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More supersymmetric Wilson loops | We present a large new family of Wilson loop operators in N=4 supersymmetric
Yang-Mills theory. For an arbitrary curve on the three dimensional sphere one
can add certain scalar couplings to the Wilson loop so it preserves at least
two supercharges. Some previously known loops, notably the 1/2 BPS circle,
belong to this class, but we point out many more special cases which were not
known before and could provide further tests of the AdS/CFT correspondence.
|
Grothendieck rings of basic classical Lie superalgebras | The Grothendieck rings of finite dimensional representations of the basic
classical Lie superalgebras are explicitly described in terms of the
corresponding generalised root systems. We show that they can be interpreted as
the subrings in the weight group rings invariant under the action of certain
groupoids called Weyl groupoids.
|
Boundaries and the Casimir effect in non-commutative space-time | We calculate modifications to the scalar Casimir force between two parallel
plates due to space-time non-commutativity. We devise a heuristic approach to
overcome the difficulties of describing boundaries in non-commutative theories
and predict that boundary corrections are of the same order as non-commutative
volume corrections. Further, both corrections have the form of more
conventional finite surface effects.
|
Negative differential conductivity in Heisenberg XXZ chain far from
equilibrium | Negative differential conductivity is reported for the far from equilibrium
quantum spin transport in the insulating regime (J_x < J_z) of finite
Heisenberg XXZ spin 1/2 chains. The phenomenon is reproduced analytically for
small chains of N=4 spins and further analyzed numerically, for up to N=16,
using an efficient pure-state simulation with stochastic spin baths.
|
Representations of Lie algebras arising from polytopes | We present an extremely elementary construction of the simple Lie algebras
over the complex numbers in all of their minuscule representations, using the
vertices of various polytopes. The construction itself requires no complicated
combinatorics and essentially no Lie theory other than the definition of a Lie
algebra; in fact, the Lie algebras themselves appear as by-products of the
construction.
|
Irreducible representations and Artin L-functions of quasi-cyclotomic
fields | We determine all irreducible representations of primary quasi-cyclotomic
fields in this paper. The methods can be applied to determine the irreducible
representations of any quasi-cyclotomic field. We also compute the Artin
L-functions for a class of quasi-cyclotomic fields.
|
Graphs with chromatic roots in the interval (1,2) | We present an infinite family of 3-connected non-bipartite graphs with
chromatic roots in the interval (1,2) thus resolving a conjecture of Jackson's
in the negative. In addition, we briefly consider other graph classes that are
conjectured to have no chromatic roots in (1,2).
|
Finite-size correction and bulk hole-excitations for special case of an
open XXZ chain with nondiagonal boundary terms at roots of unity | Using our solution for the open spin-1/2 XXZ quantum spin chain with N spins
and two arbitrary boundary parameters at roots of unity, the central charge and
the conformal dimensions for bulk hole excitations are derived from the 1/N
correction to the energy (Casimir energy).
|
Inverse Scattering for Gratings and Wave Guides | We consider the problem of unique identification of dielectric coefficients
for gratings and sound speeds for wave guides from scattering data. We prove
that the "propagating modes" given for all frequencies uniquely determine these
coefficients. The gratings may contain conductors as well as dielectrics and
the boundaries of the conductors are also determined by the propagating modes.
|
Gersten's conjecture | The purpose of this article is to prove that Gersten's conjecture for a
commutative regular local ring is true. As its applications, we will prove the
vanishing conjecture for certain Chow groups, generator conjecture for certain
$K$-groups and Bloch's formula for absolute case.
|
On the width of collective excitations in chiral soliton models | In chiral soliton models for baryons the computation of hadronic decay widths
of baryon resonances is a long standing problem. For the three flavor Skyrme
model I present a solution to this problem that satisfies large--$N_C$
consistency conditions. As an application I focus on the hadronic decay of the
$\Theta$ and $\Theta^*$ pentaquarks.
|
The Einstein relation generalized to non-equilibrium | The Einstein relation connecting the diffusion constant and the mobility is
violated beyond the linear response regime. For a colloidal particle driven
along a periodic potential imposed by laser traps, we test the recent
theoretical generalization of the Einstein relation to the non-equilibrium
regime which involves an integral over measurable velocity correlation
functions.
|
The Heaviside equation for laser heating of the fullerennes | In his paper the heating of the fullerenes by ultra-short laser pulses is
investigated. The thermal Heaviside equation is formulated and solved for the
Cauchy initial condition The effective thermal relaxation time is calculated..
