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Double Gegenbauer expansion of $|s - t|^α$Feb 21 2019We give a Gegenbauer expansion of the two variable function $| s - t |^{\alpha}$ in terms of the ultraspherical polynomials $C_l^{\lambda} (s)$ and $C^{\mu}_m (t)$. Generalization, specialization, and limits of the expansion are also discussed.
Non-cooperative Equilibria of Fermi Systems With Long Range InteractionsFeb 21 2019We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, we ... More
Conformal geometry and (super)conformal higher-spin gauge theoriesFeb 21 2019We develop a manifestly conformal approach to describe linearised (super)conformal higher-spin gauge theories in arbitrary conformally flat backgrounds in three and four spacetime dimensions. Closed-form expressions in terms of gauge prepotentials are ... More
On the absolutely continuous spectrum of generalized indefinite stringsFeb 21 2019We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite strings under rather ... More
A dynamical proof of the second law of thermodynamicsFeb 20 2019We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and Robinson. An example ... More
Sublogarithmic behaviour of the entanglement entropy in fermionic chainsFeb 20 2019In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. ... More
Comment on 'Winding around non-Hermitian singularities' by Zhong et al., Nat. Commun. 9, 4808 (2018)Feb 20 2019In a recent paper entitled "Winding around non-Hermitian singularities" by Zhong et al., published in Nat. Commun. 9, 4808 (2018), a formalism is proposed for calculating the permutations of eigenstates that arise upon encircling (multiple) exceptional ... More
Wick squares of the Gaussian Free Field and Riemannian rigidityFeb 19 2019In this short note, we show that on a compact Riemannian manifold $(M,g)$ of dimension $(d=2,3)$ whose metric has negative curvature, the partition function $Z_g(\lambda)$ of a massive Gaussian Free Field or the fluctuations of the integral of the Wick ... More
Quantum Position-Dependent Mass and Smooth Boundary Forces from Constrained GeometriesFeb 19 2019We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is illustrated with the ... More
Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systemsFeb 19 2019We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to $D>2$ dimensions. We obtain a local gap threshold of $\frac{3}{n}$, independent of $D$, for nearest-neighbor interactions. The $\frac{1}{n}$ scaling ... More
Fermion-current basis and correlation functions for the integrable spin 1 chainFeb 19 2019We use the fermion-current basis in the space of local operators for the computation of the expectation values for the integrable spin chain of spins 1. Our main tool consists in expressing a given local operators in the fermion-current basis. For this ... More
Similarity Solutions For The Complex Burgers' HierarchyFeb 19 2019A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the Complex Burgers` Hierarchy is performed. Moreover, a detailed application of the reduction process through the Lie point symmetries ... More
Geometric wave propagator on Riemannian manifoldsFeb 19 2019We study the propagator of the wave equation on a closed Riemannian manifold $M$. We propose a geometric approach to the construction of the propagator as a single oscillatory integral global both in space and in time with a distinguished complex-valued ... More
Generalized geometric Hamilton-Jacobi theorem on Lie algebroidsFeb 19 2019In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi theorem for Hamiltonian ... More
Constant curvature holomorphic solutions of the supersymmetric grassmannian sigma model: the case of $G(2,4)$Feb 19 2019We explore the constant curvature holomorphic solutions of the supersymmetric grassmannian sigma model $G(M,N)$ using in particular the gauge invariance of the model. Supersymmetric invariant solutions are constructed via generalizing a known result for ... More
Massless Rarita-Schwinger field from a divergenceless anti-symmetric-tensor spinor of pure spin-$3/2$Feb 19 2019We construct the Rarita-Schwinger basis vectors, $U^\mu$, spanning the direct product space, $U^\mu:=A^\mu\otimes u_M$, of a massless four-vector, $ A^\mu $, with massless Majorana spinors, $u_M$, together with the associated field-strength tensor, ${\mathcal ... More
Spinning extensions of $D(2,1;α)$ superconformal mechanicsFeb 19 2019As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup $D(2,1;\alpha)$, which is the most general $\mathcal{N}{=}\,4$ supersymmetric extension of the conformal group ... More
Differentiability of the van der Waals interaction between two atomsFeb 18 2019In this work we improve upon previous results on the expansion of the interaction energy of two atoms. On the one hand we prove the van der Waals-London's law, assuming that only one of the ground state eigenspaces of the atoms is irreducible in an appropriate ... More
Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS$_5$ blackholesFeb 18 2019Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like limit of the superconformal index of the 4d $\mathcal{N}=4$ theory with complexified fugacities which encodes the entropy of the dual supersymmetric AdS$_5$ blackholes. Here ... More
