Series over fat partitions: matrix models and discrete ensemblesWe consider series over Young diagrams of products of Schur functions sλλ, marked with ``fat partitions'' λλ, which appear in matrix models associated with…A. Yu. Orlov·Nov 20, 2023SaveLearn
Bosonized Momentum Distribution of a Fermi Gas via Friedrichs DiagramsRecently, Benedikter and the author proved an approximate formula for the momentum distribution of a 3d fermionic gas interacting by a short-range pair potential in the mean-field regime, within a…Sascha Lill·Nov 20, 2023SaveLearn
x-y duality in Topological Recursion for exponential variables via Quantum DilogarithmFor a given spectral curve, the theory of topological recursion generates two different families ωg,n and ωg,n of multi-differentials, which are for algebraic spectral curves…Alexander Hock·Nov 20, 2023SaveLearn
Generalised eigenfunction expansion and singularity expansion methods for two-dimensional acoustic time-domain wave scattering problemsTime-domain wave scattering in an unbounded two-dimensional acoustic medium by sound-hard scatterers is considered. Two canonical geometries, namely a split-ring resonator (SRR) and an array of…Ben Wilks, Michael H. Meylan, Fabien Montiel et al.·Nov 20, 2023SaveLearn
The Jacobian conjectureThe Jacobian conjecture involves the map y= x - V(x) where y, x are n-dimensional vectors, V(x) is a symmetric polynomial of degree d for which the Jacobian hypothesis holds: $ eTr (1-…Jacques Magnen·Nov 19, 2023SaveLearn
Canonical Quantization of the Scalar Field: The Measure Theoretic PerspectiveThis review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study…José Velhinho·Nov 19, 2023SaveLearn
On the inverse scattering transform to the discrete Hirota equation with nonzero boundary conditionsUnder investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order…Guixian Wang, Xiu-Bin Wang, Bo Han·Nov 18, 2023SaveLearn
Hadamard states for linearized gravity on spacetimes with compact Cauchy surfacesWe consider the quantization of linearized Einstein equations. We prove the existence of Hadamard states in the harmonic gauge on any Einstein spacetime with compact Cauchy surfaces.Christian Gérard·Nov 18, 2023SaveLearn
Higher Topos Theory in PhysicsA brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.Urs Schreiber·Nov 18, 2023SaveLearn
A Tale of Three CoauthorsWe tell the story of the discovery of an interesting bound on finite sums and its application to comparison of Ising models.Barry Simon·Nov 16, 2023SaveLearn
Deficiency indices for singular magnetic Schr\"odinger operatorsWe show that the deficiency indices of magnetic Schr\"odinger operators with several local singularities can be computed in terms of the deficiency indices of operators carrying just one singularity…Michele Correggi, Davide Fermi·Nov 16, 2023SaveLearn
Typical dropping asymptotics of quasiclassical approximations to solutions of the nonlinear Schr\"odinger equationFormal asymptotics are substantiated that describe typical dropping cusp singularity of quasiclassical approximations to solutions of two cases of the integrable nonlinear Schr\"odinger equation…Sergej Melikhov, Bulat Suleimanov, Azamat Shavlukov·Nov 16, 2023SaveLearn
Massless field equations for spin 3/2 in dimension 6Main topic of the paper is a study of properties of massless fields of spin 3/2 in its Euclidean version. A lot of information is available already for massless fields in dimension 4. Here, we…Roman Lavicka, Vladimir Soucek, Wei Wang·Nov 16, 2023SaveLearn
Geometry and quasi-classical quantization of magnetic monopolesWe present the basic physical and mathematical ideas (P. Curie, Darboux, Poincare, Dirac) that led to the concept of magnetic charge, the general construction of magnetic Laplacians for magnetic…I. A. Taimanov·Nov 16, 2023SaveLearn
Singular Lagrangians and the Faddeev-Jackiw Formalism in Classical MechanicsClassical mechanical systems with internal constraints will be examined using the extended symplectic formalism of Faddeev-Jackiw. We will derive the generalized brackets of the theory and the…Jorge Paulin Fuente, Carlos Manuel López Arellano, Jaime Manuel Cabrera·Nov 15, 2023SaveLearn
Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problemsThe generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the…Ben Wilks, Michael H. Meylan, Fabien Montiel et al.·Nov 15, 2023SaveLearn
Lagrangian intersections and glancing points: typical transitions of phase in semiclassical approximationsGiven a semiclassical distribution fh microlocalized on a Lagrangian manifold 0, H∈ C∞( T Rn), and H=E a regular energy surface, we find asymptotic solutions of…Ilya Bogaevskii, Michel Rouleux·Nov 15, 2023SaveLearn
Dissipative dynamics for infinite lattice systemsWe study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of…Shreya Mehta, Boguslaw Zegarlinski·Nov 14, 2023SaveLearn
Quantum field theory at finite temperature for 3D periodic backgroundsThe one-loop quantum corrections to the internal energy of some lattices due to the quantum fluctuations of the scalar field of phonons are studied. The band spectrum of the lattice is characterised…Lucia Santamaria-Sanz·Nov 14, 2023SaveLearn
Control Theory and Parametrizations of Linear Partial Differential OperatorsWhen D: → η is a linear OD or PD operator, a "direct problem" is to find compatibility conditions (CC) as an operator D1:η → ζ such that…Jean-Francois Pommaret·Nov 13, 2023SaveLearn
Nonholonomic reduction for mechanical systems with collisionsThis paper studies nonsmooth variational problems on principal bundles for nonholonomic systems with collisions taking place in the boundary of the manifold configuration space of the nonholonopmic…Álvaro Rodríguez Abella, Leonardo J. Colombo·Nov 13, 2023SaveLearn
Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regimeFor a translation invariant system of N bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy EN. While the leading, order N, contribution to EN…Cristina Caraci, Alessandro Olgiati, Diane Saint Aubin et al.·Nov 13, 2023SaveLearn
Notes on Smooth and Singular Volumetric GrowthThe material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body…Vladimir Goldshtein, Reuven Segev·Nov 12, 2023SaveLearn
Fisher-Hartwig Asymptotics and Log-Correlated Fields in Random Matrix TheoryThis thesis is based on joint work with Jon Keating [FK21], Tom Claeys and Jon Keating [CFK23], and Isao Sauzedde [FS22], and is concerned with establishing and studying connections between random…Johannes Forkel·Nov 11, 2023SaveLearn
Lattice sums of I-Bessel functions, theta functions, linear codes and heat equationsWe extend a certain type of identities on sums of I-Bessel functions on lattices, previously given by G. Chinta, J. Jorgenson, A. Karlsson and M. Neuhauser. Moreover we prove that, with continuum…Takehiro Hasegawa, Hayato Saigo, Seiken Saito et al.·Nov 11, 2023SaveLearn