Key words: fullerenes, Heaviside thermal equation, effective thermal
relaxation time.
|
Probing Alpha-Vacua of Black Holes in LHC | Motivated by the idea of alpha-vacua in Schwarzschild spacetime, we studied
the deformed spectrum of Hawking radiation. Such a deformation would leave
signatures on the small black hole evaporation in LHC because their vacuum
deviates from the Unruh state.
|
Factorization of the Non-Stationary Schrodinger Operator | We consider a factorization of the non-stationary Schrodinger operator based
on the parabolic Dirac operator introduced by Cerejeiras/ Kahler/ Sommen. Based
on the fundamental solution for the parabolic Dirac operators, we shall
construct appropriated Teodorescu and Cauchy-Bitsadze operators. Afterwards we
will describe how to solve the nonlinear Schrodinger equation using Banach
fixed point theorem.
|
ATLAS Discovery Potential for the Charged Higgs Boson in H+ to tau nu
Decays | This paper has been withdrawn by the authors in order to comply with the
ATLAS publication policy and is now only available via the CERN cdsweb
(http://cdsweb.cern.ch/record/984015)
|
Coulomb scattering of the Dirac field on de Sitter expanding universe | The lowest order contribution of the amplitude of the Dirac-Coulomb
scattering in de Sitter spacetime is calculated assuming that the initial and
final states of the Dirac field are described by exact solutions of the free
Dirac equation on de Sitter spacetime with a given momentum and helicity. One
studies the difficulties that arises when one passes from the amplitude to
cross section.
|
On a multi-resonant origin of high frequency quasiperiodic oscillations
in the neutron-star X-ray binary 4U 1636-53 | The results we presented were biased because of the typing error in the code
transcription of the equation (A.12). We will replace by the corrected version
soon. The brief of the corrected results can be found at
http://www.physics.cz/research/doc/posters/1181038112_0.pdf
|
Symmetries in the system of type $A_5^{(2)}$ | In this paper, we propose a 3-parameter family of coupled Painlev\'e III
systems in dimension four with affine Weyl group symmetry of type $A_5^{(2)}$.
We also propose its symmetric form in which the $A_5^{(2)}$-symmetries become
clearly visible.
|
Cutting surfaces and applications to periodic points and chaotic-like
dynamics | In this paper we propose an elementary topological approach which unifies and
extends various different results concerning fixed points and periodic points
for maps defined on sets homeomorphic to rectangles embedded in euclidean
spaces. We also investigate the associated discrete semidynamical systems in
view of detecting the presence of chaotic-like dynamics.
|
CdZnTe:Cl crystals for X-ray computer tomography detectors | Processes of growth of semi-insulating Cd(1-x)Zn(x)Te:Cl crystals (x = 0.0002
and 0.1) of n-type conductivity are investigated. From the grown crystals
detectors for X-ray computer tomography with small value of photocurrent memory
(afterglow) (0.1-0.3%) are obtained.
|
Symmetries in the system of type $D_4^{(1)}$ | In this paper, we propose a 4-parameter family of coupled Painlev\'e III
systems in dimension four with affine Weyl group symmetry of type $D_4^{(1)}$.
