2619 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 presents the general solutions for variable-coefficient linear ODEs and Riccati equations by utilizing convergent and reversible integral series E(X) and F(X), which serve as generalized 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 presents a unified space-time variational principle of minimum for dynamic dissipative systems, inspired by the works of Brezis, Ekeland, and Nayroles, and demonstrates its application to plasticity, friction contact, and fracture mechanics through theoretical and numerical examples.
This paper derives the exact solutions of the inverted Dirac-Moshinsky oscillator in dimensions, revealing a purely continuous spectrum governed by symmetry and identifying Gamow resonances that signal vacuum instability and spontaneous pair production analogous to the Schwinger effect.
This paper introduces temporal matrix scale invariance (tMSI) as a mathematical framework for analyzing multivariate time series near tipping points, deriving a classification scheme that distinguishes between recoverable and catastrophic transitions based on the relationship between dynamical and spectral relaxation exponents and providing a matrix-valued early warning diagnostic applicable to conditions like epilepsy and myocardial infarction.
This paper revisits the Salecker–Wigner–Peres stationary quantum clock to identify and remove a universal low-energy threshold singularity, thereby isolating the true resonant delay contribution and providing a refined observable that distinguishes kinematic threshold effects from pole-sensitive scattering dynamics.
This paper proves the global in time regularity of solutions to the Navier-Stokes equations defined in complex space.