math-ph papers | Gist.Science

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.

On the Numerical Treatment of an Abstract Nonlinear System of Coupled Hyperbolic Equations Associated with the Timoshenko Model

This paper proposes and validates a second-order accurate, symmetric three-layer semi-discrete time-stepping scheme combined with a Legendre-Galerkin spectral spatial discretization for solving an abstract nonlinear system of coupled hyperbolic equations associated with the Timoshenko model, demonstrating its convergence and efficiency through theoretical analysis and numerical experiments.

Jemal Rogava, Zurab Vashakidze2026-02-24🔢 math-ph

The heat equation and independence of the spectrum of the Hodge Laplacian on $\ell^p$

This paper establishes Davies-Gaffney-Grigoryan estimates for the heat kernel of the Hodge Laplacian on simplicial complexes, extends the associated semigroup to $\ell^p$ spaces under specific curvature and volume growth conditions, and proves the independence of the spectrum from $p$ for $p \in [1, \infty]$ .

Philipp Bartmann, Matthias Keller2026-02-24🔢 math-ph

Some effective operators for graphene monolayer superlattices, from variational perturbation theory

This paper develops precise effective operators for monolayer graphene superlattices by combining variational approximation, perturbation theory, and multiscale methods to replace the standard massless Dirac operator with new operators that account for both microscopic and macroscopic periodic potentials.

Louis Garrigue2026-02-24🔢 math-ph

Schauder estimates for germs of distributions on smooth manifolds

This paper extends multi-level Schauder estimates and a reconstruction theorem for germs of distributions from Euclidean space to smooth Riemannian manifolds by utilizing the exponential map and introducing a novel concept of $\beta$ -regularizing kernels, all without imposing additional geometric assumptions.

Beatrice Costeri, Claudio Dappiaggi, Paolo Rinaldi, Matteo Savasta2026-02-24🔢 math-ph

The multinomial dimer model

This paper establishes a variational principle for a large $N$ limit of the dimer model in any dimension $d$ , proving that random configurations concentrate on a unique limit shape determined by Euler-Lagrange equations and explicitly computable surface tension, thereby providing one of the first explicit solutions for limit shapes in statistical mechanics models of dimension three and higher.

Richard Kenyon, Catherine Wolfram2026-02-23🔢 math-ph

Characterizing the Kirkwood-Dirac positivity on second countable LCA groups

This paper extends the characterization of Kirkwood-Dirac positivity to second countable locally compact abelian groups by linking the representation to Kohn-Nirenberg quantization, identifying positive pure states as Haar measures on closed subgroups, and establishing that the associated classical fragment is non-trivial if and only if the group possesses a compact identity component.

Matéo Spriet2026-02-23🔢 math-ph

Exploring quantum fields in rotating black holes

This paper extends the proof of the Hadamard property for the Unruh state of a free scalar field on Kerr-de Sitter spacetime to any subextreme black-hole rotation by generalizing geometric analysis of the trapped set, while also discussing its applications in numerical studies of inner horizon quantum effects and related universality results.

Christiane K. M. Klein2026-02-23🔢 math-ph

Bethe equations for the critical three-state Potts spin chain with toroidal boundary conditions

This paper derives Bethe ansatz equations for the spectra of the critical three-state Potts quantum chain with integrable twisted boundary conditions, demonstrating the completeness of the spectrum for small lattices and confirming that low-lying excitations exhibit fractional spins consistent with conformal field theory predictions.

M. J. Martins2026-02-23🔢 math-ph

Chern-Simons deformations of the gauged O(3) Sigma model on compact surfaces

This paper establishes the existence of solutions to the gauged Chern-Simons-O(3)-Sigma model on compact Riemann surfaces using topological methods, demonstrating that solutions exist for small deformation parameters with multiple solutions when vortex and antivortex counts differ, while proving global existence for any parameter value when these counts are equal, alongside numerical investigations on the sphere.

Rene I. Garcia-Lara2026-02-23🔢 math-ph

Nonlocal-to-local $L^p$ -convergence of convolution operators with singular, anisotropic kernels

This paper establishes and quantifies the strong $L^p$ -convergence of nonlocal convolution operators with singular, anisotropic kernels to local differential operators with natural boundary conditions, extending previous results to include stronger singularities and providing explicit convergence rates.

Helmut Abels, Christoph Hurm, Patrik Knopf2026-02-23🔢 math-ph

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