3190 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 measuring the lifetime and decay law of metastable helium offers a promising avenue for detecting deviations from standard quantum mechanics, as even small quartic deformations can produce significant, observable changes in mean lifetime and non-exponential decay patterns within the Wigner–Weisskopf approximation.
This paper extends the central limit theorem for linear statistics of Gaussian -ensembles to general by proving convergence for functions in the Sobolev space , utilizing the Helffer-Sjöstrand representation for covariance and characteristic flow estimates for Dyson Brownian motion.
This paper establishes lower bounds on the magnetic tunneling splitting and hopping coefficient for two identical, non-symmetric potential wells at asymptotically large separation in a constant magnetic field, showing that these quantities decay no faster than for almost all separations.
Motivated by Nelson's construction, this paper develops a stochastic analysis framework for the massive two-dimensional free Dirac field using Grassmann-valued Gaussian white noise to construct Euclidean Fermi fields, derive their fundamental solutions, and establish the time-translation semigroup on Wick sectors.
This paper investigates noisy dynamical systems on a two-dimensional torus governed by Möbius transformations, utilizing WKB methods, large-deviation theory, and weak-noise analysis to characterize the fate of Arnold tongues, quantify metastable phase-locking, and establish conditions for canard persistence in the presence of noise.
This paper derives the covariant polynomial symmetry algebra of a charged harmonic oscillator in the field of a Dirac magnetic monopole, identifying a shifted rank-2 tensor that generates a cubic Heun–Racah algebra and classifying its finite-dimensional representations for both integer and half-integer charges.
This paper demonstrates that local gauge theories with identical degrees of freedom but distinct gauge structures are related by "topological deformations"—the systematic gauging of symmetries within a presymplectic BV-AKSZ framework—which couples the system to a BF-type sector to either identify global symmetry-related solutions or generate new global degrees of freedom like the cosmological constant.
This paper establishes a rigorous response theory for weakly interacting quantum spin systems at positive temperature by leveraging the locality property of local indistinguishability to extend adiabatic expansions beyond Fermi systems.
This paper introduces an accurate zeroth-order perturbation theory using the Asymptotic Iteration Method with exponential and hyperbolic ansatz substitutions to solve the Schrödinger equation for spherically symmetric power-law potentials, effectively avoiding oscillatory behaviors and demonstrating high agreement with other methods for quartic and sextic singularities.
This paper proposes a near-term implementable scheme for approximately preparing quantum thermal states using local driving and ancilla resets, providing rigorous guarantees on the deviation from the exact Gibbs state based on protocol parameters and mixing time.