2}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+\delta}$ (superconducting transition
temperature is 34 K) is studied by scanning tunneling spectroscopy at 4.2 K in
zero magnetic field. Two-dimensional density-of-states modulation aligned with
the Cu-O-Cu bond with a periodicity of about five lattice constants is
observed. It is found that this modulation accompanies the appearance of a new
energy gap of approximately 10 meV, whose gap edge peak is spatially modulated
in intensity. This gap coexists with the superconducting gap, the value of
which ranges from 10 meV to 60 meV.",0607099v3
2006-08-16,Simulation-based equation of state of the hard disk fluid and prediction of higher-order virial coefficients,"We present new molecular dynamics results for the pressure of the pure hard
disk fluid up to the hexatic transition (about reduced density 0.9). The data
combined with the known virial coefficients (up to $B_{10}$) are used to build
an equation of state, to estimate higher-order virial coefficients, and also to
obtain a better value of $B_{10}$. Finite size effects are discussed in detail.
The ``van der Waals-like'' loop reported in literature in the vicinity of the
fluid/hexatic transition is explained by suppressed density fluctuations in the
canonical ensemble. The inflection point on the pressure-density dependence is
predicted by the equation of state even if the hexatic phase simulation data
are not considered.",0608356v1
1993-01-18,Jacobi's Action and the Density of States,"The authors have introduced recently a ``microcanonical functional integral""
which yields directly the density of states as a function of energy. The phase
of the functional integral is Jacobi's action, the extrema of which are
classical solutions at a given energy. This approach is general but is
especially well suited to gravitating systems because for them the total energy
can be fixed simply as a boundary condition on the gravitational field. In this
paper, however, we ignore gravity and illustrate the use of Jacobi's action by
computing the density of states for a nonrelativistic harmonic oscillator.
(Festschrift for Dieter Brill)",9301018v2
2001-02-25,Towards An Accurate Calculation of the Neutralino Relic Density,"We compute the neutralino relic density in the minimal supersymmetric
standard model by using exact expressions for the neutralino annihilation cross
section into all tree-level final states, including all contributions and
interference terms. We find that several final states may give comparable
contributions to the relic density, which illustrates the importance of
performing a complete calculation. We compare the exact results with those of
the usual expansion method and demonstrate a sizeable discrepancy (of more than
10%) over a significant range of the neutralino mass of up to several tens of
GeV which is caused by the presence of resonances and new final-state
thresholds. We perform several related checks and comparisons. In particular,
we find that the often employed approximate iterative procedure of computing
the neutralino freeze-out temperature gives generally very accurate results,
except when the expansion method is used near resonances and thresholds.",0102308v1
2000-11-07,Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials,"We study a non-relativistic charged particle on the Euclidean plane R^2
subject to a perpendicular constant magnetic field and an R^2-homogeneous
random potential in the approximation that the corresponding random Landau
Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a
single but arbitrary Landau level. For a wide class of Gaussian random
potentials we rigorously prove that the associated restricted integrated
density of states is absolutely continuous with respect to the Lebesgue
measure. We construct explicit upper bounds on the resulting derivative, the
restricted density of states. As a consequence, any given energy is seen to be
almost surely not an eigenvalue of the restricted random Landau Hamiltonian.",0011010v3
2002-11-09,Lewenstein-Sanpera decomposition of a generic 2x2 density matrix by using Wootters's basis,"The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix
is obtained by using Wootters's basis. It is shown that the average concurrence
of the decomposition is equal to the concurrence of the state. It is also shown
that all the entanglement content of the state is concentrated in the
Wootters's state $|x_1>$ associated with the largest eigenvalue $\lambda_1$ of
the Hermitian matrix $\sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}}$ >. It is shown
that a given density matrix $\rho$ with corresponding set of positive numbers
$\lambda_i$ and Wootters's basis can transforms under $SO(4,c)$ into a generic
$2\times2$ matrix with the same set of positive numbers but with new Wootters's
basis, where the local unitary transformations correspond to $SO(4,r)$
transformations, hence, $\rho$ can be represented as coset space
$SO(4,c)/SO(4,r)$ together with positive numbers $\lambda_i$. By giving an
explicit parameterization we characterize a generic orbit of group of local
unitary transformations.",0211051v1
2007-04-26,Tuning Spontaneous Emission versus Forster Energy Transfer in Biological Systems by Manipulating the Density of Photonic States,"We theoretically discuss how to tune the competition between Forster transfer
and spontaneous emission in a continuous and nondestructive fashion. The
proposed approach is especially suitable for delicate biological systems like
light harvesting complexes and fluorescent protein oligomers. We demonstrate
that the manipulation of the density of photonic states at the emission
frequency of the energy donor results in a change of the quantum efficiencies
of the competing energy transfer and spontaneous emission processes. This
change will be manifested in a modification of the donor and acceptor emission
intensities. Thus, by controlling the local density of photonic states Forster
coupled systems can be manipulated and analyzed without the need to physically
separate donor and acceptor chromophores for individual analysis, which is of
interest, for example, for oligomeric reef coral fluorescent proteins.",0704.3560v2
2008-04-07,Density of electron states in a rectangular lattice under uniaxial stress,"The closed analytical expression for the electron density of states function
in a rectangular lattice is derived in an elementary way in terms of complete
elliptic integrals of the first kind. The lattice can be treated as a deformed
square lattice under uniform uniaxial stress (or strain). In contrast to
hydrostatic case the uniaxial pressure, say along axis y, modifies a length of
the y-bonds while the x-bonds remain intact. It also alters the corresponding
tight-binding transfer integral gamma_2 between two y-nearest-neighbours
leaving unchanged the gamma_1 for x-nn interactions. Due to stress-induced
lowering symmetry of this simple model one can get an insight into the
decoupling of its density of states on dependence of the lattice deformation or
transfer integrals anisotropy.",0804.1037v2
2008-04-17,"Electronic and magnetic properties of a quasi-one-dimensional spin chain system, Sr$_{3}$NiRhO$_{6}$","We investigate the electronic structure of Sr$_3$NiRhO$_6$, a
quasi-one-dimensional spin chain system using \emph{ab initio} band structure
calculations. Spin polarized calculations within GGA reveal that Ni and Rh have
finite moments and they are antiferromagnetically coupled along the chain axis
in the ground state. While these results obtained within the local spin density
approximations provide remarkable representation of the magnetic phase, the
experimentally observed insulating behavior could not be captured within this
method. GGA+$U$ calculations show that opening up of an insulating gap requires
on-site Coulomb interaction among the Rh 4$d$ electrons, $U_{dd}^{Rh}$
$\approx$ 2.5 eV and the correlation among Ni 3$d$ electrons, $U_{dd}^{Ni}$
$\approx$ 4.5 eV suggesting this system to be a Mott insulator. Electron
correlation among $d$ electrons leads to significant enhancement of the O 2$p$
character in the energy bands in the vicinity of the Fermi level and the $d$
bands appear at lower energies. Energy gap in the up spin density of states
appears to be significantly small ($\sim$ 0.12 eV) while it is $>$ 2 eV in the
down spin density of states suggesting possibility of spin polarized conduction
in the semiconducting phase.",0804.2781v1
2008-11-21,Variational Theory of Hot Nucleon Matter II : Spin-Isospin Correlations and Equation of State of Nuclear and Neutron Matter,"We apply the variational theory for fermions at finite temperature and high
density, developed in an earlier paper, to symmetric nuclear matter and pure
neutron matter. This extension generalizes to finite temperatures, the many
body technique used in the construction of the zero temperature
Akmal-Pandharipande-Ravenhall equation of state. We discuss how the formalism
can be used for practical calculations of hot dense matter. Neutral pion
condensation along with the associated isovector spin longitudinal sum rule is
analyzed. The equation of state is calculated for temperatures less than 30 MeV
and densities less than three times the saturation density of nuclear matter.
The behavior of the nucleon effective mass in medium is also discussed.",0811.3528v1
2009-05-25,Density of states in solid deuterium: Inelastic neutron scattering study,"The dynamics of solid deuterium (sD2) is studied by means of inelastic
scattering (coherent and incoherent) of thermal and cold neutrons at different
temperatures and para-ortho ratios. In this paper, the results for the
generalized density of states (GDOS) are presented and discussed. The
measurements were performed at the thermal neutron time-of-flight (TOF)
instrument IN4 at ILL Grenoble and at the cold neutron TOF instrument TOFTOF at
FRM II Garching. The GDOS comprises besides the hcp phonon excitations of the
sD2 the rotational transitions J = 0 ->1 and J = 1 -> 2. The intensities of
these rotational excitations depend strongly on the ortho-D2 molecule
concentration co in sD2. Above E = 10 meV there are still strong excitations,
which very likely may originate from higher energy damped optical phonons and
multi-phonon contributions. A method for separating the one- and multi-phononon
contributions to the density of states willbe presented and discussed.",0905.4017v1
2009-10-14,Decoherence and thermalization of a pure quantum state in quantum field theory,"We study the real-time evolution of a self-interacting O(N) scalar field
initially prepared in a pure quantum state. We present a complete solution of
the nonequilibrium quantum dynamics from a 1/N-expansion of the
two-particle-irreducible effective action at next-to-leading order, which
includes scattering and memory effects. Restricting one's attention (or ability
to measure) to a subset of the infinite hierarchy of correlation functions, the
system is described by an effective (reduced) density matrix which, unlike the
full density matrix, has a nontrivial time evolution. In particular, starting
from a pure quantum state, we observe the loss of putity/coherence and, on
longer time scales, thermalization of the reduced density matrix. We point out
that the physics of decoherence is well described by classical statistical
field theory.",0910.2570v2
2010-07-03,Photon position measure,"The positive operator valued measure (POVM) for a photon counting array
detector is derived and found to equal photon flux density integrated over
pixel area and measurement time. Since photon flux density equals number
density multiplied by the speed of light, this justifies theoretically the
observation that a photon counting array provides a coarse grained measurement
of photon position. The POVM obtained here can be written as a set of
projectors onto a basis of localized states, consistent with the description of
photon position in a recent quantum imaging proposal [M. Tsang, Phys. Rev.
Lett. \textbf{102}, 253601 (2009)]. The wave function that describes a photon
counting experiment is the projection of the photon state vector onto this
localized basis. Collapse is to the electromagnetic vacuum and not to a
localized state, thus violating the text book rules of quantum mechanics but
compatible with the theory of generalized observables and the nonlocalizability
of an incoming photon.",1007.0460v1
2010-09-22,A new parametric equation of state and quark stars,"It is still a matter of debate to understand the equation of state of cold
supra-nuclear matter in compact stars because of unknown on-perturbative strong
interaction between quarks. Nevertheless, it is speculated from an
astrophysical view point that quark clusters could form in cold quark matter
due to strong coupling at realistic baryon densities. Although it is hard to
calculate this conjectured matter from first principles, one can expect the
inter-cluster interaction to share some general features to nucleon-nucleon
interaction. We adopt a two-Gaussian component soft-core potential with these
general features and show that quark clusters can form stable simple cubic
crystal structure if we assume Gaussian form wave function. With this
parameterizing, Tolman-Oppenheimer-Volkoff equation is solved with reasonable
constrained parameter space to give mass-radius relation of crystalline solid
quark star. With baryon densities truncated at 2 times nuclear density at
surface and range of interaction fixed at 2fm we can reproduce similar
mass-radius relation to that obtained with bag model equations of state. The
maximum mass ranges from about 0.5 to 3 solar mass. Observed maximum pulsar
mass (about 2 solar mass) is then used to constrain parameters of this simple
interaction potential.",1009.4247v1
2011-04-27,Phonon structures in the electronic density of states of graphene in magnetic field,"Unlike in ordinary metals, in graphene, phonon structure can be seen in the
quasiparticle electronic density of states, because the latter varies on the
scale of the phonon energy. In a magnetic field, quantization into Landau
levels creates even more significant variations. We calculate the density of
states incorporating electron-phonon coupling in this case and find that the
coupling has pronounced new effects: shifting and broadening of Landau levels,
creation of new peaks, and splitting of any Landau levels falling near one of
the new peaks. Comparing our calculations with a recent experiment, we find
evidence for a phonon with energy similar to but somewhat greater than the
optical $E_{2g}$ mode and a coupling corresponding to a mass enhancement
parameter $\lambda \simeq 0.07$.",1104.5169v1
2011-06-29,Non-equilibrium Steady States of Quantum Systems on Star Graphs,"Non-equilibrium steady states of quantum fields on star graphs are explicitly
constructed. These states are parametrized by the temperature and the chemical
potential, associated with each edge of the graph. Time reversal invariance is
spontaneously broken. We study in this general framework the transport
properties of the Schroedinger and the Dirac systems on a star graph, modeling
a quantum wire junction. The interaction, which drives the system away from
equilibrium, is localized in the vertex of the graph. All point-like vertex
interactions, giving rise to self-adjoint Hamiltonians possibly involving the
minimal coupling to a static electromagnetic field in the ambient space, are
considered. In this context we compute the exact electric steady current and
the non-equilibrium charge density. We investigate also the heat transport and
derive the Casimir energy density away from equilibrium. The appearance of
Friedel type oscillations of the charge and energy densities along the edges of
the graph is established. We focus finally on the noise power and discuss the
non-trivial impact of the point-like interactions on the noise.",1106.5871v1
2013-07-04,Tight-binding couplings in microwave artificial graphene,"We experimentally study the propagation of microwaves in an artificial
honeycomb lattice made of dielectric resonators. This evanescent propagation is
well described by a tight-binding model, very much like the propagation of
electrons in graphene. We measure the density of states, as well as the wave
function associated with each eigenfrequency. By changing the distance between
the resonators, it is possible to modulate the amplitude of
next-(next-)nearest-neighbor hopping parameters and to study their effect on
the density of states. The main effect is the density of states becoming
dissymmetric and a shift of the energy of the Dirac points. We study the basic
elements: An isolated resonator, a two-level system, and a square lattice. Our
observations are in good agreement with analytical solutions for corresponding
infinite lattice.",1307.1421v2
2014-07-03,Edge magnetization and local density of states in chiral nanoribbons,"We study the edge magnetization and the local density of states of chiral
graphene nanoribbons using a {\pi}-orbital Hubbard model in the mean-field
approximation. We show that the inclusion of a realistic next-nearest hopping
term in the tight-binding Hamiltonian changes the graphene nanoribbons band
structure significantly and affects its magnetic properties. We study the
behavior of the edge magnetization upon departing from half filling as a
function of the nanoribbon chirality and width. We find that the edge
magnetization depends very weakly in the nanoribbon width, regardless of
chirality as long as the ribbon is sufficiently wide. We compare our results to
recent scanning tunneling microscopy experiments reporting signatures of
magnetic ordering in chiral nanoribbons and provide an interpretation for the
observed peaks in the local density of states, that does not depend on the
antiferromagnetic interedge interaction.",1407.0766v1
2014-12-10,Multifractality and electron-electron interaction at Anderson transitions,"Mesoscopic fluctuations and correlations of the local density of states are
studied near metal-insulator transitions in disordered interacting electronic
systems. We show that the multifractal behavior of the local density of states
survives in the presence of Coulomb interaction. We calculate the spectrum of
multifractal exponents in $2+\epsilon$ spatial dimensions for symmetry classes
characterized by broken (partially or fully) spin-rotation invariance and show
that it differs from that in the absence of interaction. We also estimate the
multifractal exponents at the Anderson metal-insulator transition in 2D systems
with preserved spin-rotation invariance. Our results for multifractal
correlations of the local density of states are in qualitative agreement with
recent experimental findings.",1412.3306v1
2015-11-23,Density of states techniques for lattice field theories using the functional fit approach (FFA),"We discuss a variant of density of states (DoS) techniques for lattice field
theories, the so-called ""functional fit approach"" (FFA). The DoS FFA is based
on a density of states rho(x) which is parameterized on small intervals of the
argument x of rho(x). On these intervals restricted Monte Carlo simulations
with an additional Boltzmann factor exp(lambda x) allow to determine rho(x)
very precisely by obtaining its parameters from fitting the Monte Carlo data to
a known function of lambda. We describe the method in detail and show its
applicability in four different systems, three of which have a complex action
problem: The SU(3) spin model with a chemical potential, U(1) lattice gauge
theory, the Z(3) spin model with chemical potential, and 2-dimensional U(1)
lattice gauge theory with a topological term. In all cases we compare to
reference calculations, which partly were done in a dual formulation where the
complex action problem is absent. In all four cases we find a very encouraging
performance of the DoS FFA.",1511.07176v1
2016-03-24,Optimal large-scale quantum state tomography with Pauli measurements,"Quantum state tomography aims to determine the state of a quantum system as
represented by a density matrix. It is a fundamental task in modern scientific
studies involving quantum systems. In this paper, we study estimation of
high-dimensional density matrices based on Pauli measurements. In particular,
under appropriate notion of sparsity, we establish the minimax optimal rates of
convergence for estimation of the density matrix under both the spectral and
Frobenius norm losses; and show how these rates can be achieved by a common
thresholding approach. Numerical performance of the proposed estimator is also
investigated.",1603.07559v1
2016-07-25,Developing and testing the density of states FFA method in the SU(3) spin model,"The Density of States Functional Fit Approach (DoS FFA) is a recently
proposed modern density of states technique suitable for calculations in
lattice field theories with a complex action problem. In this article we
present an exploratory implementation of DoS FFA for the SU(3) spin system at
finite chemical potential $\mu$ - an effective theory for the Polyakov loop.
