2656 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 a complete Lie symmetry classification of time-fractional telegraph systems with variable coefficients, identifying three distinct symmetry classes and deriving exact invariant solutions in terms of Mittag-Leffler, generalized Wright, and Fox -functions to model transport phenomena with memory and nonlocal effects.
This paper establishes a novel a posteriori error estimation framework for the enriched Galerkin method applied to linear parabolic equations, proving its reliability and efficiency while demonstrating its effectiveness in adaptive mesh refinement strategies.
This conceptual work establishes a unified derivative hierarchy linking force fields and density functional theory by demonstrating how the Born-Oppenheimer energy surface, forces, and nuclear Hessians arise from pulling back the energy functional and its density-based response derivatives from external potential space to nuclear configuration space.
This paper derives an asymptotic equivalent of the free energy and estimates the spin vector mean via an AMP algorithm for a generalized sparse Sherrington-Kirkpatrick spin glass model at high temperatures, adapting dynamical approaches originally developed for the classical SK model.
This work investigates Hamiltonian vortex dynamics on a catenoid and demonstrates that curvature gradients drive a rigid rotation and a secular drift for co-rotating vortex pairs, with numerical simulations confirming a linear instability in symmetric states as well as a reduced dynamics for generic configurations.
This paper investigates the asymptotic distribution of level crossings for random matrix pencils , deriving a deterministic limit for the empirical measure of crossings in complex and real ensembles by connecting spectral degeneracies to logarithmic energy and universality principles analogous to Girko's circular and Wigner's semicircle laws.
This paper resolves the long-standing anomaly of the purely real spectrum of the non-Hermitian Nakajima-Zwanzig projected Liouvillian in the Jaynes-Cummings model by demonstrating its pseudo-Hermiticity under a positive-definite metric, a structural property that persists through bath truncation and extends to the full Rabi model with re-entrant exceptional-point boundaries.
This paper proposes that the symmetry category of a 2D quantum field theory with a 0-form -symmetry and 't Hooft anomaly is equivalent to the category of twisted measurable fields of Hilbert spaces over , and demonstrates that its Drinfeld center corresponds to the representation category of a twisted groupoid -algebra, thereby enabling the computation of bulk 3D SymTFT braiding and providing physical examples for both abelian and non-abelian Lie groups.
This paper explores the use of two-parameter quasi-probability densities to identify quantum behavior in states with fractional mean angular momentum, demonstrating that while negative values in these densities can signal quantum superpositions, experimental uncertainty data can also reveal these unique quantum features.
This paper proposes and validates a two-species multiscale model for the Poisson-Nernst-Planck system that accounts for the simultaneous, Coulomb-coupled motion of positive and negative ions interacting with a small-scale surface trap.