2670 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 demonstrates that every fusion category containing a non-invertible, self-dual object generates a Temperley-Lieb integrable anyonic chain, establishing a connection to Pasquier's ADE lattice models and arguing that these systems are gapped when the object's quantum dimension exceeds 2, while noting that large finite-size effects can complicate numerical analysis for dimensions close to 2.
This paper establishes that in non-critical Bernoulli bond percolation for dimensions , the maximum diameter of finite clusters scales asymptotically as almost surely, where the constant is determined by the exponential decay rate of large cluster probabilities, and further analyzes the asymptotic behavior of the number of vertices in such large-diameter clusters.
This paper introduces two new off-shell indecomposable supersymmetric mechanics models with spin variables derived from nonlinearly deformed scalar superfields, demonstrating that while they differ off-shell, they are equivalent on-shell and describe spin variables in the adjoint representation of the SO(8) R-symmetry group.
This paper establishes the global existence of weak entropy solutions for 1D isentropic gas dynamics with general pressure laws by introducing a "Synchronized Dual Translation" regularization that preserves structural isomorphism with the standard Euler equations, thereby eliminating the restrictive higher-order derivative constraints required by previous flux-modification methods.
This paper establishes a novel real-space formula for the Zak phase of one-dimensional periodic Jacobi operators using Weyl -functions, which bypasses Floquet-Bloch theory to explicitly highlight boundary term dependencies and recover classical quantization under inversion symmetry.
This manuscript introduces the quadratic-phase Fourier-Bessel transform, establishes its fundamental properties and associated convolution structures, and proves a Donoho-Stark-type uncertainty principle to extend classical results to this generalized framework.
This paper introduces the algebraic concept of Leonard trios as an extension of Leonard pairs, establishes their connection to bispectral rational functions and Heun operators, and initiates their classification by demonstrating that Wilson's rational functions serve as overlap coefficients with specific recurrence and summation properties.
By generalizing a quantitative monogamy-of-entanglement argument to arbitrary convex bodies via a new relative entropy notion, this paper establishes a finite de Finetti theorem that enables a convergent conic hierarchy with certified interior points for solving polynomial optimization problems with both equality and inequality constraints.
This paper establishes the existence of non-hydrodynamic solutions to the linear density-dependent BGK equation in dimensions by employing spectral analysis and complex contour integration to demonstrate that specific initial conditions yield a macroscopic mass density dissipation rate diverging as for any Knudsen number.
This paper establishes a van den Berg-Kesten-type correlation inequality for the KPZ line ensemble and continuum directed random polymer by leveraging the integrability of the log gamma polymer and the geometric RSK correspondence, while demonstrating that such an inequality fails for non-integrable models.