Enumeration of hypermaps and Hirota equations for extended rationally constrained KPWe consider the Hurwitz Dubrovin--Frobenius manifold structure on the space of meromorphic functions on the Riemann sphere with exactly two poles, one simple and one of arbitrary order. We prove that…G. Carlet, J. van de Leur, H. Posthuma et al.·Nov 22, 2022SaveLearn
The Potts model on a Cayley tree: the new class of Gibbs measuresFor the Potts model on Cayley trees, a very wide class of new Gibbs measures is given. We give a review of all known Gibbs measures of the Potts model on trees and compare them with our new measures.Muzaffar M. Rahmatullaev, Dekhkonov D. Jasur·Nov 22, 2022SaveLearn
Semiclassical resonance asymptotics for systems with degenerate crossings of classical trajectoriesThis paper is concerned with the asymptotics of resonances in the semiclassical limit h 0+ for 2× 2 matrix Schr\"odinger operators in one dimension. We study the case where the two…Marouane Assal, Setsuro Fujiié, Kenta Higuchi·Nov 21, 2022SaveLearn
On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problemSpectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's…Olga Boyko, Olga Martynyuk, Vyacheslav Pivovarchik·Nov 21, 2022SaveLearn
New techniques to solve the 1-dimensional random flightWe present here two new techniques to solve the one-dimensional random flight. The first one is an expansion in the number of collisions. The second one is the obtention of a Fourier series. This…Ricardo García-Pelayo·Nov 20, 2022SaveLearn
Fourier series for the three-dimensional random flightThe probability density function of the random flight with isotropic initial conditions is obtained by an expansion in the number of collisions and the in the spatial harmonics of the solution, as in…Ricardo García-Pelayo·Nov 20, 2022SaveLearn
Enumerative geometry of surfaces and topological stringsThis survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs (X,D) with X a complex algebraic surface and D a singular anticanonical divisor in it. I will…Andrea Brini·Nov 20, 2022SaveLearn
Multisymplectic Formalism for Cubic Horndeski TheoriesWe present the covariant multisymplectic formalism for the so-called cubic Horndeski theories and discuss the geometrical and physical interpretation of the constraints that arise in the unified…M. Doniz, J. Gaset·Nov 19, 2022SaveLearn
D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of K\"ahler-Einstein surfacesD3-brane solutions of type IIB supergravity can be obtained by means a classical ansatz involving a harmonic warp factor and two summands, the first being the flat Minkowskian metric of the D3 brane…Ugo Bruzzo, Pietro Fré, Umar Shahzad et al.·Nov 18, 2022SaveLearn
Ultraviolet finite non-local Hamiltonian perturbation Quantum Field Theories and their weak adiabatic limitThe non-local quantum field theories attract interest in the mathematical and physical community as candidates for effective description of the reality taking into account the quantum gravity…Aleksei Bykov·Nov 18, 2022SaveLearn
Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma modelWe study the Integrated Density of States (IDS) of the random Schr\"odinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model. We…Margherita Disertori, Valentin Rapenne, Constanza Rojas-Molina et al.·Nov 18, 2022SaveLearn
Phase transition in the Peierls model for polyacetyleneWe consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existence of a critical…David Gontier, Adéchola Kouande, Eric Séré·Nov 17, 2022SaveLearn
The Boltzmann equation for hard potentials with integrable angular transition: Coerciveness, exponential tails rates, and Lebesgue integrabilityThis manuscript focus on an extensive survey with new techniques on the problem of solving the Boltzmann flow by bringing a unified approach to the Cauchy problem to homogeneous kinetic equations…Ricardo J. Alonso, Irene M. Gamba·Nov 16, 2022SaveLearn
Fusion hierarchies, T-systems and Y-systems for the dilute A2(2) loop models on a stripWe study the dilute A2(2) loop models on the geometry of a strip of width N. Two families of boundary conditions are known to satisfy the boundary Yang-Baxter equation. Fixing the boundary…Florence Boileau, Alexi Morin-Duchesne, Yvan Saint-Aubin·Nov 16, 2022SaveLearn
Infinite volume Gibbs states and metastates of the random field mean-field spherical modelFor the discrete random field Curie-Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general,…Kalle Koskinen·Nov 16, 2022SaveLearn
A simple formula for the x-y symplectic transformation in topological recursionLet Wg,n be the correlators computed by Topological Recursion for some given spectral curve (x,y) and Wg,n for (y,x), where the role of x,y is inverted. These two sets of…Alexander Hock·Nov 16, 2022SaveLearn
Kac-Schwarz Operators of Type B, Quantum Spectral Curves, and Spin Hurwitz NumbersGiven a tau-function τ(t) of the BKP hierarchy satisfying τ(0)=1, we discuss the relation between its BKP-affine coordinates on the isotropic Sato Grassmannian and its BKP-wave function.…Ce Ji, Zhiyuan Wang, Chenglang Yang·Nov 16, 2022SaveLearn
On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operatorsWe propose and prove a set of identities for GLM elliptic R-matrix (in the fundamental representation). In the scalar case (M=1) these are elliptic function identities derived by S.N.M.…M. Matushko, A. Zotov·Nov 15, 2022SaveLearn
Traveling waves and effective mass for the regularized Landau-Pekar equationsWe consider the regularized Landau-Pekar equations with positive speed of sound and prove the existence of subsonic traveling waves. We provide a definition of the effective mass for the regularized…Simone Rademacher·Nov 15, 2022SaveLearn
A new light on the FKMM invariant and its consequences"Quaternionic" vector bundles are the objects which describe the topological phases of quantum systems subjected to an odd time-reversal symmetry (class AII). In this work we prove that the FKMM…Giuseppe De Nittis, Kiyonori Gomi·Nov 15, 2022SaveLearn
Bost-Connes-Marcolli system for the Siegel modular varietyWe construct a quantum satisitical mechanical system which generalizes the Connes-Marcolli GL2 system. In particular we introduce the Connes-Marcolli system associated to the Siegel modular…Ismail Abouamal·Nov 14, 2022SaveLearn
A Block-diagonal form for four-component operators describing Graphene Quantum DotsWe consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary conditions are defined…Rafael D. Benguria, Edgardo Stockmeyer, Cristóbal Vallejos et al.·Nov 14, 2022SaveLearn
Mean-field approach to Random Apollonian PackingWe revisit the scaling properties of growing spheres randomly seeded in d=2,3 and 4 dimensions using a mean-field approach. We model the insertion probability without assuming a priori a functional…Pierre Auclair·Nov 14, 2022SaveLearn
Multiscale Loop Vertex Expansion for Cumulants, the T34 ModelWe construct cumulants up to a finite order of a tensor field theory perturbed by a quartic term, nicknamed the T34 model. The method we use is the multi-scale loop vertex expansion. We prove…Vincent Rivasseau·Nov 14, 2022SaveLearn
On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative planeIn this paper, we provide a mathematically and physically consistent minimal prescription for a charged spinless point particle coupled to a constant magnetic field in a 2-dimensional noncommutative…S. Hasibul Hassan Chowdhury, Talal Ahmed Chowdhury·Nov 14, 2022SaveLearn