We also propose its symmetric form in which the $D_4^{(1)}$-symmetries become
clearly visible.
|
A new class of rank one transformations with singular spectrum | We introduce a new tool to study the spectral type of rank one
transformations using the method of central limit theorem for trigonometric
sums. We get some new applications.
|
Navier-Stokes equations with periodic boundary conditions and pressure
loss | We present in this note the existence and uniqueness results for the Stokes
and Navier-Stokes equations which model the laminar flow of an incompressible
fluid inside a two-dimensional channel of periodic sections. The data of the
pressure loss coefficient enables us to establish a relation on the pressure
and to thus formulate an equivalent problem.
|
Solutions fortes de l'\'equation de l'\'energie | In this paper, we give some existence results of stong solutions for the
energy equation associated to the Navier-Stokes equations with nonhomogeneous
boundary conditions in two dimension.
|
On Brownian flights | Let K be a compact subset of ${\mathbb R}^n$. We choose at random with
uniform law a point at distance $\epsilon$ of K and start a Brownian motion
(BM) from this point. We study the probability that this BM hits K for the
first time at a distance $\geq r$ from the starting point.
|
Analogy electromagnetism-acoustics: Validation and application to local
impedance active control for sound absorption | An analogy between electromagnetism and acoustics is presented in 2D. The
propagation of sound in presence of absorbing material is modeled using an open
boundary microwave package. Validation is performed through analytical and
experimental results. Application to local impedance active control for free
field sound absorption is finally described.
|
Coupled Painlev\'e VI systems in dimension four with affine Weyl group
symmetry of type $D_6^{(1)}$, II | We give a reformulation of a six-parameter family of coupled Painlev\'e VI
systems with affine Weyl group symmetry of type $D_6^{(1)}$ from the viewpoint
of its symmetry and holomorphy properties.
|
Growing Directed Networks: Estimation and Hypothesis Testing | Based only on the information gathered in a snapshot of a directed network,
we present a formal way of checking if the proposed model is correct for the
empirical growing network under study. In particular, we show how to estimate
the attractiveness, and present an application of the model presented in
[arxiv:0704.1847] to the scientific publications network from the ISI dataset.
|
Catalan Traffic and Integrals on the Grassmannians of Lines | We prove that certain numbers occurring in a problem of paths enumeration,
studied by Niederhausen (Catlan Traffic at the Beach, The Electronic Journal of
Combinatorics, 9, (2002), 1--17), are top intersection numbers in the
cohomology ring of the grassmannians of the lines in the complex projective
(n+1)-space.
|
A note on Seshadri constants on general $K3$ surfaces | We prove a lower bound on the Seshadri constant $\epsilon (L)$ on a $K3$
surface $S$ with $\Pic S \simeq \ZZ[L]$. In particular, we obtain that
$\epsilon (L)=\alpha$ if $L^2=\alpha^2$ for an integer $\alpha$.
|
Local well-posedness of Musiela's SPDE with L\'evy noise | We determine sufficient conditions on the volatility coefficient of Musiela's
stochastic partial differential equation driven by an infinite dimensional
L{\'e}vy process so that it admits a unique local mild solution in spaces of
functions whose first derivative is square integrable with respect to a weight.
|
L'indice de Maslov dans les $JB^*$-triples | We construct a homotopy invariant index for pathes in the set of invertible
tripotents in a JB*-triple that satisfy a Fredholm type condition with respect
to a fixed invertible tripotent. That index generalizes the Maslov index in the
Fredholm-Lagrangian of a symplectic Hilbert space.
|
Symmetry in the Painlev\'e systems and their extensions to
four-dimensional systems | We give a new approach to the symmetries of the Painlev\'e equations
$P_{V},P_{IV},P_{III}$ and $P_{II}$, respectively. Moreover, we make natural
extensions to fourth-order analogues for each of the Painlev\'e equations
$P_{V}$ and $P_{III}$, respectively, which are natural in the sense that they
preserve the symmetries.
|
Multivariate Wavelet Frames | We proved that for any matrix dilation and for any positive integer $n$,
there exists a compactly supported tight wavelet frame with approximation order
$n$. Explicit methods for construction of dual and tight wavelet frames with a
given number of vanishing moments are suggested.
|
An English translation o Bertrand's theorem | A beautiful theorem due to J. L. F. Bertrand concerning the laws of
attraction that admit bounded closed orbits for arbitrarily chosen initial
conditions is translated from French into English.
