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.

The consecutive lifting-projection flow as an approximation of Boltzmann and Landau flow

This paper introduces the consecutive lifting-projection (LP) flow as a novel framework that approximates spatially homogeneous Boltzmann and Landau equations by lifting nonlinear collision operators to a higher-dimensional linear Kac master equation, thereby preserving physical conservation laws and entropy while enabling the development of new, stable, and accurate numerical solvers such as the Green's function method.

Kun Huang2026-05-06🔢 math-ph

Dimer models on astroidal zig-zag graphs

This paper introduces a new family of finite subgraphs called astroidal zig-zag graphs associated with periodic planar bipartite graphs, for which the authors derive explicit inverse Kasteleyn matrices via double contour integrals and use them to establish phase separation, compute limit shapes, and prove local correlation convergence for dimer models with arbitrary Newton polygons.

Tomas Berggren, Alexei Borodin, Terrence George2026-05-06🌀 nlin

Law of Large Numbers and Central Limit Theorem for random sets of solitons of the focusing nonlinear Schrödinger equation

This paper establishes a Law of Large Numbers and a Central Limit Theorem for random configurations of $N$ solitons in the focusing nonlinear Schrödinger equation, demonstrating that as $N$ increases, the random solution converges to a deterministic soliton gas limit with quantifiable fluctuations and correlation functions.

Manuela Girotti, Tamara Grava, Ken D. T-R McLaughlin, Joseph Najnudel2026-05-05🔢 math-ph

Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces

This paper establishes a Lorentzian analogue of Reshetnyak's Majorisation Theorem for spaces with upper curvature bounds, demonstrating that any two timelike curves with the same endpoints can be mapped from a convex region in model Minkowski space via a 1-anti-Lipschitz map, thereby providing a discrete-friendly four-point characterization of such curvature bounds.

Tobias Beran, Felix Rott2026-05-05🔢 math-ph

Compactness and least energy solutions to the super-Liouville equation on the sphere

This paper investigates the super-Liouville equation on the sphere by establishing a generalized Pohozaev-type identity, deriving uniform bounds for spinor components, proving solution compactness in low-energy and Möbius-invariant regimes, and demonstrating the existence of nontrivial least-energy solutions under even coefficient functions via variational methods.

Mingyang Han, Chunqin Zhou2026-05-05🔢 math-ph

Spatiotemporally Localized Optical Links and Knots

This paper proposes and experimentally demonstrates a novel scheme for generating spatiotemporally localized optical knots and links within a paraxial field by superposing toroidal light vortices, thereby overcoming the longitudinal space-filling limitations of traditional spatial modes and offering robust topological structures for advanced information transfer and storage applications.

Yaning Zhou, Nianjia Zhang, Ao Zhou, Zhao Zhang, Jinsong Liu, Chunhao Liang, Sergey A. Ponomarenko, Qiwen Zhan, Yangjian Cai, Xin Liu2026-05-05🔢 math-ph

Pulsation of quantum walk between two arbitrary graphs with weakly connected bridge

This paper demonstrates that a Grover quantum walk on two arbitrary graphs connected by a weak bridge exhibits a pulsation phenomenon characterized by periodic transfer between the graphs with a period of $O(\epsilon^{-1/2})$ , where the transfer probability depends solely on the number of edges in each graph rather than their specific structures.

Taisuke Hosaka, Etsuo Segawa2026-05-05🔢 math-ph

Gauge Symmetries, Contact Reduction, and Singular Field Theories

This paper extends the formalism of scale-invariant symmetry reduction to singular Lagrangian systems of both particles and fields by utilizing the De Donder-Weyl multisymplectic framework to construct dynamically equivalent frictional theories, with applications to physical models and implications for classical General Relativity.

Callum Bell, David Sloan2026-05-05🔢 math-ph

A kinetic interpretation of thermomechanical restrictions of continua

This paper bridges continuum thermodynamics and kinetic theory by demonstrating that the Rajagopal–Srinivasa principle of maximal entropy production is kinetically equivalent to a minimal relaxation-time principle, and proposes a hybrid Chapman–Enskog–Rajagopal–Srinivasa framework that successfully recovers standard fluid laws while offering enhanced insights for complex materials like liquid crystals.

Patrick E. Farrell, Josef Málek, Ondřej Souček, Umberto Zerbinati2026-05-05🔢 math-ph

The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure

This paper introduces a mesoscopic partition function based on combined spatial and phase-space coarse-graining that recovers the standard canonical limit and establishes a unified framework linking the factorization of this function to the extensivity of free energy, with deviations quantified by inter-cell correlations and mutual information.

Bob Osano2026-05-05🔬 cond-mat

← Previous Next →