The loop equation for the Burgers--KdV hierarchyThe Burgers--KdV hierarchy was introduced towards understanding intersection numbers on the moduli space of Riemann surfaces with boundaries. The goal of this paper is to derive the Dubrovin--Zhang…Di Yang, Chunhui Zhou·Sep 19, 2024SaveLearn
On the Hilbert Space of the Chern-Simons Matrix Model, Deformed Double Current Algebra Action, and the Conformal LimitA Chern-Simons matrix model was proposed by Dorey, Tong, and Turner to describe non-Abelian fractional quantum Hall effect. In this paper we study the Hilbert space of the Chern-Simons matrix model…Sen Hu, Si Li, Dongheng Ye et al.·Sep 19, 2024SaveLearn
Kadomtsev-Petviashvili hierarchies with non-formal pseudo-differential operators, non-formal solutions, and a Yang-Mills--like formulationWe start from the classical Kadomtsev-Petviashvili hierarchy posed on formal pseudo-differential operators, and we produce two hierarchies of non-linear equations posed on non-formal…Jean-Pierre Magnot, Enrique G. Reyes·Sep 18, 2024SaveLearn
Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D SpaceA mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity…Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka et al.·Sep 18, 2024SaveLearn
The geometry of dissipationDissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to…Asier López-Gordón·Sep 18, 2024SaveLearn
Density-functional theory for the Dicke HamiltonianA detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to…Vebjørn H. Bakkestuen, Mihály A. Csirik, Andre Laestadius et al.·Sep 18, 2024SaveLearn
Determination of Fisher and Shannon Information for 1D Fractional Quantum Harmonic OscillatorThis study employs the Riesz-Feller fractional derivative to determine Fisher and Shannon parameters for a one-dimensional harmonic oscillator. By deriving the Riesz fractional derivative of the…A. Boumali, K. Zazoua, F. Serdouk·Sep 18, 2024SaveLearn
A Geometric Perspective on Kinetic Matter-Radiation Interaction and Moment SystemsWe provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with…Brian K. Tran, Joshua W. Burby, Ben S. Southworth·Sep 17, 2024SaveLearn
Principal binetsConjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geometry, two…Niklas Christoph Affolter, Jan Techter·Sep 17, 2024SaveLearn
Deformations in spinor bundles: Lorentz violation and further physical implicationsThis paper delves into the deformation of spinor structures within nontrivial topologies and their physical implications. The deformation is modeled by introducing real functions that modify the…J. M. Hoff da Silva, R. T. Cavalcanti, G. M. Caires da Rocha·Sep 17, 2024SaveLearn
Geometric Formula for 2d Ising Zeros: Examples & NumericsA geometric formula for the zeros of the partition function of the inhomogeneous 2d Ising model was recently proposed in terms of the angles of 2d triangulations embedded in the flat 3d space. Here…Iñaki Garay, Etera R. Livine·Sep 17, 2024SaveLearn
Asymptotics of the divisor for the good Boussinesq equationWe consider a third order operator under the three-point Dirichlet condition. Its spectrum is the so-called auxiliary spectrum for the good Boussinesq equation, as well as the Dirichlet spectrum for…Andrey Badanin, Evgeny Korotyaev·Sep 17, 2024SaveLearn
A review of a work by Raymond: Sturmian Hamiltonians with a large coupling constant -- periodic approximations and gap labelsWe present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an…Ram Band, Siegfried Beckus, Barak Biber et al.·Sep 17, 2024SaveLearn
Upper bounds in non-autonomous quantum dynamicsWe prove upper bounds on outside probabilities for generic non-autonomous Schr\"odinger operators on lattices of arbitrary dimension. Our approach is based on a combination of commutator method…Jingxuan Zhang·Sep 17, 2024SaveLearn
An Observer-Based View of Euclidean GeometryInfluence network of events is a view of the universe based on events that may be related to one another via influence. The network of events form a partially-ordered set which, when quantified…Newshaw Bahreyni, Carlo Cafaro, Leonardo Rossetti·Sep 17, 2024SaveLearn
U(1)n Chern-Simons theory: partition function, reciprocity formula and Chern-Simons dualityThe U(1) Chern-Simons theory can be extended to a topological U(1)n theory by taking a combination of Chern-Simons and BF actions, the mixing being achieved with the help of a…Han-Miru Kim, Philippe Mathieu, Michail Tagaris et al.·Sep 16, 2024SaveLearn
On the thermodynamic limit of interacting fermions in the continuumWe study the dynamics of non-relativistic fermions in Rd interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we identify…Oliver Siebert·Sep 16, 2024SaveLearn
Variational closures for composite homogenised fluid flowsHomogenisation theory has seen recent applications in deriving stochastic transport models for fluid dynamics. In this work, we first derive the stochastic Lagrange-to-Euler map that underpins…Theo Diamantakis, Ruiao Hu, James-Michael Leahy·Sep 16, 2024SaveLearn
Mesoscopic Universality for Circular Orthogonal Polynomial EnsemblesWe study mesoscopic fluctuations of orthogonal polynomial ensembles on the unit circle. We show that asymptotics of such fluctuations are stable under decaying perturbations of the recurrence…Jonathan Breuer, Daniel Ofner·Sep 15, 2024SaveLearn
Quantized Kepler-Coulomb dynamical models on two-dimensional constant curvature spacesThe paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have…Agnieszka Martens·Sep 15, 2024SaveLearn
On the Novikov problem for superposition of periodic potentialsWe consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the…A. Ya. Maltsev·Sep 15, 2024SaveLearn
On the critical finite-size gap scaling for frustration-free HamiltoniansWe prove that the critical finite-size gap scaling for frustration-free Hamiltonians is of inverse-square type. The result covers general graphs embedded in RD and general finite-range…Marius Lemm, Angelo Lucia·Sep 15, 2024SaveLearn
Bethe ansatz approach for the steady state of the asymmetric simple exclusion process with open boundariesWe study the asymmetric simple exclusion process with non-diagonal boundary terms under a specific constraint. A symmetric chiral basis is constructed and a special string solution of the Bethe…Xin Zhang, Fa-Kai Wen·Sep 15, 2024SaveLearn
A class of exactly solvable Convection-Diffusion-Reaction equations in similarity form with intrinsic supersymmetryIn this work we would like to point out the possibility of generating a class of exactly solvable convection-diffusion-reaction equation in similarity form with intrinsic supersymmetry, i.e., the…Choon-Lin Ho·Sep 14, 2024SaveLearn
Neumann Series-based Neural Operator for Solving Inverse Medium ProblemThe inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within…Ziyang Liu, Fukai Chen, Junqing Chen et al.·Sep 14, 2024SaveLearn