3324 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 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.
This paper proposes a spectral approach to identifying uniqueness pairs for unitary transforms by mapping two-sided sampling problems to lower-bound spectral problems of confined Hamiltonians, thereby generalizing existing Wirtinger-Poincaré-based criteria to a broader class of transforms including the fractional Fourier and Hankel transforms.
This paper presents an exact solution for the ferromagnetic Ising model on random regular graphs by expressing the partition function as a generating function of labeled edge-bicolored graphs, thereby deriving the free energy and confirming a second-order phase transition with mean-field critical exponents through analytic combinatorics.
This paper utilizes linear programming to establish a separable version of Ky Fan's majorization relation for the sum of two tensor products of positive semidefinite operators, while demonstrating that such a relation fails for sums involving three or more tensor products.