2560 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 argues that modern world models are functionally identical to decades-old reduced-order models from control theory, and proposes unifying these lineages to solve the critical challenge of verifiability required for deploying world models in safety-critical physical systems.
This paper presents a case study where a mathematician directs an AI system to formalize the mean-field derivation of the Vlasov equation in Lean 4, framing the process as a "strategy game" that successfully produced a complete, axiom-clean proof and a reusable optimal-transport library within approximately one month.
This paper introduces TokaGrad, the first end-to-end differentiable tokamak simulator that self-consistently models full-discharge scenarios—including ramp-up, L-mode, and H-mode transitions—to enable efficient, gradient-based optimization of reactor designs and autonomous plasma control.
This study investigates the inertial Kuramoto model to reveal that intrinsic frequency distributions dictate distinct synchronization pathways, where unimodal Gaussian distributions lead to smooth, hierarchical cluster entrainment, while multimodal uniform distributions produce discrete, Devil's staircase-like synchronization via successive peripheral cluster mergers.
This paper establishes the nonlinear stability of the Einstein-de Sitter universe by proving that initial data sets with near-flat metrics and positive fluid energy density on converge to a flat metric under the Einstein-Euler flow with a polytropic equation of state, thereby confirming that the model can be stable for an appropriate matter description despite its known linear instability under pressureless conditions.
This paper demonstrates that despite the Landau Hamiltonian on the half-plane possessing a purely absolutely continuous spectrum (unlike the full plane's pure point spectrum), its ground states still obey a strict area law for entanglement entropy, prompting an investigation into the specific spectral conditions required to produce a logarithmically enhanced area law.
This paper presents a certified refinement and asymptotic analysis of the Kuznetsov-Sahinidis diameter bound for Lennard-Jones clusters, offering a rigorous tightening of the bound for and resolving its asymptotic behavior as , while noting that the improvement serves primarily as a theoretical advancement rather than an immediate practical boost for current deterministic solvers.
This paper introduces H-cloud, a cloud-accessible, open-source finite-element framework built on Firedrake that enables rigorous, reproducible, and portable electromagnetic modeling of applied superconductors with accuracy comparable to commercial software while supporting forward simulation, adjoint differentiation, and optimization in both local and browser-based environments.
This paper establishes sharp and endpoint two-weight fractional integral estimates for Schrödinger operators with inverse-square potentials, demonstrating that while strong and weighted estimates fail at origin-critical boundaries, the Lorentz space estimate remains valid, alongside derived weighted Sobolev consequences for the Hardy-critical Friedrichs case.
This paper introduces a complete ultrametric structure on the set of von Neumann's incomplete tensor products to rigorously quantify the operational distinctness of quantum branches, demonstrating how product unitaries displace these states and interpreting the metric as a decoherence exponent that measures the rate at which universal state branches become distinguishable.