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Line Singularities and Hopf Indices of Electromagnetic MultipolesApr 22 2019Electromagnetic multipoles can be continuously mapped to tangent vectors on the momentum sphere, the topology of which guarantees the existence of isolated singularities. For pure (real or imaginary) vectors, those singularities correspond to zeros of ... More
Morawetz estimates and spacetime bounds for quasilinear Schrödinger equations with critical Sobolev exponentApr 22 2019In this paper, we study the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t=\Delta u + 2uh'(|u|^2)\Delta h(|u|^2) + F(|u|^2)u\mp A[h(|u|^2]^{2^*-1} h'(|u|^2)u,\ x\in \mathbb{R}^N, \ t>0\\ u(x,0)=u_0(x), \quad x\in \mathbb{R}^N. ... More
Morawetz estimates as well as spacetime bounds based on pseudoconformal conservation law and interaction Morawetz estimates for a quasilinear Schrödinger equationApr 22 2019In this paper, we consider the Cauchy problem of the quasilinear Sch\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t = \Delta u+2uh'(|u|^2)\Delta h(|u|^2)+V(x)u+F(|u|^2)u+(W*|u|^2)u,\ x\in \mathbb{R}^N,\ t>0\\ u(x,0) = u_0(x),\quad ... More
On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular caseApr 21 2019We study a substitute for the matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the ``singular case'' $\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product ansatz of Derrida, Evans, Hakim and Pasquier ... More
Induced dynamicsApr 20 2019Induced dynamics is defined as dynamics of real zeros with respect to $x$ of equation $f(q_1-x,\ldots,q_N-x,p_1,\ldots,p_N)=0$, where $f$ is a function, and $q_i$ and $p_j$ are canonical variables obeying some (free) evolution. Identifying zero level ... More
Comparison of discrete and continuum Liouville first passage percolationApr 19 2019Discrete and continuum Liouville first passage percolation (DLFPP, LFPP) are two approximations of the conjectural $\gamma$-Liouville quantum gravity (LQG) metric, obtained by exponentiating the discrete Gaussian free field (GFF) and the circle average ... More
Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on latticeApr 19 2019We study a cyclic Leibniz rule, which provides a systematic approach to lattice supersymmetry, using a numerical method with a transfer matrix. The computation is carried out in N=2 supersymmetric quantum mechanics with the phi^6-interaction for weak ... More
Magnetization in the zig-zag layered Ising model and orthogonal polynomialsApr 19 2019We discuss the magnetization $M_m$ in the $m$-th column of the zig-zag layered 2D Ising model on a half-plane using Kadanoff-Ceva fermions and orthogonal polynomials techniques. Our main result gives an explicit representation of $M_m$ via $m\times m$ ... More
Universality for critical kinetically constrained models: infinite number of stable directionsApr 19 2019Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb{Z}^d$ with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with random initial ... More
High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graphApr 19 2019The Kubo-Martin-Schwinger condition is a widely studied fundamental property in quantum statistical mechanics which characterises the thermal equilibrium states of quantum systems. In the seventies, G. Gallavotti and E. Verboven, proposed an analogue ... More
On Itzykson-Zuber AnsatzApr 19 2019We apply the renormalized coupling constants and Virasoro constraints to derive the Itzykson-Zuber Ansatz on the form of the free energy in topological 2D gravity. We also treat the topological 1D gravity and the Hermitian one-matrix models in the same ... More
The $x_i$-eigenvalue problem on some new fuzzy spheresApr 18 2019We study the eigenvalue equation for the 'Cartesian coordinates' observables $x_i$ on the fully $O(2)$-covariant fuzzy circle $\{S^1_\Lambda\}_{\Lambda\in\mathbb{N}}$ ($i=1,2$) and on the fully $O(3)$-covariant fuzzy 2-sphere $\{S^2_\Lambda\}_{\Lambda\in\mathbb{N}}$ ... More
Entropy Production in Random Billiards and the Second Law of ThermodynamicsApr 18 2019We introduce a class of random mechanical systems called random billiards to study the problem of quantifying the irreversibility of nonequilibrium macroscopic systems. In a random billiard model, a point particle evolves by free motion through the interior ... More
On the finite-size Lyapunov exponent for the Schroedinger operator with skew-shift potentialApr 18 2019It is known that a one-dimensional quantum particle is localized when subjected to an arbitrarily weak random potential. It is conjectured that localization also occurs for an arbitrarily weak potential generated from the nonlinear skew-shift dynamics: ... More
Critical Robertson-Walker universesApr 18 2019The integral of the energy density function $\mathfrak m$ of a closed Robertson-Walker (RW) spacetime with source a perfect fluid and cosmological constant $\Lambda$ gives rise to an action functional on the space of scale functions of RW spacetime metrics. ... More
Hamiltonian Floer theory for nonlinear Schrödinger equations and the small divisor problemApr 18 2019We prove the existence of infinitely many time-periodic solutions of nonlinear Schr\"odinger equations using pseudo-holomorphic curve methods from Hamiltonian Floer theory. For the generalization of the Gromov-Floer compactness theorem to infinite dimensions, ... More
Removal of spurious solutions encountered in Helmholtz scattering resonance computations in R^dApr 18 2019In this paper we consider a sorting scheme for the removal of spurious scattering resonant pairs in two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a Lippmann-Schwinger type of ... More
Phase transition in the exclusion process on the Sierpinski gasket with slowed boundary reservoirsApr 18 2019We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process evolving on the Sierpinski gasket in the presence of a slow boundary. Depending on the slowness of the boundary we obtain, at the hydrodynamics ... More
Uniqueness and Non-Degeneracy of Minimizers of the Pekar Functional on a BallApr 18 2019We consider the Pekar functional on a ball in R^3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from non-degeneracy of the Hessian at the minimum.