Homogenization for Generalized Langevin Equations with Applications to Anomalous DiffusionFeb 18 2019We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the ... More
The Arctic curve for Aztec rectangles with defects via the Tangent MethodFeb 18 2019The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path configurations are ... More
2-parameter $τ$-function for the first Painlevé equation -Topological recursion and direct monodromy problem via exact WKB analysis-Feb 18 2019We show that a 2-parameter family of $\tau$-functions for the first Painlev\'e equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a family of elliptic curves. We also perform an exact WKB ... More
${\boldsymbolπ}$-systems of symmetrizable Kac-Moody algebrasFeb 18 2019As part of his classification of regular semisimple subalgebras of semisimple Lie algebras, Dynkin introduced the notion of a $\pi$-system. This is a subset of the roots such that pairwise differences of its elements are not roots. These arise as simple ... More
On self-force in higher-order electrodynamicsFeb 18 2019This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order derivative theory proposed by Bopp, Land\'e--Thomas, and Podolsky. We rigorously derive a world-line integral expression for the ... More
Bi-orthogonal Polynomials and the Five parameter Asymmetric Simple Exclusion ProcessFeb 18 2019We apply the bi-moment determinant method to compute a representation of the matrix product algebra -- a quadratic algebra satisfied by the operators $\mathbf{d}$ and $\mathbf{e}$ -- for the five parameter ($\alpha$, $\beta$, $\gamma$, $\delta$ and $q$) ... More
Conservation laws and line soliton solutions of a family of modified KP equa tionsFeb 18 2019A family of modified Kadomtsev-Petviashvili equations which includes the integrable case is studied. The explicit line soliton solution and all conservation laws of low order are derived and compared to their counterparts in the integrable case.
Repartition of the quasi-stationary distribution and first exit point density for a double-well potentialFeb 17 2019Let $f: \mathbb R^{d} \to \mathbb R$ be a smooth function and $(X_t)_{t\ge 0}$ be the stochastic process solution to the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t.$$ Let $\Omega\subset \mathbb R^d$ be a smooth bounded ... More
A C*-algebraic approach to interacting quantum field theoriesFeb 16 2019A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag-Kastler axioms, with insights gained in the perturbative approach to quantum ... More
On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equationFeb 16 2019Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2n+2n-dimensional integrable partial differential equation with the associated eigenfunction constituting an ... More
$Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometryFeb 15 2019In this paper we introduce the bosonic generators of the $sp(4,R)$ algebra and study some of their properties, based on the $SU(1,1)$ and $SU(2)$ group theory. With the developed theory of the $Sp(4,R)$ group, we solve the interaction part of the most ... More
Non-local Lagrangians from Renormalons and Analyzable FunctionsFeb 15 2019We embed in a generalized Borel procedure the notion of renormalization and renormalons. While there are several efforts in literature to have a semi-classical understanding of the renormalons, here we argue that this is not the fundamental issue and ... More
Entanglement of boundary conditions giving rise to spontaneous symmetry breaking in quantum mechanicsFeb 15 2019We study spontaneous symmetry breaking in one dimensional quantum mechanical problems in terms of two-point boundary problems which lead to singular potentials containing Dirac delta functions and its derivatives. We search for broken-symmetry bound states. ... More
Matrix solitons solutions of the modified Korteweg-de Vries equationFeb 15 2019Nonlinear non-Abelian Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations and their links via Baecklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified Korteweg-de Vries ... More
Alexander and Jones polynomials of surgerized tst linksFeb 15 2019Feb 19 2019This paper is a continuation on the 2012 paper on "Cutting Twisted Solid Tori (TSTs)", in which we considered twisted solid torus links (tst links). We generalize the notion of tst links to "surgerized tst links": recall that when performing $\Phi^\mu(n(\tau), ... More
Alexander and Jones polynomials of surgerized tst linksFeb 15 2019Feb 18 2019This paper is a continuation on the HLMA paper published in 2012 on twisted solid torus links (tst links). We generalize the notion of tst links to "surgerized tst links": recall that when performing $\Phi^\mu(n(\tau), d(\tau), M)$ on a tst $\langle \tau ... More
$\mathbb{Z}_2 \times \mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensionsFeb 15 2019We introduce a class of novel $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of ... More
Perturbation theory of KMS statesFeb 15 2019We extend the new perturbation formula of equilibrium states by Hastings to KMS states of general $W^*$-dynamical systems.