This model has a complex action problem similar to the one of QCD but also
allows for a dual simulation in terms of worldlines where the complex action
problem is solved. Thus we can compare the DoS FFA results to the reference
data from the dual simulation and assess the performance of the new approach.
We find that the method reproduces the observables from the dual simulation for
a large range of $\mu$ values, including also phase transitions, illustrating
that DoS FFA is an interesting approach for exploring phase diagrams of lattice
field theories with a complex action problem.",1607.07340v2
2019-05-06,Eigenstate thermalization from the clustering property of correlation,"The clustering property of an equilibrium bipartite correlation is one of the
most general thermodynamic properties in non-critical many-body quantum
systems. Herein, we consider the thermalization properties of a system class
exhibiting the clustering property. We investigate two regimes, namely, regimes
of high and low density of states corresponding to high and low energy regimes,
respectively. We show that the clustering property is connected to several
properties on the eigenstate thermalization through the density of states.
Remarkably, the eigenstate thermalization is obtained in the low-energy regime
with sparse density of states, which is typically seen in gapped systems. For
the high-energy regime, we demonstrate the ensemble equivalence between
microcanonical and canonical ensembles even for subexponentially small energy
shell with respect to the system size, which eventually leads to the weak
version of eigenstate thermalization.",1905.01886v2
2017-04-16,Highly anisotropic quasiparticle interference patterns in the spin-density wave state of the iron pnictides,"We investigate the impurity scattering induced quasiparticle interference in
the ($\pi, 0$) spin-density wave phase of the iron pnictides. We use a five
orbital tight binding model and our mean field theory in the clean limit
captures key features of the Fermi surface observed in angle-resolved
photoemission. We use a t-matrix formalism to incorporate the effect of doping
induced impurities on this state. The impurities lead to a spatial modulation
of the local density of states about the impurity site, with a periodicity of
$\sim 8a_{{\rm Fe}-{\rm Fe}}$ along the antiferromagnetic direction. The
associated momentum space quasiparticle interference pattern is anisotropic,
with major peaks located at $\sim (\pm \pi/4,0)$, consistent with spectroscopic
imaging scanning tunneling microscopy. We trace the origin of this pattern to
an elliptical contour of constant energy around momentum (0,0), with major axis
oriented along the (0,1) direction, in the mean field electronic structure.",1704.04783v1
2017-09-28,A DMRG study: Pair-density wave in spin-valley locked systems,"Interest in modulated paired states, long sought since the first proposals by
Fulde and Ferrell and by Larkin and Ovchinnikov, has grown recently in the
context of strongly coupled superconductors under the name of pair density
wave. However, there is little theoretical understanding of how such a state
might arise out of strong coupling physics in simple models. Although density
matrix renormalization group has been a powerful tool for exploring strong
coupling modulation phenomena of spin and charge stripe in the Hubbard model
and the t-J model, there has been no numerical evidence of PDW within these
models using DMRG. Here we note that a system with inversion breaking, C3v
point group symmetry may host a PDW-like state. Motivated by the fact that
spin-valley locked band structure of hole-doped group VI transition metal
dichalcogenides materializes such a setting, we use DMRG to study the
superconducting tendencies in spin-valley locked systems with strong
short-ranged repulsion. Remarkably we find robust evidence for a PDW and the
first of such evidence within DMRG studies of a simple fermionic model.",1709.10058v1
2017-10-25,Exceptional Lattice Green's Functions,"The three exceptional lattices, $E_6$, $E_7$, and $E_8$, have attracted much
attention due to their anomalously dense and symmetric structures which are of
critical importance in modern theoretical physics. Here, we study the
electronic band structure of a single spinless quantum particle hopping between
their nearest-neighbor lattice points in the tight-binding limit. Using Markov
chain Monte Carlo methods, we numerically sample their lattice Green's
functions, densities of states, and random walk return probabilities. We find
and tabulate a plethora of Van Hove singularities in the densities of states,
including degenerate ones in $E_6$ and $E_7$. Finally, we use brute force
enumeration to count the number of distinct closed walks of length up to eight,
which gives the first eight moments of the densities of states.",1710.10260v1
2019-04-01,Dependence of the density of states on the probability distribution -- part II: Schrödinger operators on $\mathbb{R}^d$ and non-compactly supported probability measures,"We extend our results in \cite{hislop_marx_1} on the quantitative continuity
properties, with respect to the single-site probability measure, of the density
of states measure and the integrated density of states for random Schr\""odinger
operators. For lattice models on $\mathbb{Z}^d$, with $d \geq 1$, we treat the
case of non-compactly supported probability measures with finite first moments.
For random Schr\""odinger operators on $\mathbb{R}^d$, with $d \geq 1$, we prove
results analogous to those in \cite{hislop_marx_1} for compactly supported
probability measures. The method of proof makes use of the Combes-Thomas
estimate and the Helffer-Sj\""ostrand formula.",1904.01118v2
2020-10-21,Density of States Graph Kernels,"A fundamental problem on graph-structured data is that of quantifying
similarity between graphs. Graph kernels are an established technique for such
tasks; in particular, those based on random walks and return probabilities have
proven to be effective in wide-ranging applications, from bioinformatics to
social networks to computer vision. However, random walk kernels generally
suffer from slowness and tottering, an effect which causes walks to
overemphasize local graph topology, undercutting the importance of global
structure. To correct for these issues, we recast return probability graph
kernels under the more general framework of density of states -- a framework
which uses the lens of spectral analysis to uncover graph motifs and properties
hidden within the interior of the spectrum -- and use our interpretation to
construct scalable, composite density of states based graph kernels which
balance local and global information, leading to higher classification
accuracies on a host of benchmark datasets.",2010.11341v3
2021-02-15,Quantum Monge-Kantorovich problem and transport distance between density matrices,"A quantum version of the Monge--Kantorovich optimal transport problem is
analyzed. The transport cost is minimized over the set of all bipartite
coupling states $\rho^{AB}$, such that both of its reduced density matrices
$\rho^A$ and $\rho^B$ of dimension $N$ are fixed. We show that, selecting the
quantum cost matrix to be proportional to the projector on the antisymmetric
subspace, the minimal transport cost leads to a semidistance between $\rho^A$
and $\rho^B$, which is bounded from below by the rescaled Bures distance and
from above by the root infidelity. In the single qubit case we provide a
semi-analytic expression for the optimal transport cost between any two states
and prove that its square root satisfies the triangle inequality and yields an
analogue of the Wasserstein distance of order two on the set of density
matrices. We introduce an associated measure of proximity of quantum states,
called SWAP-fidelity, and discuss its properties and applications in quantum
machine learning.",2102.07787v2
2021-04-06,B12C2N Interstitial Boron subcarbonitride with peculiar magnetic properties: First principles investigations,"The subcarbides B12C3 and B13C2 known for their abrasive properties, can be
structurally considered as carbon inserted rhombohedral alpha-B12 and expressed
as B12{C-C-C} and B12(C-B-C). Using density functional theory DFT computations,
the substitution of the central atom in the linear triatomic interstitials by N
leads to an original new boron subcarbonitride B12C2N or B12(C-N-C) identified
as slightly more cohesive than the two subcarbides. While B12C3 is insulating
with a E(Gap) close to 0.2 eV, and B13C2 a weak metal with small density of
state DOS at the Fermi level, B12C2N ground state is a half-metallic
ferromagnet with M= 1 BM. From the equation of state, the magnetization is
found unchanged over a broad volume range around equilibrium. Total and
magnetic charge density projections, in accordance with charge transfer
calculations, show the charge envelopes to be concentrated on (C:N:C) and the
magnetic charge having the shape of a torus centered on N. The triatomic
interstitials interact through terminal carbons specifically with one of the
two boron substructures of alpha-B12 forming 3B1-C-N-C-3B1-like complex.
Further syntheses and experimental characterizations are expected to extend the
field of investigation of such an original class of materials.",2104.02315v1
2021-05-22,Electrically charged compact stars with an interacting quark equation of state,"We investigate the properties of non-rotating, electrically charged strange
quark stars in four-dimensional Einstein-Maxwell theory. For quark matter we
adopt the well-motivated quantum chromodynamics (QCD) equation-of-state, while
for the charge density we assume it is proportional to the mass density. The
system of coupled structure equations are integrated numerically, and we
compute the mass, the radius as well as the total electric charge of the stars.
Moreover, we perform a detailed numerical study of the effect of electric
charge using the interacting quark equation-of-state. We find that stars as
heavy as two solar masses can be supported, and that the highest radius and
highest mass of the stars increase with the charge density.",2105.10638v1
2022-09-16,Out of Equilibrium Majoranas in Interacting Kitaev Chains,"We employ a time-dependent real-space local density-of-states method to study
the movement and fusion of Majorana zero modes in the 1D interacting Kitaev
model, based on the time evolution of many-body states.
  We analyze the dynamics and both fusion channels of Majoranas using
time-dependent potentials, either creating {\it Walls} or {\it Wells}. %
focusing on the local density-of-states and charge-density of fermions varying
with time. For fast moving Majoranas, we unveil non-equilibrium signatures of
the ``strong-zero mode'' operator (quasi parity degeneracy in the full
spectrum) and its breakdown in the presence of repulsive Coulomb interactions.
Focusing on forming a full electron after fusion, we also discuss upper and
lower limits on the Majorana speed needed to reduce non-adiabatic effects and
to avoid poisoning due to decoherence.",2209.07913v2
2022-10-03,An approximate local modular quantum energy inequality in general quantum field theory,"For every local quantum field theory on a static, globally hyperbolic
spacetime of arbitrary dimension, assuming the Reeh-Schlieder property, local
preparability of states, and the existence of an energy density as
operator-valued distribution, we prove an approximate quantum energy inequality
for a dense set of vector states. The quantum field theory is given by a net of
von Neumann algebras of observables, and the energy density is assumed to
fulfill polynomial energy bounds and to locally generate the time translations.
While being approximate in the sense that it is controlled by a small parameter
that depends on the respective state vector, the derived lower bound on the
expectation value of the spacetime averaged energy density has a universal
structure. In particular, the bound is directly related to the Tomita-Takesaki
modular operators associated to the local von Neumann algebras. This reveals
general, model-independent features of quantum energy inequalities for a large
class of quantum field theories on static spacetimes.",2210.01145v2
2023-04-06,Random Lindblad operators obeying detailed balance,"We introduce different ensembles of random Lindblad operators $\cal L$, which
satisfy quantum detailed balance condition with respect to the given stationary
state $\sigma$ of size $N$, and investigate their spectral properties. Such
operators are known as `Davies generators' and their eigenvalues are real;
however, their spectral densities depend on $\sigma$. We propose different
structured ensembles of random matrices, which allow us to tackle the problem
analytically in the extreme cases of Davies generators corresponding to random
$\sigma$ with a non-degenerate spectrum for the maximally mixed stationary
state, $\sigma = \mathbf{1} /N$. Interestingly, in the latter case the density
can be reasonably well approximated by integrating out the imaginary component
of the spectral density characteristic to the ensemble of random unconstrained
Lindblad operators. The case of asymptotic states with partially degenerated
spectra is also addressed. Finally, we demonstrate that similar universal
properties hold for the detailed balance-obeying Kolmogorov generators obtained
by applying superdecoherence to an ensemble of random Davies generators. In
this way we construct an ensemble of random classical generators with imposed
detailed balance condition.",2304.02960v1
2023-07-19,Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4,"The pairing symmetry of Sr$_2$RuO$_4$ is a long-standing fundamental question
in the physics of superconducting materials with strong electronic
correlations. We use the functional renormalization group to investigate the
behavior of superconductivity under uniaxial strain in a two-dimensional
realistic model of Sr$_2$RuO$_4$ obtained with density functional theory and
incorporating the effect of spin-orbit coupling. We find a dominant
$d_{x^2-y^2}$ superconductor mostly hosted by the $d_{xy}$-orbital, with no
other closely competing superconducting state. Within this framework we
reproduce the experimentally observed enhancement of the critical temperature
under strain and propose a simple mechanism driven by the density of states to
explain our findings. We also investigate the competition between
superconductivity and spin-density wave ordering as a function of interaction
strength. By comparing theory and experiment, we discuss constraints on a
possible degenerate partner of the $d_{x^2-y^2}$ superconducting state.",2307.10006v1
2001-03-13,On the two types of steady hard X-ray states of GRS 1915+105,"Using the data of 5 years of RXTE observations we investigate the X-ray
spectral and timing properties of GRS 1915+105 during the hard steady states.
