3210 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 investigates the algebraic structure of neural network conformal theories by analyzing their correlator properties and providing a systematic method to construct the theory's underlying operator algebra.
This paper extends stochastic path-space thermodynamics by analyzing the fluctuation statistics of an Ornstein-Uhlenbeck process with asymmetric drift and a step penalty potential, utilizing the Feynman-Kac formalism and parabolic cylinder theory to derive high-precision eigenvalues and formulate a modified Gallavotti-Cohen fluctuation theorem for a combination of residence time and integral current functionals relevant to molecular motors and ion channels.
This paper demonstrates that momentum-dependent symmetry actions can enforce odd-integer topological invariants in systems with classifications, establishing that such nontrivial phases are unavoidable when symmetry matrices possess odd parity, while locality constraints determine whether these odd values can be realized by finite-range, quasilocal, or no physical actions.
This paper constructs a complete ultrametric geometry on the space of quantum histories by demonstrating that the decay of normalized interference in the infinite registration limit is governed by the accumulated Bures distance of quantum records, thereby establishing a "consistency rate" that defines superselection sectors and quantifies the distinguishability of cumulative records.
This paper proves that below the Nishimori point, the ferromagnetic boundary of biased Ising spin glasses can be either vertical or reentrant—meaning cooling at fixed disorder can destroy order—across Sherrington-Kirkpatrick, -spin, and specific decorated lattice models, utilizing computer-assisted methods and a new proof regarding the Parisi measure's support.
This paper proves that the rescaled root lattice uniquely minimizes both the theta and Epstein zeta functions among all unit-covolume lattices in dimension four, thereby confirming a 2006 conjecture by Sarnak and Strömbergsson and resolving the Rankin-Sobolev problem in this dimension.
This paper proves that for Bernoulli bond percolation on regular trees of degree at least three, infinite clusters emerge strictly before the appearance of absolutely continuous spectrum, thereby establishing that the critical probability is strictly less than 1.
This paper presents a diagrammatic algorithm to construct GKZ hypergeometric systems for polygonal functions, which are conjectured to evaluate multipoint one-loop conformal integrals, by deriving a finite subsystem of second- and third-order equations from a transition matrix that encodes the underlying toric structure.
This paper demonstrates that the molecule reduction algorithm used by Deng, Hani, and Ma to prove a rigidity theorem for the Boltzmann equation is fundamentally a Kruskal-style graph traversal algorithm that constructs a Kruskal spanning tree.
The paper establishes that for gapped non-periodic insulators, the existence of an orthogonal basis of Wannier functions with finite second moments is a sufficient condition for the vanishing of the Chern marker, thereby implying topological triviality.