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Random matrix products: Universality and least singular valuesFeb 08 2018We establish local universality of the $k$-point correlation functions associated with products of independent iid random matrices, as the sizes of the matrices tend to infinity, under a moment matching hypothesis. We also prove Gaussian limits for the ... More
Approximation of fractals by manifolds and other graph-like spacesFeb 08 2018We define a distance between energy forms on a graph-like metric measure space and on a discrete weighted graph using the concept of quasi-unitary equivalence. We apply this result to metric graphs and graph-like manifolds (e.g. a small neighbourhood ... More
Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperatureFeb 08 2018We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is purely atomic ... More
The n body matrix and its determinantFeb 08 2018The purpose of this note is to prove two recent conjectures concerning the $n$ body matrix that arises in recent papers of Escobar--Ruiz, Miller, and Turbiner on the classical and quantum $n$ body problem in $d$-dimensional space. First, whenever the ... More
Low-lying eigenvalues of semiclassical Schrödinger operator with degenerate wellsFeb 08 2018In this article, we consider the semiclassical Schr\"odinger operator $P = - h^{2} \Delta + V$ in $\mathbb{R}^{d}$ with confining non-negative potential $V$ which vanishes, and study its low-lying eigenvalues $\lambda_{k} ( P )$ as $h \to 0$. First, we ... More
Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformationsFeb 08 2018We study the fully nonlinear dynamical Cosserat micropolar elasticity problem in space with three dimensionals with various energy functionals dependent on the microrotation $\overline{R}$ and the deformation gradient tensor $F$ . We derive a set of coupled ... More
3D Current Algebra and Twisted K TheoryFeb 08 2018Equivariant twisted K theory classes on compact Lie groups $G$ can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra $LG$ using a supersymmetric ... More
On matrix modified KP hierarchyFeb 08 2018Using the bilinear formalism, we consider multicomponent and matrix modified KP hierarchies. The main tool is the bilinear identity for the tau-function which is realized as an expectation value of a Clifford group element composed from multicomponent ... More
Sharp operator-norm asymptotics for linearised elastic plates with rapidly oscillating periodic propertiesFeb 07 2018We analyse a system of partial differential equations describing the behaviour of an elastic plate with periodic moduli in the two planar directions. We assume that the displacement gradients of the points of the plate are small enough for the equations ... More
Disconnection by level sets of the discrete Gaussian free field and entropic repulsionFeb 07 2018We derive asymptotic upper and lower bounds on the large deviation probability that the level set of the Gaussian free field on $Z^d$, d bigger or equal to three, below a given level disconnects the discrete blow-up of a compact set A from the boundary ... More
Quasi-exactly solvable Schrödinger equations, symmetric polynomials, and functional Bethe ansatz methodFeb 07 2018For applications to quasi-exactly solvable Schr\"odinger equations in quantum mechanics, we consider the general conditions that have to be satisfied by the coefficients of a second-order differential equation with at most $k+1$ singular points in order ... More
Generalized localization operators: Cohen's class and trace class operatorsFeb 07 2018We study generalized localization operators from the perspective of Werner's operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase space is approached ... More
Two Dimensional Plane, Modified Symplectic Structure and QuantizationFeb 07 2018Noncommutative quantum mechanics on the plane has been widely studied in the literature. Here, we consider the problem using Isham's canonical group quantization scheme for which the primary object is the symmetry group that underlies the phase space. ... More
Scalar products of the elliptic Felderhof model and elliptic Cauchy formulaFeb 07 2018We analyze the scalar products of the elliptic Felderhof model introduced by Foda-Wheeler-Zuparic as an elliptic extension of the trigonometric face-type Felderhof model by Deguchi-Akutsu. We derive the determinant formula for the scalar products by applying ... More
$\infty$-topoi and Natural Phenomena: GenerationFeb 07 2018We show that the Segal topos of derived stacks over simplicial commutative $k$-algebras, which can be used to model natural phenomena, has a subobject classifier, something we regard as being a source from which dynamics is generated. This is done by ... More
The ultimate precision of quantum illuminationFeb 06 2018Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric ... More
Conformal invariance and the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence: Refuting a recent claimFeb 06 2018The recent claim by Grebenev et al. [J. Phys. A: Math. Theor. 50, 435502 (2017)] that the inviscid 2D Lundgren-Monin-Novikov (LMN) equations on a zero vorticity characteristic naturally would reveal local conformal invariance when only analyzing these ... More