According to the results of our simultaneous X-ray spectral and timing analysis
the behavior the source during the hard steady states can be reduced to a
couple of major distinct types. i) Type I states: The dominant hard component
of the energy spectrum has characteristic quasi- exponential cut-off at 50-120
keV. The broad-band power density spectrum of the source shows significant high
frequency noise component with a cut-off at 60-80 Hz. ii) Type II states: The
hard spectral component has a break in its slope at ~12-20 keV. The high
frequency part of the power density spectrum fades quickly lacking significant
variability at frequencies higher than ~30 Hz. These two types of the X-ray
hard states are also clearly distinguished by their properties in the radio
band: while during the type I observations the source tends to be
'radio-quiet', the type II observations are characterized by high level of
radio flux ('plateau' radio states). In this work we demonstrate aforementioned
differences using the data of 12 representative hard steady state observations.
We conclude that the difference between these two types can be probably
explained in terms of different structure of the accretion flow in the
immediate vicinity of the compact object due to presence of relativistic
outflow of matter.",0103182v1
2002-07-05,Interacting Bosons at Finite Temperature: How Bogolubov Visited a Black Hole and Came Home Again,"The structure of the thermal equilibrium state of a weakly interacting Bose
gas is of current interest. We calculate the density matrix of that state in
two ways. The most effective method, in terms of yielding a simple, explicit
answer, is to construct a generating function within the traditional framework
of quantum statistical mechanics. The alternative method, arguably more
interesting, is to construct the thermal state as a vector state in an
artificial system with twice as many degrees of freedom. It is well known that
this construction has an actual physical realization in the quantum
thermodynamics of black holes, where the added degrees of freedom correspond to
the second sheet of the Kruskal manifold and the thermal vector state is a
state of the Unruh or the Hartle-Hawking type. What is unusual about the
present work is that the Bogolubov transformation used to construct the thermal
state combines in a rather symmetrical way with Bogolubov's original
transformation of the same form, used to implement the interaction of the
nonideal gas in linear approximation. In addition to providing a density
matrix, the method makes it possible to calculate efficiently certain
expectation values directly in terms of the thermal vector state of the doubled
system.",0207032v1
2017-08-25,On the hydrodynamics of Bose-condensed fluids subject to density-dependent gauge potentials,"When the energy functional of a Bose-condensed state of matter features an
effective gauge potential which depends on the density $\rho$ of the
condensate, the kinetic energy density of the matter field becomes nonlinear in
$\rho$ and additional flow-dependent terms enter the wave equation for the
phase of the condensate wavefunction. To begin with, we consider a certain
class of density-dependent `single-component' gauge potentials, and later
extend this class to encompass more general `multi-component' potentials. The
nonlinear flow terms are cast into the general form of an inner-product between
the velocity field of the fluid and the gauge potential. This is achieved by
introducing a coupling matrix of dimensionless functions $\gamma_{ij}\left(
\rho \right)$, which characterises the particular functional form of the gauge
potential and regulates the strengths of the nonlinear terms accordingly. In
the momentum-transport equation of the fluid, two non-trivial terms emerge due
to the density-dependent vector potential. A body-force of dilation appears as
a product of the gauge potential and the dilation rate of the fluid, while the
fluid stress tensor features a flow-dependent pressure contribution given by
the inner-product of the gauge potential and the current density of the fluid.
This explicit dependence of the fluid pressure on the flow highlights the lack
of Galilean invariance of the nonlinear fluid.",1708.07712v1
2008-01-09,Turbo charging time-dependent density-functional theory with Lanczos chains,"We introduce a new implementation of time-dependent density-functional theory
which allows the \emph{entire} spectrum of a molecule or extended system to be
computed with a numerical effort comparable to that of a \emph{single} standard
ground-state calculation. This method is particularly well suited for large
systems and/or large basis sets, such as plane waves or real-space grids. By
using a super-operator formulation of linearized time-dependent
density-functional theory, we first represent the dynamical polarizability of
an interacting-electron system as an off-diagonal matrix element of the
resolvent of the Liouvillian super-operator. One-electron operators and density
matrices are treated using a representation borrowed from time-independent
density-functional perturbation theory, which permits to avoid the calculation
of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated
through a newly developed algorithm based on the non-symmetric Lanczos method.
Each step of the Lanczos recursion essentially requires twice as many
operations as a single step of the iterative diagonalization of the unperturbed
Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients
allows for a dramatic reduction of the number of Lanczos steps necessary to
obtain well converged spectra, bringing such number down to hundreds (or a few
thousands, at worst) in typical plane-wave pseudopotential applications. The
resulting numerical workload is only a few times larger than that needed by a
ground-state Kohn-Sham calculation for a same system. Our method is
demonstrated with the calculation of the spectra of benzene, C$_{60}$
fullerene, and of chlorofyll a.",0801.1393v1
2015-11-27,Influence of the weakly interacting light U boson on the properties of massive PNS,"Considering the octet baryons in relativistic mean field theory and selecting
entropy per baryon S=1, we calculate and discuss the influence of U boson on
the equation of state, mass-radius, moment of inertia and gravitational
redshift of massive protoneutron star (PNS). The effective coupling constant
$g_{U}$ of U bosons and nucleons is selected from 0GeV$^{-2}$ to 70GeV$^{-2}$.
The results point that U bosons will stiffen the equation of state (EOS). The
influence of U bosons on the pressure is more obvious at low density than high
density, while, the influence of U bosons on the energy density is more obvious
at high density than low density. The U bosons play a significant role in
increasing the maximum mass and radius of PNS. When the value of $g_{U}$
changes from 0GeV$^{-2}$ to 70GeV$^{-2}$, the maximum mass of massive PNS
increases from 2.11 $M_{\odot}$ to 2.58 $M_{\odot}$, and the radius of PNS
corresponding PSR J0348+0432 increases from 13.71 km to 24.35 km. The U bosons
will increase the moment of inertia and decrease the gravitational redshift of
PNS. For PNS of the massive PSR J0348+0432, the radius and moment of inertia
vary directly with $g_{U}$, the gravitational redshift vary inversely with
$g_{U}$ approximately.",1601.02850v1
2019-06-05,Equation of state effects in the core collapse of a $20$-$M_\odot$ star,"Uncertainties in our knowledge of the properties of dense matter near and
above nuclear saturation density are among the main sources of variations in
multi-messenger signatures predicted for core-collapse supernovae (CCSNe) and
the properties of neutron stars (NSs). We construct 97 new finite-temperature
equations of state (EOSs) of dense matter that obey current experimental,
observational, and theoretical constraints and discuss how systematic
variations in the EOS parameters affect the properties of cold nonrotating NSs
and the core collapse of a $20\,M_\odot$ progenitor star. The core collapse of
the $20\,M_\odot$ progenitor star is simulated in spherical symmetry using the
general-relativistic radiation-hydrodynamics code GR1D where neutrino
interactions are computed for each EOS using the NuLib library. We conclude
that the effective mass of nucleons at densities above nuclear saturation
density is the largest source of uncertainty in the CCSN neutrino signal and
dynamics even though it plays a subdominant role in most properties of cold NS
matter. Meanwhile, changes in other observables affect the properties of cold
NSs, while having little effect in CCSNe. To strengthen our conclusions, we
perform six octant three-dimensional CCSN simulations varying the effective
mass of nucleons at nuclear saturation density. We conclude that neutrino
heating and, thus, the likelihood of explosion is significantly increased for
EOSs where the effective mass of nucleons at nuclear saturation density is
large.",1906.02009v1
2021-03-18,Coherence of oscillations in matter and supernova neutrinos,"We study the propagation coherence for neutrino oscillations in media with
different density profiles. For each profile, we find the dependence of the
coherence length, $L_{coh}$, on neutrino energy and address the issue of
correspondence of results in the distance and energy-momentum representations.
The key new feature in matter is existence of energy ranges with enhanced
coherence around the energies $E_0$ of ""infinite coherence"" at which $L_{coh}
\rightarrow \infty$. In the configuration space, the infinite coherence
corresponds to equality of the (effective) group velocities of the eigenstates.
In constant density medium, there is a unique $E_0$, which coincides with the
MSW resonance energy of oscillations of mass states and is close to the MSW
resonance energy of flavor states. In the case of massless neutrinos or
negligible masses in a very dense medium the coherence persists continuously.
In the adiabatic case, the infinite coherence is realized for periodic density
change. Adiabaticity violation changes the shape factors of the wave packets
(WPs) and leads to their spread. In a medium with sharp density changes
(jumps), splitting of the eigenstates occurs at crossing of each jump. We study
the increase of the coherence length in a single jump and periodic density
jumps - castle-wall (CW) profiles. For the CW profile, there are several $E_0$
corresponding to parametric resonances. We outlined applications of the results
for supernova neutrinos. In particular, we show that coherence between two
shock wave fronts leads to observable oscillation effects, and our analysis
suggests that the decoherence can be irrelevant for flavor transformations in
the central parts of collapsing stars.",2103.10149v1
2007-12-30,Local quasiparticle lifetimes in a d-wave superconductor,"Scanning tunnelling spectroscopy (STS) measurements find that the surface of
Bi-2212 is characterized by nanoscale sized regions, ""gap patches,"" which have
different magnitudes for the d-wave energy gap. Recent studies have shown that
the tunnelling conductance can be fit using a BCS-type density of states for a
d-wave superconductor with a local quasiparticle scattering rate. The fit is
made with a scattering rate which varies linearly with energy and has a slope
that is positively correlated with the local value of the gap. We revisit a
model of quasiparticle scattering by impurities and spin fluctuations which was
previously used to describe the lifetimes of nodal quasiparticles measured by
angle-resolved photoemission (ARPES). We argue that the broadening of the local
density of states is in general determined by the imaginary part of the
self-energy of the system averaged over a small region. The size of this region
is set by a mean free path which depends upon the energy. At low energies, this
region is found to be significantly larger than a gap ""patch"", so that the
density of states measured by STS is homogeneous in this energy range. At
higher energies where the mean free path is comparable with the patch size, the
density of states is inhomogeneous. We show that a local self-energy in the
impurity-plus-spin fluctuation model, while not strictly linear, yields a local
density of states (LDOS) nearly identical to the full theory, and argue that it
is consistent with the STS data as well as the phenomenological linear
scattering rate extracted from experiment. We also explore the qualitative
consequences of this phenomenology for the spectral widths observed in ARPES
and predict the existence of Fermi arcs in the superconducting state.",0801.0101v1
1994-09-13,Improved Mean-Field Scheme for the Hubbard Model,"Ground state energies and on-site density-density correlations are calculated
for the 1-D Hubbard model using a linear combination of the Hubbard projection
operators. The mean-field coefficients in the resulting linearized Equations of
Motion (EOM) depend on both one-particle static expectation values as well as
static two-particle correlations. To test the model, the one particle
expectation values are determined self-consistently while using Lanczos
determined values for the two particle correlation terms. Ground state energies
and on-site density-density correlations are then compared as a function of $U$
to the corresponding Lanczos values on a 12 site Hubbard chain for 1/2 and 5/12
fillings. To further demonstrate the validity of the technique, the static
correlation functions are also calculated using a similar EOM approach, which
ignores the effective vertex corrections for this problem, and compares those
results as well for a 1/2 filled chain. These results show marked improvement
over standard mean-field techniques.",9409053v1
1997-07-29,Excitation energies from density functional perturbation theory,"We consider two perturbative schemes to calculate excitation energies, each
employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate
exchange-correlation potentials generated from essentially exact densities and
their exchange components determined by a recently proposed method, we evaluate
energy differences between the ground state and excited states in first-order
perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was
recently observed that the zeroth-order excitations energies, simply given by
the difference of the Kohn-Sham eigenvalues, almost always lie between the
singlet and triplet experimental excitations energies, corrected for
relativistic and finite nuclear mass effects. The first-order corrections
provide about a factor of two improvement in one of the perturbative schemes
but not in the other. The excitation energies within perturbation theory are
compared to the excitations obtained within $\Delta$SCF and time-dependent
density functional theory. We also calculate the excitation energies in
perturbation theory using approximate functionals such as the local density
approximation and the optimized effective potential method with and without the
Colle-Salvetti correlation contribution.",9707304v1
2002-07-31,Charge and Salt Driven Reentrant Order-Disorder and Gas-Solid Transitions in Charged Colloids,"Monte Carlo simulations have been performed for aqueous charged colloidal
suspensions as a function of charge density on the particles and salt
concentration. We vary the charge density in our simulations over a range where
a reentrant solid-liquid transition in suspensions of silica and polymer latex
particles has been reported by Yamanaka et al. [Phys. Rev. Lett. 80 5806
(1998)]. We show that at low ionic strengths a homogeneous liquid-like ordered
suspension undergoes crystallization upon increasing charge density . Further
increase in charge density resulted once again a disordered state which is in
agreement with experimental observations. In addition to this reentrant
order-disorder transition, we observe an inhomogeneous to homogeneous
transition in our simulations when salt is added to the disordered
inhomogeneous state. This inhomogeneous to homogeneous disordered transition is
analogous to the solid-gas transition of atomic systems and has not yet been
observed in charged colloids. The reported experimental observations on charged
colloidal suspensions are discussed in the light of present simulation results.",0207728v1
2011-09-24,Connecting the Reentrant Insulating Phase and the Zero Field Metal-Insulator Transition in a 2D Hole System,"We present the transport and capacitance measurements of 10nm wide GaAs
quantum wells with hole densities around the critical point of the 2D
metal-insulator transition (critical density $p_c$ down to
0.8$\times10^{10}$/cm$^2$, $r_s\sim$36). For metallic hole density $p_c < p
<p_c +0.15\times10^{10}$/cm$^2$, a reentrant insulating phase (RIP) is observed
between the $\nu$=1 quantum Hall state and the zero field metallic state and is
attributed to the formation of pinned Wigner crystal. Through studying the
evolution of the RIP versus 2D hole density by transport and capacitance
experiments, we show that the RIP is incompressible and continuously connected
to the zero field insulator, suggesting a similar origin for these two phases.",1109.5232v1
2012-09-22,Real-time calculations of many-body dynamics in quantum systems,"Real-time computation of time-dependent quantum mechanical problems are
presented for nuclear many-body problems. Quantum tunneling in nuclear fusion
at low energy is described using a time-dependent wave packet. A real-time
method of calculating strength functions using the time-dependent Schroedinger
equation is utilized to properly treat the continuum boundary condition. To go
beyond the few-body models,we resort to the density-functional theory. The
nuclear mean-field models are briefly reviewed to illustrate its foundation and
necessity of state dependence in effective interactions. This state dependence
is successfully taken into account by the density dependence, leading to the
energy density functional. Photoabsorption cross sections in 238U are
calculated with the real-time method for the time-dependent density-functional
theory.",1209.5384v1
2015-03-15,Reentrant Superfluidity and Pair Density Wave in Single Component Dipolar Fermi Gases,"We study the superfluidity of single component dipolar Fermi gases in three
dimensions within a pairing fluctuation theory. The transition temperature
$T_{c}$ for the dominant $p_z$ wave superfluidity exhibits a remarkable
re-entrant behavior as a function of the pairing strength induced by the
dipole-dipole interaction (DDI), which leads to an anisotropic pair dispersion.