Axially-Symmetric Exact Solutions for Majorana Fermions with GravityApr 18 2019In this paper, we consider Majorana spinor fields in interaction with their own gravitational field: for this case we present axially-symmetry exact solutions. Final comments are given.
The Zilch Electromagnetic Conservation Law in Variational Characteristic FormApr 18 2019In this paper we consider the zilch conservation laws for Maxwell theory and demonstrate that in the duality-symmetric version of Maxwell theory, the zilch arises as a Noether current for a variational symmetry of the duality symmetric Lagrangian which ... More
Classification of simple weight modules for the $N=2$ superconformal algebraApr 18 2019In this paper, we classify all simple weight modules with finite dimensional weight spaces over the $N=2$ superconformal algebra. As an application, we give a new proof of the classification of such modules for the $N=1$ superconformal algebra, which ... More
The Navier-Stokes - End-Functionalized Polymer System: Global Regularity and Polymer Drag ReductionApr 17 2019Reducing wall drag in turbulent pipe and channel flows is an issue of great practical importance. In engineering applications, end-functionalized polymer chains are often employed as agents to reduce drag. These are polymers which are floating in the ... More
Bounds on eigenvalues of perturbed Lamé operators with complex potentialsApr 17 2019Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. This paper provides ... More
Steady filtration of Peng-Robinson gas in a porous mediumApr 17 2019Filtration of real gases described by Peng-Robinson equations of state in 3-dimensional space is studied. Thermodynamic states are considered as either Legendrian submanifolds in contact space, or Lagrangian submanifolds in symplectic space. The correspondence ... More
Preservation of no-signalling principle in parity-time symmetric quantum systemsApr 17 2019We look into the possibility of entanglement generation in a parity(P)-time(T)-symmetric framework and demonstrate the non-violation of non-signalling principle for the case of bipartite systems when at least one is guided by PT-symmetric quantum mechanics. ... More
Diffraction of a model set with complex windowsApr 17 2019The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the associated control ... More
Exact Solution of the F-TASEPApr 17 2019We obtain the exact solution of the facilitated totally asymmetric simple exclusion process (F-TASEP) in 1D. The model is closely related to the conserved lattice gas (CLG) model and to some cellular automaton traffic models. In the F-TASEP a particle ... More
Exact Solution of the F-TASEPApr 17 2019Apr 21 2019We obtain the exact solution of the facilitated totally asymmetric simple exclusion process (F-TASEP) in 1D. The model is closely related to the conserved lattice gas (CLG) model and to some cellular automaton traffic models. In the F-TASEP a particle ... More
On the modular operator of mutli-component regions in chiral CFTApr 17 2019We introduce an approach to find the Tomita-Takesaki modular flow for multi-component regions in chiral conformal field theory. Our method is based only locality (or braid-relations) of primary fields and the so-called Kubo-Martin-Schwinger (KMS) condition. ... More
The Long ans Short Time Asymptotics of the Two-Time Distribution in Local Random GrowthApr 17 2019The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be universal in ... More
d-orthogonal polynomials, Toda Lattice and Virasoro symmetriesApr 17 2019The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d >1$. Any such ... More
Kaluza-Klein Reduction of the 6 Dimensional \\ Dirac Equation on $\mathbb{S}^3 \cong SU(2)$ and \\ Non-abelian Topological InsulatorsApr 17 2019In this work, the Kaluza-Klein reduction of the Dirac equation on a 6 dimensional spacetime $\mathbb{M}^{1+5} := \mathbb{M}^{1+2} \times \mathbb{S}^3$ is studied. Because of the group structure on $\mathbb{S}^3$, $\mathbb{M}^{1+5}$ can be seen as a principal ... More
A microscopic derivation of Gibbs measures for nonlinear Schrödinger equations with unbounded interaction potentialsApr 17 2019We study the derivation of the Gibbs measure for the nonlinear Schr\"{o}dinger equation (NLS) from many-body quantum thermal states in the high-temperature limit. In this paper, we consider the nonlocal NLS with defocusing and unbounded $L^p$ interaction ... More
Identifying variations of magnetic anomalies using geomagnetic monitoringApr 17 2019We are concerned with the inverse problem of identifying magnetic anomalies with varing parameters beneath the Earth using geomagnetic monitoring. Observations of the change in Earth's magnetic field--the secular variation--provide information about the ... More
