1695 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 novel Gaussian process-based framework that learns probabilistic Dirichlet-to-Neumann maps on graphs by integrating discrete exterior calculus and nonlinear optimal recovery to enforce conservation laws, thereby enabling accurate, uncertainty-quantified predictions in data-scarce multiphysics applications like subsurface fracture networks and arterial blood flow.
This paper introduces a general framework for stochastically generated matrix product states with stationary local tensors, proving that under natural conditions on transfer operators, local observables possess thermodynamic limits and two-point correlations exhibit almost-sure exponential or mixing-dependent decay rates, thereby unifying and extending previous results on random MPS ensembles.
This paper demonstrates that for 1-dimensional reaction-diffusion equations with nonzero random drift and FKPP nonlinearity, a positive average drift can push both wave fronts toward negative infinity, a phenomenon proven via Large Deviations Principles and Feynman-Kac analysis which reveals the drift acts as an external field shifting the free-energy reference level.
This paper presents an algorithmic construction of a -graded differential variety that extends a given positively graded structure by incorporating an arborescent Koszul-Tate resolution in its negative part, utilizing explicit homotopy data to minimize homological computations and providing a concrete application to Lie-Rinehart algebras.
This paper generalizes the covariant quasilinear wave equation for the Riemann curvature tensor, originally established for Levi-Civita connections, to spacetimes with generic affine connections featuring torsion and nonmetricity, and analyzes its specific forms within Einstein spaces, teleparallel gravity, and Einstein-Cartan theory.
This paper extends the spectral theory of Markov chains beyond the classical birth-and-death setting by applying a spectral Favard theorem to chains with transition matrices admitting a positive stochastic bidiagonal factorization, thereby deriving Karlin-McGregor representations, establishing recurrence conditions, and characterizing stationary distributions and ergodicity through associated orthogonal polynomials and spectral measures.
This paper analyzes the asymptotic escape rate of non-uniformly expanding interval maps with a parabolic fixed point as a hole containing that fixed point shrinks, utilizing transfer operator techniques to generalize previous results on systems with finite or infinite ergodic absolutely continuous invariant measures.
This paper establishes a geometric mechanics framework using Euler-Poincaré reduction to derive 3-dimensional Eulerian equations of motion and Kelvin-Noether circulation conservation laws for self-gravitating barotropic fluids within the 3+1 ADM formulation of general relativity, thereby bridging relativistic hydrodynamics with Newtonian fluid dynamics and offering potential applications for numerical relativity.
This paper proposes a formal framework for a Lorentzian, $SU(3)$-covariant noncommutative Kadomtsev–Petviashvili hierarchy constructed from Dirac-type operators and hypercomplex gauge fields, which describes integrable sectors of nonabelian gauge theories in dimensions.
This paper investigates the spectral properties and resonance behavior of the acoustic operator with piecewise constant coefficients by deriving a resolvent difference formula to establish a Limiting Absorption Principle and characterize the spectrum, while also providing analytic expansions for resonances in the asymptotic regime where the domain shrinks and material parameters vanish.