|
Dynamics of the universe in the modified unimodular theory of gravity | The equations that govern the dynamics of the universe in the modified
unimodular theory of gravity are derived. We find a mechanism for inflation in
the early universe without postulating a false vacuum state during the first
$10^{-35}$ seconds after the Big Bang. In addition, we find a natural
explanation for the acceleration of the universe without resorting to dark
energy.
|
The Invariant Ring of Triples of 3x3 Matrices over a Field of Arbitrary
Characteristic | Let R_{n,d} be the ring of invariants of d-tuples of n x n matrices under the
simultaneous conjugation action of the general linear group. A minimal
generating system and a homogeneous system of parameters for R_{3,3} are
determined. Homogeneous systems of parameters for R_{3,2}, R_{4,2} are also
pointed out.
|
Indecomposable invariants of quivers for dimension (2,...,2) and maximal
paths | An upper bound on degrees of elements of a minimal generating system for
invariants of quivers of dimension (2,...,2) is established over a field of
arbitrary characteristic and its precision is estimated. The proof is based on
the reduction to the problem of description of maximal paths satisfying certain
condition.
|
Hopf algebras of dimension pq, II | Let H be a Hopf algebra of dimension pq over an algebraically closed field of
characteristic zero, where p, q are odd primes with p < q < 4p+12. We prove
that H is semisimple and thus isomorphic to a group algebra, or the dual of a
group algebra.
|
The Topological Theory of the Milnor Invariant $\bar{\mu}(1,2,3)$ | We study a topological Abelian gauge theory that generalizes the Abelian
Chern-Simons one, and that leads in a natural way to the Milnor's link
invariant $\bar{\mu}(1,2,3)$ when the classical action on-shell is calculated.
|
Integrable Nonautonomous Nonlinear Schrodinger Equations | We show that a recently given nonautonomous nonlinear Schrodinger equation
(NLSE) can be transformed into the autonomous NLSE.
|
New $_5F_4$ hypergeometric transformations, three-variable Mahler
measures, and formulas for $1/\pi$ | New relations are established between families of three-variable Mahler
measures. Those identities are then expressed as transformations for the
$_5F_4$ hypergeometric function. We use these results to obtain two explicit
$_5F_4$ evaluations, and several new formulas for $1/\pi$.
|
Superfield formulation of 4D, N=1 massless higher spin gauge field
theory and supermatrix model | We study the relation between a supermatrix model and the free 4D, N=1
supersymmetric field theory of a massless supermultiplet with spins (3, 5/2).
In order to do this, we construct a superfield formulation of the theory. We
show that solutions of the equations of motion for the supermultiplet (3, 5/2)
satisfy the equations of motion of a supermatrix model.
|
An Abstract Regularity Lemma | We extend Szemeredi's Regularity Lemma (SRL) to abstract measure spaces. Our
main aim is to find general conditions under which the original proof of
Szemeredi still works. To illustrate that our approach has some merit, we
outline several applications. Some of these applications seem to be tailored to
our approach: in particular, we are not aware of any alternative proofs.
|
On Carmichael's Conjecture | In this article we prove that equation $\phi(x)=n$, for a fixed $n$, admits a
finite number of solutions, we find the general form of these solutions, and we
show that: if $x_0$ is a unique solution of this equation then $x_0$ is a
product of a very large number of primes (we conjecture that the number of such
primes is infinite).
|
Another Odd Thing About Unparticle Physics | The peculiar propagator of scale invariant unparticles has phases that
produce unusual patterns of interference with standard model processes. We
illustrate some of these effects in $e^+e^-\to\mu^+\mu^-$.
|
Ultra-High Energy Cosmic Rays and the GeV-TeV Diffuse Gamma-Ray Flux | Ultra-high energy cosmic ray protons accelerated in astrophysical objects
produce secondary electromagnetic cascades during propagation in the cosmic
microwave and infrared backgrounds. We show that such cascades can contribute
between ~1% and ~50% of the GeV-TeV diffuse photon flux measured by the EGRET
experiment. The GLAST satellite should have a good chance to discover this
flux.
|
Fermionic formulas for (1,p) logarithmic model characters in \Phi_{2,1}
quasiparticle realisation | We give expressions for the characters of $(1,p)$ logarithmic conformal field
models in the Gordon-type form. The formulas are obtained in terms of
``quasiparticles'' that are Virasoro $\Phi_{2,1}$ primary fields and generalize
the symplectic fermions.
|
N=2 supergravity in three dimensions and its Godel supersymmetric
background | The four dimensional Godel spacetime is known to have the structure M_3 x R.