Variational principles for nonlinear Kirchhoff rodsFeb 15 2019The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented in a systematic ... More
Detection of Hermitian connections in wave equations with cubic non-linearityFeb 15 2019We consider the geometric non-linear inverse problem of recovering a Hermitian connection $A$ from the source-to-solution map of the cubic wave equation $\Box_{A}\phi+\kappa |\phi|^{2}\phi=f$, where $\kappa\neq 0$ and $\Box_{A}$ is the connection wave ... More
Discrete eigenvalues of the spin-boson Hamiltonian with two photons: on a conjecture of Minlos and SpohnFeb 14 2019Under minimal regularity conditions on the photon dispersion and the coupling function, we prove that the spin-boson model with two massless photons in $\mathbb{R}^d$ can not have more than two bound state energies for any coupling strength. This solves ... More
An exactly solvable quantum-metamaterial type modelFeb 14 2019The key difficulty in the modelling of large quantum coherent structures lies in keeping track of nonlocal, multipoint quantum correlations between their constituent parts. Here we consider a special case of such a system, a fractal quantum metamaterial ... More
Spectral Action in Noncommutative GeometryFeb 14 2019What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry \`a la Connes, deliberately unveiling the answers to these questions. After a brief ... More
A stable quantum Darmois-Skitovich theoremFeb 14 2019The Darmois-Skitovich theorem is a simple characterization of the normal distribution in terms of the independence of linear forms. We present here a non-commutative version of this theorem in the context of Gaussian bosonic states and show that this ... More
Shrinking scale equidistribution for monochromatic random waves on compact manifoldsFeb 14 2019We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With ... More
Note on the retarded van der Waals potential within the dipole approximationFeb 14 2019We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. By an exact diagonalization method, we prove that the binding energy of the two hydrogen atoms behaves as $R^{-7}$, provided that the distance between atoms $R$ is ... More
Accelerating dynamical peakons and their behaviourFeb 14 2019A wide class of nonlinear dispersive wave equations are shown to possess a novel type of peakon solution in which the amplitude and speed of the peakon are time-dependent. These novel dynamical peakons exhibit a wide variety of different behaviours for ... More
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered MediaFeb 13 2019The growing need for smaller electronic components has recently sparked the interest in the breakdown of the classical conductivity theory near the atomic scale, at which quantum effects should dominate. In 2012, experimental measurements of electric ... More
Semigroups for One-Dimensional Schrödinger Operators with Multiplicative White NoiseFeb 13 2019Let $ H:=-\tfrac12\Delta+V$ be a one-dimensional continuum Schr\"odinger operator. Consider ${\hat H}:= H+\xi$, where $\xi$ is a Gaussian white noise. We prove that if the potential $V$ is locally integrable, bounded below, and grows faster than $\log$ ... More
Heat Kernel Estimates for Fractional Heat EquationFeb 13 2019We study the long-time behavior of the Cesaro means of fundamental solutions for fractional evolution equations corresponding to random time changes in the Brownian motion and other Markov processes. We consider both stable subordinators leading to equations ... More
Self-Adjointness of two dimensional Dirac operators on corner domainsFeb 13 2019We study the self-adjointenss of the two-dimensional Dirac operator with Quantum-dot and Lorentz-scalar $\delta$-shell boundary conditions, on piecewise $C^2$ domains with finitely many corners. For both models, we prove the existence of a unique self-adjoint ... More
Operational causality in spacetimeFeb 13 2019We consider the general evolution of binary statistics in a, possibly curved, spacetime with the help of the optimal transport theory. It covers a wide range of models including classical statistics, quantum wave-packets and general, possibly non-linear, ... More
