3210 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 constructs a sequence of finite Rodriguez-Villegas transforms that converge locally uniformly to the Riemann -function by utilizing a specific Stieltjes profile derived from the Riemann theta kernel, whose Bernstein polynomials yield reciprocal numerators satisfying exact finite functional equations and admit interpretations as both fermionic supertraces and normalized Gibbs traces.
This paper presents an exact and computationally efficient analytic formula for the potential and current density in a 2D rectangular domain with point source and sink, overcoming the slow convergence of traditional Fourier series by employing -analysis techniques related to Gaussian polynomials and Jacobi's theta-functions.
This paper introduces a practical framework for performing controlled, systematically improvable diagrammatic many-body calculations directly on the real frequency axis by utilizing pole representations and a recompression procedure to avoid numerical bottlenecks associated with imaginary-time formulations.
This paper establishes that determining whether a generic Markovian open quantum system governed by a time-independent Lindblad master equation admits a decoherence-free subspace is computationally intractable, specifically proving the problem is QMA-hard for localities by generalizing Kitaev's clock construction to encode quantum circuit executions into the system's steady-state subspace.
The paper proves that for non-periodic insulators in two and three dimensions, the existence of an orthonormal basis for the Fermi projection with finite second moment (algebraic localization) necessarily implies the existence of an orthonormal basis that decays exponentially fast in space, thereby supporting the Localization Dichotomy Conjecture.
This paper develops the necessary harmonic and microlocal analysis tools, including a novel Cole-Hopf transform with random bundle maps, to support the construction of the measure on arbitrary closed Riemannian manifolds as an invariant measure of a singular stochastic partial differential equation.
This paper introduces a direct and explicit construction of a scalar pseudodifferential operator of order $-3$, termed the asymmetry operator, which characterizes the spectral asymmetry of the curl operator on a closed oriented Riemannian 3-manifold and generalizes the classical eta invariant.
This paper investigates Locally Rotationally Symmetric spacetimes within gravity by employing the covariant formalism to analyze the effects of nonmetricity on kinematic quantities, deriving conditions for homogeneous and static spherically symmetric solutions, and exploring elementary gravastar models via covariant junction conditions.
This study extends Kirchhoff's kinetic analogy to planar soft ferromagnetic rods under external magnetic fields, revealing distinct bifurcation behaviors and novel localized equilibrium solutions driven by homoclinic and heteroclinic orbits that are absent in purely elastic systems.
This paper establishes that a matched pair of actions on a Hopf algebra induces an involutive Yang-Baxter operator if and only if its associated intrinsic Hopf algebra is braided commutative, thereby resolving an open problem by Ferri and Sciandra and applying this characterization to classify such operators on the 8-dimensional non-semisimple Hopf algebra .