Fifty years of the finite nonperiodic Toda lattice: A geometric and topological viewpointFeb 06 2018In 1967, Japanese physicist Morikazu Toda published a pair of seminal papers in the Journal of the Physical Society of Japan that exhibited soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the fifty years ... More
Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump processFeb 06 2018We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The first is a direct connection between the VRJP and sigma models whose target ... More
Control of fluctuations and heavy tails for heat variation in the two-time measurement frameworkFeb 06 2018We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier ... More
Local Energy Optimality of Periodic SetsFeb 06 2018We study the local optimality of periodic point sets in $\mathbb{R}^n$ for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-c r}$ with $c>0$. By considering suitable parameter spaces for $m$-periodic ... More
Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operatorsFeb 06 2018We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials $SP_\lambda((z_1,\ldots,z_n),(w_1,\ldots,w_m);\theta)$ with respect to a natural positive semi-definite, but degenerate, Hermitian product $\langle\cdot,\cdot\rangle_{n,m}^\prime$. ... More
Atiyah classes of Lie bialgebrasFeb 06 2018The Atiyah class was originally introduced by M.F. Atiyah. It has many developments in recent years. One important case is the Atiyah classes of Lie algebra pairs. In this paper, we study the Atiyah class of the Lie algebra pair associated with a Lie ... More
Blow-up profile of rotating 2D focusing Bose gasesFeb 06 2018We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the ground state when ... More
Breakdown of Ehrenfest theorem for free particle constrained on a hypersurfaceFeb 06 2018There is a belief that the Ehrenfest theorem holds true universally. We demonstrate that for a classically nonrelativistic particle constrained on an $N-1$ ($N\geq 2$) curved hypersurface embedded in $N$ flat space, the theorem breaks down.
Gagliardo-Nirenberg-Sobolev inequalities for convex domains in $\mathbb{R}^d$Feb 06 2018A special type of Gagliardo-Nirenberg-Sobolev (GNS) inequalities in $\mathbb{R}^d$ has played a key role in several proofs of Lieb-Thirring inequalities. Recently, a need for GNS inequalities in convex domains of $\mathbb{R}^d$, in particular for cubes, ... More
Renormalization for a Scalar Field in an External Scalar PotentialFeb 05 2018The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated ... More
Bernstein operators and super-Schur functions: combinatorial aspectsFeb 05 2018The Bernstein vertex operators, which can be used to build recursively the Schur functions, are extended to superspace. Four families of super vertex operators are defined, corresponding to the four natural families of Schur functions in superspace. Combinatorial ... More
Large deviations of avalanches in the raise and peel modelFeb 05 2018We study the large deviation functions for two quantities characterizing the avalanche dynamics in the Raise and Peel model: the number of tiles removed by avalanches and the number of global avalanches extending through the whole system. To this end, ... More
All unital qubit channels are $4$-noisy operationsFeb 05 2018We show that any unital qubit channel can be implemented by letting the input system interact unitarily with a $4$-dimensional environment in the maximally mixed state and then tracing out the environment. We also provide an example where the dimension ... More
Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnetsFeb 03 2018We solve the non-stationary Schrodinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as ... More
Vector Hamiltonians in Nambu mechanicsFeb 03 2018We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in $\mathbb{R}^n$ can be represented as a generalized Nambu mechanics with $n-1$ integral invariants. For the case when ... More
Unitarity issues in higher derivative field theoriesFeb 03 2018We analyze the unitarity properties of higher derivative quantum field theories which are free of ghosts and ultraviolet singularities. We point out that in spite of the absence of ghosts most of these theories are not unitary. This result confirms the ... More
A low-frequency variational model for energetic particle effects in the pressure-coupling schemeFeb 03 2018Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different kinetic-fluid coupling ... More
Differential invariants of Einstein-Weyl structures in 3DFeb 02 2018Einstein-Weyl structures on a three-dimensional manifold $M$ is given by a system $E$ of PDEs on sections of a bundle over $M$. This system is invariant under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two Einstein-Weyl structures are locally ... More
Hopf solitons on compact manifoldsFeb 02 2018Hopf solitons in the Skyrme-Faddeev system on $R^3$ typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the Skyrme term (the ... More
On the rattleback dynamicsFeb 01 2018In this paper we present some relevant dynamical properties of the rattleback, from the Poisson geometry point of view.
