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 announces limit shape theorems for the height function of the six-vertex model under domain-wall boundary conditions, specifically covering the antiferroelectric regime () and a restricted range of the disordered regime ().
This paper establishes the integrability of a long-range deformation of the quantum open Toda system by constructing explicit Lax operators, demonstrating the deformation's applicability across classical and quantum, non-relativistic and relativistic regimes, and showing its compatibility with the algebraic Bethe ansatz.
This paper establishes the existence of absolutely continuous spectrum and the absence of singular spectrum for the Anderson model on a specific hyperbolic square lattice at weak disorder and under certain bounded density conditions, demonstrating Anderson delocalization in this geometric setting.
This paper presents a Hamiltonian framework for regularizing and linearizing central-force dynamics by introducing a new canonical extension of projective decomposition, which yields closed-form solutions for inverse-square and inverse-cubic forces while being numerically validated for the two-body problem with J2 perturbations.
This paper introduces "free mutual information" (FMI), a new diagnostic for quantum chaos derived from free probability theory that quantifies operator spreading in the doubly exponential Hilbert space via a Coulomb gas formula and a weighted sum of higher-point OTOCs, thereby offering a sharper and more universal measure of chaos than standard four-point OTOCs.
This paper establishes the theoretical well-posedness of an inverse problem for identifying a time-dependent potential coefficient in a one-dimensional diffusion equation and evaluates the accuracy and robustness of three distinct numerical methods—an integration-based scheme, a Newton-Raphson solver, and a physics-informed neural network—for solving it.
This paper extends closed-form relative entropy calculations to multi-mode squeezed states in a free scalar quantum field, demonstrating that while spatially local squeezing yields unphysical divergences, spacetime-local squeezing produces a physically reasonable class of states with finite relative entropy.
This paper investigates both unitary and nonunitary A-D-E minimal models with topological defects on the cylinder, demonstrating that a specific coset graph encodes key boundary conformal field theory structures like fusion algebras and g-factors, while also establishing their lattice realization through integrable restricted solid-on-solid models and deriving effective central charges via dilogarithm identities from Y-system asymptotics.
This paper constructs the eigensections and eigenvalues of commuting monodromy operators for a qKZ-type discrete flat connection with a root-of-unity step by representing the connection as a discrete Gauss-Manin connection.
This paper introduces a reinforcement learning-based framework that dynamically adapts the fidelity of coupled full-order and reduced-order models within an overlapping Schwarz alternating method, enabling efficient and accurate online resolution of transient problems with propagating features without requiring reference solutions.