Tightness of Liouville first passage percolation for $γ\in (0,2)$Apr 16 2019We study Liouville first passage percolation metrics associated to a Gaussian free field $h$ mollified by the two-dimensional heat kernel $p_t$ in the bulk, and related star-scale invariant metrics. For $\gamma \in (0,2)$ and $\xi = \frac{\gamma}{d_{\gamma}}$, ... More
Cluster Structures on Double Bott-Samelson CellsApr 16 2019We introduce double Bott-Samelson cells defined by a symmetrizable generalized Cartan matrix $C$ and a pair of positive braids $(b,d)$ in the braid group associated to $C$. We prove that the coordinate rings of double Bott-Samelson cells are upper cluster ... More
On the Convergence of Random Tridiagonal Matrices to Stochastic SemigroupsApr 16 2019We develop an improved version of the stochastic semigroup approach to study the edge of $\beta$-ensembles pioneered by Gorin and Shkolnikov, and later extended to rank-one additive perturbations by the author and Shkolnikov. Our method is applicable ... More
Integrable semi-discretizations of the Davey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system. IApr 16 2019The integrable Davey-Stewartson system is a linear combination of the two elementary flows that commute: $\mathrm{i} q_{t_1} + q_{xx} + 2q\partial_y^{-1}\partial_x (|q|^2) =0$ and $\mathrm{i} q_{t_2} + q_{yy} + 2q\partial_x^{-1}\partial_y (|q|^2) =0$. ... More
On superstatistics of energy for a free quantum Brownian particleApr 16 2019We consider energetics of a free quantum Brownian particle coupled to thermostat of temperature $T$ and study this problem in terms of the lately formulated quantum analogue of the energy equipartition theorem. We show how this quantum counterpart can ... More
Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitionsApr 16 2019We study the discrete-to-continuum variational limit of the $J_{1}$-$J_{3}$ spin model on the square lattice in the vicinity of the helimagnet/ferromagnet transition point as the lattice spacing vanishes. Carrying out the $\Gamma$-convergence analysis ... More
Glassy dynamics in strongly anharmonic chains of oscillatorsApr 16 2019We review the mechanism for transport in strongly anharmonic chains of oscillators near the atomic limit where all oscillators are decoupled. In this regime, the motion of most oscillators remains close to integrable, i.e. quasi-periodic, on very long ... More
Quasi-Exactly Solvable Scattering Problems, Exactness of the Born Approximation, and Broadband Unidirectional Invisibility in Two DimensionsApr 16 2019Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open problem of scattering ... More
On solving the Thomas Bargman-Michel-Telegdi equation using the Bogoliubov Krylov method of averages and the calculation of the Berry phasesApr 16 2019Several proposals aimed at measuring the Electric Dipole Moment (EDM) for charged particles require very precise simulations and understanding of the systematic errors that can contribute to a spin buildup mimicking the EDM signal to be detected. In what ... More
Uniform matrix product states from an algebraic geometer's point of viewApr 16 2019We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equations and identifiability. By an interplay of theorems from algebra, geometry ... More
Partition of energy for a dissipative quantum oscillatorApr 16 2019We reveal a new face of the old clich\'ed system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems.Both mean kinetic energy $E_k$ and mean potential ... More
Quantum partition of energy for a free Brownian particle: Impact of dissipationApr 16 2019We study the quantum counterpart of the theorem on energy equipartition for classical systems. We consider a free quantum Brownian particle modelled in terms of the Caldeira-Leggett framework: a system plus thermostat consisting of an infinite number ... More
Non-integrable dimers: Universal fluctuations of tilted height profilesApr 16 2019We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer model with plaquette ... More
Dirac Equation In The Curved Spacetime and Generalized Uncertainty Principle: A fundamental quantum mechanical approach with energy dependent potentialsApr 16 2019In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime ... More
Damping modes of harmonic oscillator in open quantum systemsApr 16 2019Through a set of generators that preserves the hermiticity and trace of density matrices, we analyze the damping of harmonic oscillator in open quantum systems into four modes, distinguished by their specific effects on the covariance matrix of position ... More
