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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

Uncertainty Quantification for Geometry Deformations of Superconducting Cavities using Eigenvalue TrackingFeb 08 2018The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities are sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators ... 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

Fourier Analysis and Evaluation of DG, FD and Compact Difference Methods for Conservation LawsFeb 08 2018Large eddy simulation (LES) has been increasingly used to tackle vortex-dominated turbulent flows. In LES, the quality of the simulation results hinges upon the quality of the numerical discretizations in both space and time. It is in this context we ... 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

Recovering the full Navier Stokes equations with lattice Boltzmann schemesFeb 07 2018We consider multi relaxation times lattice Boltzmann scheme with two particle distributions for the thermal Navier Stokes equations formulated with conservation of mass and momentum and dissipation of volumic entropy.Linear stability is taken into consideration ... More

A Schematic Definition of Quantum Polynomial Time ComputabilityFeb 07 2018In the past four decades, the notion of quantum polynomial-time computability has been realized by the theoretical models of quantum Turing machines and quantum circuits. Here, we seek a third model, which is a quantum analogue of the schematic (inductive ... 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

Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)Jan 31 2018The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The system of contextually labeled random variables describing this experiment forms a cyclic system of rank 4, formally the same as ... 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

The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEsJan 30 2018We present the Maple package TDDS (Thomas Decomposition of Differential Systems) for decomposition of polynomially nonlinear differential systems, which in addition to equations may contain inequations, into a finite set of differentially triangular and ... 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

Brain-to-brain heteroclinic coordination: model of sequential episodic memory initiationJan 29 2018Retrieval of episodic memory is a dynamical process in the large scale brain networks. In social groups, the neural patterns, associated to specific events directly experienced by single members, are encoded, recalled and shared by all participants. Here ... More

Matrix product states and the quantum max-flow/min-cut conjecturesJan 27 2018In this note we discuss the geometry of matrix product states with periodic boundary conditions and provide three infinite sequences of examples where the quantum max-flow is strictly less than the quantum min-cut. In the first we fix the underlying graph ... More

Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequenciesJan 27 2018We develop a non-overlapping domain decomposition method (DDM) for the solution of quasi-periodic scalar transmission problems in layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout ... 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

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitionsJan 25 2018Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting ... More

Energy-constrained two-way assisted private and quantum capacities of quantum channelsJan 24 2018Jan 25 2018With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to ... 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

Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic TomographyJan 22 2018Feb 08 2018The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate ... 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

A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part IIJan 20 2018Recent years have witnessed a significant trend towards filling the gap between Social Network Analysis (SNA) and control theory. This trend was enabled by the introduction of new mathematical models describing dynamics of social groups, the development ... 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

Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-Ray CTJan 19 2018Statistical image reconstruction (SIR) methods for X-ray CT produce high-quality and accurate images, while greatly reducing patient exposure to radiation. When further reducing X-ray dose to an ultra-low level by lowering the tube current, photon starvation ... 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

Eventually Entanglement Breaking MapsJan 17 2018We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor ... 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