Universal optimality of the $E_8$ and Leech lattices and interpolation formulasFeb 13 2019We prove that the $E_8$ root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions $8$ and $24$, respectively. In other words, they minimize energy for every potential function that is a completely ... More
Factorization of KdV Schrödinger operators using differential subresultantsFeb 13 2019We address the classical factorization problem of a one dimensional Schr\"odinger operator $-\partial^2+u-\lambda$, for a stationary potential $u$ of the KdV hierarchy but, in this occasion, a "parameter" $\lambda$. Inspired by the more effective approach ... More
Comment on "Quantization of the damped harmonic oscillator" [Serhan et al, J. Math. Phys. 59, 082105 (2018)]Feb 13 2019A recent paper [J. Math. Phys. {\bf 59}, 082105 (2018)] constructs a Hamiltonian for the (dissipative) damped harmonic oscillator. We point out that non-Hermiticity of this Hamiltonian has been ignored to find real discrete eigenvalues which are actually ... More
Curvature stabilized Skyrmions with angular momentumFeb 13 2019We examine skyrmionic field configurations on a spherical ferromagnet with large normal anisotropy. Exploiting variational concepts of angular momentum we find a new family of localized solutions to the Landau-Lifshitz equation that are topologically ... More
A Partial Data Problem in Linear ElasticityFeb 13 2019We discuss the determination of the Lam\'e parameters of an elastic material by the means of boundary measurements. We will combine previous results of Eskin-Ralston and Isakov to prove inverse results in the case of bounded domains with partial data. ... More
Sparsity pattern of the self-energy for classical and quantum impurity problemsFeb 13 2019We prove that for various impurity models, in both classical and quantum settings, the self-energy matrix is a sparse matrix with a sparsity pattern determined by the impurity sites. In the quantum setting, such a sparsity pattern has been known since ... More
Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel DerivationFeb 13 2019Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to study wide random ... More
Random positive operator valued measuresFeb 13 2019We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting eigenvalue distributions ... More
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, BrieflyFeb 12 2019In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due to Damanik--Sims--Stolz, and it ... More
On the information content of the difference from hamiltonian evolutionFeb 12 2019A dissipative version of hamiltonian mechanics is proposed via a principle of minimal information content of the deviation from hamiltonian evolution. We show that we can cover viscosity, plasticity, damage and unilateral contact. This article continues ... More
Exterior powers of the adjoint representation and the Weyl ring of $E_8$Feb 12 2019I derive explicitly all polynomial relations in the character ring of $E_8$ of the form $\chi_{\wedge^k \mathfrak{e}_8} - \mathfrak{p}_{k} (\chi_{1}, \dots, \chi_{r})=0$, where $\wedge^k \mathfrak{e}_8$ is an arbitrary exterior power of the adjoint representation ... More
Effective dynamics of a conditioned generalized linear Glauber modelFeb 12 2019In order to study the stochastic Markov processes conditioned on a specific value of a time-integrated observable, the concept of ensembles of trajectories has been recently used extensively. In this paper, we consider a generic reaction-diffusion process ... More
Potentials with Identical Scattering Properties Below a Critical EnergyFeb 12 2019A pair of scattering potentials are called $\alpha$-equivalent if they have identical scattering properties for incident plane waves with wavenumber $k\leq\alpha$ (energy $k^2\leq\alpha^2$.) We use a recently developed multidimensional transfer-matrix ... More
Variational nonlinear WKB in the Eulerian frameFeb 12 2019Nonlinear WKB is a multiscale technique for studying locally-plane-wave solutions of nonlinear partial differential equations (PDE). Its application comprises two steps: (1) replacement of the original PDE with an extended system separating the large ... More
