Theoretical and Numerical Study of Self-Organizing Processes In a Closed System Classical Oscillator + Random EnvironmentA self-organizing joint system classical oscillator + random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential…A. S. Gevorkyan, A. V. Bogdanov, V. V. Mareev et al.·Sep 6, 2022SaveLearn
Generalizations of the Pfaffian to non-antisymmetric matricesWe study two generalizations of the Pfaffian to non-antisymmetric matrices and derive their properties and relation to each other. The first approach is based on the Wigner normal-form, applicable to…Daniel Varjas·Sep 6, 2022SaveLearn
A Lieb-Thirring inequality for extended anyonsWe derive a Pauli exclusion principle for extended fermion-based anyons of any positive radius and any non-trivial statistics parameter. That is, we consider 2D fermionic particles coupled to…Théotime Girardot, Nicolas Rougerie·Sep 6, 2022SaveLearn
Reconstruction of vertex algebras in even higher dimensionsVertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any…Bojko N. Bakalov, Nikolay M. Nikolov·Sep 6, 2022SaveLearn
A Riemann Hilbert approach to the study of the generating function associated to the Pearcey processUsing Riemann-Hilbert methods, we establish a Tracy-Widom like formula for the generating function of the occupancy numbers of the Pearcey process. This formula is linked to a coupled vector…Thomas Chouteau·Sep 6, 2022SaveLearn
Ground state energies of the Hubbard models and the Hartree Fock approximationAccording to the `folk knowledge', the Hartree-Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling U (the smaller |U|, the better is the H-F…Jacek Wojtkiewicz, Piotr H. Chankowski·Sep 6, 2022SaveLearn
Stochastic dynamics for Group Field TheoriesPhase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium…Vincent Lahoche, Dine Ousmane Samary·Sep 6, 2022SaveLearn
Supersymmetry and Convection-Diffusion-Reaction equationsIn this work we are concerned with generating solutions of a class of Convection-Diffusion-Reaction equation from the solutions of another CDR equation through the Darboux transformations. The method…Choon-Lin Ho·Sep 4, 2022SaveLearn
Infinite Chain of Harmonic Oscillators Under the Action of the Stationary Stochastic ForceWe consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on…Alexandr Lykov, Margarita Melikian·Sep 4, 2022SaveLearn
Rigged Hilbert Space Approach for Non-Hermite Systems with Positive Definite MetricWe investigate Dirac's bra-ket formalism based on a rigged Hilbert space for a non-Hermite quantum system with a positive-definite metric. First, the rigged Hilbert space, characterized by…Shousuke Ohmori, Junichi Takahashi·Sep 4, 2022SaveLearn
Affine geometric description of thermodynamicsThermodynamics provides a unified perspective of thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described…Shin-itiro Goto·Sep 4, 2022SaveLearn
On the Perturbed Second Painlev\'e EquationWe consider a perturbed version of the second Painlev\'e equation (PII), which arises in applications, and show that it possesses solutions analogous to the celebrated…Joshua Holroyd, Nalini Joshi·Sep 4, 2022SaveLearn
From pinned billiard balls to partial differential equationsWe discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billiard balls is assumed to be large but finite and we assume…Krzysztof Burdzy, Jeremy G. Hoskins, Stefan Steinerberger·Sep 3, 2022SaveLearn
Watermelons on the half-planeWe study the watermelon probabilities in the uniform spanning forests on the two-dimensional semi-infinite square lattice near either open or closed boundary to which the forests can or cannot be…Khaydar Nurligareev, Alexander Povolotsky·Sep 3, 2022SaveLearn
Arithmetic Phase Transitions For Mosaic Maryland ModelWe give a precise description of spectral types of the Mosaic Maryland model with any irrational frequency, which provides a quasi-periodic unbounded model with non-monotone potential has arithmetic…Jiawei He, Xu Xia·Sep 3, 2022SaveLearn
Supersymmetric Quantum Potentials Analogs of Classical Electrostatic FieldsA relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be…Juan D. García-Muñoz, A Raya·Sep 2, 2022SaveLearn
Stability of the spectral gap and ground state indistinguishability for a decorated AKLT modelWe use cluster expansions to establish local indistiguishability of the finite-volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our…Angelo Lucia, Alvin Moon, Amanda Young·Sep 2, 2022SaveLearn
Somonodromic Deformations Along the Caustic of a Dubrovin-Frobenius ManifoldWe study the family of ordinary differential equations associated to a Dubrovin-Frobenius manifold along its caustic. Upon just loosing an idempotent at the caustic and under a non-degeneracy…Felipe Reyes·Sep 2, 2022SaveLearn
Feynman checkers: external electromagnetic field and asymptotic propertiesWe study Feynman chekers - one of the most elementary models of electron motion. It is also known as one-dimensional quantum walk or an Ising model at imaginary temperature. We add the simpliest…Fedor Ozhegov·Sep 2, 2022SaveLearn
Generalized Frobenius Manifolds with Non-flat Unity and Integrable HierarchiesFor any generalized Frobenius manifold with non-flat unity, we construct a bihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of the Principal Hierarchy of a Frobenius…Si-Qi Liu, Haonan Qu, Youjin Zhang·Sep 1, 2022SaveLearn
Monodromy of Complexified Planar Kepler ProblemThe planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.Shanzhong Sun, Peng You·Aug 31, 2022SaveLearn
Using stochastic order to compare different Euclidean Random Assignment ProblemsThis paper provides a theorem to compare the minimum total cost of two different Euclidean Random Assignment Problems with the same number of points, using the stochastic order of the costs of one of…Matteo D'Achille, Yuqi Liu·Aug 31, 2022SaveLearn
Local Laws and a Mesoscopic CLT for β-ensemblesWe study the statistical mechanics of the log-gas, or β-ensemble, for general potential and inverse temperature. By means of a bootstrap procedure, we prove local laws on the next order energy…Luke Peilen·Aug 31, 2022SaveLearn
Symmetry-induced quasicrystalline waveguidesIntroducing an axis of reflectional symmetry in a quasicrystal leads to the creation of localised edge modes that can be used to build waveguides. We develop theory that characterises…Bryn Davies, Richard V Craster·Aug 31, 2022SaveLearn
Ginzburg-Landau equations and their generalizationsThe Ginzburg-Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the…Armen Sergeev·Aug 31, 2022SaveLearn