🔢 Category

math-ph

3210 papers

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

Restricted (Relative) Rota-Baxter operators on restricted Lie algebras and restricted Lie triple systems and related structures

This paper defines and investigates restricted Rota-Baxter operators on restricted Lie algebras and restricted Lie triple systems, establishing their connections to pre-Lie structures, proving that the pre-Lie triple system operad splits the Lie triple system operad, and demonstrating that Jacobson identities hold in pre-Lie triple systems in positive characteristic to introduce the concept of restricted pre-Lie triple systems.

Jon Beristain, Abdenacer Makhlouf2026-09-21
🔢 mathematics

Homogenization and averaging in the Bourgain-Brezis-Mironescu limit

This paper characterizes the Γ\Gamma-limit of quadratic fractional energies with periodic coefficients as both the period and the fractional exponent approach their local limits, demonstrating that the resulting energy is determined by the relative scaling of these parameters, ranging from pure homogenization or averaging in extreme regimes to a convex combination of both at a critical logarithmic scaling.

Andrea Braides, Stefano Mannella, Alec Jacopo Almo Schiavoni Piazza2026-09-21
🔢 mathematics

2D Torus defocusing NLSE with a potential and random initial data

This paper establishes the almost sure global well-posedness in a weak sense for the 2D defocusing cubic nonlinear Schrödinger equation with a potential and random initial data in H0−H^{0^-}, demonstrating that the solution remains close to the linear evolution in a higher regularity space and arises as the limit of truncated approximations, thereby generalizing Bourgain's earlier results.

Nicolas Lindstrom2026-09-21
🔢 mathematics

A variational approach for the 2D Abelian Yang-Mills-Higgs measure

This paper presents the first rigorous construction of the interacting Abelian Yang-Mills-Higgs measure on the two-dimensional torus with polynomial potentials by applying the Boué-Dupuis variational method to both the Higgs and gauge fields, while also establishing exponential integrability, gauge covariance, and a large-deviation principle for gauge-invariant observables.

Nikolay Barashkov, Ajay Chandra, Ilya Chevyrev, Andreas Koller, Abdulwahab Mohamed2026-09-21
🔢 mathematics

Comparative analysis of Neural Networks approaches for Initial Orbit Determination of Near-Earth Objects

This paper presents a comparative analysis demonstrating that a physics-informed neural network outperforms both a purely data-driven neural network and classical methods (Gauss's and Laplace's) in Initial Orbit Determination for Near-Earth Objects using Very Short Arcs, particularly by achieving higher rates of dynamically admissible predictions and superior performance on fast, nearby objects.

Francesco Geroni, Roberto Paoli, Riccardo Massidda, Giacomo Tommei2026-09-21
🌀 nonlinear sciences

Generalized Hamiltonian formalism for spatially nonlocal nonlinear differential equations

This paper establishes a unified generalized Hamiltonian formalism for spatially nonlocal field theories by deriving Euler-Lagrange equations with reflected-field contributions and applying the framework to construct the first standard Lagrangian and complete Hamiltonian formulation for the Ablowitz-Musslimani equation, alongside consistent formulations for two other nonlocal nonlinear Schrödinger equations.

Ali Pazarci, Nadir Ghazanfari, Ilmar Gahramanov2026-09-21
🔢 mathematics

dd-dimensional spherical ferromagnets in random fields: Metastates, continuous symmetry breaking, and spin-glass features

This paper investigates the large-volume behavior of dd-dimensional spherical ferromagnets in random fields for d≥2d \geq 2, demonstrating that while metastates are supported on a continuum of random product states, the non-scaled model exhibits unique mixture behaviors in two dimensions and the scaled model displays chaotic, non-self-averaging spin-glass characteristics with replica symmetry breaking.

Kalle Koskinen, Christof Külske2026-09-18
🔬 mesoscale physics

Beyond symmetry protection: Robust feedback-enforced edge states in non-Hermitian stacked quantum spin Hall systems

This paper demonstrates that intermediate inter-layer coupling combined with competitive non-Hermitian directed amplification can enforce robust helical edge states in stacked quantum spin Hall systems without relying on symmetry protection, thereby challenging the conventional view that such coupled layers inevitably form trivial phases.

Mengjie Yang, Ching Hua Lee2026-09-18
🔢 mathematics

The power of quantum catalytic local operations

This paper investigates the distinct roles of quantum catalysis and classical communication in state transformations by demonstrating that the class of catalytic local operations (CLO) is incomparable to both LOCC and stochastic LOCC with bounded quantum communication, thereby revealing that these mechanisms capture fundamentally different facets of quantum state manipulation.

Patryk Lipka-Bartosik, Jessica Bavaresco, Nicolas Brunner, Pavel Sekatski2026-09-18