It is also known that the three-dimensional factor M_3 is an exact solution of
three-dimensional gravity coupled to a Maxwell-Chern-Simons theory. We build in
this paper a N=2 supergravity extension for this action and prove that the
Godel background preserves half of all supersymmetries.
|
Coupled Painlev\'e III systems with affine Weyl group symmetry of types
$B_5^{(1)},D_5^{(1)}$ and $D_6^{(2)}$ | We find and study four kinds of five-parameter family of six-dimensional
coupled Painlev\'e III systems with affine Weyl group symmetry of types
$D_5^{(1)},B_5^{(1)}$ and $D_6^{(2)}$. We show that each system is equivalent
by an explicit birational and symplectic transformation, respectively. We also
show that we characterize each system from the viewpoint of holomorphy.
|
Discontinuity of the Lempert function and the Kobayashi--Royden metric
of the spectral ball | Some results on the discontinuity properties of the Lempert function and the
Kobayashi pseudometric in the spectral ball are given.
|
Coupled Painlev\'e III systems with affine Weyl group symmetry of types
$B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$ | We find and study four kinds of a 4-parameter family of four-dimensional
coupled Painlev\'e III systems with affine Weyl group symmetry of types
$B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$. We also show that these systems are
equivalent by an explicit birational and symplectic transformation,
respectively.
|
Lineare Rekurrenzen, Potenzreihen und ihre erzeugenden Funktionen | Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen
versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele
ausfuehrliche Beispiele angegeben.
This short introduction to theory and usage of linear recurrences tries to
fill a gap in the literature by giving many extensive examples.
|
Un module inversible associ\'e au ruban de M\"obius, et quelques autres | After attaching explicitly to the M\"obius strip an invertible module over
the ring of real polynomial functions on the real circle, we expound as
directly as possible the many faces and the main algebraic properties of
invertible modules. The goal is to make this algebraic concept accessible to a
wide mathematical audience.
|
Substrate temperature changes during MBE growth of GaMnAs | Remarkably big increase of the substrate temperature during the
low-temperature MBE growth of GaMnAs layers is observed by means of band gap
spectroscopy. It is explained and simulated in terms of changes in the
absorption/emission characteristics of the growing layer. Options for the
temperature variation damping are discussed.
|
Supersymmetry breaking by constant superpotentials and O'Raifeartaigh
model in warped space | Supersymmetry breaking together by constant boundary superpotentials and by
the O'Raifeartaigh model is studied in a warped space model. It is shown that
the contribution of constant boundary superpotentials enables the moduli of
chiral supermultiplets to be stabilized and that the vacuum at the stationary
point has zero cosmological constant in a wide region of parameters.
|
On the Stability Functional for Conservation Laws | This note is devoted to the explicit construction of a functional defined on
all pairs of $\L1$ functions with small total variation, which is equivalent to
the $\L1$ distance and non increasing along the trajectories of a given system
of conservation laws. Two different constructions are provided, yielding an
extension of the original stability functional by Bressan, Liu and Yang.
|
Pure Point spectrum for measure dynamical systems on locally compact
Abelian groups | We show equivalence of pure point diffraction and pure point dynamical
spectrum for measurable dynamical systems build from locally finite measures on
locally compact Abelian groups. This generalizes all earlier results of this
type. Our approach is based on a study of almost periodicity in a Hilbert
space. It allows us to set up a perturbation theory for arbitrary equivariant
measurable perturbations.
|
Homotopy coherent nerve in Deformation theory | In this note we explain that homotopy coherent simplicial nerve has to used
intead of the standard definition in the author's papers on formal deformation
theory. A convenient version of the notion of fibered category is presented
which is useful once one works with simplicial categories.
