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Mathematical Physics papers — page 244

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Log-Sobolev inequality for the 42 and 43 measures
The continuum 42 and 43 measures are shown to satisfy a log-Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that their susceptibility is…
Roland Bauerschmidt, Benoit DagallierFeb 4, 2022
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Quantum number towers for the Hubbard and Holstein models
In 1989, Elliott Lieb published a Physical Review Letter proving two theorems about the Hubbard model. This paper used the concept of spin-reflection positivity to prove that the ground state of the…
Janes K. FreericksFeb 4, 2022
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A Markov Chain Surrogate Model for a Two-Dimensional Interacting Particle System with Internal Collisions
A probabilistic Markov Chain (MC) surrogate model for a two-dimensional system of interacting particles within a square domain having inherent symmetries is developed. Particles are assumed to be…
Tricity Andrew, James D. Nance, Mansoor A. HaiderFeb 4, 2022
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Heat coefficients for magnetic Laplacians on the complex projective space Pn(C)
Denoting by Δν the Fubini-Study Laplacian perturbed by a uniform magnetic field strength proportional to ν, this operator has a discrete spectrum consisting on eigenvalues $βm, \…
K. Ahbli, A. Hafoud, Z. MouaynFeb 4, 2022
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The new simplest proof of Ceyley's formula and connections with Kirkwood-Salzburg equations
A new very simple proof of the number of labeled rooted forest-graphs with a given number of vertices is given. As a partial case of this formula we have Cayley's formula.
Alexei L. RebenkoFeb 4, 2022
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Conjugation Matters. Bioctonionic Veronese Vectors and Cayley-Rosenfeld Planes
Motivated by the recent interest in Lie algebraic and geometric structures arising from tensor products of division algebras and their relevance to high energy theoretical physics, we analyze…
Daniele Corradetti, Alessio Marrani, David Chester et al.Feb 4, 2022
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Shape Dynamics of N Point Vortices on the Sphere
We give a geometric account of the relative motion or the shape dynamics of N point vortices on the sphere exploiting the SO(3)-symmetry of the system. The main idea is to bypass the…
Tomoki OhsawaFeb 3, 2022
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Bose-Einstein condensation on hyperbolic spaces
A well-known conjecture in mathematical physics asserts that the interacting Bose gas exhibits Bose-Einstein condensation (BEC) in the thermodynamic limit. We consider the Bose gas on certain…
Marius Lemm, Oliver SiebertFeb 3, 2022
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Statistical mechanics of Coulomb systems: From electrons and nuclei to atoms and molecules
This article is dedicated to Elliott Lieb in celebration of his 90th birthday. I recount briefly some history of our joint work on the existence of the thermodynamic limit for Coulomb systems and…
Joel L. LebowitzFeb 3, 2022
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Eyring-Kramers type formulas for some piecewise deterministic Markov processes
In this work, we give sharp asymptotic equivalents in the small temperature regime of the smallest eigenvalues of the generator of some piecewise deterministic Markov processes (including the ZigZag…
Dorian Le Peutrec, Laurent Michel, Boris NectouxFeb 3, 2022
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The Madelung Constant in N Dimensions
We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and representations of sums rN(m) of squares for N-dimensional Madelung constants, MN(s),…
Antony Burrows, Shaun Cooper, Peter SchwerdtfegerFeb 3, 2022
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Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Ruijsenaars-Macdonald…
M. Matushko, A. ZotovFeb 2, 2022
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Winding number and homotopy for quaternionic curves
Following a recent approach to quaternionic curves, we defined the quaternionic polar angle that enabled us to define global properties of quaternionic curves, namely the winding number and the…
Sergio GiardinoFeb 2, 2022
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The Role of Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited
Second law of thermodynamics imposes that in any thermodynamic process the entropy production must be nonnegative. In continuum physics such a requirement is fulfilled by postulating the constitutive…
V. A. Cimmelli, P. RogolinoFeb 2, 2022
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Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph
We consider the inverse scattering problems for two types of Schrödinger operators on locally perturbed periodic lattices. For the discrete Hamiltonian, the knowledge of the S-matrix for all energies…
Emilia Blåsten, Pavel Exner, Hiroshi Isozaki et al.Feb 2, 2022
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Ballistic transport in periodic and random media
We prove ballistic transport of all orders, that is, xme-itHψ tm, for the following models: the adjacency matrix on Zd, the Laplace operator on…
Anne Boutet de Monvel, Mostafa SabriFeb 2, 2022
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Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups
This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and,…
Álvaro Rodríguez Abella, Melvin LeokFeb 1, 2022
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On Products of Random Matrices
We introduce a family of models, which we name matrix models associated with children's drawings -- the so-called dessin d'enfant. Dessins d'enfant are graphs of a special kind drawn on a…
Natalia Amburg, Aleksandr Yu. Orlov, Dmitry VasilievFeb 1, 2022
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On the Pernici-Wanless Expansion for the Entropy ( and Virial Coefficients ) of a Dimer Gas on an Infinite Regular Lattice
We work with the following expression for the entropy (density) of a dimer gas on an infinite r-regular lattice lambda(p) = 1/2 [ pln(r)-ln(p)-2(1-p)ln(1-p)-p ]+sumk=2(dk)(pk) where the…
Paul FederbushFeb 1, 2022
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Generalized forms, metrics and Ricci flat four-metrics
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat…
D C RobinsonFeb 1, 2022
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Spectral Analysis of the Quantum Random Energy Model
The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type which describes effects of a transversal magnetic field on Derrida's spin glass. The model exhibits a glass phase as…
Chokri Manai, Simone WarzelFeb 1, 2022
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Trajectories of charged particles in knotted electromagnetic fields
We investigate the trajectories of point charges in the background of finite-action vacuum solutions of Maxwell's equations known as knot solutions. More specifically, we work with a basis of…
Kaushlendra Kumar, Olaf Lechtenfeld, Gabriel Picanço CostaFeb 1, 2022
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Ground state energy of the low density Bose gas with three-body interactions
We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined…
Phan Thành Nam, Julien Ricaud, Arnaud TriayJan 31, 2022
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Nambu-Goldstone Modes for Superconducting Lattice Fermions
We present a lattice model for superconducting fermions whose nearest-neighbour two-body interactions are a Bardeen-Cooper-Schrieffer-type pairing on the hypercubic lattice Zd with the…
Tohru KomaJan 31, 2022
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Current correlations, Drude weights and large deviations in a box-ball system
We explore several aspects of the current fluctuations and correlations in the box-ball system (BBS), an integrable cellular automaton in one space dimension. The state we consider is an ensemble of…
Atsuo Kuniba, Grégoire Misguich, Vincent PasquierJan 31, 2022
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