Mode solutions for a Klein-Gordon field in anti-de Sitter with dynamical boundary conditions of Wentzell typeFeb 01 2018We study a real, massive Klein-Gordon field in the Poincar\'e fundamental domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary ... More
Invariance and conservation laws of some nonlinear Schrodinger equation with PT-symmetric potentials and inhomogeneous nonlinearityFeb 01 2018In this paper, we construct and analyse the symmetries and conservation laws (conserved densities) of a model of a nonlinear Scrodinger equation with PT-symmetric potentials and inhomogeneity.
KdV hierarchy via Abelian coverings and operator identitiesJan 31 2018We establish precise spectral criteria for potential functions $V$ of reflectionless Schr\"odinger operators $L_V = -\partial_x^2 + V$ to admit solutions to the Korteweg de-Vries (KdV) hierarchy with $V$ as an initial value. More generally, our methods ... More
Lindbladians with multiple steady states: theory and applicationsJan 31 2018Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum properties, an engineered ... More
The Maxwell operator with periodic coefficients in a cylinderJan 31 2018In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is ... More
Green Function of the Poisson Equation: D=2,3,4Jan 30 2018We study the Green function of the Poisson equation in two, three and four dimensions. The solution g of the equation nabla^2 g(x - x') = \delta^(D)(x - x'), where x and x are D-dimensional position vectors, is customarily expanded into radial and angular ... More
Standard modules, Jones-Wenzl projectors, and the valenced Temperley-Lieb algebraJan 30 2018This article concerns a generalization of the Temperley-Lieb algebra, motivated by applications to conformal field theory. We call this algebra the valenced Temperley-Lieb algebra. We prove salient facts concerning this algebra and its representation ... More
Nonlinear stability of 2-solitons of the Sine-Gordon equation in the energy spaceJan 30 2018In this article we prove that 2-soliton solutions of the sine-Gordon equation (SG) are orbitally stable in the natural energy space of the problem. The solutions that we study are the {\it 2-kink, kink-antikink and breather} of SG. In order to prove this ... More
Quasiperiodic granular chains and Hofstadter butterfliesJan 30 2018We study quasiperiodicity-induced localization of waves in strongly precompressed granular chains. We propose three different setups, inspired by the Aubry--Andr\'e (AA) model, of quasiperiodic chains; and we use these models to compare the effects of ... More
Kähler fibrations in quantum information theoryJan 29 2018We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible K\"ahler structure. The case of the unitary group allows us to reformulate the geometric framework of quantum information theory. In particular, ... More
Higher rank isomonodromic deformations and W-algebrasJan 29 2018We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest example is given ... More
Nonlinear Excitations in Magnetic Lattices with Long-Range InteractionsJan 29 2018We study - experimentally, theoretically, and numerically - nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying ... More
R-matrix-valued Lax pairs and long-range spin chainsJan 26 2018In this paper we discuss $R$-matrix-valued Lax pairs for ${\rm sl}_N$ Calogero-Moser model and its relation to integrable quantum long-range spin chain of the Haldane-Shastry-Inozemtsev type. First, we construct the $R$-matrix-valued Lax pairs for the ... More
The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre typeJan 26 2018Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In "Painlev\'e III and a singular linear statistics in Hermitian random matrix ensembles, I", the authors proved that this deformation ... More
Concentration without measureJan 26 2018Although there doesn't exist the Lebesgue measure in the ball $M$ of $C[0,1]$ with $p-$norm, the average values (expectation) $EY$ and variance $DY$ of some functionals $Y$ on $M$ can still be defined through the procedure of limitation from finite dimension ... More
Biorthogonal Polynomial System Composed of X-Jacobi Polynomials from Different SequencesJan 26 2018The paper examines rational Darboux transformations (RDTs) of the Jacobi equation written in the canonical form, with emphasis on the Sturm-Liouville problems (SLPs) solved under the Dirichlet boundary conditions (DBCs) at the ends of the infinite interval ... More