The anisotropy and the long range nature of the DDI cause $T_c$ to vanish for a
narrow range of intermediate interaction strengths, where a pair density wave
state emerges as the ground state. The superfluid density and thermodynamics
below $T_{c}$, along with the density profiles in a harmonic trap, are
investigated as well, throughout the BCS-BEC crossover. Implications for
experiments are discussed.",1503.04453v3
2017-06-07,Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system,"Quantum Hall ferromagnetic transitions are typically achieved by increasing
the Zeeman energy through in-situ sample rotation, while transitions in systems
with pseudo-spin indices can be induced by gate control. We report here a
gate-controlled quantum Hall ferromagnetic transition between two real spin
states in a conventional two-dimensional system without any in-plane magnetic
field. We show that the ratio of the Zeeman splitting to the cyclotron gap in a
Ge two-dimensional hole system increases with decreasing density owing to
inter-carrier interactions. Below a critical density of $\sim2.4\times 10^{10}$
cm$^{-2}$, this ratio grows greater than $1$, resulting in a ferromagnetic
ground state at filling factor $\nu=2$. At the critical density, a resistance
peak due to the formation of microscopic domains of opposite spin orientations
is observed. Such gate-controlled spin-polarizations in the quantum Hall regime
opens the door to realizing Majorana modes using two-dimensional systems in
conventional, low-spin-orbit-coupling semiconductors.",1706.02044v1
2023-06-15,Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens,"The quantum separability problem consists in deciding whether a bipartite
density matrix is entangled or separable. In this work, we propose a machine
learning pipeline for finding approximate solutions for this NP-hard problem in
large-scale scenarios. We provide an efficient Frank-Wolfe-based algorithm to
approximately seek the nearest separable density matrix and derive a systematic
way for labeling density matrices as separable or entangled, allowing us to
treat quantum separability as a classification problem. Our method is
applicable to any two-qudit mixed states. Numerical experiments with quantum
states of 3- and 7-dimensional qudits validate the efficiency of the proposed
procedure, and demonstrate that it scales up to thousands of density matrices
with a high quantum entanglement detection accuracy. This takes a step towards
benchmarking quantum separability to support the development of more powerful
entanglement detection techniques.",2306.09444v2
1995-11-06,Consistent Construction of Realistic One-Body Density Matrix in Nuclei,"A phenomenological method based on the natural orbital representation is
applied to construct the ground state one-body density matrix which describes
correctly both density and momentum distributions in $^{4}He$, $^{16}O$ and
$^{40}Ca$ nuclei. The parameters of the matrix are fixed by a best fit to the
experimental density distribution and to the correlated nucleon momentum
distribution. The method allows the natural orbitals, the occupation
probabilities and the depletion of the Fermi sea to be obtained. Ground-state
characteristics of $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei, such as rms radii
and mean kinetic energies are calculated, as well.",9511006v1
2000-12-12,Analysis of Density Matrix reconstruction in NMR Quantum Computing,"Reconstruction of density matrices is important in NMR quantum computing. An
analysis is made for a 2-qubit system by using the error matrix method. It is
found that the state tomography method determines well the parameters that are
necessary for reconstructing the density matrix in NMR quantum computations.
Analysis is also made for a simplified state tomography procedure that uses
fewer read-outs. The result of this analysis with the error matrix method
demonstrates that a satisfactory accuracy in density matrix reconstruction can
be achieved even in a measurement with the number of read-outs being largely
reduced.",0012047v2
2009-09-04,Dyadic Green's functions and electromagnetic local density of states,"A formal proof to relate the concept of electromagnetic local density of
states (LDOS) to the electric and magnetic dyadic Green's functions is
provided. The expression for LDOS is obtained by relating the electromagnetic
energy density at any location in a medium at uniform temperature $T$ to the
electric and magnetic dyadic Green's functions. With this the concept of LDOS
is also extended to material media. The LDOS is split into two terms -- one
that originates from the energy density in an infinite, homogeneous medium and
the other that takes into account scattering from inhomogenieties. The second
part can always be defined unambiguously, even in lossy materials. For lossy
materials, the first part is finite only if spatial dispersion is taken into
account.",0909.0788v1
2011-07-12,One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory,"We extend the density matrix renormalization group to compute exact ground
states of continuum many-electron systems in one dimension with long-range
interactions. We find the exact ground state of a chain of 100 strongly
correlated artificial hydrogen atoms. The method can be used to simulate 1d
cold atom systems and to study density functional theory in an exact setting.
To illustrate, we find an interacting, extended system which is an insulator
but whose Kohn-Sham system is metallic.",1107.2394v3
2012-03-09,Critical Reinvestigation on Vibronic Couplings in Picene from View of Vibronic Coupling Density Analysis,"Vibronic coupling constants in the monoanionic, trianionic, and excited
states of picene are evaluated from the total energy gradients using the
density functional theory. Employing the calculated vibronic coupling constants
in the excited state of the neutral molecule, electron energy loss spectrum
(EELS) is simulated to be compared with the experimental spectrum. The
calculated vibronic coupling constants are analyzed in terms of the vibronic
coupling density which enables us to analyze vibronic couplings based on the
relation between the electronic and vibrational structures. The vibronic
coupling constants reported by Kato et al. [J. Chem. Phys. 116, 3420 (2002) and
Phys. Rev. Lett. 107, 077001 (2011)] are critically discussed based on the
vibronic coupling density analysis.",1203.2013v1
2012-08-07,"Metallic behavior at YBaCuO7/ZAs interfaces (Z=Ga, Al)","We present the electronic band structure of the interfaces
$YBa_2Cu_3O_7/GaAs$ (direct gap) and $YBa_2Cu_3O_7/AlAs$ (indirect gap) in
different configurations calculated using the Density Functional Theory as in
the Wien2k code within the local density approximation. We have projected the
density of states at the atomic layers forming the interface. We concentrated
in the semiconductor side. The two first atomic layers in the semiconductor
side of the interface present a clear metallic behavior. We found for both
semiconductors considered that it converges towards the bulk atomic-layer
projected density of states at the fifth atomic layer from the interface. We
considered an ideal non-reconstructed interface in the (001) direction in this
work. This behavior is interesting and could be used in several technological
applications.",1208.1312v1
2018-06-05,Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t',"We report a large-scale density-matrix renormalization group study of the
lightly doped Hubbard model on 4-leg cylinders at hole doping concentration
$\delta=12.5\%$. By keeping a large number of states for long system sizes, we
are able to reveal a delicate interplay between superconductivity and charge
and spin density wave orders tunable via next-nearest neighbor hopping t'. For
finite t', the ground state is consistent with that of a Luther-Emery liquid,
having `half-filled' charge stripes with power-law superconducting and
charge-density-wave correlations of wave-length $\lambda=1/2\delta$, but
short-range spin correlations. This is in direct contrast to the case with
t'=0, where superconducting correlations fall off exponentially while charge-
and spin-density modulations are dominant. Our results indicate that a route to
robust long-range superconductivity involves destabilizing insulating charge
stripes in the doped Hubbard model.",1806.01465v2
2018-06-09,Pressure induced collapse of the charge density wave and Higgs mode visibility in 2H-TaS$_2$,"The pressure evolution of the Raman active electronic excitations of the
transition metal dichalcogenides 2H-TaS$_2$ is followed through the pressure
phase diagram embedding incommensurate charge-density-wave and superconducting
states. At high pressure, the charge-density-wave is found to collapse at
8.5~GPa. In the coexisting charge-density-wave and superconducting orders, we
unravel a strong in-gap superconducting mode, attributed to a Higgs mode,
coexisting with the expected incoherent Cooper-pair breaking signature. The
latter remains in the pure superconducting state reached above 8.5~GPa. Our
report constitutes the first observation of such Raman active Higgs mode since
the longstanding unique case 2H-NbSe$_2$.",1806.03433v1
2018-06-18,Phase space density limitation in laser cooling without spontaneous emission,"We study the possibility to enhance the phase space density of
non-interacting particles submitted to a classical laser field without
spontaneous emission. We clearly state that, when no spontaneous emission is
present, a quantum description of the atomic motion is more reliable than
semi-classical description which can lead to large errors especially if no care
is taken to smooth structures smaller than the Heisenberg uncertainty
principle. Whatever the definition of position - momentum phase space density,
its gain is severely bounded especially when started from a thermal sample.
More precisely, the maximum phase space density, can only be improved by a
factor M for M-level atoms. This bound comes from a transfer between the
external and internal degrees of freedom. To circumvent this limit, one can use
non-coherent light fields, informational feedback cooling schemes, involve
collectives states between fields and atoms, or allow a single spontaneous
emission even",1806.06906v2
2014-05-25,How to experimentally detect a GGE? - Universal Spectroscopic Signatures of the GGE in the Tonks gas,"In this work we study the properties of the density density correlation
function of the 1-D Lieb-Liniger model with infinite repulsion in the GGE
regime. The GGE describes the equilibrated system in the long time limit after
a quench from a generic initial state. In the case that the initial and hence
the final state has low entropy per particle we find that the density density
correlation function has a universal form, in particular it depends on a few
parameters corresponding to ""key"" momenta and has power law dependence on the
distance. This provides an experimental signature of the GGE which may readily
be identified through spectroscopy. These signatures are universal and robust
to initial sate preparation.",1405.6365v2
2017-09-28,A density-driven first-order phase transition in liquid sulfur,"First-order phase transitions are characterized by a discontinuous first
derivative of the Gibbs free energy, so that volumes and entropies are
discontinuous. Such transitions are common in the crystalline state, but
extremely rare in liquid substances and experimentally evidenced in only one
pure element, phosphorus. Here we report combined in-situ Raman scattering,
X-ray diffraction and density measurements that support the existence of a
first-order liquid-liquid transition in sulfur at high pressures and
temperatures. The transformation involves a sharp density jump between two
structurally and dynamically distinct liquids. The first-order phase transition
proceeds through an initial stage of temperature induced polymerization and a
final stage where the low-density liquid abruptly converts to a denser
polymeric state. This unique feature is explained by competing effects of
pressure and temperature.",1709.09996v1
2018-10-30,Machine learning density functional theory for the Hubbard model,"The solution of complex many-body lattice models can often be found by
defining an energy functional of the relevant density of the problem. For
instance, in the case of the Hubbard model the spin-resolved site occupation is
enough to describe the system total energy. Similarly to standard density
functional theory, however, the exact functional is unknown and suitable
approximations need to be formulated. By using a deep-learning neural network
trained on exact-diagonalization results we demonstrate that one can construct
an exact functional for the Hubbard model. In particular, we show that the
neural network returns a ground-state energy numerically indistinguishable from
that obtained by exact diagonalization and, most importantly, that the
functional satisfies the two Hohenberg-Kohn theorems: for a given ground-state
density it yields the external potential and it is fully variational in the
site occupation.",1810.12700v1
2020-01-16,Orbital-collaborative Charge Density Wave in Monolayer VTe2,"Charge density waves in transition metal dichalcogenides have been
intensively studied for their close correlation with Mott insulator,
charge-transfer insulator, and superconductor. VTe2 monolayer recently comes
into sight because of its prominent electron correlations and the mysterious
origin of CDW orders. As a metal of more than one type of charge density waves,
it involves complicated electron-electron and electron-phonon interactions.
Through a scanning tunneling microscopy study, we observed triple-Q 4-by-4 and
single-Q 4-by-1 modulations with significant charge and orbital separation. The
triple-Q 4-by-4 order arises strongly from the p-d hybridized states, resulting
in a charge distribution in agreement with the V-atom clustering model.
Associated with a lower Fermi level, the local single-Q 4-by-1 electronic
pattern is generated with the p-d hybridized states remaining 4-by-4 ordered.
In the spectroscopic study, orbital- and atomic- selective charge-density-wave
gaps with the size up to ~400 meV were resolved on the atomic scale.",2001.05649v1
2022-04-11,"Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands","Twisted double- and mono-bilayer graphene are graphene-based moir\'e
materials hosting strongly correlated fermions in a gate-tunable conduction
band with a topologically non-trivial character. Using unbiased exact
diagonalization complemented by unrestricted Hartree-Fock calculations, we find
that the strong electron-electron interactions lead to a non-coplanar magnetic
state, which has the same symmetries as the tetrahedral antiferromagnet on the
triangular lattice and can be thought of as a skyrmion lattice commensurate
with the moir\'e scale, competing with a set of ferromagnetic, topological
charge density waves featuring an approximate emergent O(3) symmetry,
""rotating"" the different charge density wave states into each other. Direct
comparison with exact diagonalization reveals that the ordered phases are
accurately described within the unrestricted Hartree-Fock approximation.
Exhibiting a finite charge gap and Chern number $|C|=1$, the formation of
charge density wave order which is intimately connected to a skyrmion lattice
phase is consistent with recent experiments on these systems.",2204.05317v2
2023-06-21,Two species $k$-body embedded Gaussian unitary ensembles: $q$-normal form of the eigenvalue density,"Eigenvalue density generated by embedded Gaussian unitary ensemble with
$k$-body interactions for two species (say $\mathbf{\pi}$ and $\mathbf{\nu}$)
fermion systems is investigated by deriving formulas for the lowest six
moments. Assumed in constructing this ensemble, called EGUE($k:\mathbf{\pi}
\mathbf{\nu}$), is that the $\mathbf{\pi}$ fermions ($m_1$ in number) occupy
$N_1$ number of degenerate single particle (sp) states and similarly
$\mathbf{\nu}$ fermions ($m_2$ in number) in $N_2$ number of degenerate sp
states. The Hamiltonian is assumed to be $k$-body preserving $(m_1,m_2)$.