Damping modes of harmonic oscillator in open quantum systemsApr 16 2019Apr 21 2019Through a set of generators that preserves the hermiticity and trace of density matrices, we analyze the damping of harmonic oscillator in open quantum systems into four modes, distinguished by their specific effects on the covariance matrix of position ... More
Combinatorial Conversion and Moment Bisimulation for Stochastic Rewriting SystemsApr 15 2019We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship between the combinatorics ... More
Quantum toroidal algebra associated with $\mathfrak{gl}_{m|n}$Apr 15 2019We introduce and study the quantum toroidal algebra $\mathcal{E}_{m|n}(q_1,q_2,q_3)$ associated with the superalgebra $\mathfrak{gl}_{m|n}$ with $m\neq n$, where the parameters satisfy $q_1q_2q_3=1$. We give an evaluation map. The evaluation map is a ... More
Hyperbolicity of the modulation equations for the Serre-Green-Naghdi modelApr 15 2019Serre-Green-Naghdi equations (SGN equations) is the most simple dispersive model of long water waves having "good" mathematical and physical properties. First, the model is a mathematically justified approximation of the exact water wave problem. Second, ... More
Mean value properties of harmonic functions and related topics (a survey)Apr 15 2019Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes of functions. ... More
Construction of complex potentials for multiply connected domainsApr 15 2019The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential --- an analytic function in an infinite multiply connected domain with a simple pole at infinity which maps the domain onto ... More
Bulk eigenvalue fluctuations of sparse random matricesApr 15 2019We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graphs $\mathcal G(N,p)$ for $p \in [N^{\varepsilon-1},N^{-\varepsilon}]$. We identify the joint limiting distributions of the eigenvalues away from ... More
Accurate modelling of the low-order secondary resonances in the spin-orbit problemApr 15 2019We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To this end we extend ... More
Double-Graded Supersymmetric Quantum MechanicsApr 15 2019A quantum mechanical model that realizes the $ \mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is related to parasupersymmetric ... More
The Lieb-Yau Conjecture for Ground States of Pseudo-Relativistic Boson StarsApr 15 2019It is known that ground states of the pseudo-relativistic Boson stars exist if and only if the stellar mass $N>0$ satisfies $N<N^*$, where the finite constant $N^*$ is called the critical stellar mass. Lieb and Yau conjecture in [Comm. Math. Phys., 1987] ... More
A generally covariant measurement scheme for quantum field theory in curved spacetimesApr 15 2019We propose and develop a measurement scheme for quantum field theory (QFT) in curved spacetimes, in which the QFT of interest, the "system", is dynamically coupled to another, the "probe", in a compact spacetime region. Measurements of observables in ... More
Composite fermions, rectangular Young tableaux and Gelfand-Tsetlin basis in multicomponent fractional quantum Hall systemsApr 15 2019We put forward a group-theoretical approach to describe the Hilbert space of $M$ fermions, with $N$ components (spin, layer, valley, sub-lattice, etc), per Landau site in the lowest Landau level, at fractional filling factor $\nu=M/\lambda$. The Hilbert ... More
Some results on double triangle descendants of $K_5$Apr 15 2019Double triangle expansion is an operation on $4$-regular graphs with at least one triangle which replaces a triangle with two triangles in a particular way. We study the class of graphs which can be obtained by repeated double triangle expansion beginning ... More
Symmetry breaking and lattice kirigami: finite temperature effectsApr 15 2019Recent work has analysed how deformations due to the insertion of a defect in a flat hexagonal lattice affect the ground state structure of an interacting fermion field theory. Such modifications result in an increase of the order parameter in the vicinity ... More
Non-Weyl Microwave GraphsApr 15 2019One of the most important characteristics of a quantum graph is the average density of resonances, $\rho = \frac{\mathcal{L}}{\pi}$, where $\mathcal{L}$ denotes the length of the graph. This is a very robust measure. It does not depend on the number of ... More
From minimal gravity to open intersection theoryApr 15 2019We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with boundaries is defined in terms of boundary cosmological constant $\mu_B$ ... More
Nonsymmetric Macdonald polynomials via integrable vertex modelsApr 15 2019Starting from an integrable rank-$n$ vertex model, we construct an explicit family of partition functions indexed by compositions $\mu = (\mu_1,\dots,\mu_n)$. Using the Yang-Baxter algebra of the model and a certain rotation operation that acts on our ... More