Representations of meromorphic open-string vertex algebrasJan 26 2018We study representations of the meromorphic open-string vertex algebra (MOSVAs hereafter) defined in [H3], a noncommutative generalization of vertex (operator) algebra. We start by recalling the definition of a MOSVA $V$ and left $V$-modules in [H3]. ... More
A Curie-Weiss Theory of the Continuum Widom-Rowlinson ModelJan 25 2018A version of the continuum Widom-Rowlinson model is introduced and studied. It is a two-component gas of point particles placed in $\mathbf{R}^d$ in which like particles do not interact and unlike particles contained in a given vessel of volume $V$ repel ... More
Energy-parity from a bicomplex algebraJan 24 2018By replacing the field of complex numbers with the commutative ring of bicomplex numbers, we attempt to construct interacting scalar quantum field theories that feature both positive- and negative-energy states. This work places the tentative ideas proposed ... More
Doi-Peliti Path Integral Methods for Stochastic Systems with Partial ExclusionJan 24 2018Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct ... More
Existence of solutions to non-homogeneous higher order differential equation in the Schwartz spaceJan 24 2018There is studied problem on existence of solutions to non-homogeneous differential equation of higher even order. Similar problem arises while studying soliton and soliton-like solutions to partial differential equations of integrable type. By means of ... More
Stability of the 2+2 fermionic system with point interactionsJan 24 2018We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m_c \approx 0.58 such that the system is stable, ... More
On geometric estimates for some problems arising from modeling pull-in voltage in MEMSJan 23 2018In this paper for all $p>1$ we prove that the pull-in voltage of the $p$-MEMS (micro-electro mechanical systems) problems in a smooth bounded domain of $\mathbb R^{d}, d\geq1,$ is minimized by symmetrizing the domain and the permittivity profile. The ... More
Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equationJan 22 2018Jan 23 2018We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics ... More
Ballistic transport in the classical Toda chain with harmonic pinningJan 22 2018We investigate, via numerical simulation, heat transport in the nonequilibrium stationary state (NESS) of the 1D classical Toda chain with an additional pinning potential, which destroys momentum conservation. The NESS is produced by coupling the system, ... More
New variational and multisymplectic formulations of the Euler-Poincaré equation on the Virasoro-Bott group using the inverse mapJan 22 2018Jan 25 2018We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincar\'e equations defined on the Virasoro-Bott group, by using the inverse map (also called `back-to-labels' map). This ... More
Entanglement entropy in the Long-Range Kitaev chainJan 22 2018In this paper we complete the study on the asymptotic behaviour of the entanglement entropy for Kitaev chains with long range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic ... More
Weighted local Weyl laws for elliptic operatorsJan 22 2018Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $\mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $d\mu_\mathcal{X}$. Then, the spectrum of $A$ is made up ... More
Beautiful mathematics for beauty-full and other multi-heavy hadronic systemsJan 21 2018In most non-perturbative methods in hadron physics the calculations are started with a correlation function in terms of some interpolating and transition currents in $ x $-space. For simplicity, the calculations are then transformed to the momentum space ... More
Integrability and correspondence of classical and quantum non-linear three-mode systemJan 20 2018The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the quantum system ... More
On the asymptotic behavior of static perfect fluidsJan 20 2018Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite ... More
Scalar-torsion theories of gravity I: general formalism and conformal transformationsJan 19 2018We discuss the most general class of teleparallel scalar-torsion theories of gravity in their covariant formulation. The only restrictions we impose are the invariance of the action under diffeomorphisms and local Lorentz transformations, as well as vanishing ... More
