3324 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 reviews recent advances in the entanglement of free-fermion systems on graphs by leveraging signal processing techniques to identify commuting tridiagonal matrices and utilizing the irreducible decomposition of Terwilliger algebras from -polynomial association schemes to simplify the analysis.
This paper demonstrates that the stationary diffusion of an effective energy-enstrophy process in a two-dimensional cone serves as the inviscid limit of an -dimensional Galerkin-Navier-Stokes system with Brownian forcing and random stirring, thereby establishing quantitative bounds on the attrition of all but the lowest modes in the inviscid limit.
This paper constructs an elliptic diffusion process on with Gaussian coefficients representing energy and enstrophy, proving the existence of a unique stationary distribution and deriving a condensation bound that controls the ratio of expected energy to expected enstrophy, while establishing this model as the inviscid limit of a stochastic Galerkin-Navier-Stokes system in a companion study.
This paper establishes sufficient conditions for the invariance of Bernoulli and Markov measures in soliton systems generated by Mealy automata, applies these findings to prove measure invariance for three specific box-ball system variants, and computes their fundamental soliton characteristics to lay the groundwork for studying generalized hydrodynamics in these systems.
This paper systematically organizes rank-two difference-differential Lax pairs for classical Painlevé equations into a standardized matrix form and applies a general method to derive a countable family of integrals of motion in finite characteristic for each relevant equation.
This paper introduces a geometric reduction mechanism that utilizes families of particular integrals with linearly closed time derivatives to construct invariant submanifolds, thereby establishing a direct link between particular integrability, presymplectic reduction, and lower-dimensional Hamiltonian dynamics.
This paper derives a hydrodynamic description for a bulk-driven nonlinear energy diffusion model and demonstrates through simulations that specific driving fields can induce the formation of robust, traveling energy condensates exhibiting continuous time-crystalline order.
This paper investigates the dimer model on two families of non-bipartite torus graphs by establishing the relationship between their Newton polygons and those of underlying bipartite graphs, identifying edge vectors with zig-zag path homology classes, proving the real-rootedness of specific marginal polynomials, and introducing new local moves that preserve dimer partition functions.
This paper establishes the existence of a rare, adiabatically conserved extra invariant in the magnetohydrodynamics of rotating and stratified fluid layers, which is notably linked to the dynamo phenomenon in planets and stars.
This paper presents a general strategy to derive rigorous error bounds and explicit error constants for truncated Baker--Campbell--Hausdorff and Zassenhaus formulas specifically applied to skew-adjoint operators in quantum evolution problems.