1695 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 investigates the Householder tridiagonalization of a GE process governed by -Dyson Brownian motion, proving that the limit of its fixed-size upper-left minors yields a dynamical -stochastic Airy operator whose eigenvalues correspond to the asymptotic behavior of the largest eigenvalues of the original process.
This paper establishes that specific unitary matrix integrals relevant to random permutation statistics and the Riemann zeta function satisfy both first-order matrix and higher-order scalar linear differential equations, offering an efficient computational alternative to nonlinear Painlevé characterizations while demonstrating that these results extend to natural -generalizations.
This paper provides a rigorous mathematical justification for damped-driven wave turbulence theory by proving that the stochastic dynamics of the nonlinear Schrödinger equation converge to a deterministic kinetic equation under specific scaling limits, thereby establishing a formal framework for the turbulent energy cascade observed in empirical studies.
This paper demonstrates that unitary cocycle deformations of covariant -differential calculi preserve complex structures and Chern connections as twists of their original forms, while establishing that the Levi-Civita connection on deformed Kähler manifolds decomposes into the direct sum of twisted holomorphic and anti-holomorphic Chern connections.
This paper investigates the analytical properties and presents an efficient Galerkin-based numerical solution using B-splines for the Bardeen-Cooper-Schrieffer equation describing unconventional superconductors with long-range power-law interactions on a -dimensional lattice, with specific results demonstrated for a nodal superconductor on a two-dimensional square lattice.
This paper proposes and validates a finite-element space discretization combined with implicit-explicit time marching to simulate salt crystallization in stone artifacts, extending previous one-dimensional models to higher dimensions while conducting sensitivity analysis, stability considerations, and convergence testing.
This paper introduces Feature-Enriched Kolmogorov-Arnold Networks (FEKAN), a parameter-efficient extension that enhances the computational efficiency, convergence speed, and predictive accuracy of existing KAN architectures through feature enrichment while maintaining their interpretability.
This paper establishes a Lorentzian equivariant index theorem for twisted Dirac operators on compact globally hyperbolic spacetimes with timelike boundaries, demonstrating that the equivariant index under APS boundary conditions follows the same fixed-point integral formula as in the Riemannian case through a novel reduction technique linking the equivariant index to spectral flow.
This paper extends classical edge-triangle Exponential Random Graph Models to inhomogeneous block-structured settings, establishing a large deviation principle and deriving a variational formula for the limiting free energy that, under ferromagnetic conditions, reduces to a scalar optimization problem and yields uniqueness and a law of large numbers for edge density under specific parameter constraints.
These Les Houches lecture notes, delivered in Summer 2024, provide an accessible, foundational introduction to the topological recursion framework, aiming to clarify its core concepts for readers encountering it across diverse fields like matrix models, string theory, and gauge theories without attempting to exhaustively detail every specific application.