1677 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 investigates the long-time behavior of exact and numerical solutions for linear stochastic evolution equations on the sphere, demonstrating that while forward and backward Euler-Maruyama schemes fail to preserve the correct evolution of physical quantities like energy and momentum, the stochastic exponential integrator successfully maintains these properties.
This paper derives and analyzes a unidirectional asymptotic model for one-dimensional blood flow in viscoelastic arteries, establishing local well-posedness of strong solutions, proving global existence and exponential decay in the purely elastic regime for small data, and providing a numerical study of the model's dynamics across various viscoelastic and amplitude regimes.
This paper employs exact WKB analysis and resurgence theory to unify the quantization of non-Hermitian inverted triple-well systems, deriving exact median-summed spectra that clarify PT-symmetry breaking, characterize exceptional points via algebraic relations between bounce and bion actions, and demonstrate the complex conjugate relationship between resonance and anti-resonance spectra.
This paper establishes the well-posedness of a two-dimensional incompressible vorticity equation driven by fractional transport noise by adapting the sewing lemma to construct Young integrals, and subsequently derives a statistical estimator for the Hurst parameter based on quadratic functionals of the solution.
This paper introduces the first rigorous framework for efficiently preparing Gibbs states of infinite-dimensional bosonic systems, such as Bose-Hubbard models, by proving that their dissipative generators possess a positive spectral gap, thereby enabling mathematically controlled quantum algorithms for thermal property simulation on qubit hardware.
This paper derives stochastic differential equations for the coupled system of eigenvalues and eigenvector-overlaps in non-Hermitian matrix-valued Brownian motion, establishes their scale-transformation invariance, and utilizes a regularized Fuglede-Kadison determinant to formulate stochastic partial differential equations linking the time-dependent eigenvalue point process to the logarithmic variations of the determinant.
This paper proves a global well-posedness and asymptotic convergence theorem for the -dimensional vacuum Einstein equations with a positive cosmological constant on globally hyperbolic spacetimes with negative Yamabe type manifolds, demonstrating that large initial data leads to solutions converging to a constant negative scalar curvature metric via a new integrable damping mechanism, thereby confirming Ringström's conjecture that such dynamics do not canonically encode the Thurston geometrization of the underlying three-manifold.
This paper establishes that the quantized Coulomb branch of 4d $Sp(N)$ gauge theory with specific matter content is isomorphic to the spherical double affine Hecke algebra of -type, a result rigorously proven for the rank-one case and conjectured for higher ranks with supporting evidence from 't Hooft loop operators.
This paper presents and simplifies two formulations for computing the dyadic Green's functions of Maxwell's equations in layered media, demonstrating their equivalence while highlighting the second formulation's advantages in decoupling interface conditions and facilitating far-field approximations for both electromagnetic and elastic wave equations.
This paper provides a unified pedagogical treatment of the first-passage problem for a Poisson counting process with a linear moving boundary by reconciling time-domain and Laplace-domain approaches to derive new exact analytical results, including an explicit large deviation function and closed-form expressions for the conditional mean first-passage time.