Stochastic differential equations for Lie group valued moment mapsApr 14 2019The celebrated result by Biane-Bougerol-O'Connell relates Duistermaat-Heckman (DH) measures for coadjoint orbits of a compact Lie group $G$ with the multi-dimensional Pitman transform of the Wiener process on its Cartan subalgebra. The DH theory admits ... More
Time Global Finite-Energy Weak Solutions to the Many-Body Maxwell-Pauli EquationsApr 14 2019We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the electrons and ... More
Connection Formulae for Asymptotics of the Fifth Painlevé Transcendent on the Imaginary Axis: IApr 14 2019Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\'e equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \frac{d}{d\lambda}Y= \left(\frac ... More
Duality in a hyperbolic interaction model integrable even in a strong confinement: Multi-soliton solutions and field theoryApr 14 2019Models that remain integrable even in confining potentials are extremely rare and almost non-existent. Here, we consider a one-dimensional hyperbolic interaction model, which we call as the Hyperbolic Calogero (HC) model. This is classically integrable ... More
Tensorization of the strong data processing inequality for quantum chi-square divergencesApr 13 2019Quantifying the contraction of classical and quantum states under noisy channels is an important topic in the information theory. Among various techniques, the strong data processing inequality, as a refinement of the well-known data processing inequality, ... More
Boundary correlations for the six-vertex model with reflecting end boundary conditionApr 12 2019We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the Sklyanin's reflection ... More
Shaken dynamics for the 2d ising modelApr 12 2019We define a Markovian parallel dynamics for a class of nearest neighbors spin systems. In the dynamics, beside the two usual parameters $J$, the strength of the interaction, and $\lambda$, the external field, it appears an inertial parameter $q$, measuring ... More
Minimal energy cost of entanglement extractionApr 12 2019We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase in the system resulting from replacing an entangled pair of modes, sharing ... More
Quantum features of macroscopic fields. Entropy and dynamicsApr 12 2019Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism ... More
Surface energy and boundary layers for a chain of atoms at low temperatureApr 12 2019We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ ... More
The energy of dilute Bose gasesApr 12 2019For a dilute system of non-relativistic bosons interacting through a positive $L^1$ potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+ \frac{128}{15\sqrt{\pi}} \sqrt{\rho ... More
Semi-conformal structure on certain vertex superalgebras associated to vertex superalgebroidsApr 12 2019In this paper, we first give the definiton of a vertex superalgebroid. Then we construct a family of vertex superalgebras associated to vertex superalgebroids. As a main result, we find a sufficient and necessary condition that this vertex superalgebras ... More
A two-variable series for knot complementsApr 12 2019The physical 3d $\mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $\hat{Z}_{a}(q)$ that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the ... More
Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl TensorApr 12 2019We derive a superpotential for null electromagnetic fields in which the field line structure is in the form of an arbitrary torus knot. These fields are shown to correspond to single copies of a class of anti-self-dual Kerr-Schild spacetimes containing ... More
From variational to bracket formulations in nonequilibrium thermodynamics of simple systemsApr 11 2019A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. ... More
Constructive expansion for quartic vector fields theories. I. Low dimensionsApr 11 2019This paper is the first of a series aiming at proving rigorously the analyticity and the Borel summability of generic quartic bosonic and fermionic vector models (generalizing the O(N) vector model) in diverse dimensions. Both non-relativistic (Schr\"odinger) ... More
Variational integrators for stochastic dissipative Hamiltonian systemsApr 11 2019Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for the stochastic ... More
Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potentialApr 11 2019In this paper we examine the semiclassical behaviour of the scattering data of a non-self-adjoint Dirac operator with analytic potential decaying at infinity. In particular, employing the exact WKB method, we provide the complete rigorous uniform semiclassical ... More
