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 provides estimates for the lower bound of the self-adjoint operator associated with a three-coefficient Sturm-Liouville differential expression within the weighted -Hilbert space .
This paper introduces a two-stage, geometry-agnostic neural framework that infers dynamical constraints directly from observational data to discover and transfer rare, high-impact coherent structures—such as solitons and instantons—across varying dimensions and geometric manifolds without requiring prior knowledge of the governing equations.
This paper constructs a collection of differential-difference operators acting on the space of smooth functions on the two-dimensional sphere, which correspond to the action of the Lie algebra of and involve shifts in the spherical harmonic degree and fourth-order derivatives in a complex variable.
This paper establishes the existence of the first known strictly convex ergodic billiards by demonstrating that sufficiently asymmetric lemon billiards possess uniformly hyperbolic returns and controlled singularity curves, thereby satisfying the Bernoulli property.
This paper proves that for any real-analytic drive acting on an system, the Fer expansion of the propagator cannot terminate beyond the first order unless the first exponential factor already provides the exact solution.
This paper introduces DeHNSSo-v2, a major open-source update to the Delft Harmonic Navier-Stokes Solver that extends its capabilities to compressible flows on curvilinear grids while significantly reducing computational costs through efficient assembly and factorization techniques, thereby enabling high-fidelity nonlinear stability analysis across diverse compressibility regimes and complex geometries.
This paper establishes central limit theorems for polynomial linear statistics of continuous -particle systems in both fixed- and high-temperature regimes by deriving necessary and sufficient conditions via logarithmic Bessel generating functions and a ribbon graph topological expansion that reveals distinct contributions from genus-zero and higher-genus surfaces, respectively.
This paper identifies all soft modes of soft shells within the Sonnet-Virga variational framework by establishing their connection to Bonnet families of isometric deformations, providing a general existence criterion and a path-integration method to construct these energy-preserving deformations.
This paper develops a hypercomplex method using a family of two-dimensional commutative associative algebras and a hodograph transformation to construct solutions for a broad class of nonlinear second-order partial differential equations by reducing them to solvable linear equations.
This paper extends the recursive construction of free-field realizations to supersymmetric -algebras associated with the Lie superalgebras and , providing explicit realizations for specific cases including new results for and , and utilizing these to compute central charges, conformal weights, and construct local integrals of motion.