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 unit-invariant generalizations of von Neumann entanglement entropy based on the Unit-Invariant Singular Value Decomposition (UISVD), demonstrating their stability and physical relevance across diverse frameworks including biorthogonal quantum mechanics, random matrix theory, and Chern-Simons theory.
This paper introduces a rigorous framework for defining the probability of a quantum state being fully contained within a subspace by uniquely decomposing a non-negative operator into orthogonal components, yielding a measure that is more restrictive than standard overlap probability while offering new insights for quantum information and cryptography.
This paper presents asymptotic expressions for a solid Cauchy transform with a rapidly oscillating phase and a Cauchy singularity, utilizing Stokes' theorem to decompose the integral into three terms that are analyzed via special functions on steepest descent contours in .
The paper investigates how irreversible behavior emerges from underlying deterministic, invertible, and reversible dynamics by analyzing the second law of thermodynamics through the lens of combinatorial processes.
This paper rigorously demonstrates that an equiprobable superposition of high-energy eigenstates in an infinite square well converges exactly to the uniform classical probability distribution and reproduces the classical triangular trajectory in the limit of a large number of states, with residual quantum effects confined to vanishing boundary layers.
This survey paper compiles existing results on spectral bounds for deterministic and random non-self-adjoint Schrödinger operators with complex potentials on Euclidean spaces and compact manifolds, while also presenting a new theorem extending these bounds to fractional Laplacians using -norm estimates of the potentials.
This paper establishes the polynomial long-time stability of polynomially weighted -norms for solutions to the -dimensional nonlinear Maryland model under small perturbations and suitable Diophantine conditions, utilizing a Birkhoff normal form procedure to show that the norm remains bounded for timescales of order .
This paper establishes that the action of super charges in the shifted quantum toroidal algebra of type on the level zero super Fock module yields a Pieri rule for super Macdonald polynomials, which is expressed via differential operators to derive supersymmetric Hamiltonians that recover previously known results.
This paper introduces "variational openness" as a conservative extension of classical variational principles that unifies bulk and boundary stationarity by requiring the cancellation of total first variation rather than separate contributions, thereby enabling the analysis of regulated systems where bulk and boundary displacements are linked through compatibility operators and revealing critical thresholds for stability loss via a projected Rayleigh–Ritz criterion.
This paper introduces the weighted spectral fidelity, a one-parameter family of quantum state distinguishability measures based on the weighted spectral geometric mean that interpolates between trivial overlap and Uhlmann fidelity, and characterizes its structural properties, explicit violations of the data processing inequality for non-midpoint parameters, and partial extensions of the Fuchs–van de Graaf inequalities.