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 extends Enrico Fermi's 1932 procedure to the transverse electromagnetic field by using a quantum canonical transformation to derive a gauge-respecting, matter-only Hamiltonian with incoherent current interactions, thereby circumventing Haag's theorem and providing a quantum origin for the longitudinal-transverse splitting of phonons and other excitations.
This paper establishes that sandwiched and - Rényi divergences on arbitrary von Neumann algebras can be represented as averages of ordinary relative entropy over a canonical family of fixed-ray escort states, a result derived using Haagerup spaces that enables new reformulations of one-shot testing converses and work-extraction reliability.
This paper establishes a particle-number-uniform Poincaré inequality for repulsive mean-field Coulomb gases in dimensions under a weak-coupling condition, thereby proving exponential relaxation for their overdamped Langevin dynamics.
This paper establishes the polynomial decay of spin-spin correlations and the interchangeability of thermodynamic and infinite-volume limits for the spin-1/2 Heisenberg XXZ chain in the range by employing novel probabilistic couplings between the Lorentz mirror model and the six-vertex model, thereby providing rigorous results independent of Bethe Ansatz techniques.
This paper defines a family of Turaev-Viro type invariants for hyperbolic 3-manifolds with totally geodesic boundary using the modular double of and proves that their asymptotic behavior is governed by the manifold's hyperbolic volume and the adjoint twisted Reidemeister torsion of its double.
This paper analytically characterizes the adjacency matrix spectra of random graphs with discrete scale invariance and infinite-mean node fitness, revealing that their leading eigenvalues form a logarithmic spiral with alternating signs and that their eigenvectors exhibit log-periodicity, distinguishing them from typical finite-rank random graph models.
This paper proposes a fast, stable, and direct analytic method using one-dimensional shallow water equations to reconstruct underwater channel topography from surface wave measurements at a single instant, demonstrating high accuracy and Lipschitz stability under specific discharge conditions.
This paper investigates the implications of modified Painlevé-Gullstrand coordinates for Kiselev black holes surrounded by quintessence by constructing a static line element with a deformation parameter, analyzing radiation and dust effects via the barotropic index, and deriving closed-form expressions for Hawking temperature and entropy.
This paper provides a simple and elementary proof, utilizing high-temperature expansion, random-cluster, and random current representations, that the truncated two-point function of the near-critical planar Ising model on with external field decays exponentially.
This paper derives exact solutions to the one-dimensional Schrödinger equation for compactly supported parabolic and hyperbolic secant potential barriers (including their combinations), providing explicit expressions for transmission and reflection coefficients as well as specific dwell times.