Formulas with finite $(N_1,N_2)$ corrections and asymptotic limit formulas both
show that the eigenvalue density takes $q$-normal form with the $q$ parameter
defined by the fourth moment. The EGUE($k:\mathbf{\pi} \mathbf{\nu}$) formalism
and results are extended to two species boson systems. Results in this work
show that the $q$-normal form of the eigenvalue density established only
recently for identical fermion and boson systems extends to two species fermion
and boson systems.",2306.12513v2
2024-03-20,Forecasting density-valued functional panel data,"We introduce a statistical method for modeling and forecasting functional
panel data, where each element is a density. Density functions are nonnegative
and have a constrained integral and thus do not constitute a linear vector
space. We implement a center log-ratio transformation to transform densities
into unconstrained functions. These functions exhibit cross-sectionally
correlation and temporal dependence. Via a functional analysis of variance
decomposition, we decompose the unconstrained functional panel data into a
deterministic trend component and a time-varying residual component. To produce
forecasts for the time-varying component, a functional time series forecasting
method, based on the estimation of the long-range covariance, is implemented.
By combining the forecasts of the time-varying residual component with the
deterministic trend component, we obtain h-step-ahead forecast curves for
multiple populations. Illustrated by age- and sex-specific life-table death
counts in the United States, we apply our proposed method to generate forecasts
of the life-table death counts for 51 states.",2403.13340v1
1998-04-24,Analytical Results For The Steady State Of Traffic Flow Models With Stochastic Delay,"Exact mean field equations are derived analytically to give the fundamental
diagrams, i.e., the average speed - car density relations, for the
Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high
speed vehicles $(v_{max}=M>1) $ with stochastic delay. Starting with the basic
equation describing the time evolution of the number of empty sites in front of
each car, the concepts of inter-car spacings longer and shorter than $M$ are
introduced. The probabilities of having long and short spacings on the road are
calculated. For high car densities $(\rho \geq 1/M)$, it is shown that
inter-car spacings longer than $M$ will be shortened as the traffic flow
evolves in time, and any initial configurations approach a steady state in
which all the inter-car spacings are of the short type. Similarly for low car
densities $(\rho \leq 1/M)$, it can be shown that traffic flow approaches an
asymptotic steady state in which all the inter-car spacings are longer than
$M-2$. The average traffic speed is then obtained analytically as a function of
car density in the asymptotic steady state. The fundamental diagram so obtained
is in excellent agreement with simulation data.",9804269v1
2007-04-25,Wang-Landau molecular dynamics technique to search for low-energy conformational space of proteins,"Multicanonical molecular dynamics (MD) is a powerful technique for sampling
conformations on rugged potential surfaces such as protein. However, it is
notoriously difficult to estimate the multicanonical temperature effectively.
Wang and Landau developed a convenient method for estimating the density of
states based on a multicanonical Monte Carlo method. In their method, the
density of states is calculated autonomously during a simulation. In this paper
we develop a set of techniques to effectively apply the Wang-Landau method to
MD simulations. In the multicanonical MD, the estimation of the derivative of
the density of states is critical. In order to estimate it accurately, we
devise two original improvements. First, the correction for the density of
states is made smooth by using the Gaussian distribution obtained by a short
canonical simulation. Second, an approximation is applied to the derivative,
which is based on the Gaussian distribution and the multiple weighted histogram
technique. A test of this method was performed with small polypeptides,
Met-enkephalin and Trp-cage, and it is demonstrated that Wang-Landau MD is
consistent with replica exchange MD but can sample much larger conformational
space.",0704.3365v3
2008-08-22,Single crystal growth and physical properties of the layered arsenide BaRh_2As_2,"Single crystals of BaRh_2As_2 have been synthesized from a Pb flux. We
present the room temperature crystal structure, single crystal x-ray
diffraction measurements as a function of temperature T, anisotropic magnetic
susceptibility \chi versus T, electrical resistivity in the ab-plane \rho
versus T, Hall coefficient versus T and magnetic field H, and heat capacity C
versus T measurements on the crystals. The single crystal structure
determination confirms that BaRh_2As_2 forms in the tetragonal ThCr_2Si_2 type
structure (space group I4/mmm) with lattice parameters a = b = 4.0564(6)\AA and
c = 12.797(4) \AA. Band structure calculations show that BaRh_2As_2 should be
metallic with a small density of states at the Fermi energy N(E_ F) = 3.49
states/eV f.u. (where f.u. \equiv formula unit) for both spin directions.
\rho(T) data in the ab-plane confirm that the material is indeed metallic with
a residual resistivity \rho(2K) = 29 \mu \Omega cm, and with a residual
resistivity ratio \rho(310K)/\rho(2K) = 5.3. The observed \chi(T) is small
(\sim 10^{-5} cm^3/mol) and weakly anisotropic with \chi_{ab}/\chi_ c \approx
2. The C(T) data indicate a small density of states at the Fermi energy with
the low temperature Sommerfeld coefficient \gamma = 4.7(9) mJ/mol K^2. There
are no indications of superconductivity, spin density wave, or structural
transitions between 2K and 300K. We compare the calculated density of states
versus energy of BaRh_2As_2 with that of BaFe_2As_2.",0808.3116v1
2013-07-29,Effects of electronic correlations and magnetic field on a molecular ring out of equilibrium,"We study effects of electron-electron interactions on the steady-state
characteristics of a hexagonal molecular ring in a magnetic field, as a model
for a benzene molecular junction. The system is driven out of equilibrium by
applying a bias voltage across two metallic leads. We employ a model
Hamiltonian approach to evaluate the effects of on-site as well as
nearest-neighbour density-density type interactions in a physically relevant
parameter regime. Results for the steady-state current, charge density and
magnetization in three different junction setups (para, meta and ortho) are
presented. Our findings indicate that interactions beyond the mean-field level
renormalize voltage thresholds as well as current plateaus. Electron-electron
interactions lead to substantial charge redistribution as compared to the
mean-field results. We identify a strong response of the circular current on
the electronic structure of the metallic leads. Our results are obtained by
steady-state Cluster Perturbation Theory, a systematically improvable
approximation to study interacting molecular junctions out of equilibrium, even
in magnetic fields. Within this framework general expressions for the current,
charge density and magnetization in the steady-state are derived. The method is
flexible and fast and can straight-forwardly be applied to effective models as
obtained from ab-initio calculations.",1307.7530v2
2015-01-30,Random Matrix Theory with U(N) Racah Algebra for Transition Strengths,"For finite quantum many-particle systems, a given system, induced by a
transition operator, makes transitions from its states to the states of the
same system or to those of another system. Examples are electromagnetic
transitions (then the initial and final systems are same), nuclear beta and
double beta decay (then the initial and final systems are different), particle
addition to or removal from a given system and so on. Working towards
developing a complete statistical theory for transition strength densities
(transition strengths multiplied by the density of states at the initial and
final energies), we have started a program to derive formulas for the lower
order bivariate moments of the strength densities generated by a variety of
transition operators. In this paper results are presented for a transition
operator that removes $k_0$ number of particle by considering $m$ spinless
fermions in $N$ single particle states. The Hamiltonian that is $k$-body is
represented by EGUE($k$) [embedded Gaussian unitary ensemble of $k$-body
interactions] and similarly the transition operator by an appropriate
independent EGUE. Employing the embedding $U(N)$ algebra, finite-$N$ formulas
for moments up to order four are derived and they show that in general the
smoothed (with respect to energy) bivariate transition strength densities take
bivariate Gaussian form. Extension of these results to particle addition
operator and beta decay type operators are discussed.",1501.07670v1
2023-07-06,Strong Purcell enhancement of an optical magnetic dipole transition,"Engineering the local density of states with nanophotonic structures is a
powerful tool to control light-matter interactions via the Purcell effect. At
optical frequencies, control over the electric field density of states is
typically used to couple to and manipulate electric dipole transitions.
However, it is also possible to engineer the magnetic density of states to
control magnetic dipole transitions. In this work, we experimentally
demonstrate the optical magnetic Purcell effect using a single rare earth ion
coupled to a nanophotonic cavity. We engineer a new single photon emitter,
Er$^{3+}$ in MgO, where the electric dipole decay rate is strongly suppressed
by the cubic site symmetry, giving rise to a nearly pure magnetic dipole
optical transition. This allows the unambiguous determination of a magnetic
Purcell factor $P_m=1040 \pm 30$. We further extend this technique to realize a
magnetic dipole spin-photon interface, performing optical spin initialization
and readout of a single Er$^{3+}$ electron spin. This work demonstrates the
fundamental equivalence of electric and magnetic density of states engineering,
and provides a new tool for controlling light-matter interactions for a broader
class of emitters.",2307.03022v1
2002-02-10,Filling Control of the Pyrochlore Oxide Y2Ir2O7,"We report the filling control of the pyrochlore oxide Y2Ir2O7. Metallic
ground state appears with increasing substitution content x (x >= 0.3). We have
revealed that the density of states at the Fermi level rapidly changes with x
by this filling control of Y2Ir2O7.",0202169v2
2007-02-08,"Cylindrically Symmetric, Static, Perfect-Fluid Solutions of Einstein's Field Equations","Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field
equations are obtained for the equations of state $\rho+3p=0$ and $\rho=p$. In
the former case, the density and the pressure turn out to be constant while in
the later case, they depend on the radial parameter $r$. Evan's solution
corresponding to the equation of state $\rho=p$ is included in the solutions
discussed here.",0702045v1
2003-06-14,Open-Closed Duality at Tree Level,"We study decay of unstable D-branes in string theory in the presence of
electric field, and show that the classical open string theory results for
various properties of the final state agree with the properties of closed
string states into which the system is expected to decay. This suggests a
duality between tree level open string theory on unstable D-branes and closed
strings at high density.",0306137v1
2005-11-02,Can tetraneutron exist from theoretical point of view?,"A theoretical possibility is shown for the bound state of a tetraneutron to
exist in the case of the proposed neutron-neutron potentials in the singlet
state with two attractive wells separated by a repulsive barrier. The anomalous
behaviours are revealed for the calculated size, density distribution, and pair
correlation functions of a hypothetical tetraneutron.",0511006v1
1997-07-11,On the Localization of One-Photon States,"Single photon states with arbitrarily fast asymptotic power-law fall-off of
energy density and photodetection rate are explicitly constructed. This goes
beyond the recently discovered tenth power-law of the Hellwarth-Nouchi photon
which itself superseded the long-standing seventh power-law of the Amrein
photon.",9707027v1
2004-11-13,Non-decomposable quantum dynamical semigroups and bound entangled states,"We use open quantum system techniques to construct one-parameter semigroups
of positive maps and apply them to study the entanglement properties of a class
of 16-dimensional density matrices, representing states of a 4x4 bipartite
system.",0411095v1
2006-04-10,Canonical Coset Parameterization and the Bures Metric of the Three-level Quantum Systems,"An explicit parameterization for the state space of an $n$-level density
matrix is given. The parameterization is based on the canonical coset
decomposition of unitary matrices. We also compute, explicitly, the Bures
metric tensor over the state space of two- and three-level quantum systems.",0604063v2
2008-11-03,Equation of state for QCD matter in a quasiparticle model,"A phenomenological QCD quasiparticle model provides a means to map lattice
QCD results to regions relevant for a variety of heavy-ion collision
experiments at larger baryon density. We report on effects of collectives modes
and damping on the equation of state.",0811.0274v1
2010-03-21,Symmetry energy in the structure and in reactions,"Efforts to extract information on magnitude and density dependence of the
nuclear symmetry energy are discussed. The utilized data include those on mass
dependence of the excitation energies to the isobaric analog states of ground
states, as well as data on the diffusion of isospin in heavy-ion reactions.
Results following from different observables are compared.",1003.4011v1
2012-08-30,On the ground state energy scaling in quasi-rung-dimerized spin ladders,"On the basis of periodic boundary conditions we study perturbatively a large
N asymptotics (N is the number of rungs) for the ground state energy density
and gas parameter of a spin ladder with slightly destroyed rung-dimerization.
Exactly rung-dimerized spin ladder is treated as the reference model. Explicit
perturbative formulas are obtained for three special classes of spin ladders.",1208.6192v1
2015-12-02,Point-contact spectroscopy of superconductors in the nonequilibrium state,"A phase transition of the region of the superconductor near the point contact
into a new nonequi- librium state at the critical density of
nonequilibriumquasiparticles is observed.",1512.00684v2
2019-12-15,Unitarity of quantum tunneling decay for an analytical exact non-Hermitian resonant-state approach,"By using an exact analytical non-Hermitian formalism involving the full set
of resonance (quasinormal) states and complex energy eigenvalues for quantum
tunneling decay, we show that unitarity holds at any instant of time for the
nonstationary decaying probability density in the whole space, thus providing a
fundamental description of the quantum mechanical decay process.",1912.07069v2
2022-06-19,Quantum states defined by using the finite frame quantization,"Finite frame quantization is a discrete version of the coherent state
quantization. In the case of a quantum system with finite-dimensional Hilbert
space, the finite frame quantization allows us to associate a linear operator
to each function defined on the discrete phase space of the system. We
investigate the properties of the density operators which can be defined by
using this method.",2206.10602v2
2014-10-31,"One-dimensional Hubbard model with pair-hopping term: Pair-density wave, pair-superconductor and orthogonal metal","As the simplest non-Fermi liquids, orthogonal metals have gapped
single-particle excitations but show normal metallic behaviors in thermodynamic
and transport quantities. Such an exotic metallic state could be realized in a
Hubbard model with pair-hopping term. However, it is difficult to solve this
model in higher dimension, here we focus on its one-dimension version, in which
a powerful U(1) abelian bosonization technique is available to capture
\textit{analytically} its universal low-energy physics. It is found that the
one-dimensional system is unable to provide an appropriate precursor for the
desirable orthogonal metals in higher dimension and the occurrence of the
featureless orthogonal metallic phase needs \textit{at least} a
quasi-one-dimensional multi-leg ladder model. Nevertheless, two interesting
quantum liquid phases are identified for the present one-dimensional model,
namely, pair-density wave (PDW) state and pair-superconducting (PSC) state. The
former describes the charge-density-wave order of cooper pairs while the latter
shows the superfluidity of two cooper pairs. Needing not any explicit
calculation, these two phases could have further implications in the
two-dimensional case, namely, the PDW state may give rise to quantum electron
liquid crystal states, which is believed to be responsible for the complex
pseudogap phase in cuprate, and the PSC state with charge 4e can be related to
certain nematic superconducting state. These predications call for further
investigation on this model in higher dimension by available analytical methods
and/or numerical calculations.",1410.8666v2
2006-12-04,Entanglement in phase space,"Classical surfaces in phase space correspond to quantum states in Hilbert
space. Subsystems specify factor spaces of the Hilbert space. An entangled
state corresponds semiclassically to a surface that cannot be decomposed into a
product of lower dimensional surfaces. Such a classical factorization never
exists for ergodic eigenstates of a chaotic Hamiltonian. The space of quantum
operators corresponds to a double phase space. The various representations of
the density operator then result from alternative choices of allowed coordinate
planes. In the case of the Wigner function and its Fourier transform, the chord
function, or the quantum characteristic function, this is a phase space on its
own. The reduced Wigner function, representing the partial trace of a density
operator over a subsystem is the projection of the original Wigner function;
the reduced chord function is obtained as a section. The purity of the reduced
density operator, the square of its trace, is a measure of entanglement,
obtained by integrating either the square of the reduced Wigner function, or
the square-modulus of the reduced chord function. Bell inequalities for general
parity measurements can be violated even for classical looking states with
positive Wigner functions that have evolved classically from product states.
