2656 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 proposes using the Hausdorff dimension of the spectral form factor's associated random walk as a fractal diagnostic to distinguish chaotic Hamiltonians (dimension ) from integrable ones (dimension $1$), while providing exact moment calculations and proving Gaussian or log-Normal distributions under specific degeneracy conditions.
This paper improves a singularity theorem by Galloway and Ling for globally hyperbolic spacetimes satisfying the null energy condition with 2-convex Cauchy surfaces, establishing that such spacetimes are either past null geodesically incomplete or possess specific topological structures (spherical spaces or surface bundles), while also relaxing convexity requirements under isometry and strengthening conclusions for non-orientable, non-prime, or specific Haken manifolds without needing finite covers.
This paper resolves an open problem by establishing necessary and sufficient conditions for the Law of Large Numbers of -particle ensembles at fixed temperature through Bessel generating function asymptotics, thereby proving that the limiting behaviors of -sums, -corners, and time-slices of -Dyson Brownian motion correspond to free convolution and free projection regardless of the inverse temperature parameter .
This paper reviews recent progress on state-dependent Lieb-Robinson bounds for Bose-Hubbard Hamiltonians and provides a simplified proof establishing a polynomial velocity bound of for general bounded-density initial states.
This paper demonstrates that the integral means spectrum of the primitive of the randomized Riemann zeta-function and holomorphic Gaussian multiplicative chaos almost surely follows the Kraetzer conjecture, despite neither function being injective.
This paper establishes the local well-posedness of a Camassa-Holm type equation with time-dependent weak dissipation using Kato's theory and derives two blowup criteria along with a universal $-2$ blowup rate through energy estimates and characteristic methods, thereby extending wave breaking analysis to variable dissipation regimes.
This paper derives a nonperturbative bound on the distance between evolutions of open quantum systems with time-dependent generators, which is then applied to establish explicit upper bounds on the errors of the rotating-wave and secular approximations in the presence of dissipation and decoherence.
This paper extends the scaling limit theory for one-dimensional random Schrödinger operators with critically decaying potentials by characterizing the limits of transfer matrices and eigenvalue point processes for intermediate decaying profiles via coupled stochastic differential equations, thereby identifying new point processes with properties similar to the process and describing the corresponding eigenfunction shapes.
Motivated by conformal bootstrap principles and space-time supersymmetry, this paper presents a new method for constructing Gepner model orbifolds by utilizing spectral flow generators to define an admissible group and its mirror counterpart, thereby generating modular invariant models with mutually local physical fields.
This paper establishes a systematic framework for gauging non-invertible symmetries in two-dimensional quantum field theories by formulating the process through topological interfaces, thereby extending standard gauging properties to general fusion categories, deriving key mathematical theorems from physical axioms, and identifying new self-dualities and a generalized orbifold groupoid structure.