2548 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 single-site Glauber dynamics for the Sherrington-Kirkpatrick model mixes in optimal time for any fixed inverse temperature , utilizing a novel deterministic criterion for Poincaré inequalities and a modified log-Sobolev inequality framework, with key proof concepts generated by GPT-5.6 Sol Ultra.
This paper presents a validated 2D axisymmetric multi-domain model implemented in MATLAB/Simulink that successfully simulates the coupled thermal, fluid, and electromagnetic dynamics of DC arcs across a 10–1500 A range, offering a robust tool for analyzing arc behavior in applications like circuit breakers and welding.
This paper investigates an open XXZ spin chain with unparallel boundary fields under a special gauge-invariant condition, demonstrating that its transfer matrix can be diagonalized via a generalized Separation of Variables approach using bases dependent on gauge parameters only through their difference, and utilizing this framework to compute elementary correlation blocks and overlaps with eigenstates of related models.
This paper demonstrates that the mean-field limit and the zero-noise limit can be commuted for Anderson-Hermite operators in dimensions 1, 2, and 3 by adapting the Knowles-Pickl derivation and establishing uniform energy estimates for the resulting Anderson-Hartree equations.
This paper proves that for arbitrary bounded variation data with at least one jump, the density of the free Schrödinger evolution on a torus exhibits fractality with an upper box dimension of 3/2 at almost every time, while its critical Sobolev mass diverges logarithmically at a rate determined solely by the jump content of the initial datum.
This paper introduces a cooperative-decay graph framework that reformulates the Pauli master equation as a time-dependent edge flux conservation law, enabling the derivation of exact Bateman solutions for arbitrary finite directed acyclic graphs and linking total cooperative rates to the descent speed of a graph depth function.
This paper establishes the well-posedness and kinetic behavior of the one-dimensional quasilinear Majda–McLaughlin–Tabak (MMT) equation on a large torus, demonstrating a dichotomy in solution existence times and kinetic limits based on the dispersion exponent by combining probabilistic randomness propagation with deterministic energy estimates to overcome derivative loss.
This paper offers a unified pedagogical framework to clarify the distinct mathematical roles of position and time in the quantum wavefunction by separating background coordinates from spectral labels, thereby resolving common student misconceptions about time operators and Dirac notation without proposing a new interpretation of time.
This paper demonstrates that the renormalization of a three-dimensional quartic model on a manifold with a boundary requires extending the classical action to include singular boundary coefficients and renormalizing a boundary operator to ensure consistency under manifold gluing.
This paper derives the asymptotic behavior of joint cumulants for real and non-real eigenvalue counts in the real Ginibre ensemble across various regimes, establishing a joint central limit theorem and revealing a universality phenomenon where combined fluctuations match those of complex and symplectic ensembles despite individual dependencies on symmetry classes.