On inclusive Racah matrices $\bar S$ for rectangular representationsFeb 11 2019We use the recent observation about the evolution formula for twist knots to provide a nearly explicit answer for Racah matrix $\bar S$ in arbitrary rectangular representation $R=[r^s]$. The answer is expressed through the eigenvectors of a simply-looking ... More
On exclusive Racah matrices $\bar S$ for rectangular representationsFeb 11 2019Feb 15 2019We use the recent observation about the evolution formula for twist knots to provide a nearly explicit answer for Racah matrix $\bar S$ in arbitrary rectangular representation $R=[r^s]$. The answer is expressed through the eigenvectors of a simply-looking ... More
On the analytical evaluation of the magnetization of ferromagnetic latticesFeb 11 2019We investigate analytically the magnetization of Heisenberg ferromagnetic lattices in one and two dimensions, and we derive approximate expressions that are valid at high and low temperatures. In the case of the spin-$\frac{1}{2}$ Heisenberg XX chain ... More
Renormalizing the Kardar-Parisi-Zhang equation in $d\geq 3$ in weak disorderFeb 11 2019We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random limit as the smoothing ... More
Divergence of the effective mass of a polaron in the strong coupling limitFeb 11 2019We consider the Fr\"ohlich model of a polaron, and show that its effective mass diverges in the strong coupling limit.
Dirac operators and shell interactions: a surveyFeb 11 2019In this survey we gather recent results on Dirac operators coupled with $\delta$-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterward we switch to an approximation question: ... More
Discretization and superintegrability all rolled into oneFeb 11 2019Abelian integrals arise in the mathematical description of various physical processes. According to Abel's theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are relatively little used in physics ... More
On Fermionic walkers interacting with a correlated structured environmentFeb 11 2019We study the large-time behaviour of a sample $\mathcal{S}$ consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions $\mathcal{E}$ through an exchange of particles in preferred states. We describe ... More
3d Mirror Symmetry and Elliptic Stable EnvelopesFeb 10 2019We consider a pair of quiver varieties (X;X') related by 3d mirror symmetry, where X =T*Gr(k,n) is the cotangent bundle of the Grassmannian of k-planes of n-dimensional space. We give formulas for the elliptic stable envelopes on both sides. We show an ... More
Expansion of the resolvent in a Feshbach modelFeb 10 2019Feb 12 2019In this paper we extend the results proved in (Carlone, R., Correggi, M., Finco, D., Teta, A.: A model for Feshbach Resonances arXiv:1901.08282 [math-ph]) about Feshbach resonances in a multichannel Hamiltonian $\mathcal{H}$, proving a low energy expansion ... More
Expansion of the resolvent in a Feshbach modelFeb 10 2019In this paper we extend the results proved in (Carlone, R., Correggi, M., Finco, D., Teta, A.: A model for Feshbach Resonances arXiv:1901.08282 [math-ph]) about Feshbach resonances in a multichannel Hamiltonian $\mathcal{H}$, proving a low energy expansion ... More
Drift of spectrally stable shifted states on star graphsFeb 10 2019When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a certain constraint, the nonlinear Schr\"{o}dinger (NLS) equation on the star graph can be transformed to the NLS equation ... More
Symmetry Breaking in Density Functional Theory due to Dirac Exchange for a Hydrogen MoleculeFeb 09 2019We study symmetry breaking in the mean field solutions to the 2 electron hydrogen molecule within Kohn Sham (KS) local spin density function theory with Dirac exchange (the XLDA model). This simplified model shows behavior related to that of the (KS) ... More
A combinatorial identityFeb 09 2019We prove an interesting combinatorial identity, which we came across in counting contributions from forest graphs to a cluster expansion for classical gas correlation functions, but may be of more general interest.
