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 establishes a nonasymptotic training theory for quantum physics-informed neural networks (QPINNs) solving elliptic PDEs, proving that sufficiently wide parameterized quantum circuits converge via gradient flow to a linearized neural tangent kernel model with explicit bounds dependent on circuit and domain parameters.
This paper presents a general method for computing Bragg peaks in diffraction theory as limits by utilizing the Eberlein convolution as an inner product to derive a Cauchy–Schwarz-type inequality that yields quantitative Bombieri–Taylor results.
This paper establishes a geometric foundation for large deviation theory by developing a contact framework on stochastic vector bundles, where rate functions, fluctuation symmetries, and Gallavotti--Cohen-type dualities are derived from a contact 1-form and a coupled Hamilton--Jacobi--transport system.
This paper introduces a three-level hierarchy of upper bounds—Structural, Effective, and Physical Reconstruction Dimensions—to distinguish between the theoretical limits of reconstructability imposed by symmetry, the constraints of specific reconstruction maps, and the degeneracies inherent in physical processes, thereby providing a framework to identify where information is lost in inverse problems.
This paper investigates asymmetric phase transitions in random noncommutative geometries by employing the Riemann-Hilbert approach, bootstrapping with positivity, and Hamiltonian Monte Carlo simulations to derive explicit formulae and reconstruct the intricate phase structure of quartic (0, 1) and (1, 0) Dirac ensembles, with all three methods demonstrating excellent agreement for large matrix sizes.
This paper provides a rigorous nonperturbative proof of chiral anomaly cancellation and its universality in a lattice Kogut-Susskind regularization of the multiflavor Schwinger model, demonstrating that irrelevant lattice operators play an essential role in this mechanism through their convergence properties in the renormalized expansion.
This paper develops a Dirichlet-to-Neumann spectral formalism for restricted diffusion with multiple targets by decomposing the governing operator into target-restricted blocks to derive convergent switching expansions and operator-valued renewal equations that resolve boundary local times and inter-target transfers.
This paper resolves a long-standing open problem by proving the first existence of non-simple blow-up solutions for the self-dual Chern--Simons--Higgs equation in the finite-height regime, characterizing their regular-polygonal structure, equal core masses, and mass-gap constraints through detailed a priori analysis and explicit construction.
This paper establishes a sharp-interface Gamma-limit for heterogeneous anisotropic Kac interactions on general rectifiable cut spaces by resolving microscopic bank-crossing information through measure-theoretic methods, thereby characterizing the limit energy without requiring standard geometric regularity assumptions or boundary concentration terms.
This paper proposes a factorization method for reconstructing an unknown clamped obstacle from near-field measurements of the biharmonic Helmholtz equation by introducing an obstacle-independent far-field transformation that enables a symmetric factorization of the operator, thereby providing a rigorous characterization and a practical spectral reconstruction algorithm.