1706 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 establishes a novel real-space formula for the Zak phase of one-dimensional periodic Jacobi operators using Weyl -functions, which bypasses Floquet-Bloch theory to explicitly highlight boundary term dependencies and recover classical quantization under inversion symmetry.
This manuscript introduces the quadratic-phase Fourier-Bessel transform, establishes its fundamental properties and associated convolution structures, and proves a Donoho-Stark-type uncertainty principle to extend classical results to this generalized framework.
This paper introduces the algebraic concept of Leonard trios as an extension of Leonard pairs, establishes their connection to bispectral rational functions and Heun operators, and initiates their classification by demonstrating that Wilson's rational functions serve as overlap coefficients with specific recurrence and summation properties.
By generalizing a quantitative monogamy-of-entanglement argument to arbitrary convex bodies via a new relative entropy notion, this paper establishes a finite de Finetti theorem that enables a convergent conic hierarchy with certified interior points for solving polynomial optimization problems with both equality and inequality constraints.
This paper establishes the existence of non-hydrodynamic solutions to the linear density-dependent BGK equation in dimensions by employing spectral analysis and complex contour integration to demonstrate that specific initial conditions yield a macroscopic mass density dissipation rate diverging as for any Knudsen number.
This paper establishes a van den Berg-Kesten-type correlation inequality for the KPZ line ensemble and continuum directed random polymer by leveraging the integrability of the log gamma polymer and the geometric RSK correspondence, while demonstrating that such an inequality fails for non-integrable models.
This paper presents a simplified proof demonstrating that the Newell-Whitehead-Segel equation yields a null solution by utilizing recent insights into convolution integrals to avoid complex nested calculations and confirming the result through alternative representations like expansions and Fujita-type solutions.
This paper investigates the limiting spectral distribution of a -deformed random unitary ensemble associated with the little- Laguerre weight, deriving a -deformation of the Marchenko-Pastur law that exhibits a phase transition at a critical value and establishing its convergence and large deviation properties through moment methods, equilibrium problems, and orthogonal polynomial asymptotics.
This paper addresses the challenge of modeling stiff forces in soft matter systems by providing a practical summary of constrained Brownian dynamics equations with "soft" constraints and a novel singular perturbation theory derivation that validates these equations over relevant timescales, while also extending the framework to scenarios with spatially varying mobility.
This paper unifies the Cartan and Weil models of equivariant cohomology with BRST quantization to establish a transparent analytic proof of the Atiyah--Bott--Berline--Vergne localization formula, demonstrating how gauge-fixing procedures naturally lead to equivariant Witten deformation and illustrating the framework through explicit computations on complex projective spaces.