1605 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 new Thomson-type variational principle that characterizes the diffusion coefficient of reversible interacting particle systems as the supremum of a functional, offering a more natural framework for deriving lower bounds compared to the standard infimum formulation, and demonstrates its application to a kinetically constrained lattice gas.
This paper demonstrates that while neither homotopy to Minkowski space nor global hyperbolicity alone ensures conicality, causally simple, future cohesive spacetimes of dimension ()—including TIP spacetimes representing an observer's timelike past—do satisfy this property, thereby validating the conjecture for a physically relevant class of spacetimes.
This paper derives exact distributional identities and asymptotic behavior for the maximal minimal spacing between points selected from random points on a line by reformulating the problem as a threshold-resetting random walk, where the optimal spacing probability corresponds to the likelihood of completing at least reset cycles within steps.
This paper employs Hirota's bilinear method to derive novel time-periodic solutions, regular breathers, and rogue waves for both scalar and coupled defocusing Ablowitz-Ladik systems on a nonzero background, while also establishing the correspondence between Hirota's parameters and inverse scattering spectral parameters.
This paper presents the general solutions for variable-coefficient linear ordinary differential equations and Riccati equations by utilizing integral series and , which serve as generalized, convergent, and reversible forms of the exponential function.
This paper investigates apparent bifurcation phenomena, specifically the existence of multiple solutions with quadratic folds, in the conformal formulations of the Einstein constraint equations by applying modern bifurcation theory and numerical homotopy methods using the AUTO software to verify these findings.
This paper establishes a central limit theorem for tensor products of free variables, demonstrating that the limiting distribution is the semi-circle law for centered variables and a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws for non-centered variables.
This paper establishes that the operator derived from the fundamental solution of the quantum difference equation for Nakajima varieties is regular at primitive -th roots of unity, thereby providing an explicit description of the spectrum of the -curvature for the associated quantum connection via its relationship to Frobenius twists.
This paper establishes limit theorems for a generalized step-reinforced random walk with regularly varying memory, proving a law of large numbers and characterizing a phase transition between diffusive and superdiffusive behaviors based on the reinforcement probability and memory index , while providing novel almost sure and distributional convergence results for the critical regime under linear and time-independent scalings.
This paper synthesizes works inspired by Brezis, Ekeland, and Nayroles to develop a unified space-time variational principle of minimum for dynamic dissipative systems, applying convex analysis and symplectic geometry to model plasticity, friction contact, and fracture mechanics.