2619 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 resolves the long-standing ghost instability problem in the Pais-Uhlenbeck model by leveraging Lie symmetries and its Bi-Hamiltonian structure to construct positive-definite formulations and equivalent first-order systems, while also analyzing how interaction terms typically disrupt this underlying structure.
This paper establishes an -loss version of Pólya's conjecture for bounded Lipschitz domains by providing explicit quantitative estimates for the Weyl law remainder without relying on Neumann eigenvalues, thereby reducing the conjecture to a computational problem and identifying broader classes of domains, including irregular shapes and strip-tiling domains, that satisfy the conjecture or even exhibit stronger eigenvalue bounds.
This paper derives exact, explicit formulas for the average relative entropy between random quantum states drawn from Hilbert-Schmidt and Bures-Hall ensembles, utilizing unitary integral factorization to complement existing asymptotic results.
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.
This paper constructs explicit -adapted Hilbert spaces using 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.
This paper presents exact analytical solutions for the gravitational collapse of a massive scalar field coupled with perfect fluid and dissipative matter in a conformally flat spacetime, demonstrating that such configurations evolve asymptotically without forming shell-focusing singularities within finite proper time, even when exhibiting effective exotic matter behavior.
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.