|
Analyticity of strictly static and strictly stationary, inheriting and
non-inheriting Einstein-Maxwell solutions | Following the technique of M\"uller-zum-Hagen, refs [1,2], we show that
strictly static and strictly stationary solutions of the Einstein-Maxwell
equations are analytic in harmonic coordinates. This holds whether or not the
Maxwell field inherits the symmetry.
|
Postnikov-Stability for Complexes | We present a novel notion of stable objects in the derived category of
coherent sheaves on a smooth projective variety. As one application we
compactify a moduli space of stable bundles using genuine complexes.
|
Substitution tilings with statistical circular symmetry | Two new series of substitution tilings are introduced in which the tiles
appear in infinitely many orientations. It is shown that several properties of
the well-known pinwheel tiling do also hold for these new examples, and, in
fact, for all substitution tilings showing tiles in infinitely many
orientations.
|
Quelques plats pour la m\'etrique de Hofer | We show, by an elementary and explicit construction, that the group of
Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with
Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of
arbitrary dimension.
|
Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations
for the KdV Hierarchy | We study the Whitham equations for all the higher order KdV equations. The
Whitham equations are neither strictly hyperbolic nor genuinely nonlinear. We
are interested in the solution of the Whitham equations when the initial values
are given by a step function.
|
Self-dual tilings with respect to star-duality | The concept of star-duality is described for self-similar cut-and-project
tilings in arbitrary dimensions. This generalises Thurston's concept of a
Galois-dual tiling. The dual tilings of the Penrose tilings as well as the
Ammann-Beenker tilings are calculated. Conditions for a tiling to be self-dual
are obtained.
|
Integration on moduli spaces of stable curves through localization | We introduce a new method of calculating intersections on \bar{M}_{g,n},
using localization of equivariant cohomology. As an application, we give a
proof of Mirzakhani's recursion relation for calculating intersections of mixed
psi and kappa_1 classes.
|
Introduction to Phase Transitions in Random Optimization Problems | Notes of the lectures delivered in Les Houches during the Summer School on
Complex Systems (July 2006).
|
Note on charge interaction in NQED | The interaction of charges in NQED is discussed. It is shown that the
relativistic correction have the same form as in the commutative case provided
the Weyl ordering rule is used.
|
Local Energy Velocity of Classical Fields | It is proposed to apply a recently developed concept of local wave velocities
to the dynamical field characteristics, especially for the canonical field
energy density. It is shown that local energy velocities can be derived from
the lagrangian directly. The local velocities of zero- and first- order for
energy propagation has been obtained for special cases of scalar and vector
fields. Some important special cases of these results are discussed.
|
Metastable String Vacua | We argue that tachyon-free type I string vacua with supersymmetry breaking in
the open sector at the string scale can be interpreted, via S and T-duality
arguments, as metastable vacua of supersymmetric type I superstring. The
dynamics of the process can be partially captured via nucleation of
brane-antibrane pairs out of the non-supersymmetric vacuum and subsequent
tachyon condensation.
|
A tree without leaves | The puzzle presented by the famous stumps of Gilboa, New York, finds a
solution in the discovery of two fossil specimens that allow the entire
structure of these early trees to be reconstructed.
|
Characteristic forms of complex Cartan geometries | We calculate relations on characteristic classes which are obstructions
preventing closed K\"ahler manifolds from carrying holomorphic Cartan
geometries. We apply these relations to give global constraints on the phase
spaces of complex analytic determined and underdetermined systems of
differential equations.
|
On the quark propagator singularity | Using the method of Fukuda and Kugo \cite{FUKKUG} the continuation of
Euclidean solution is performed to the timelike axis of fourmomenta. It is
shown that assumed presence of the real simple pole in quark propagator is not
in agreement with the solution. The simple pole disappears because of the
discontinuity in the resulting quark mass function.
|
Homomorphic images of Branch groups, and Serre's property (FA) | It is shown that a finitely generated branch group has Serre's property (FA)
if and only if it does not surject onto the infinite cyclic group or the
infinite dihedral group. An example of a finitely generated self-similar branch
group surjecting onto the infinite cyclic group is constructed.
|
Higher order Painleve system of type D^{(1)}_{2n+2} arising from
integrable hierarchy | A higher order Painleve system of type D^{(1)}_{2n+2} was introduced by Y.
