🔢 Category

math-ph

2563 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

One- and two-particle spectral gap identities for the symmetric inclusion process and related models

This paper establishes that while the spectral gap of the conservative symmetric inclusion process generally deviates from the single-particle gap outside the log-concave regime, the identity universally holds for the non-conservative variant, with the authors providing sharp bounds and a two-particle gap identity for the former case using refined Dirichlet form comparisons and slow-fast system analysis.

Seonwoo Kim, Federico Sau2026-06-23
🔢 mathematics

Logarithmic Spectral Distribution of a Non-Hermitian β\beta-Ensemble

This paper introduces a non-Hermitian β\beta-ensemble defined by tridiagonal complex random matrices, derives its large-nn and large-β\beta logarithmic spectral density on a compact disc using free probability and characteristic polynomial analysis, and confirms via numerical simulations that its local eigenvalue statistics follow two-dimensional Poisson behavior independent of β\beta, distinguishing it from previously studied ensembles.

Gernot Akemann, Francesco Mezzadri, Patricia Päßler, Henry Taylor2026-06-23
🔢 mathematics

Breakdown of the thermodynamic limit in quantum spin and dimer models

This paper demonstrates that the thermodynamic limit can break down in quantum spin and dimer models by constructing Hamiltonians on square and square-octagon lattices where the ground state phases on diamond-shaped domains differ fundamentally from those on square domains, exhibiting geometry-dependent macroscopic regions with distinct ordering and correlation behaviors.

Jeet Shah, Laura Shou, Jeremy Shuler, Victor Galitski2026-06-23
🔢 mathematics

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces

This paper establishes that the Hawking quasi-local energy satisfies nonnegativity and rigidity properties under the dominant energy condition when evaluated on area-constrained critical surfaces, providing the first such theorems for the fully dynamical case and extending these results to charged, cosmological constant, and higher-dimensional variants in the time-symmetric setting.

Alejandro Peñuela Diaz2026-06-23