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 establishes the equivalence between the Borodin-Gorin interlacing integral presentation of the Heckman-Opdam hypergeometric function and two other integral representations, while also examining related Baxter operators and the limiting procedure from the Ruijsenaars hyperbolic model.
This paper investigates the relationship between relative Abelian BF torsion and knot Floer homology within the BV-BFV formalism, establishing connections to the Alexander polynomial and analyzing specific algebraic obstructions, though it concludes that a full geometric equivalence between the two frameworks remains unproven.
This paper rigorously derives the hydrodynamic limit for heat conduction in a finite one-dimensional chain coupled to Langevin heat baths, establishing that the macroscopic energy profile evolves according to a fractional heat equation with a non-local Lévy-type operator and explicitly identifying the boundary conditions that govern phonon absorption, reflection, and transmission at the endpoints.
This paper establishes normal forms for elliptic automorphic Lie algebras with dihedral symmetry of order 4 to classify them over , demonstrating their role in realizing key algebras associated with Landau-Lifshitz type equations and applying this framework to a specific three-component generalization of the Landau-Lifshitz equation.
This paper presents a tight-binding framework for computing subwavelength guided modes in high-contrast periodic media with line defects, leveraging the proven exponential decay of quasi-periodic capacitance matrix elements to enable efficient spectral analysis through banded approximations.
This paper establishes maximal velocity estimates for the fractional Laplacian with subcritical Hardy and external potentials, which are then applied to provide an alternative proof of the nonexistence of wave operators intertwining Hardy operators with and without long-range Coulomb perturbations.
This paper establishes the global small-data stability of nonlinear Dirac systems, specifically semilinear tensorial wave--Dirac and Maxwell--Dirac models, on the Schwarzschild black hole background by developing a spinor-adapted geometric approach that overcomes derivative-loss difficulties through intrinsic Clifford-algebraic structures and energy hierarchies without requiring independent null conditions.
This paper demonstrates that an adaptation of the Fröhlich-Pizzo model, utilizing local algebras of a chiral current, effectively captures the non-Markovian features of the horizon-induced decoherence mechanism identified by Danielson, Satishchandran, and Wald in the limit of large holding time.
This paper develops a generalized coordinate Bethe ansatz framework for the time-dependent massive Thirring model featuring a rapidity lattice and Ruijsenaars-type difference equations, which reveals that exponential mass evolution is required for integrability and establishes a new realization of the time-dependent integrability-renormalization group correspondence.
This paper presents a computer-assisted proof demonstrating that the body-centered cubic lattice uniquely minimizes the renormalized Coulomb energy among all three-dimensional Bravais lattices of fixed covolume.