🔢 Category

math-ph

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.

🔢 mathematics

The dynamical structure of the Earth co-orbital region and implications for the near-Earth asteroid population

This study utilizes a semi-analytical model to map the dynamical structure of Earth's co-orbital region, revealing that horseshoe orbits dominate the phase space with significant inhomogeneities and varying levels of chaos, which implies that a large fraction of the Earth co-orbital asteroid population remains undiscovered and poses potential challenges for planetary defense.

Marco Fenucci, Óscar Rodríguez, Melaine Saillenfest, Laura Faggioli2026-05-28
🔢 mathematics

From geodesic flow to wave dynamics on hyperbolic surfaces

This paper constructs explicit XX-adapted Hilbert spaces using SL2(R)SL_2(\mathbb{R}) representation theory to decompose the geodesic flow on a closed hyperbolic surface into a damped harmonic oscillator and a transverse wave group, thereby providing a unified spectral framework that explicitly links classical geodesic dynamics, Ruelle resonances, and the Laplace spectrum through a dynamical derivation of the Selberg trace formula.

Frédéric Faure2026-05-28
🔢 mathematics

Dissipative Spectral Form Factor of the Complex Elliptic Ginibre Ensemble across Various Non-Hermiticity Regimes

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.

Gernot Akemann, Sung-Soo Byun, Seungjoon Oh2026-05-28
🔢 mathematics

Gauge Geometry of Hodge Zero-Mode Transport in Parameter-Dependent Topological Data Analysis

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.

Satoshi Kanno, Rei Nishimura, Hiroshi Yamauchi, Yoshi-aki Shimada2026-05-28
🔢 mathematics

Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds

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.

Jan Střeleček, Jakub Novotný, Pavel Cejnar2026-05-28
🔢 mathematics

Determinantal point processes on complex manifolds: Construction and limit theorems

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.

Thibaut Lemoine2026-05-27
🔢 mathematics

Illposedness for dispersive equations: Degenerate dispersion and Takeuchi--Mizohata condition

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.

In-Jee Jeong, Sung-Jin Oh2026-05-27