These include the original EPR state. Entanglement with an unknown environment
results in decoherence. An example is that of the centre of mass of a large
number of independent particles, entangled with internal variables. In this
case, the Central Limit Theorem for Wigner functions leads to some aspects of
Markovian evolution for the reduced system.",0612029v1
2019-05-08,Stability analysis of ground states in a one-dimensional trapped spin-1 Bose gas,"In this work we study the stability properties of the ground states of a
spin-1 Bose gas in presence of a trapping potential in one spatial dimension.
To set the stage we first map out the phase diagram for the trapped system by
making use of a, so-called, continuous-time Nesterov method. We present an
extension of the method, which has been previously applied to one-component
systems, to our multi-component system. We show that it is a powerful and
robust tool for finding the ground states of a physical system without the need
of an accurate initial guess. We subsequently solve numerically the Bogoliubov
de-Gennes equations in order to analyze the stability of the ground states of
the trapped spin-1 system. We find that the trapping potential retains the
overall structure of the stability diagram, while affecting the spectral
details of each of the possible ground state waveforms. It is also found that
the peak density of the trapped system is the characteristic quantity
describing dynamical instabilities in the system. Therefore replacing the
homogeneous density with the peak density of the trapped system leads to good
agreement of the homogeneous Bogoliubov predictions with the numerically
observed maximal growth rates of dynamically unstable modes. The stability
conclusions in the one-dimensional trapped system are independent of the spin
coupling strength and the normalized trap strength over several orders of
magnitude of their variation.",1905.03069v2
2018-10-05,Duistermaat-Heckman measure and the mixture of quantum states,"In this paper, we present a general framework to solve a fundamental problem
in Random Matrix Theory (RMT), i.e., the problem of describing the joint
distribution of eigenvalues of the sum $\bsA+\bsB$ of two independent random
Hermitian matrices $\bsA$ and $\bsB$. Some considerations about the mixture of
quantum states are basically subsumed into the above mathematical problem.
Instead, we focus on deriving the spectral density of the mixture of adjoint
orbits of quantum states in terms of Duistermaat-Heckman measure, originated
from the theory of symplectic geometry. Based on this method, we can obtain the
spectral density of the mixture of independent random states. In particular, we
obtain explicit formulas for the mixture of random qubits. We also find that,
in the two-level quantum system, the average entropy of the equiprobable
mixture of $n$ random density matrices chosen from a random state ensemble
(specified in the text) increases with the number $n$. Hence, as a physical
application, our results quantitatively explain that the quantum coherence of
the mixture monotonously decreases statistically as the number of components
$n$ in the mixture. Besides, our method may be used to investigate some
statistical properties of a special subclass of unital qubit channels.",1810.02630v2
2013-10-10,Spin entanglement and nonlocality of multifermion systems,"Spin density matrices of the system, containing arbitrary even number N of
indistinguishable fermions with spin S = 1/2, described by antisymmetric wave
function, have been calculated. The indistinguishability and the Pauli
principles are proved to determine uniquely spin states, spin correlations and
entanglement of fermion spin states. Increase of the particle number in the
multifermion system reduces the spin correlation in any pair of fermions. The
fully entangled system of N electrons are shown to be composed by pairs with
nonentangled spin states that is the incoherent superposition of the singlet
and triplet states. Any large system of N fermions, such as electrons with spin
S = 1/2, the spin state of any particle are shown to be entangled with the
other part of the system containing N-1 particle. However, the spin state of
this electron is not entangled with any other particle, and spin state of any
electron pair is not entangled. These properties of spin states manifest in the
Einstein-Podolsky-Rosen as confirmation or violation of the Bell inequalities
indicating the presence of non-local quantum spin correlations.",1310.2863v3
2022-08-16,Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions,"We investigate the charge-density wave (CDW) transition for one-dimensional
spinless fermions at half band-filling with nearest-neighbor electron transfer
amplitude $t$ and interaction $V$. The model is equivalent to the anisotropic
XXZ Heisenberg model for which the Bethe Ansatz provides an exact solution. For
$V> V_{\rm c}= 2t$, the CDW order parameter and the single-particle gap are
finite but exponentially small, as is characteristic for a Kosterlitz-Thouless
transition. It is notoriously difficult to locate such infinite-order phase
transitions in the phase diagram using approximate analytical and numerical
approaches. Second-order Hartree-Fock theory is qualitatively applicable for
all interaction strengths, and predicts the CDW transition to occur at $V_{\rm
c,2}^{(2)}\approx 1.5t$. Second-order Hartree Fock theory is almost variational
because the density of quasi-particle excitations is small. We apply the
density-matrix renormalization group (DMRG) for periodic boundary conditions
for system sizes up to 514 sites which permits a reliable extrapolation of all
physical quantities to the thermodynamic limit, apart from the critical region.
We investigate the ground-state energy, the gap, the order parameter, the
momentum distribution, the quasi-particle density, and the density-density
correlation function to locate $V_{\rm c}$ from the DMRG data. Tracing the
breakdown of the Luttinger liquid and the peak in the quasi-particle density at
the band edge permits us to reproduce $V_{\rm c}$ with an accuracy of one
percent.",2208.07620v3
2018-11-01,Construction of quantum dark soliton in one-dimensional Bose gas,"Dark soliton solutions in the one-dimensional classical nonlinear
Schr\""odinger equation has been considered to be related to the yrast states
corresponding to the type-II excitations in the Lieb-Liniger model. However,
the relation is nontrivial and remains unclear because a dark soliton localized
in space breaks the translation symmetry, while yrast states are
translationally invariant. In this work, we construct a symmetry-broken quantum
soliton state and investigate the relation to the yrast states. By interpreting
a quantum dark soliton as a Bose-Einstein condensation to the wave function of
a classical dark soliton, we find that the quantum soliton state has a large
weight only on the yrast states, which is analytically proved in the free-boson
limit and numerically verified in the weak-coupling regime. By extending these
results, we derive a parameter-free expression of a quantum soliton state that
is written as a superposition of yrast states with Gaussian weights. The
density profile of this quantum soliton state excellently agrees to that of the
classical dark soliton. The dynamics of a quantum dark soliton is also studied,
and it turns out that the density profile of a dark soliton decays, but the
decay time increases as the inverse of the coupling constant in the
weak-coupling limit.",1811.00211v1
1994-07-02,The Dynamics of the Bean Critical State,"A simple one dimensional model to simulate the establishment of the Bean
critical state is introduced. It is shown that the dynamics of the flux lines
as they enter the superconductor are dominated by `avalanches'. The
distribution of distances moved by vortices in the avalanches obeys a power law
with an exponent of -1. This suggests that the Bean state is a self-organised
critical state. The density of flux lines is parabolic.",9407008v1
1999-05-28,Ground state of the hard-core Bose gas on lattice I. Energy estimates,"We investigate the properties of the ground state of a system of interacting
bosons on regular lattices with coordination number $k\geq 2$. The interaction
is a pure, infinite, on-site repulsion. Our concern is to give an improved
upper bound on the ground state energy per site. For a density $\rho$ a trivial
upper bound is known to be $-k\rho(1-\rho)$. We obtain a smaller variational
bound within a reasonably large family of trial functions. The estimates make
use of a large deviation principle for the energy of the Ising model on the
same lattice.",9905421v1
2000-09-05,Establishment of a stable vortex state in the peak effect region in a weakly pinned superconductor CeRu_2,"We present magnetization data on a weakly pinned CeRu_2 single crystal
showing the existence of a stable state of the vortex lattice in the peak
effect region. The stable state is achieved by cycling the magnetic field by
small amplitude. This stable state is characterized by a unique value of
critical current density (J_c), independent of the magnetic history of the
sample. The results support the recent model proposed by Ravikumar et al
\cite{r39} on the history dependence of the J_c.",0009069v1
2000-10-28,One-dimensional Surface Bound States in d-wave Superconductors,"We present an {\it exact} quantum theory for the bound states in the vicinity
of an edge or a line of impurities in a $d_{x^2-y^2}$ superconductor. For a
(110)-surface we show that a finite dispersion of the one dimensional band of
bound states leads to a two peak structure in the density of states (DOS). We
study the effect of an applied magnetic field and a subdominant $id_{xy}$ order
parameter on the DOS and discuss the implications of our results for tunneling
experiments.",0010460v1
2001-06-06,Gap Fluctuations in Inhomogeneous Superconductors,"Spatial fluctuations of the effective pairing interaction between electrons
in a superconductor induce variations of the order parameter which in turn lead
to significant changes in the density of states. In addition to an overall
reduction of the quasi-particle energy gap, theory suggests that mesoscopic
fluctuations of the impurity potential induce localised tail states below the
mean-field gap edge. Using a field theoretic approach, we elucidate the nature
of the states in the `sub-gap' region. Specifically, we show that these states
are associated with replica symmetry broken instanton solutions of the
mean-field equations.",0106109v1
2004-05-11,Failure of Scattering Interference in the Pseudogap State of Cuprate Superconductors,"We calculate scattering interference patterns for various electronic states
proposed for the pseudogap regime of the cuprate superconductors. The
scattering interference models all produce patterns whose wavelength changes as
a function of energy, in contradiction to the energy-independent wavelength
seen by scanning tunneling microscopy (STM) experiments in the pseudogap state.
This suggests that the patterns seen in STM local density of states
measurements are not due to scattering interference, but are rather the result
of some form of ordering.",0405204v1
2006-06-17,The effect of electron-electron interactions on the conditions of surface state existence,"Electronic surface states in one-dimensional two-band TBA model are studied
by use of the Green function method. The local density of states (LDOS) at
successive atoms in a semi-infinite chain, even in the case of atoms distant
from the surface, is found to be clearly different from that observed in an
unperturbed (infinite) chain. The surface atom occupancy is calculated
self-consistently, with the effect of electron-electron interactions taken into
account. The electron-electron interactions are shown to have a significant
impact on the conditions of surface state existence.",0606467v1
2001-12-20,A Note on the Tachyon State in Vacuum String Field Theory,"We re-examine the recent proposal of Rastelli, Sen and Zwiebach on the
tachyon fluctuation of the vacuum string field theory representing a D25 brane,
originally considered by Hata and Kawano. We show that the tachyon state
satisfies the linearized equations of motion on-shell in the strong sense
thereby allowing us to calculate the ratio of energy density to the tension of
the D-brane to be $E_c/T_{25}\simeq \pi^2/3[1/16(ln2)^3]\simeq 0.62$. Our proof
relies on a careful handling of the limits ($n\to\infty$) involved in the
conformal theory description of the sliver and tachyon states. We conjecture
that the sliver state represents a single D25 brane.",0112202v1
1995-04-04,Quantum Coding Theorem for Mixed States,"We prove a theorem for coding mixed-state quantum signals. For a class of
coding schemes, the von Neumann entropy $S$ of the density operator describing
an ensemble of mixed quantum signal states is shown to be equal to the number
of spin-$1/2$ systems necessary to represent the signal faithfully. This
generalizes previous works on coding pure quantum signal states and is
analogous to the Shannon's noiseless coding theorem of classical information
theory. We also discuss an example of a more general class of coding schemes
which {\em beat} the limit set by our theorem.",9504004v2
2000-02-18,Beyond single-photon localization at the edge of a Photonic Band Gap,"We study spontaneous emission in an atomic ladder system, with both
transitions coupled near-resonantly to the edge of a photonic band gap
continuum. The problem is solved through a recently developed technique and
leads to the formation of a ``two-photon+atom'' bound state with fractional
population trapping in both upper states. In the long-time limit, the atom can
be found excited in a superposition of the upper states and a ``direct''
two-photon process coexists with the stepwise one. The sensitivity of the
effect to the particular form of the density of states is also explored.",0002051v1
2001-01-16,Quantum State Tomography of Complex Multimode Fields using Array Detectors,"We demonstrate that it is possible to use the balanced homodyning with array
detectors to measure the quantum state of correlated two-mode signal field. We
show the applicability of the method to fields with complex mode functions,
thus generalizing the work of Beck (Phys. Rev. Letts. 84, 5748 (2000)) in
several important ways. We further establish that, under suitable conditions,
array detector measurements from one of the two outputs is sufficient to
determine the quantum state of signals. We show the power of the method by
reconstructing a truncated Perelomov state which exhibits complicated structure
in the joint probability density for the quadratures.",0101070v1
2001-10-05,Comment on relationship between atomic squeezed and entangled states,"The ability of parameter recently proposed by Sorensen et al. (Nature, 409,
63 (2001)) to characterize entanglement or inseparability is investigated for a
system of two two-level atoms interacting with a single mode of radiation
field. For comparison we employ the necessary and sufficient criterion of Peres
and Horodecki for inseparability of bipartite states. We show that for diagonal
atomic density matrix the parameter of Sorensen et al. fails to show entangled
nature of collective atomic state whereas same state is inseparable in
accordance with Peres-Horodecki criterion.",0110032v1
2007-05-05,Mixing and decoherence to nearest separable states in quantum measurements,"We illustrate through numerical results a number of features of
environment-induced decoherence under a broad class of apparatus-environment
interactions in quantum measurements wherein the reduced system-apparatus
density matrix evolves towards the nearest separable state and, in addition,
there occurs a mixing in relevant groups of apparatus microstates (see below).
