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.

Euler--Poincaré reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics

This paper develops a discrete Euler-Poincaré reduction framework for mechanical systems with advected parameters and additional dynamics using group difference maps, extends the Kelvin-Noether theorem to this discrete setting, and demonstrates the method's effectiveness in preserving geometric properties through applications to underwater vehicle dynamics and numerical simulations.

Yusuke Ono, Simone Fiori, Linyu Peng2026-04-24🔢 math-ph

On the subcritical self-catalytic branching Brownian motions

This paper constructs self-catalytic branching Brownian motions with an infinite number of initial particles for the subcritical case and establishes their coming down from infinity property along with characterizing the associated convergence rates.

Haojie Hou, Zhenyao Sun2026-04-24🔢 math-ph

A new perspective on the equivalence between Weak and Strong Spatial Mixing in two dimensions

This paper provides a new proof extending the equivalence between weak and strong spatial mixing to a broader family of two-dimensional lattice models by introducing a "percolative picture" of information propagation.

Sébastien Ott2026-04-24🔢 math-ph

Discontinuous transition in 2D Potts: I. Order-Disorder Interface convergence

This paper establishes that the order-disorder interface in the 2D $q$ -state Potts model (for $q>4$ ) at the critical temperature is a well-defined object with $\sqrt{N}$ fluctuations that converges to a Brownian bridge under diffusive scaling, a result proven by coupling the model to the Ashkin-Teller and six-vertex models to derive a renewal picture for the interface.

Moritz Dober, Alexander Glazman, Sébastien Ott2026-04-24🔢 math-ph

Chimera states on m-directed hypergraphs

This paper demonstrates that non-reciprocal higher-order interactions on m-directed hypergraphs facilitate the emergence of chimera states over a broader parameter range and enable new dynamical patterns not observed in reciprocal or pairwise systems, a finding validated through numerical simulations and phase reduction theory.

Rommel Tchinda Djeudjo, Timoteo Carletti, Hiroya Nakao, Riccardo Muolo2026-04-24🌀 nlin

Interfaces of discrete systems - spectral and index properties

This paper establishes a general operator algebraic framework using Hilbert $C^*$ -modules to analyze discrete systems on interfaces, demonstrating how the essential spectrum and topological properties of such mixtures can be derived from the asymptotic behavior of their constituent bulk systems.

Chris Bourne2026-04-24🔢 math-ph

Gauss Principle in Incompressible Flow: Unified Variational Perspective on Pressure and Projection

This paper clarifies that the Gauss-Appell principle, when applied at a fixed time to incompressible inviscid flow, yields a variational minimization that uniquely determines the reaction pressure as the Lagrange multiplier enforcing kinematic constraints, thereby recovering the Euler equations and the Leray-Hodge projection without inherently selecting global flow features like circulation.

Karthik Duraisamy2026-04-24🔢 math-ph

A natural decomposition of the Jacobi equation for some classes of $N$ -body problems

This paper presents a natural and simple criterion for decoupling the Jacobi equation in various $N$ -body problems, which unifies known decompositions for homographic motions and provides a concise proof of the linear instability of elliptic Lagrange solutions under specific mass conditions.

Renato Iturriaga, Ezequiel Maderna2026-04-24🔢 math-ph

Black holes and black regions, horizons and barriers in Lorentzian manifolds

This paper establishes that the semi-permeability of time-oriented null hypersurfaces is a fundamental geometric consequence of their null nature, leading to the introduction of "barriers" and "black regions" as simplified, locally defined tools for characterizing and locating event horizons and black holes in Lorentzian manifolds.

Cristina Giannotti, Andrea Spiro2026-04-24🔢 math-ph

Heisenberg-Euler and the Quantum Dilogarithm

This paper derives a dispersion integral representation of the Heisenberg-Euler QED effective lagrangian using Faddeev's quantum dilogarithm as a generalized Borel kernel, expressing its nonperturbative imaginary part via the quantum dilogarithm and its real part through a duality manifestation involving both the quantum dilogarithm and its modular dual.

Gerald V. Dunne2026-04-24🔢 math-ph

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