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

Vortex patterns of a two-dimensional Bose-Einstein condensate at the almost critical rotation speed

This paper numerically investigates vortex patterns in a two-dimensional Bose-Einstein condensate near critical rotation, demonstrating that repulsive interactions yield Abrikosov vortex lattices consistent with Thomas-Fermi theory, while attractive interactions preclude vortex lattices in favor of collapsing giant vortex solitons whose stability thresholds are determined by equivariant Gagliardo-Nirenberg inequalities.

Bao-Duy Le, Dinh-Thi Nguyen2026-08-18

🔢 mathematics

Approximate pushforward designs and image bounds on approximations

This paper extends the framework of quantum pushforward designs to approximate settings by establishing general transfer theorems and deriving sharp Schatten-norm bounds for partial traces on symmetric subspaces, which yield tighter error estimates for mixed-state and channel designs.

Jakub Czartowski, Adam Sawicki, Karol Życzkowski2026-08-18

🔢 mathematics

Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture

This paper derives an irreversibility condition for brittle fracture in one-dimensional elastic bars using the inverse-deformation approach and the second law of thermodynamics, proving that fixing crack locations in the reference configuration ensures local stability for all broken equilibria under hard loading.

Arnav Gupta2026-08-18

🔢 mathematics

Differential calculus on bigraded spaces and Koszul duality

This paper resolves the discrepancy in Koszul duality for superspaces by introducing a bigraded framework that establishes isomorphisms between the differential calculus structures, Poisson (co)homology, and Batalin-Vilkovisky algebras of a superspace and its dual.

Ruobing Chen, Sirui Yu2026-08-18

🔢 mathematics

From the planar Ising model to quasiconformal mappings

This paper establishes that the scaling limits of full-plane Kadanoff-Ceva fermions and energy-energy correlations for generic, non-degenerate $s$ -embeddings of the (near-)critical planar Ising model are described by solutions to conjugate Beltrami equations and Green kernels of uniformly elliptic operators, thereby revealing a richer conformal structure involving quasiconformal mappings and spacelike surfaces in Minkowski space that extends beyond classical Euclidean conformal covariance.

Rémy Mahfouf2026-08-18

⚛️ general relativity

The space spinor formalism and estimates for spinor fields

This paper demonstrates how the space spinor formalism can be adapted to construct estimates for spinor fields satisfying first-order equations, drawing parallels with the positive commutator method for second-order hyperbolic equations while recasting concepts of hyperbolicity within the spinor context.

Mariem Magdy, Juan A. Valiente Kroon2026-08-18

🔢 mathematics

A formal framework for higher-order spin models via hypergraphs, polymatroids, and the Tutte polynomial

This paper establishes a rigorous mathematical framework for higher-order spin models on hypergraphs by demonstrating how their partition functions relate to generalized Tutte polynomials and polymatroids, thereby extending the classical graph-theoretic connection between Potts models and the Tutte polynomial to a broader class of hypergraphical interactions.

Khallil Berrekkal, Joanna A. Ellis-Monaghan, Merijn Moody, Clélia de Mulatier2026-08-18

🔢 mathematics

Integrability of Hamiltonian systems on COLCS Manifold

This paper establishes a Lie-type integrability framework for Hamiltonian systems on con-locally conformal symplectic (COLCS) manifolds by introducing a COLCS bracket, identifying Poisson subalgebras, and proving that systems with sufficient first integrals and scaling symmetries are integrable by quadratures.

Antonio J. Pan-Collantes, Xuefeng Zhao2026-08-18

🔢 mathematics

Dynamical Gibbs-non-Gibbs transitions for finite-alphabet models on trees

This paper investigates dynamical Gibbs-non-Gibbs transitions for finite-alphabet spin models on trees under symmetric spin-flip dynamics, demonstrating that while $f$ -stable initial states lead to a recovery of the Gibbs property at large times, $f$ -saddle initial states result in the persistent non-quasilocality of the time-evolved measures.

Sebastian Bergmann, Christof Külske, Niklas Schubert2026-08-18

🔢 mathematics

On the kinetic Fokker--Planck equation in curved geometry

This self-contained paper investigates the kinetic Fokker-Planck equation on the tangent bundle of a compact Riemannian manifold by unifying and simplifying existing results while establishing new global hypoelliptic regularization and hypocoercive exponential equilibration properties in both $L^2$ and $L^1$ settings.

Cédric Villani2026-08-18

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