Hardy-Lieb-Thirring Inequalities for Fractional Pauli OperatorsJan 19 2018We provide lower bounds for the sum of the negative eigenvalues of the operator $|\sigma\cdot p_A|^{2s} - C_s/|x|^{2s} + V$ in three dimensions, where $s\in (0, 1]$, covering the interesting physical cases $s = 1$ and $s = 1/2$. Here $\sigma$ is the vector ... More
The equivalence of the Power-Zineau-Woolley picture and the Poincaré gauge from the very first principlesJan 17 2018In reply to the paper Sci. Rep. 7:11115 (2017) by Rousseau and Felbacq, it is here shown at the level of the action that the Power-Zineau-Woolley picture of the electrodynamics of nonrelativistic neutral particles (atoms) is equivalent with the Poincar\'e ... More
An existence result and evolutionary $Γ$-convergence for perturbed gradient systemsJan 16 2018The initial-value problem for the perturbed gradient flow \[ B(t,u(t)) \in \partial\Psi_{u(t)}(u'(t))+\partial \mathcal E_t(u(t)) \text{ for a.a. } t\in (0,T),\qquad u(0)=u_0 \] with a perturbation $B$ in a Banach space $V$ is investigated, where the ... More
Two-dimensional Dirac fermion in presence of an asymmetric vector potentialJan 15 2018We introduce an exactly solvable model of two-dimensional Dirac fermion in presence of an asymmetric vector potential. Fundamental solutions of its stationary equation are represented by an irreducible combination of two Gauss hypergeometric functions. ... More
Nonlocal Representation of the $sl(2,R)$ Algebra for the Chazy equationJan 15 2018A demonstration of how the point symmetries of the Chazy Equation become nonlocal symmetries for the reduced equation is discussed. Moreover we construct an equivalent third-order differential equation which is related to the Chazy Equation under a generalized ... More
Rational Solutions of the Painlevé-III EquationJan 13 2018All of the six Painlev\'e equations except the first have families of rational solutions, which are frequently important in applications. The third Painlev\'e equation in generic form depends on two parameters $m$ and $n$, and it has rational solutions ... More
Multiplication of Distributions and Nonperturbative Calculations of Transition ProbabilitiesJan 10 2018In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so called "`infinite ... More
Global fluctuations for 1D log-gas dynamics. (2) Covariance kernel and supportJan 09 2018We consider the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, $ d\lambda_t^i=\frac{1}{\sqrt{N}} dW_t^i - V'(\lambda_t^i) dt+ \frac{\beta}{2N} \sum_{j\not=i} \frac{dt}{\lambda^i_t-\lambda^j_t}, ... More
Mean-field evolution of fermions with singular interactionJan 09 2018We consider a system of N fermions in the mean-field regime interacting though an inverse power law potential $V(x)=1/|x|^{\alpha}$, for $\alpha\in(0,1]$. We prove the convergence of a solution of the many-body Schr\"{o}dinger equation to a solution of ... More
Wigner function of noninteracting trapped fermionsJan 08 2018We study analytically the Wigner function $W_N({\bf x},{\bf p})$ of $N$ noninteracting fermions trapped in a smooth confining potential $V({\bf x})$ in $d$ dimensions. At zero temperature, $W_N({\bf x},{\bf p})$ is constant over a finite support in the ... More
On the Szegő formulas for truncated Wiener-Hopf operatorsJan 08 2018We consider functions of multi-dimensional versions of truncated Wiener--Hopf operators with smooth symbols, and study the scaling asymptotics of their traces. The obtained results extend the asymptotic formulas obtained by H. Widom in the 1980's to non-smooth ... More
Magnetic oscillations in a model of grapheneJan 05 2018We consider a quantum graph as a model of graphene in constant magnetic field and describe the density of states in terms of relativistic Landau levels satisfying a Bohr--Sommerfeld quantization condition. That provides semiclassical corrections (with ... More
A Phase Transition in a Widom-Rowlinson Model with Curie-Weiss InteractionJan 04 2018An analog of the continuum Widom-Rowlinson model is introduced and studied. Its two-component version is a gas of point particles of types 0 and 1 placed in $\mathds{R}^d$, in which like particles do not interact and unlike particles contained in a vessel ... More
Spectral properties of 2D Pauli operators with almost periodic electromagnetic fieldsJan 04 2018We consider a 2D Pauli operator with almost periodic field $b$ and electric potential $V$. First, we study the ergodic properties of $H$ and show, in particular, that its discrete spectrum is empty if there exists a magnetic potential which generates ... More