Sasano. It is an extension of the sixth Painleve equation for the affine Weyl
group symmetry. It is also expressed as a Hamiltonian system of order 2n with a
coupled Painleve VI Hamiltonian. In this paper, we discuss a derivation of this
system from a Drinfeld-Sokolov hierarchy.
|
Strong photon non-linearities and photonic Mott insulators | We show, that photon non-linearities in electromagnetically induced
transparency can be at least one order of magnitude larger than predicted in
all previous approaches. As an application we demonstrate that, in this regime
they give rise to very strong photon - photon interactions which are strong
enough to make an experimental realization of a photonic Mott insulator state
feasible in arrays of coupled ultra high-Q micro-cavities.
|
Formal completions of N\'eron models for algebraic tori | We calculate the formal group law which represents the completion of the
N\'eron model of an algebraic torus over the rationals that splits in a tamely
ramified abelian extension. As a tools in the proof, we define and give
criterions to compute the Weil restriction of a formal group law and the analog
of the fixed part of a formal group law with respect to the action of a
(finite) group.
|
Distributions of Roots of Reduced Cubic Equations with Random
Coefficients | If the coefficients of polynomials are selected by some random process, the
zeros of the resulting polynomials are in some sense random. In this paper the
author rephrases the above in more precise language, and calculates the joint
conditional densities of a random vector whose values determine almost surely
the zeros of a "random" reduced cubic.
|
Uniform convergence in the mapping class group | We characterize convex cocompact subgroups of the mapping class group of a
surface in terms of uniform convergence actions on the zero locus of the limit
set. We also construct subgroups that act as uniform convergence groups on
their limit sets, but are not convex cocompact.
|
Phases of three dimensional large N QCD on a continuum torus | It is established by numerical means that continuum large N QCD defined on a
three dimensional torus can exist in four different phases. They are (i)
confined phase; (ii) deconfined phase; (iii) small box at zero temperature and
(iv) small box at high temperatures.
|
Computing Extensions of Linear Codes | This paper deals with the problem of increasing the minimum distance of a
linear code by adding one or more columns to the generator matrix. Several
methods to compute extensions of linear codes are presented. Many codes
improving the previously known lower bounds on the minimum distance have been
found.
|
Regions without complex zeros for chromatic polynomials on graphs with
bounded degree | We prove that the chromatic polynomial $P_\mathbb{G}(q)$ of a finite graph
$\mathbb{G}$ of maximal degree $\D$ is free of zeros for $\card q\ge C^*(\D)$
with $$ C^*(\D) = \min_{0<x<2^{1\over \D}-1} {(1+x)^{\D-1}\over x [2-(1+x)^\D]}
$$ This improves results by Sokal (2001) and Borgs (2005). Furthermore, we
present a strengthening of this condition for graphs with no triangle-free
vertices.
|
Recent Developments in Maser Theory | This review covers selected developments in maser theory since the previous
meeting, "Cosmic Masers: From Proto-Stars to Black Holes" (Migenes & Reid
2002). Topics included are time variability of fundamental constants, pumping
of OH megamasers and indicators for differentiating disks from bi-directional
outflows.
|
Isolated fixed points and moment maps of symplectic manifolds | Withdrawn due to an incompleteness of the main results.
|
Unobservable Higgs Boson and Spontaneous Violation of Lorentz Invariance | The standard theory of elementary particle physics is modified in such a way
that the Higgs boson becomes unobservable and Lorentz invariance is slightly
violated at the level of the S-matrix. The basic technique of realizing these
properties without violating the unitarity of the physical S-matrix is the use
of the complex-ghost quantum field theory.
|
On Multiplier Hermitian Structures on Compact Kahler Manifolds | Mabuchi introduced multiplier Hermitian structures on compact Kahler
manifolds and defined metrics similar to Kahler-Einstein metrics under these
structures. In this note we generalize the inequality of Moser-Trudinger type
on Kahler-Einstein manifolds to this case.
