New bounds on the excess charge for atomic systemsIn this manuscript, using a technique introduced by P.~T.~Nam in 2012 and the Coulomb Uncertainty Principle, we prove new bounds on the excess charge for non relativistic atomic systems,…Rafael D. Benguria, Juan Manuel Gonzalez-Brantes, Trinidad Tubino·Jul 18, 2022SaveLearn
Deformation quantization of the simplest Poisson OrbifoldWhenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new…Alexey Sharapov, Evgeny Skvortsov, Arseny Sukhanov·Jul 18, 2022SaveLearn
Computer Algebra and Hypergeometric Structures for Feynman IntegralsWe present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the…Johannes Bluemlein, Marco Saragnese, Carsten Schneider·Jul 18, 2022SaveLearn
Tau functions, infinite Grassmannians and lattice recurrencesThe addition formulae for KP τ-functions, when evaluated at lattice points in the KP flow group orbits in the infinite dimensional Sato-Segal-Wilson Grassmannian, give infinite parametric…S. Arthamonov, J. Harnad, J. Hurtubise·Jul 17, 2022SaveLearn
Deformation Quantisation via Kontsevich Formality TheoremThis dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the…Peize Liu·Jul 16, 2022SaveLearn
Two Comments on the Derivation of the Time-Dependent Hartree-Fock EquationWe revisit the derivation of the time-dependent Hartree-Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comments to the result…Niels Benedikter, Davide Desio·Jul 16, 2022SaveLearn
Weak Markov Blankets in High-Dimensional, Sparsely-Coupled Random Dynamical SystemsThis paper formulates a notion of high-dimensional random dynamical systems that couple to another system, like an embedding environment, in such a way that each system engages in controlled exchange…Dalton A R Sakthivadivel·Jul 15, 2022SaveLearn
Non-Abelian correlation inequalities and stable determinantal polynomialsWe consider the correlations of invariant observables for the O(N) and CPN-1 models at zero coupling, namely, with respect to the natural group-invariant measure. In the…Abdelmalek Abdesselam·Jul 15, 2022SaveLearn
Combinatorics of generalized Dyck and Motzkin pathsWe relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficients of particles obeying generalized exclusion statistics, and obtain explicit expressions for the…Li Gan, Stéphane Ouvry, Alexios P. Polychronakos·Jul 15, 2022SaveLearn
A class of weak pseudo-bosons and their bi-coherent statesIn this paper we extend some previous results on weak pseudo-bosons and on their related bi-coherent states. The role of compatible functions is discussed in details, and some examples are…Fabio Bagarello·Jul 15, 2022SaveLearn
Evolution of channel flow and Darcy law beyond the critical Reynolds numberChannel flow is usually described by Darcy law with the Poiseuille flow profile. However, for incompressible channel flow there is a critical state, characterized by a critical Reynolds number Rec…Xiaohui Deng, Ping Sheng·Jul 14, 2022SaveLearn
Mathematical aspects and simulation of electron-electron scattering in grapheneSome properties of the electron-electron collision operator in graphene are analyzed along with the evaluation of collision rate. Monte Carlo simulations complete the study and highlight the…Giovanni Nastasi, Vittorio Romano·Jul 14, 2022SaveLearn
Boundary Condition and the Auxiliary Phase in Feynman Path IntegralWhen employing Feynman path integrals to compute propagators in quantum physics, the concept of summing over the set of all paths is not always naive. In fact, an auxiliary phase often has to be…Chung-Ru Lee·Jul 14, 2022SaveLearn
Contact dynamics, contact Poisson bracket, and symplectic integrator -- Even Arnold noddsBy introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are…Kiyoshi Sogo, Shuhei Ohnishi·Jul 14, 2022SaveLearn
An effective fractional paraxial wave equation for wave-fronts in randomly layered media with long-range correlationsThis work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the 3D physical…Christophe Gomez·Jul 13, 2022SaveLearn
Spontaneous stochasticity and renormalization group in discrete multi-scale dynamicsWe introduce a class of multi-scale systems with discrete time, motivated by the problem of inviscid limit in fluid dynamics in the presence of small-scale noise. These systems are…Alexei A. Mailybaev, Artem Raibekas·Jul 13, 2022SaveLearn
Yang-Mills as a Constrained GaussianYang-Mills is reformulated in terms of the logarithmic derivative of the holonomies. The classical equations of motion are recovered, and the path integral is rewritten in two ways, both of which are…Tamer Tlas·Jul 13, 2022SaveLearn
Toda systems for Takiff algebrasWe study completely integrable systems attached to Takiff algebras gN, extending open Toda systems of split simple Lie algebras g. With respect to Darboux coordinates on…Michael Lau·Jul 13, 2022SaveLearn
Seven Useful Questions in Density Functional TheoryWe explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward…Steven Crisostomo, Ryan Pederson, John Kozlowski et al.·Jul 12, 2022SaveLearn
Quantization, dequantization, and distinguished statesGeometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques…Eli Hawkins, Christoph Minz, Kasia Rejzner·Jul 12, 2022SaveLearn
Quasi-Linear Criticality Theory and Green's Functions on GraphsWe study energy functionals associated with quasi-linear Schrödinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of…Florian Fischer·Jul 12, 2022SaveLearn
One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation lawsA recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional…Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman V. Kozlov et al.·Jul 12, 2022SaveLearn
Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and AF algebrasIn this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an AF-algebra. One aim of this paper is to lift arrows of a Bratteli…Thierry Masson, Gaston Nieuviarts·Jul 10, 2022SaveLearn
Half-plane diffraction problems on a triangular latticeWe investigate thin-slit diffraction problems for two-dimensional lattice waves. The peculiar structure allows us to consider the problems on the semi-infinite triangular lattice, consequently, we…David Kapanadze, Ekaterina Pesetskaya·Jul 10, 2022SaveLearn
Airy ideals, transvections and W(sp2N)-algebrasIn the first part of the paper we propose a different viewpoint on the theory of higher Airy structures (or Airy ideals) which may shed light on its origin. We define Airy ideals in the -adic…Vincent Bouchard, Thomas Creutzig, Aniket Joshi·Jul 9, 2022SaveLearn