Modular Nekrasov-Okounkov formulasFeb 09 2019Using Littlewood's map, which decomposes a partition into its $r$-core and $r$-quotient, Han and Ji have shown that many well-known hook-length formulas admit modular analogues. In this paper we present a variant of the Han-Ji `multiplication theorem' ... More
Large deviations and entropy production in viscous fluid flowsFeb 08 2019We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair (velocity field, ... More
Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution EquationsFeb 08 2019For a scalar evolution equation $u_t=K(t,x,u,u_x,\ldots, u_n), n\geq 2$ the cohomology spaces $H^{1,s}({\mathcal R}^\infty)$ vanishes for $s\geq 3$ while the space $H^{1,2}({\mathcal R}^\infty)$ is isomorphic to the space of variational operators. The ... More
Quantum Markov States on Cayley treesFeb 08 2019It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-neighbor interactions. In our previous results, we have investigated quantum ... More
Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley treeFeb 08 2019The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QMC) scheme. In this scheme, we employ the $C^*$-algebraic approach to the ... More
Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More
Regularization by ε-metricFeb 08 2019The regularization of propagators by means of a complex metric is considered. (The paper is an English translation of the first of two articles in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization by {\epsilon}-metric. I, Izvestiya ... More
Spectral geometry in a rotating frame: properties of the ground stateFeb 08 2019We investigate spectral properties of the operator describing a quantum particle confined to a planar domain $\Omega$ rotating around a fixed point with an angular velocity $\omega$ and demonstrate several properties of its principal eigenvalue $\lambda_1^\omega$. ... More
Deformations of Kupershmidt operators on Leibniz algebras and Leibniz bialgebrasFeb 08 2019In this paper, we study (proto-, quasi-)twilled Leibniz algebras and the associated L-infty-algebras and differential graded Lie algebras. As applications, first we study the twilled Leibniz algebra corresponding to the semidirect product of a Leibniz ... More
Scattering for a particle interacting with a Bose gasFeb 08 2019We study the asymptotic behavior of solutions to an ODE - Schr\"{o}dinger type system that models the interaction of a particle with a Bose gas. We show that the particle has a ballistic trajectory asymptotically, and that the wave function describing ... More
Spectral theory of first-order systems: from crystals to Dirac operatorsFeb 08 2019Let $$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj}, \quad x\in\Rn,$$ be a constant coefficient first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous part is strongly ... More
Proper treatment of scalar and vector exponential potentials in the Klein-Gordon equation: Scattering and bound statesFeb 07 2019We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of scalar and vector ... More
W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branesFeb 07 2019We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the $W$ algebra defined using nilpotent orbit with partition $[q^m,1^s]$. Gauging above AD matters, we can ... More
Classical Dimers on Penrose TilingsFeb 07 2019We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead, their maximum ... More
Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum ElectrodynamicsFeb 07 2019Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure calculations, and ... More
Topological quantum field theory and polynomial identities for graphs on the torusFeb 07 2019We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.
Two-dimensional non-abelian BF theory in Lorenz gauge as a solvable logarithmic TCFTFeb 07 2019We study two-dimensional non-abelian BF theory in Lorenz gauge and prove that it is a topological conformal field theory. This opens the possibility to compute topological string amplitudes (Gromov-Witten invariants). We found that the theory is exactly ... More
Weak Solutions of the Relativistic Vlasov-Maxwell System with External CurrentsFeb 07 2019The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma consists of ... More
Near-integrability of periodic Klein-Gordon latticesFeb 07 2019In this paper we study the Klein-Gordon (KG) lattice with periodic boundary conditions. It is an $N$ degrees of freedom Hamiltonian system with linear inter-site forces and nonlinear on-site potential, which here is taken to be of the $\phi^4$ form. First, ... More
A short introduction to Monstrous MoonshineFeb 07 2019This paper is an introduction to the Monstrous Moonshine correspondence aiming at an undergraduate level. We review first the classification of finite simple groups and some properties of the monster $\mathbb{M}$, and then the theory of classical modular ... More
A short introduction to Monstrous MoonshineFeb 07 2019Feb 18 2019This paper is an introduction to the Monstrous Moonshine correspondence aiming at an undergraduate level. We review first the classification of finite simple groups and some properties of the monster $\mathbb{M}$, and then the theory of classical modular ... More