|
A Wegner estimate for multi-particle random Hamiltonians | We prove a Wegner estimate for a large class of multiparticle Anderson
Hamiltonians on the lattice. These estimates will allow us to prove Anderson
localization for such systems. A detailed proof of localization will be given
in a subsequent paper.
|
Local quantum mechanics with finite Planck mass | In this paper the motion of quantum particles with initial mass m is
investigated. The quantum mechanics equation is formulated and solved. It is
shown that the wave function contains the component which is depended on the
gravitation fine structure constant
|
D-brane superpotentials and RG flows on the quintic | The behaviour of D2-branes on the quintic under complex structure
deformations is analysed by combining Landau-Ginzburg techniques with methods
from conformal field theory. It is shown that the boundary renormalisation
group flow induced by the bulk deformations is realised as a gradient flow of
the effective space time superpotential which is calculated explicitly to all
orders in the boundary coupling constant.
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Effect of premelting on conductivity of DNA-lipid films | We have measured temperature dependent (between 20 and 80 C) electrical
conductivity and molecular structure (Raman spectroscopy) of DNA-lipid cast
film. Our findings show that the conductivity is strongly influenced by
premelting effects in the molecular structure starting near physiological
temperatures (~40 C), prior to the global DNA denaturation.
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D.E.U.S. (Dimension Embedded in Unified Symmetry) | An unified model of the Universe, Black Holes, particles .... and beyond.
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The isospin symmetry breaking effects in $K_{e4}$ decays | The Fermi-Watson theorem is generalized to the case of two coupled channels
with different masses and applied to final state interaction in $K_{e4}$
decays. The impact of considered effect on the phase of the $\pi\pi$ scattering
is estimated and shown that it can be crucial for scattering lengths extraction
from experimental data on $K_{e4}$ decays.
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CP Violation Studies at Tevatron | We present an overview of a few recent results related to CP-violation from
the Tevatron. First, we discuss a measurement of the dimuon charge asymmetry
from D{\O}that extracts the CP-violation parameter of $\Bo$ mixing and decay.
This is followed by the CDF measurement of the CP-violating asymmetry in
$\bdkpi$ decays. Finally we give the CDF result on the ratio $R = \frac{BR(B
\to D^0 K)}{BR(B \to D^0 \pi)}$
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Entanglement induced Sub-Planck structures | We study Wigner function of a system describing entanglement of two
cat-states. Quantum interferece arising due to entanglement is shown to produce
sub-Planck structures in the phase-space plots of the Wigner function. Origin
of these structures in our case depends on entanglement unlike those in Zurek
\cite{Zurek}. It is argued that the entangled cat-states are better suited for
carrying out precision measurements.
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On the Applications of a New Technique to Solve Linear Differential
Equations, with and without Source | A general method for solving linear differential equations of arbitrary
order, is used to arrive at new representations for the solutions of the known
differential equations, both without and with a source term. A new
quasi-solvable potential has also been constructed taking recourse to the above
method.
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A Channel that Heats Up | Motivated by on-chip communication, a channel model is proposed where the
variance of the additive noise depends on the weighted sum of the past channel
input powers. For this channel, an expression for the capacity per unit cost is
derived, and it is shown that the expression holds also in the presence of
feedback.
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Classification of line-transitive point-imprimitive linear spaces with
line size at most 12 | In this paper we complete a classification of finite linear spaces $\cS$ with
line size at most 12 admitting a line-transitive point-imprimitive subgroup of
automorphisms. The examples are the Desarguesian projective planes of orders
$4,7, 9$ and 11, two designs on 91 points with line size 6, and 467 designs on
729 points with line size 8.
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On matrix type corings, algebra coverings and Cech cohomology | We investigate the a matrix-type coring associated to a complete covering of
an algebra, its Amitsur complex and propose a definition for the related Cech
cohomology relative to the covering.
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Twisted Dirac Operators over Quantum Spheres | We construct new families of spectral triples over quantum spheres, with a
particular attention focused on the standard Podles quantum sphere and twisted
Dirac operators.
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