3362 papers
Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.
On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.
This paper introduces a universal algebraic framework for finite-dimensional open quantum systems that reformulates the Lindblad equation using a closed algebra of Hermitian operators, thereby revealing the richer structure of dissipative dynamics compared to unitary evolution while significantly reducing computational costs through efficient recursion relations and model-independent parametrizations.
This paper establishes sharp -linear estimates for Carleson--Sjölin oscillatory integral operators with arbitrary separated frequency scales and resolves the Burq--Gérard--Tzvetkov problem by proving log-free endpoint bilinear spectral cluster estimates on closed three-dimensional Riemannian manifolds.
This paper employs the nonlinear steepest descent method within a Riemann-Hilbert framework to derive the long-time asymptotic behavior of the defocusing nonlinear Schrödinger equation with step-like initial data, revealing that the solution in the first two transition regions is governed by Painlevé III-type formulas while the third region exhibits collisionless shock dynamics described by Riemann theta functions.
This paper introduces a wave-particle decomposition framework for kinetic relaxation equations that partitions the distribution function into a wave component and a collisionless particle component based on a local evolution timescale, yielding a unified, asymptotic-preserving numerical system that seamlessly adapts across the entire Knudsen spectrum from continuum to rarefied regimes.
This paper establishes that the short-time asymptotics of the expected Liouville quantum gravity heat trace on a bounded domain are governed by a nontrivial exponent determined by the KPZ relation, while also resolving a conjecture regarding annealed heat kernel asymptotics and proving the finiteness of its moments.
This paper derives a normal form for the simplest Lagrangian singularity arising from the projection of Hamilton-Jacacobi solutions onto space-energy, which is then utilized to construct asymptotic solutions for semiclassical equations when the energy corresponds to a critical value on the Lagrangian manifold.
This paper derives explicit, finite-sum formulas for discrete space-time wave kernels on regular trees in terms of - and -Bessel functions, providing convolution representations for solutions and analyzing their asymptotic behavior across large distances, times, and tree degrees.
This paper rigorously proves that the critical partition function of the Ising model coupled to 2D gravity converges to the -function of the string equation by utilizing a steepest-descent analysis of a Riemann-Hilbert problem associated with biorthogonal polynomials, thereby confirming long-standing conjectures by Douglas, Shenker, Brézin, Kazakov, Gross, and Migdal.
This paper demonstrates that the macroscopic fluctuation theory for a multispecies symmetric simple exclusion process on an infinite line constitutes an integrable system of Landau–Lifshitz type, allowing the derivation of the current cumulant generating function and conditioned density profiles via inverse scattering methods, ultimately revealing that the generating function depends on a single scalar variable and coincides with the single-species result regardless of the number of particle species.
This paper introduces a shell-based shortest-path anisotropy statistic for graph discretizations of black-hole geometries, demonstrating that this measure exhibits a stable radial organization strongly correlated with the logarithmic Kretschmann profile across various black-hole families, thereby serving as a curvature-sensitive diagnostic distinct from universal pointwise curvature scalars.