1605 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 derives the precise asymptotic behavior of the dissipative spectral form factor for the complex elliptic Ginibre ensemble across various non-Hermiticity regimes, explicitly characterizing its dip-ramp-plateau structure and identifying a mesoscopic regime that interpolates between non-Hermitian and Hermitian spectral statistics.
This paper proposes a computational framework that tracks homological features via Hodge zero-mode transport in a common ambient space to derive curvature and holonomy descriptors, thereby capturing dynamic structural reorganizations and cycle-level memory in parameter-dependent topological data that standard persistence diagrams miss.
This paper proposes a formalism that regularizes singularities in the Provost-Vallee metric by treating diabolic points as bridges to connect adjacent eigenstate manifolds into a single, topologically refined structure that restores numerical stability, enables new geodesic shortcuts, and facilitates Berry phase computation even along paths traversing degeneracies.
This paper introduces non-integral geometry as a generalized distribution theory where a non-symmetric integration measure yields a universal inverse operator with an additional term , which is proven to act as a regularizing contribution that eliminates complex singularities in image reconstruction.
This paper establishes a coordinate-free probabilistic framework for determinantal point processes on compact complex manifolds by rigorously defining scalar determinants for line-bundle-valued Bergman kernels, proving that finite-dimensional spaces of sections generate such processes, and deriving transfer principles that convert analytic asymptotics into probabilistic limit theorems.
This paper critiques the limitations of the standard bra-ket formalism in quantum mechanics and proposes a new, universal representation-free scheme that eliminates these drawbacks while offering flexible one-space and dual-space interpretations for practical calculations.
This paper establishes a unified framework for demonstrating strong illposedness in high-regularity Sobolev spaces for various quasilinear dispersive equations by analyzing the interplay between degenerate dispersion in the principal term and the failure of the Takeuchi--Mizohata condition in the subprincipal term, utilizing a robust energy- and duality-based method.
This paper proposes an explicit, oracle-free quantum framework that utilizes Schrödingerisation and efficient block-encoding to simulate general linear PDEs with Robin boundary conditions, inhomogeneous terms, and variable coefficients, achieving polynomial scaling in grid points and exponential advantages in spatial dimensions to overcome the classical curse of dimensionality.
This paper promotes the global symmetry of the Schwarzian derivative to a local gauge symmetry by constructing a gauge-invariant analogue of the Schwarzian derivative through a composite field method, thereby enabling the study of topological sectors and locally invariant couplings in two-dimensional gravity contexts.
This paper advances the exact-WKB formalism for general one-dimensional potentials by analyzing spectral transitions across sectors via complexification, deriving exact median quantization conditions and trans-series structures for asymmetric triple-well and tilted double-well systems, and establishing transformation rules for genus-1 resurgence data that clarify the link between path integrals and exact-WKB methods.