3190 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 demonstrates that Granger causality and Gaussian transfer entropy are substantially suppressed by correlations between variables in dynamical systems, quantifying this attenuation through a new framework that links predictive measures to operator-based causality and validates the findings across linear, nonlinear, and real-world fMRI data.
This paper proves the conjecture that northeastern antidiagonal quasideterminants associated with successive blocks of the generating matrix in a reflection equation algebra of type form a commuting family, utilizing a triangular realization and the flag property of quasideterminants while also exploring their connections to quantum cluster coordinates and generalized Toda systems.
This paper rigorously proves the existence of the thermodynamic limit for the free energy of the Hopfield model with Gaussian patterns at all loads and temperatures, deriving an explicit variational principle that resolves the replica-symmetric Amit-Gutfreund-Sompolinsky theory, identifies the annealed region boundary, and demonstrates that replica symmetry is broken below the critical temperature .
This paper establishes exact decompositions and sharp asymptotic limit laws for the trace moments and eigenvalue statistics of powers of Haar-distributed unitary matrices, utilizing tools such as Rains's power-map theorem, Charlier-Ewens convolutions, and Fredholm factorizations to characterize their behavior across various regimes of matrix dimension and power.
This paper utilizes the Ratios Theorem for random unitary matrices to derive concrete expressions for averages of up to four traces and general trace moments extending beyond the Diaconis–Shahshahani range, enabling applications such as identifying parameter ranges where these averages become negative.
This paper establishes that the Hamiltonian reduction of the big-cell differential realization of yields an intrinsic factorization where corner quasideterminants facilitate the transformation into a coproduct action of evaluation differential realizations of , thereby linking higher-rank differential realizations to lower-rank Yangian actions.
This paper derives a strongly non-linear, strain-gradient continuum model for wave propagation in two-dimensional granular media based on the Hertzian contact law, analyzes its hyperbolicity, and validates its predictions against discrete-element simulations for phenomena such as gravitational settling and depth-dependent wave speeds.
This paper derives the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors and parabolic-cylinder functions, demonstrating that these results recover the Euler-scale predictions of generalized hydrodynamics for hard rods.
This paper classifies one-dimensional disordered quantum systems with chiral symmetry by computing the partition function for a broad class of additive two-matrix models and deriving an asymptotic expansion for the average winding number that reveals universal leading features and a novel correction term distinct from the Ginibre case.
This paper constructs integrable 2d sigma models via 4d Chern-Simons theory to establish a correspondence with Hitchin systems, demonstrating that their quantized dynamics align with the Perelman operator and enabling the derivation of exact quantization conditions for the sausage model through 4d gauge theory and 2d CFT methods.