3366 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 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.
This paper demonstrates that the joint distribution of SYK Hamiltonians with partial interactions converges to a mixed -Gaussian system in the large-system limit, thereby providing a random model for asymptotic -freeness and establishing an isomorphism with graph products of diffusive abelian von Neumann algebras.
This paper establishes a generalized semiclassical analysis framework for flat Hilbert bundles over compact hyperbolic surfaces to derive uniform control estimates and prove observability for the Schrödinger equation on non-compact hyperbolic coverings with virtually Abelian deck transformation groups.
This paper proposes an explicit Poisson vertex algebra as the space of holomorphic-topological observables in pure Seiberg-Witten theory, demonstrating that its Hilbert-Poincaré series refines the Schur index and that its cohomology under a specific differential captures non-perturbative corrections.
This paper utilizes the short-wavelength instability method to demonstrate that exact, upward-propagating nonlinear mountain waves in dry adiabatic flow become linearly unstable when wave steepness exceeds a critical threshold of 1/3, leading to chaotic three-dimensional motion within a specific layer beneath the tropopause.
This paper establishes that the existence of purely electric or purely magnetic Weyl curvature tensors on compact -dimensional manifolds is obstructed by the vanishing of specific products of Pontryagin classes in the top-degree de Rham cohomology, thereby providing nontrivial topological constraints on such Lorentzian metrics and their associated Petrov subtypes.
This paper extends the Kuramoto-Sakaguchi model to general Riemannian manifolds to demonstrate that while geometry determines the critical coupling for synchronization, topology (specifically the Euler characteristic) fundamentally constrains the nature of the phase transition, permitting continuous or tricritical transitions only on manifolds with zero Euler characteristic.
This paper establishes a categorical and algebro-geometric framework for localization in cohomological theories with open-closed recollements, demonstrating that natural outputs are torsors of supported refinements rather than distinguished classes, and showing how imposing uniqueness or concentration principles recovers familiar index formulas and unifies various localization techniques like Atiyah-Bott-Berline-Vergne and Lefschetz decompositions.
This thesis provides a comprehensive and clarified derivation of analytical solutions to the Ornstein-Zernike integral equation for hard-sphere and charged hard-sphere systems under the Percus-Yevick and Mean Spherical Approximations, utilizing advanced mathematical techniques to rigorously establish macroscopic thermodynamic properties.