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

Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method

This paper presents a hybrid modeling framework that couples pre-trained, subdomain-local numerics-informed neural networks (NINNs) with classical full-order models using the overlapping Schwarz alternating method to solve advection-dominated advection-diffusion problems, demonstrating that both top-down and bottom-up training approaches yield accurate results comparable to full-order solutions.

George Chumbipuma, Irina Tezaur, Alejandro Diaz, Beatrice Riviere2026-09-17

🌀 nonlinear sciences

Two-Parameter Family of Nonlinear Dirac Equations With Scalar-Scalar plus Vector-Vector Interactions

This paper derives exact solitary wave solutions for a two-parameter family of nonlinear Dirac equations in 1+1 dimensions with scalar-scalar and vector-vector interactions, analyzing their profile transitions, energy-to-charge ratios, and stability properties while also obtaining their non-relativistic reduction to a modified nonlinear Schrödinger equation.

Avinash Khare, Fred Cooper, John F. Dawson, Avadh Saxena2026-09-17

⚛️ quantum physics

Unbounded Holevo additivity gaps in finite dimensions

This paper establishes the existence of unbounded two-use Holevo additivity gaps in finite-dimensional quantum channels by constructing specific tensor-product channels that exhibit a linear gap in output qubits with a quadratic input cost, while also demonstrating cases where the single-use Holevo quantity vanishes yet the classical capacity diverges.

Jinzhao Wang2026-09-17

🔢 mathematics

Endpoint eigenfunction restriction estimates in codimension two

This paper establishes an optimal $o(\lambda^{1/2}\sqrt{\log\lambda})$ improvement over the classical endpoint $L^2$ restriction estimates for Laplace eigenfunctions on codimension-two submanifolds while demonstrating that the logarithmic factor cannot be removed in general.

Xing Wang, Cheng Zhang2026-09-17

🔢 mathematics

Pathology-Free Real-Space Renormalization Group Theory on an Inverse Limit Space

This paper introduces a novel, pathology-free framework based on inverse limits of finite systems that rigorously implements Kenneth Wilson's original renormalization group vision, thereby overcoming decades of mathematical obstacles and opening new avenues for proving the existence of non-trivial fixed points.

Fabio Arz2026-09-17

⚛️ high-energy theory

Differential equations for Dotsenko--Fateev integrals: the case of degenerate fields $\Phi_{n,1}$

This paper investigates higher-order differential equations associated with Dotsenko--Fateev integrals for four-point correlation functions involving degenerate fields $\Phi_{n,1}$ , deriving their general structure and coefficients in terms of integral parameters while establishing their connection to hypergeometric operators.

Aleksandra Ivanova2026-09-17

🔢 mathematics

Some Considerations on the Fluid-Dynamical Limit of Particle Systems

This paper reviews and compares mathematical procedures for rigorously deriving fluid-dynamic descriptions from classical particle systems in the large-scale limit of Hamiltonian dynamics, highlighting that despite the program's longevity, most fundamental problems remain open with only a few notable exceptions.

Mario Pulvirenti, Sergio Simonella2026-09-17

🔢 mathematics

Contact canonoid maps and their conserved and dissipated quantities

This paper investigates conserved and dissipated quantities arising from contact canonoid maps and their extensions to singular smooth maps by constructing polynomial first integrals and smooth invariant endomorphisms that yield up to $n$ functionally independent trace invariants in a $(2n+1)$ -dimensional space, illustrated through various physical examples involving friction and damping.

R. Azuaje2026-09-17

🔢 mathematics

Quantum Behaviors Are Not Semialgebraic

This paper resolves Tsirelson's 1993 open question by proving that the set of quantum behaviors in a Bell scenario with four binary measurements per party is not semialgebraic, thereby demonstrating that it cannot be exactly characterized by any finite level of the Navascués-Pironio-Acín hierarchy or described by finite real-analytic equations.

Minbo Gao, Zhengfeng Ji, Chenghua Liu2026-09-17

🔢 mathematics

Polynomial rigidity of strong-field magnetic billiards

This paper proves that in the strong-field regime, a smooth strictly convex magnetic billiard admits a nonconstant polynomial first integral if and only if the domain is a disk, thereby establishing polynomial rigidity without requiring a real-analytic boundary assumption.

Dipesh Bhandari2026-09-17

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math-ph

Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method

Two-Parameter Family of Nonlinear Dirac Equations With Scalar-Scalar plus Vector-Vector Interactions

Unbounded Holevo additivity gaps in finite dimensions

Endpoint eigenfunction restriction estimates in codimension two

Pathology-Free Real-Space Renormalization Group Theory on an Inverse Limit Space

Differential equations for Dotsenko--Fateev integrals: the case of degenerate fields Φn,1\Phi_{n,1}Φn,1​

Some Considerations on the Fluid-Dynamical Limit of Particle Systems

Contact canonoid maps and their conserved and dissipated quantities

Quantum Behaviors Are Not Semialgebraic

Polynomial rigidity of strong-field magnetic billiards

Differential equations for Dotsenko--Fateev integrals: the case of degenerate fields $\Phi_{n,1}$