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.

🔢 mathematics

The Landau-Dirac operator with shell interactions: self-adjointness and clustering

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.

Badreddine Benhellal, Vincent Bruneau, Pablo Miranda2026-08-24

🔢 mathematics

On quantum channels: extreme points, topology, and categorical properties

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.

J. M. S. T. da Silva2026-08-24

🔢 mathematics

Degeneracy beyond the parity-symmetry protection in the Lipkin-Meshkov-Glick model

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 $\mathbb{Z}_2$ reflection symmetry in the classical phase space that manifests as an anti-unitary symmetry in the quantum system.

Jamil Khalouf-Rivera, Miguel Carvajal, Francisco Pérez-Bernal2026-08-24

🔢 mathematics

The transverse matter Hamiltonian

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.

Andrea Marini, Kai Wu, Riccardo Reho2026-08-24

⚛️ high-energy theory

Fixed-ray escort representations of sandwiched and $\alpha$ -- $z$ Rényi divergences on von Neumann algebras

This paper establishes that sandwiched and $\alpha$ - $z$ 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 $L^p$ spaces that enables new reformulations of one-shot testing converses and work-extraction reliability.

Tanay Kibe, Pratik Roy2026-08-24

🔢 mathematics

Spectral gaps for mean-field Coulomb gases

This paper establishes a particle-number-uniform Poincaré inequality for repulsive mean-field Coulomb gases in dimensions $d \ge 3$ under a weak-coupling condition, thereby proving exponential relaxation for their overdamped Langevin dynamics.

Simon Becker, Angeliki Menegaki2026-08-24

🔢 mathematics

The spin-1/2 Heisenberg XXZ chain and the Lorentz mirror model with loop weight 2

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 $\Delta\in[-1,1/2]$ by employing novel probabilistic couplings between the Lorentz mirror model and the six-vertex model, thereby providing rigorous results independent of Bethe Ansatz techniques.

Kieran Ryan2026-08-24

🔢 mathematics

Turaev-Viro invariant from the modular double of $\mathrm {U}_{q}\mathfrak{sl}(2;\mathbb R)$

This paper defines a family of Turaev-Viro type invariants for hyperbolic 3-manifolds with totally geodesic boundary using the modular double of $\mathrm{U}_{q}\mathfrak{sl}(2;\mathbb{R})$ and proves that their asymptotic behavior is governed by the manifold's hyperbolic volume and the adjoint twisted Reidemeister torsion of its double.

Tianyue Liu, Shuang Ming, Xin Sun, Baojun Wu, Tian Yang2026-08-21

🔢 mathematics

Spectra of random graphs with discrete scale invariance

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.

Alessio Catanzaro, Rajat Subhra Hazra, Diego Garlaschelli2026-08-21

🔢 mathematics

A Direct Approach for Detection of Bottom Topography in Shallow Water

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.

Lamsahel Noureddine, Carole Rosier2026-08-21

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math-ph

The Landau-Dirac operator with shell interactions: self-adjointness and clustering

On quantum channels: extreme points, topology, and categorical properties

Degeneracy beyond the parity-symmetry protection in the Lipkin-Meshkov-Glick model

The transverse matter Hamiltonian

Fixed-ray escort representations of sandwiched and α\alphaα--zzz Rényi divergences on von Neumann algebras

Spectral gaps for mean-field Coulomb gases

The spin-1/2 Heisenberg XXZ chain and the Lorentz mirror model with loop weight 2

Turaev-Viro invariant from the modular double of Uqsl(2;R)\mathrm {U}_{q}\mathfrak{sl}(2;\mathbb R)Uq​sl(2;R)

Spectra of random graphs with discrete scale invariance

A Direct Approach for Detection of Bottom Topography in Shallow Water

Fixed-ray escort representations of sandwiched and $\alpha$ -- $z$ Rényi divergences on von Neumann algebras

Turaev-Viro invariant from the modular double of $\mathrm {U}_{q}\mathfrak{sl}(2;\mathbb R)$