Reflection $K$ matrices associated with an Onsager coideal of $U_p(A^{(1)}_{n-1})$, $U_p(B^{(1)}_n)$, $U_p(D^{(1)}_n)$ and $U_p(D^{(2)}_{n+1})$Apr 11 2019We determine the intertwiners of a family of Onsager coideal subalgebras of the quantum affine algebra $U_p(A^{(1)}_{n-1})$ in the fundamental representations and $U_p(B^{(1)}_{n}), U_p(D^{(1)}_{n}), U_p(D^{(2)}_{n+1})$ in the spin representations. They ... More
Reflection $K$ matrices associated with an Onsager coideal of $U_p(A^{(1)}_{n-1})$, $U_p(B^{(1)}_n)$, $U_p(D^{(1)}_n)$ and $U_p(D^{(2)}_{n+1})$Apr 11 2019Apr 20 2019We determine the intertwiners of a family of Onsager coideal subalgebras of the quantum affine algebra $U_p(A^{(1)}_{n-1})$ in the fundamental representations and $U_p(B^{(1)}_{n}), U_p(D^{(1)}_{n}), U_p(D^{(2)}_{n+1})$ in the spin representations. They ... More
On Ground States and Phase Transition for $λ$-Model with the Competing Potts Interactions on Cayley TreesApr 11 2019In this paper, we consider the $\lambda$-model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if $\lambda$-function is taken as a Potts interaction function, then this model contains ... More
Ground States And Hyperuniformity Of The Hierarchical Coulomb Gas In All DimensionsApr 10 2019Large ensembles of points with Coulomb interactions arise in various settings of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, ... More
Non-autonomous Henon-Heiles system from Painleve classApr 10 2019We show how to deform separable Henon-Heiles system with isospectral Lax representation, related with the stationary flow of the $5th$-order KdV, to respective non-autonomous systems of Painleve type with isomonodromic Lax representation.
Uniqueness of the Non-Equilibrium Steady State for a $1$d BGK model in kinetic theoryApr 10 2019We continue our investigation of kinetic models of a one-dimensional gas in contact with homogeneous thermal reservoirs at different temperatures. Nonlinear collisional interactions between particles are modeled by a so-called BGK dynamics which conserves ... More
Generating functions of planar polygons from homological mirror symmetry of elliptic curvesApr 10 2019We study generating functions of certain shapes of planar polygons arising from homological mirror symmetry of elliptic curves. We express these generating functions in terms of rational functions of the Jacobi theta function and Zwegers' mock theta function. ... More
Two variations on $(A_3\times A_1\times A_1)^{(1)}$ type discrete Painlevé equationsApr 10 2019By considering the normalizers of reflection subgroups of types $A_1^{(1)}$ and $A_3^{(1)}$ in $\widetilde{W}\left(D_5^{(1)}\right)$, two normalizers: $\widetilde{W}\left(A_3\times A_1\right)^{(1)}\ltimes {W}(A_1^{(1)})$ and $\widetilde{W}\left(A_1\times ... More
Universal density matrix for the phase spaceApr 10 2019In this paper, a new representation of the Wigner function for a quantum system in the phase space is proposed. The new representation is of the form $W=\operatorname{Sp}\left[ \rho \mathcal{W} \right]$, where $\rho$ is the density matrix, and $\mathcal{W}$ ... More
The linear stability of Reissner-Nordström spacetime for small chargeApr 09 2019In this thesis, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordstr\"om family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordstr\"om ... More
Classical Influence Functionals: Rigorously Deducing Stochasticity From Deterministic DynamicsApr 09 2019The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. Using the Koopman von-Neumann formulation of classical ... More
Cartan Connections and Atiyah Lie AlgebroidsApr 09 2019This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a $H$-principal fiber ... More
BRST symmetry of doubled membrane sigma-modelsApr 09 2019Courant sigma-models encode the geometric and non-geometric fluxes of compactified closed string theory as generalized Wess-Zumino terms and exhibit their relation to Courant algebroids. In recent work, we proposed a doubled membrane sigma-model that ... More
Time evolution of concentrated vortex ringsApr 09 2019We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider $N$ disjoint vortex rings of size $\varepsilon$ and intensity of the order of $|\log\varepsilon|^{-1}$. ... More
Phase transitions in filtration of Redlich-Kwong gasesApr 09 2019In this paper we study a 3-dimensional filtration of real gases described by Redlich-Kwong equations of state. Thermodynamical states are considered as Legendrian (Lagrangian) submanifolds in contact (symplectic) space. Connection between singularities ... More