Covariant Schrödinger semigroups on noncompact Riemannian manifoldsJan 04 2018This monograph develops the theory of covariant Schr\"odinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. ... More
New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gasJan 04 2018In the context of $f\left( R\right) $-gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of $f(R)$ theories for ... More
Duffing oscillator and elliptic curve cryptographyJan 04 2018A new approach to discretization of the Duffing equation is presented. Integrable discrete maps are obtained by using well-studied encrypting operations in elliptic curve cryptography and, therefore, they do not depend upon standard small parameter assumption. ... More
The distribution of overlaps between eigenvectors of Ginibre matricesJan 04 2018We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. Well known work by Chalker and Mehlig calculated the expectation ... More
Analytic vortex solutions in generalized models of the Maxwell-Higgs typeJan 03 2018Jan 12 2018This work deals with the presence of analytical vortex configurations in generalized models of the Maxwell-Higgs type in the three-dimensional spacetime. We implement a procedure that allows to decouple the first order equations, which we use to solve ... More
Riccati-type pseudopotentials, conservation laws and solitons of deformed sine-Gordon modelsJan 03 2018Jan 05 2018Deformed sine-Gordon (DSG) models of the type $\partial_\xi \partial_\eta \, w + \frac{d}{dw}V(w) = 0$, with $V(w)$ being the deformed potential, are considered in the context of the Riccati-type pseudopotential representations. A compatibility condition ... More
Moutard transform for the conductivity equationDec 31 2017Jan 31 2018We construct Darboux-Moutard type transforms for the two-dimensional conductivity equation. This result continues our recent studies of Darboux-Moutard type transforms for generalized analytic functions. In addition, at least, some of the Darboux-Moutard ... More
Ground-state energy of one-dimensional free Fermi gases in the thermodynamic limitDec 30 2017We study the ground-state energy of one-dimensional, non-interacting fermions subject to an external potential in the thermodynamic limit. To this end, we fix some (Fermi) energy $\nu>0$, confine fermions with total energy below $\nu$ inside the interval ... More
Spectral properties of the 2+1 fermionic trimer with contact interactionsDec 29 2017Jan 08 2018We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction ... More
Remarks on multisymplectic reductionDec 28 2017Jan 15 2018The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
Variational order for forced Lagrangian systemsDec 26 2017We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, ... More
Spectral curves for the rogue wavesDec 26 2017Here we find the spectral curves, corresponding to the known rational or quasi-rational solutions of AKNS hierarchy equations, ultimately connected with the modeling of the rogue waves events in the optical waveguides and in hydrodynamics. We also determine ... More
Bruhat order in the Toda system on $\mathfrak{so}(2,4)$: an example of non-split real formDec 25 2017In our previous papers we described the structure of trajectories of the symmetric Toda system on normal real forms of various Lie algebras and showed that it was totally determined by the Hasse diagram of the Bruhat order on the corresponding Weil group. ... More
Bound states in the continuum in a two-dimensional PT-symmetric systemDec 23 2017We address a two-dimensional parity-time (PT)-symmetric structure built as a chain of waveguides, where all waveguides except for the central one are conservative, while the central one is divided into two halves with gain and losses. We show that such ... More
New scattering features in non-Hermitian space fractional quantum mechanicsDec 23 2017The spectral singularity (SS) and coherent perfect absorption (CPA) have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian standard quantum mechanics (SQM) governed by Schrodinger equation. ... More
Quadratic tomography star product algebra and its classical limitDec 23 2017We consider quadratic tomography in star product formalism. The contraction and the behavior of the associative algebra of quadratic tomographic symbols in $\hbar\rightarrow 0$ limit are discussed. A simple $k$-deformation example is illustrated.
Bianchi cosmologies with $p$-form gauge fieldsDec 23 2017In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p\,\in\,\{1,3\}$), a cosmological constant ($4$-form) and perfect ... More