The resulting final state is unique and correctly embodies the measurement
statistics even in the absence of environment-induced superselection because of
energy differences between these groups of states. The partial transpose
remains non-positive throughout the process.",0705.0733v2
2008-01-10,Measurable Concurrence of Mixed States,"We show that bipartite concurrence for rank-2 mixed states of qubits is
written by an observable which can be exactly and directly measurable in
experiment by local projective measurements, provided that four copies of the
composite quantum system are available. In addition, for a tripartite quantum
pure state of qubits, the 3-tangle is also shown to be measurable only by
projective measurements on the reduced density matrices of a pair of qubits
conditioned on four copies of the state.",0801.1576v1
2010-02-09,Numerical studies of entangled PPT states in composite quantum systems,"We report here on the results of numerical searches for PPT states with
specified ranks for density matrices and their partial transpose. The study
includes several bipartite quantum systems of low dimensions. For a series of
ranks extremal PPT states are found. The results are listed in tables and
charted in diagrams. Comparison of the results for systems of different
dimensions reveal several regularities. We discuss lower and upper bounds on
the ranks of extremal PPT states.",1002.1949v1
2011-05-25,Non-Gaussian resistance noise in the ferromagnetic insulating state of a hole doped manganite,"We report the observation of a large 1/f noise in the ferromagnetic
insulating state (FMI) of a hole doped manganite single crystal of
La0.80Ca0.20MnO3 which manifests hopping conductivity in presence of a Coulomb
gap. The temperature dependent noise magnitude shows a deep within the FMI
state, there is a sharp freeze out of the noise magnitude with temperature on
cooling. As the material enters the FMI state, the noise becomes non-Gaussian
as seen through probability density function and second spectra. It is proposed
to arise from charge fluctuations in a correlated glassy phase of the polaronic
carriers which develop in these systems as reported in recent simulation
studies.",1105.5079v1
2011-08-01,Zeeman Splitting of Photonic Angular Momentum States in Gyromagnetic Cylinder,"We show that under the presence of a static magnetic field the photon
eigen-frequencies of a circular gyromagnetic cylinder experience a splitting
that is proportional to the angular momentum density of light at the cylinder
surface. Such a splitting of the photonic states is similar to the Zeeman
splitting of electronic states in atoms. This leads to some unusual decoupling
properties of these non-degenerate photonic angular momentum states, which are
demonstrated through numerical simulations.",1108.0215v2
2011-09-09,Quantum Kinetic Equations of Many-Particle Systems in Condensed States,"This paper is devoted to the description of the evolution of states of
quantum many-particle systems within the framework of a one-particle density
operator, which enables to construct the kinetic equations in scaling limits in
the presence of correlations of particle states at initial time, for instance,
correlations characterizing the condensed states.",1109.1998v2
2012-02-01,Spin state of negative charge-transfer material SrCoO3,"We employ the combination of the density functional and the dynamical
mean-field theory (LDA+DMFT) to investigate the electronic structure and
magnetic properties of SrCoO3, monocrystal of which were prepared recently. Our
calculations lead to a ferromagnetic metal in agreement with experiment. We
find that, contrary to some suggestions, the local moment in SrCoO3 does not
arise from intermediate spin state, but is a result of coherent superposition
of many different atomic states. We discuss how attribution of magnetic
response to different atomic states in solids with local moments can be
quantified.",1202.0110v2
2013-05-09,Beam splitter and entanglement created with the squeezed coherent states of the Morse potential,"The Morse potential is relatively closed to the harmonic oscillator quantum
system. Thus, following the idea used for the latter, we study the possibility
of creating entanglement using squeezed coherent states of the Morse potential
as an input field of a beam splitter. We measure the entanglement with the
linear entropy for two types of such states and we study the dependence with
the coherence and squeezing parameters. The new results are linked with
observations made on probability densities and uncertainty relations of those
states. The dynamical evolution of the linear entropy is also explored.",1305.2100v1
2014-10-01,Equivalent sets of coherent states of the 1D infinite square well and properties,"We prove the equivalence (under some conditions) of two sets of coherent
states built for the one-dimensional infinite square well: the so-called
generalized and Gaussian Klauder coherent states. We then derive an approximate
close expression approaching their probability density and wave function to
explore their properties analytically. This process gives thereby explanation
of the quasi-classical behavior of these states in terms of the main
observables and the Heisenberg uncertainty product",1410.0305v1
2017-02-06,On the oxidation state of titanium in titanium dioxide,"The oxidation state of titanium in titanium dioxide is commonly assumed to be
+4. This assumption is used ubiquitously to rationalize phenomena observed with
TiO2. We present a comprehensive electronic structure investigation of Ti ions,
TiO2 molecules and TiO2 bulk crystals, using different density functional
theory and wave function-based approaches, which suggests a lower oxidation
state (+3). Specifically, there is evidence of a significant remaining
contribution from valence s and d electrons of Ti, including the presence of a
nuclear cusp around the Ti core. The charge corresponding to valence s and d
states of Ti amounts to 1 e. The commonly assumed picture may therefore have to
be revised.",1702.01555v1
2017-02-15,Quantum state of a frequency comb,"Uncertainties in the frequency parameters of a frequency comb laser, causes
it to represent a mixed quantum state. The formulation of such a quantum state
is compounded by the fact that it contains both particle-number degrees of
freedom and temporal degrees of freedom. Here we develop a formalism in terms
of which such a mixed quantum state can be expressed. For this purpose we also
need to compute the expression for the power spectral density of the frequency
comb laser. We do so by taking the uncertainties in the frequency parameters
into account.",1702.04514v2
2017-05-21,Separability and entanglement in the Hilbert space reference frames related through the generic unitary transform for four level system,"Quantum correlations in the state of four-level atom are investigated by
using generic unitary transforms of the classical (diagonal) density matrix.
Partial cases of pure state, $X$-state, Werner state are studied in details.
The geometrical meaning of unitary Hilbert reference-frame rotations generating
entanglement in the initially separable state is discussed. Characteristics of
the entanglement in terms of concurrence, entropy and negativity are obtained
as functions of the unitary matrix rotating the reference frame.",1705.07433v1
2018-11-13,Electronic energy state and transmission properties study of triple barrier parabolic double quantum well,"We investigate transmission properties of triple barrier parabolic double
quantum well structure using the non-equilibrium Green's function method. In
particular, we examine the effect of system parameters on transmission
coefficient. The properties of the electronic state are also studied as a
function of the system parameters (such as the well and barrier widths) and
electric field bias. We also tested energy electronic state with calculating
the density of states. It has been found that the first resonant peaks shift
towards the lower energy region as the middle barrier width increases. New
resonant peaks emerge when the well widths or depths become wider. These
structures are useful for the design of electronic devices.",1811.05470v1
2020-09-16,The electric pulses induced multi-resistance states in the hysteresis temperature range of 1T-TaS2 and 1T-TaS1.6Se0.4,"The electric pulse-induced responses of 1T-TaS2 and 1T-TaS1.6Se0.4 crystals
in the commensurate charge-density-wave (CCDW) phase in the hysteresis
temperature range have been investigated. We observed that abrupt multiple
steps of the resistance are excited by electric pulses at a fixed temperature
forming multi metastable like states. We propose that the response of the
system corresponds to the rearrangements of the textures of CCDW domains and
the multi-resistance states or the nonvolatile resistance properties excited
simply by electric pulses have profound significance for the exploration of
solid-state devices.",2009.07587v1
2016-08-16,Effect of edge vacancies on localized states in semi-infinite zigzag graphene sheet,"The effect of vacancies on the robustness of zero-energy edge electronic
states in zigzag-type graphene layer is studied at different concentrations and
distributions of defects. All calculations are performed by using the Green's
function method and the tight-binding approximation. It is found that the
arrangement of defects plays a crucial role in the destruction of the edge
states. We have specified a critical distance between edge vacancies when their
mutual influence becomes significant and affects markedly the density of
electronic states at graphene edge.",1608.04523v2
2023-07-07,State of the Art Development on Solid-State Lithium Batteries,"Solid-state lithium batteries (SLBs) offers a promising avenue for the
development of next-generation lithium-ion batteries with ultrahigh energy
density and safety performance. This review provides a quick overview of the
state-of-the-art development of anode, cathode, solid electrolyte of SLBs and
the observation of ion transport in the cell during the past half year in 2023.
Other important developments for SLIBs such as high safety and performance
strategies have also been provided.",2307.03620v2
2023-09-20,Origin of the gap in the surface states of the antiferromagnetic topological insulator,"We study the influence of the antiferromagnetic order on the surface states
of topological insulators. We derive an effective Hamiltonian for these states,
taking into account the space structure of the antiferromagnetic ordering. We
obtain a typical (gapless) Dirac Hamiltonian for the surface states if the
surface of the sample is not perturbed. However, a shift in the chemical
potential of the surface layer opens a gap in the spectrum away from Fermi
energy. Such a gap arises only in systems with a finite antiferromagnetic
order. We observe that the gap is robust against the surface disorder. The
obtained results are consistent with the recent experiments and density
functional theory calculations.",2309.11216v1
2023-12-14,Richardson-Gaudin States,"This chapter gives an overview of Richardson-Gaudin states which represent
weakly correlated pairs of electrons. They are parametrized by sets of numbers
obtained from non-linear equations. The best method to solve these equations is
presented in a straightforward manner with enough detail to implement the
method computationally. Optimal expressions for the density matrix elements are
discussed. A simple description of 1-dimensional hydrogen chains is presented
in terms of Richardson-Gaudin states. Richardson-Gaudin states are placed in
the larger context of integrable models and geminal wavefunctions of quantum
chemistry.",2312.08804v1
2024-03-06,Hermitian-preserving ansatz and variational open quantum eigensolver,"We propose a new variational quantum algorithm named Variational Open Quantum
Eigensolver (VOQE) for solving steady states of open quantum systems described
by either Lindblad master equations or non-Hermitian Hamiltonians. In VOQE,
density matrices of mixed states are represented by pure states in doubled
Hilbert space. We give a framework for building circuit ansatz which we call
the Hermitian-preserving ansatz (HPA) to restrict the searching space. We also
give a method to efficiently measure the operators' expectation values by
post-selection measurements. We show the workflow of VOQE on solving steady
states of the LMEs of the driven XXZ model and implement VOQE to solve the
spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an
imaginary field.",2403.03478v1
2003-12-11,Fractional Quantum Hall States of Clustered Composite Fermions,"The energy spectra and wavefunctions of up to 14 interacting quasielectrons
(QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are
investigated using exact numerical diagonalization. It is shown that at
sufficiently high density the QE's form pairs or larger clusters. This
behavior, opposite to Laughlin correlations, invalidates the (sometimes
invoked) reapplication of the composite fermion picture to the individual QE's.
The series of finite-size incompressible ground states are identified at the QE
filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings
nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4,
1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states
were recently discovered experimentally. Detailed analysis indicates that QE or
QH correlations in these states are different from those of well-known FQH
electron states (e.g., Laughlin or Moore-Read states), leaving the origin of
their incompressibility uncertain. Halperin's idea of Laughlin states of QP
pairs is also explored, but is does not seem adequate.",0312290v2
2004-10-26,Relaxation energies and excited state structures of poly(para-phenylene),"We investigate the relaxation energies and excited state geometries of the
light emitting polymer, poly(para-phenylene). We solve the
Pariser-Parr-Pople-Peierls model using the density matrix renormalization group
method. We find that the lattice relaxation of the dipole-active $1^1B_{1u}^-$
state is quite different from that of the $1^3B_{1u}^+$ state and the
dipole-inactive $2^1A_g^+$ state. In particular, the $1^1B_{1u}^-$ state is
rather weakly coupled to the lattice and has a rather small relaxation energy
ca. 0.1 eV. In contrast, the $1^3B_{1u}^+$ and $2^1A_g^+$ states are strongly
coupled with relaxation energies of ca. 0.5 and ca. 1.0 eV, respectively. By
analogy to linear polyenes, we argue that this difference can be understood by
the different kind of solitons present in the $1^1B_{1u}^-$, $1^3B_{1u}^+$ and
$2^1A_g^+$ states. The difference in relaxation energies of the $1^1B_{1u}^-$
and $1^3B_{1u}^+$ states accounts for approximately one-third of the exchange
gap in light-emitting polymers.",0410675v1
2007-04-20,Biordered superconductivity and strong pseudogap state,"Interrelation between the two-particle and mean-field problems is used to
describe the strong pseudogap and superconducting states in cuprates. We
present strong pseudogap state as off-diagonal short-range order (ODSRO)
originating from quasi-stationary states of the pair of repulsing particles
with large total momentum (K - pair). Phase transition from the ODSRO state
into the off-diagonal long-range ordered (ODLRO) superconducting state is
associated with Bose-Einstein condensation of the K - pairs. A checkerboard
spatial order observable in the superconducting state in the cuprates is
explained by a rise of the K - pair density wave. A competition between the
ODSRO and ODLRO states leads to the phase diagram typical of the cuprates.
Biordered superconducting state of coexisting condensates of Cooper pairs with
zero momentum and K - pairs explains some properties of the cuprates observed
below Tc: Drude optical conductivity, unconventional isotope effect and two-gap
quasiparticle spectrum with essentially different energy scales.",0704.2742v1
2008-11-22,Quantum Correlations in Multipartite States. Study Based on the Wootters-Mermin Theorem,"Decomposition of any N-partite state (density operator) into clusters (that
do not overlap) is studied in detail with a view to learn as much as possible
about the correlations implied by the state. The Wootters-Mermin theorem,
stating that the totality of all strings of cluster events (projectors)
determines the state in any finite- or infinite-dimensional state space, is a
slightly sharpened and generalized form of the original results of Wootters and
Mermin. It is applied to tensor factorization of the state into states of
clusters (uncorrelated decomposition) and it is shown that a finest
uncorrelated decomposition always exists, and that its coarsenings and only
they are other possible uncorrelated cluster decompositions. Distant effects
witin homogeneous cluster states, which are, by definition, the tensor factors
in the finest uncorrelated decomposition, are discussed. The entire study is
viewed by the author as a possible further elaboration of Mermin's Ithaca
program.",0811.3674v1
2023-02-22,Bi-directional quantum teleportation of GHZ-like states,"In this paper we propose a method through which $n$-qubit states can
simultaneously be bi-directionally transmitted between two users. We assume
that Alice and Bob, the legitimate users, each have a $n$-qubit GHZ-like state
and want to teleport it to the other party. Also, a four-qubit cluster state
plays the role of the quantum channel of this bi-directional quantum
teleportation. The protocol is based on the method that at first, each user,
through a series of $\mbox{CNOT}$ gates, converts the $n$-qubit state into a
single qubit and some $0$ qubits. Then, by means of the Bell state measurement
and proper operation, the single qubit state is transferred over the channel
between the two sides. By re-applying the $\mbox{CNOT}$ gates on the
transmitted qubits and auxiliary $0$ states, each user reconstructs the initial
GHZ-like state. Finally, we investige the effects of some kind of noises on the
density marix of the channel due to its interaction with the environment and
present a method to protect the channel against the bit-flip error.",2302.11300v1
2024-01-17,Optimal remote restoring of quantum states in communication lines via local magnetic field,"Optimal state transport across spin chains, which are proposed as quantum
wires for information transfer in solid state quantum architectures, is an
important topic for quantum technologies. In this work, we study {the remote
restoring of a quantum state transferred along a spin chain.} The structural
state-restoring technique provides proportionality between the appropriate
elements of the density matrices of the initial sender state and receiver state
at some time instant. We develop a {remote} state-restoring protocol which uses
an inhomogeneous magnetic field with step-wise time-dependent Larmor
frequencies as the state-control tool. For simulating the multiparametric
Hamiltonian we use two approximating models. First model is based on the
Trotter-Suzuki method, while the second model is based on using short pulses of
high intensity. In both cases we estimate the accuracy of the approximation and
find the optimal restoring parameters (Larmor frequencies) of the protocol
which maximize the coefficients in the proportionality for spin chains of
various lengths.",2401.09569v1
2020-01-16,PDANet: Pyramid Density-aware Attention Net for Accurate Crowd Counting,"Crowd counting, i.e., estimating the number of people in a crowded area, has
attracted much interest in the research community. Although many attempts have
been reported, crowd counting remains an open real-world problem due to the
vast scale variations in crowd density within the interested area, and severe
occlusion among the crowd. In this paper, we propose a novel Pyramid
Density-Aware Attention-based network, abbreviated as PDANet, that leverages
the attention, pyramid scale feature and two branch decoder modules for
density-aware crowd counting. The PDANet utilizes these modules to extract
different scale features, focus on the relevant information, and suppress the
misleading ones. We also address the variation of crowdedness levels among
different images with an exclusive Density-Aware Decoder (DAD). For this
purpose, a classifier evaluates the density level of the input features and
then passes them to the corresponding high and low crowded DAD modules.
