2560 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 establishes that the lower edge of the appropriately scaled Laguerre beta-ensemble converges to the process as when the parameter satisfies and , thereby completing the classification of its edge scaling limits through operator-level convergence proofs and coupling arguments.
This paper proposes a generalized definition of temperature for isolated quantum many-body systems out of equilibrium by locating non-stationary states within a family of regular states compatible with their energy-coherence structure, thereby replacing the principle of maximum entropy with a principle of minimum discrimination information and extending the framework to subsystems via induced local thermodynamic structures.
This paper establishes the unconditional stability and convergence of a mixed finite element discretization for coupling continuum and discrete diffusion models, demonstrating its effectiveness through numerical examples and its utility in solving diffusive problems with incomplete data.
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 establishes the hydrodynamic limit for heat conduction in a finite one-dimensional chain with stochastic perturbations, rigorously deriving a fractional superdiffusion equation with explicit non-local boundary conditions that describe phonon absorption, reflection, and transmission at Langevin heat baths.
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.