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 proposes a spectral approach to identifying uniqueness pairs for unitary transforms by mapping two-sided sampling problems to lower-bound spectral problems of confined Hamiltonians, thereby generalizing existing Wirtinger-Poincaré-based criteria to a broader class of transforms including the fractional Fourier and Hankel transforms.
This paper presents an exact solution for the ferromagnetic Ising model on random regular graphs by expressing the partition function as a generating function of labeled edge-bicolored graphs, thereby deriving the free energy and confirming a second-order phase transition with mean-field critical exponents through analytic combinatorics.
This paper utilizes linear programming to establish a separable version of Ky Fan's majorization relation for the sum of two tensor products of positive semidefinite operators, while demonstrating that such a relation fails for sums involving three or more tensor products.
This paper analyzes zero-modes in a one-loop semi-classical Yang-Mills theory in 3+1 dimensions, demonstrating that they arise from gauge redundancy and, through proper gauge fixing with a bosonic ghost term and zeta-function regularization, yields a finite effective theory that reproduces the known one-loop beta-function.
This paper presents a group-theoretic interpretation of the periodic table using the Lie algebra , demonstrating how its weight diagram and root system naturally explain period doubling, spin splitting, and the inclusion of antimatter through the projection of a four-dimensional 24-cell onto two isomorphic subalgebras.
This paper introduces a novel method using approximate stochastic localization to prove a weak Poincaré inequality for the Sherrington-Kirkpatrick model at , thereby demonstrating that Glauber dynamics with a warm start efficiently samples its Gibbs measure.
This paper constructs localized approximate eigenfunctions for Hamiltonians modeling aperiodic crystals, demonstrating that under specific assumptions on the associated periodic operator family, these functions yield energy estimates with a controlled error of order for small .
This paper develops a covariant reconstruction framework in teleparallel gravity to derive specific functional forms of the gravitational Lagrangian for Kantowski--Sachs geometries sourced by Chaplygin and polytropic fluids, utilizing nonlinear matter conservation laws to reverse the standard reconstruction strategy and identify viable anisotropic cosmological and black-hole-interior branches.
This paper presents exact, assumption-free analytical formulas for the evolution operators of four time-dependent Hamiltonians relevant to quantum spin batteries by employing a novel combination of -algebra, path-sums, and Omega calculus, thereby enabling the recovery and extension of existing approximations and providing explicit exact formulas for Floquet Hamiltonians at all orders.
This survey paper presents a rigorous mathematical theory for quantum filtering equations in infinite-dimensional mixed-state systems, resolves a longstanding open problem in their derivation, and explores their applications to feedback control, quantum dynamics, and mean-field games through propagation of chaos limits.