2548 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 a variational-adjoint interpretation of quantum mechanics where the interaction between forward and adjoint wavefunctions defines a general Fréchet sensitivity kernel for quantum observables, revealing the Born probability density as a specific positive-definite case within a broader class of sensitivity measures applicable to momentum, energy, and spin.
This book provides a self-contained, tutorial introduction to topology, differential geometry, and general relativity for physicists, distinguished by its use of original, runnable Mathematica notebooks to concretize abstract mathematical concepts and enable hands-on verification of theoretical results.
This paper provides a rigorous realization of the dilute instanton picture for a semiclassical Schrödinger operator with a symmetric double-well potential by using a localized Feynman–Kac representation to demonstrate that Brownian bridge passages between wells follow a Poisson distribution, thereby directly deriving the familiar instanton expansion for the eigenvalue splitting.
This paper establishes a three-term asymptotic formula for the eigenvalues of the fractional Laplacian in a bounded interval and proves the uniform boundedness of its normalized eigenfunctions, thereby confirming two long-standing conjectures regarding the remainder term and eigenfunction bounds.
This paper proves that almost every smooth minimal area-preserving flow with simple saddles on a compact orientable surface of any genus possesses a singular spectrum and is spectrally disjoint from almost every other such flow, establishing these results via a new criterion for spectral singularity and a mechanism of resonant rigidity times applied to special flows over interval exchange transformations.
This paper proposes a revised hydromechanically coupled phase-field model for poro-elastoplastic media that incorporates an associative Drucker-Prager flow rule and a specific coupling term in the free energy to ensure a continuous strength surface and accurate fracture driving force, thereby improving the simulation of both shear- and tension-dominated fractures compared to existing approaches.
This paper characterizes the one-point fluctuations of exponential directed last passage percolation conditioned on an atypically large passage time, identifying that the limiting distributions transition between GUE Tracy-Widom, Gaussian, and one-spike BBP laws depending on the observation point's location within the macroscopic spatial regions.
This paper establishes the self-adjointness and analyzes the spectral properties of a two-dimensional Landau-Dirac operator perturbed by shell interactions, demonstrating that in the non-critical case, discrete eigenvalues accumulate at Landau-Dirac levels with rates determined by the curve's logarithmic capacity and sides dependent on the coupling strength, while the critical case introduces a new essential spectrum interval.
This thesis investigates quantum channels from a mathematical perspective by constructing extreme CPTP and UCPTP maps of various ranks, analyzing the preservation of extremality under tensor products, classifying categorical products and coproducts, and exploring the topological structure of the closure of extreme CPTP maps.
This paper demonstrates that in an anharmonic Lipkin-Meshkov-Glick model, exponential degeneracy in energy doublets can persist even when parity symmetry is broken by a first-order ground-state quantum phase transition, a phenomenon attributed to an underlying reflection symmetry in the classical phase space that manifests as an anti-unitary symmetry in the quantum system.