Finally, we generate an overall density map by considering the summation of low
and high crowded density maps as spatial attention. Meanwhile, we employ two
losses to create a precise density map for the input scene. Extensive
evaluations conducted on the challenging benchmark datasets well demonstrate
the superior performance of the proposed PDANet in terms of the accuracy of
counting and generated density maps over the well-known state of the arts.",2001.05643v10
2016-10-17,Deconstruction and differentiation of squeezed kitten states in a qubit-oscillator system,"We study the evolution of the hybrid entangled squeezed states of the
qubit-oscillator system in the strong coupling domain. Following the adiabatic
approximation we obtain the reduced density matrices of the qubit and the
oscillator degrees of freedom. The oscillator reduced density matrix is
utilized to calculate the quasiprobability distributions such as the
Sudarshan-Glauber diagonal P -representation, the Wigner W -distribution, and
the nonnegative Husimi Q-function. The negativity associated with the W
-distribution acts as a measure of the nonclassicality of the state. The
existence of the multiple time scales induced by the interaction introduces
certain features in the bipartite system. In the strong coupling regime the
transient evolution to low entropy configurations reveals brief emergence of
nearly pure kitten states that may be regarded as superposition of uniformly
separated distinguishable squeezed coherent states. However, the quantum
fluctuations with a short time period engender bifurcation and subsequent
rejoining of these peaks in the phase space. The abovementioned doubling of the
number of peaks increases the entropy to its near maximal value. Nonetheless,
these states characterized by high entropy values, are endowed with a large
negativity of the W -distribution that points towards their non-Gaussian
behavior. This may be ascertained by the significantly large Hilbert-Schmidt
distance between the oscillator state and an ensemble of most general
statistical mixture of squeezed Gaussian states possessing nearly identical
second order quadrature moments as that of the oscillator.",1610.05117v1
1996-02-19,Reconstruction of cosmological density and velocity fields in the Lagrangian Zel'dovich Approximation,"We present a method for reconstructing cosmological densityn for and velocity
fields using the Lagrangian Zel'dovich formalism. . The method involves finding
the least action solution for straight line particle paths in an evolving
density field. Our starting point is the final, evolved density , so that we
are in effect carrying out the standard Zel'dovich Approximation based process
in reverse. Using a simple numerical algorithm we are able to minimise the
action for the trajectories of several million particles. We apply our method
to the evolved density taken from N-body simulations of different cold dark
matter dominated universes, testing both the prediction for the present day
velocity field and for the initial density field. The method is easy to apply,
reproduces the accuracy of the forward Zel'dovich Approximation, and also works
directly in redshift space with minimal modification.",9602100v2
2011-10-12,Charge self-consistent dynamical mean-field theory based on the full-potential linear muffin-tin orbital method: methodology and applications,"Full charge self-consistence (CSC) over the electron density has been
implemented into the local density approximation plus dynamical mean-field
theory (LDA+DMFT) scheme based on a full-potential linear muffin-tin orbital
method (FP-LMTO). Computational details on the construction of the electron
density from the density matrix are provided. The method is tested on the
prototypical charge-transfer insulator NiO using a simple static Hartree-Fock
approximation as impurity solver. The spectral and ground state properties of
bcc Fe are then addressed, by means of the spin-polarized T-matrix fluctuation
exchange solver (SPTF). Finally the permanent magnet SmCo$_5$ is studied using
multiple impurity solvers, SPTF and Hubbard I, as the strength of the local
Coulomb interaction on the Sm and Co sites are drastically different. The
developed CSC-DMFT method is shown to in general improve on materials
properties like magnetic moments, electronic structure and the materials
density.",1110.2606v1
2013-10-23,Thermodynamic properties of liquid mercury to 520 K and 7 GPa from acoustic velocity measurements,"Ultrafast acoustics measurements on liquid mercury have been performed at
high pressure and temperature in diamond anvils cell using picosecond acoustic
interferometry. We extract the density of mercury from adiabatic sound
velocities using a numerical iterative procedure. The pressure and temperature
dependence of the thermal expansion, the isothermal compressibilty, the
isothermal bulk modulus and its pressure derivative are derived up to 7 GPa and
520 K. In the high pressure regime, the sound velocity values, at a given
density, are shown to be only slightly dependent on the specific temperature
and pressure conditions. The density dependence of sound velocity at low
density is consistent with that observed with our data at high density in the
metallic liquid state.",1310.6264v1
2016-07-08,Colloids Exposed to Random Potential Energy Landscapes: from Particle Number Density to Particle-Potential and Particle-Particle Interactions,"Colloidal particles were exposed to a random potential energy landscape
(rPEL) that has been created optically via a speckle pattern. The mean particle
density as well as the potential roughness, i.e. the disorder strength, were
varied. The local probability density of the particles as well as its main
characteristics were determined. For the first time, the disorder-averaged pair
density correlation function and an analogue of the Edwards-Anderson order
parameter, which quantifies the correlation of the mean local density among
disorder realisations, were measured experimentally and shown to be consistent
with replica liquid state theory results.",1607.02288v1
2016-09-22,On the applicability of density dependent effective interactions in cluster-forming systems,"We systematically studied the validity and transferability of effective,
coarse-grained, pair potentials in ultrasoft colloidal systems. We focused on
amphiphilic dendrimers, macromolecules which can aggregate into clusters of
overlapping particles to minimize the contact area with the surrounding
(implicit) solvent. Simulations were performed for both the monomeric and
coarse-grained model in the liquid phase at densities ranging from infinite
dilution up to values close to the freezing point. For every state point, each
macromolecule was mapped onto a single interaction site and the effective pair
potential was computed using a coarse-graining technique based on
force-matching. We found excellent agreement between the spatial dendrimer
distributions obtained from the coarse-grained and microscopically detailed
simulations at low densities, where the macromolecules were distributed
homogeneously in the system. However, the agreement deteriorated significantly
when the density was increased further and the cluster occupation became more
polydisperse. Under these conditions, the effective pair potential of the
coarse-grained model can no longer be computed by averaging over the whole
system, but the local density needs to be taken into account instead.",1609.06855v1
2017-02-10,Density Functional Estimators with k-Nearest Neighbor Bandwidths,"Estimating expected polynomials of density functions from samples is a basic
problem with numerous applications in statistics and information theory.
Although kernel density estimators are widely used in practice for such
functional estimation problems, practitioners are left on their own to choose
an appropriate bandwidth for each application in hand. Further, kernel density
estimators suffer from boundary biases, which are prevalent in real world data
with lower dimensional structures. We propose using the fixed-k nearest
neighbor distances for the bandwidth, which adaptively adjusts to local
geometry. Further, we propose a novel estimator based on local likelihood
density estimators, that mitigates the boundary biases. Although such a choice
of fixed-k nearest neighbor distances to bandwidths results in inconsistent
estimators, we provide a simple debiasing scheme that precomputes the
asymptotic bias and divides off this term. With this novel correction, we show
consistency of this debiased estimator. We provide numerical experiments
suggesting that it improves upon competing state-of-the-art methods.",1702.03051v1
2019-02-07,Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation,"We prove an existence and uniqueness result for solutions to nonlinear
diffusion equations with degenerate mobility posed on a bounded interval for a
certain density $u$. In case of \emph{fast-decay} mobilities, namely mobilities
functions under a Osgood integrability condition, a suitable coordinate
transformation is introduced and a new nonlinear diffusion equation with linear
mobility is obtained. We observe that the coordinate transformation induces a
mass-preserving scaling on the density and the nonlinearity, described by the
original nonlinear mobility, is included in the diffusive process. We show that
the rescaled density $\rho$ is the unique weak solution to the nonlinear
diffusion equation with linear mobility. Moreover, the results obtained for the
density $\rho$ allow us to motivate the aforementioned change of variable and
to state the results in terms of the original density $u$ without prescribing
any boundary conditions.",1902.02764v1
2019-12-02,Density matrix based perturbative corrections for improved quantum simulation accuracy,"We present error mitigation (EM) techniques for noisy intermediate-scale
quantum computers (QC) based on density matrix purification and perturbative
corrections to the target energy. We incorporate this scheme into the
variational quantum eigensolver (VQE) and demonstrate chemically-accurate
ground state energy calculations of various alkali metal hydrides using IBM
quantum computers. Both the density matrix purification improvements and the
perturbative corrections require only meager classical computational resources,
and are conducted exclusively as post-processing of the measured density
matrix. The improved density matrix leads to better simulation accuracy at each
step of the variational optimization, resulting in a better input into the next
optimization step without additional measurements. Adding perturbative
corrections to the resulting energies further increases the accuracy, and
decreases variation between consecutive measurements. These EM schemes allow
for previously unavailable levels of accuracy over remote QC resources.",1912.01056v1
2021-03-05,Learning the sampling density in 2D SPARKLING MRI acquisition for optimized image reconstruction,"The SPARKLING algorithm was originally developed for accelerated 2D magnetic
resonance imaging (MRI) in the compressed sensing (CS) context. It yields
non-Cartesian sampling trajectories that jointly fulfill a target sampling
density while each individual trajectory complies with MR hardware constraints.
However, the two main limitations of SPARKLING are first that the optimal
target sampling density is unknown and thus a user-defined parameter and second
that this sampling pattern generation remains disconnected from MR image
reconstruction thus from the optimization of image quality. Recently,
datadriven learning schemes such as LOUPE have been proposed to learn a
discrete sampling pattern, by jointly optimizing the whole pipeline from data
acquisition to image reconstruction. In this work, we merge these methods with
a state-of-the-art deep neural network for image reconstruction, called XPDNET,
to learn the optimal target sampling density. Next, this density is used as
input parameter to SPARKLING to obtain 20x accelerated non-Cartesian
trajectories. These trajectories are tested on retrospective compressed sensing
(CS) studies and show superior performance in terms of image quality with both
deep learning (DL) and conventional CS reconstruction schemes.",2103.03559v2
2021-03-20,Adaptive deep density approximation for Fokker-Planck equations,"In this paper we present an adaptive deep density approximation strategy
based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P)
equations. F-P equations are usually high-dimensional and defined on an
unbounded domain, which limits the application of traditional grid based
numerical methods. With the Knothe-Rosenblatt rearrangement, our newly proposed
flow-based generative model, called KRnet, provides a family of probability
density functions to serve as effective solution candidates for the
Fokker-Planck equations, which has a weaker dependence on dimensionality than
traditional computational approaches and can efficiently estimate general
high-dimensional density functions. To obtain effective stochastic collocation
points for the approximation of the F-P equation, we develop an adaptive
sampling procedure, where samples are generated iteratively using the
approximate density function at each iteration. We present a general framework
of ADDA-KR, validate its accuracy and demonstrate its efficiency with numerical
experiments.",2103.11181v2
2021-09-16,Machine-Learned HASDM Model with Uncertainty Quantification,"The first thermospheric neutral mass density model with robust and reliable
uncertainty estimates is developed based on the SET HASDM density database.
This database, created by Space Environment Technologies (SET), contains 20
years of outputs from the U.S. Space Force's High Accuracy Satellite Drag Model
(HASDM), which represents the state-of-the-art for density and drag modeling.
We utilize principal component analysis (PCA) for dimensionality reduction,
creating the coefficients upon which nonlinear machine-learned (ML) regression
models are trained. These models use three unique loss functions: mean square
error (MSE), negative logarithm of predictive density (NLPD), and continuous
ranked probability score (CRPS). Three input sets are also tested, showing
improved performance when introducing time histories for geomagnetic indices.
These models leverage Monte Carlo (MC) dropout to provide uncertainty
estimates, and the use of the NLPD loss function results in well-calibrated
uncertainty estimates without sacrificing model accuracy (<10% mean absolute
error). By comparing the best HASDM-ML model to the HASDM database along
satellite orbits, we found that the model provides robust and reliable
uncertainties in the density space over all space weather conditions. A
storm-time comparison shows that HASDM-ML also supplies meaningful uncertainty
measurements during extreme events.",2109.07651v1
2022-06-01,Charge density wave and superconductivity in 6R-TaS2,"The layered transition metal dichalcogenide compounds 1T-TaS2 and 4H-TaS2 are
well known for their exotic properties, which include charge density wave,
superconductivity, Mott transition, etc., and lately quantum spin liquid. Here,
we report the magnetic, transport and transmission electron microscopy study of
the charge density wave and superconductivity in 6R-TaS2 which is a relatively
less studied polymorph of this dichalcogenide TaS2. Our high temperature
electron microscopy reveals multiple charge density wave transitions between
room temperature and 650K. Magnetization, and the electrical resistivity
measurements in the temperature range of 2-400 K reveal that 6R-TaS2 undergoes
a charge density wave transition around 305 K and is followed by a transition
to a superconducting state around 3.5 K. The low temperature specific heat
measurement exhibits anomaly associated with the superconducting transition
around 2.4 K. The estimated Ginzburg Landau parameter suggests that this
compound lies at the extreme limit of type-II superconductivity.",2206.00281v3