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.

Hirota-tau and Heun-function framework for Dirac vacuum polarization and quantum stabilization of kinks

This paper establishes a Hirota-tau and Heun-function framework for a modified affine Toda model to demonstrate that fermion-soliton interactions, governed by one-loop quantum corrections and a deformed Noether-topological current, yield stable kink configurations with a complete scattering spectrum that has implications for topologically protected states in quantum and condensed-matter systems.

Harold Blas2026-03-31🌀 nlin

Generalized quantum theory for accessing nonlinear systems: the case of Liénard and Levinson-Smith equations

This paper demonstrates that a generalized quantum theory framework connects to Liénard and Levinson-Smith nonlinear systems, yielding closed-form solutions for the former via Abel conversion and revealing solitonic-like solutions and position-dependent mass relevance for the latter.

Bijan Bagchi, Anindya Ghose-Choudhury2026-03-31🌀 nlin

Data-driven discovery and control of multistable nonlinear systems and hysteresis via structured Neural ODEs

This paper proposes a minimally structured Neural Ordinary Differential Equation architecture that enforces trajectory stability and parameterizes multistable nonlinear systems by learning a vector field with a contraction term and an implicit equilibrium map, enabling efficient data-driven discovery and gradient-based control.

Ike Griss Salas, Ethan King2026-03-31🔢 math-ph

Semiclassical shape resonances for magnetic Stark Hamiltonians

This paper establishes a one-to-one correspondence between the shape resonances of two-dimensional magnetic Stark Hamiltonians with potential wells and the discrete eigenvalues of a reference operator in the semiclassical limit, thereby deriving the Weyl law for resonance counts and characterizing their asymptotic behavior near potential well bottoms.

Kentaro Kameoka, Naoya Yoshida2026-03-31🔢 math-ph

Quantum Hall States response to toroidal geometry deformation

This paper employs complex time Hamiltonian evolution and generalized coherent state transforms to analyze the response of integer and fractional quantum Hall states to both flat and non-flat Kähler toroidal geometry deformations, deriving explicit analytic expressions for the evolution of Laughlin states up to a curvature singularity in the latter case.

Bruno Mera, José M. Mourão, João P. Nunes, Carolina Paiva2026-03-31🔢 math-ph

The Full Set of KMS-States for Abelian Kitaev Models

This paper characterizes the full set of KMS states for abelian Kitaev models by representing the quasilocal observables as a groupoid $C^\ast$ -algebra, proving the uniqueness of these states for all finite temperatures, and demonstrating that their zero-temperature limit coincides with the unique frustration-free ground state.

Danilo Polo Ojito, Emil Prodan2026-03-31🔢 math-ph

Homothetic Hodge$-$de Rham Theory and a Geometric Regularization of Elliptic Boundary Value Problems

This paper introduces a homothetic extension of Weyl integrable geometry to develop a twisted Hodge theory that provides a rigorous geometric regularization of elliptic boundary value problems, enabling consistent weak solutions for incompatible data and nonsingular models for point sources through a diffuse interface penalty layer.

Fereidoun Sabetghadam2026-03-31🔢 math-ph

Structure-Preserving Learning of Nonholonomic Dynamics

This paper introduces a structure-preserving Gaussian process framework that utilizes a novel nonholonomic matrix-valued kernel to learn dynamics while strictly enforcing nonholonomic constraints, thereby ensuring physically consistent motion and establishing theoretical guarantees on consistency and representation.

Thomas Beckers, Anthony Bloch, Leonardo Colombo2026-03-31🔢 math-ph

$q$ -Deformed Quantum Mechanics and the Thermodynamics of Black Hole/White Hole Spectral pair

This paper proposes a $q$ -deformed Wheeler--DeWitt framework for Schwarzschild black and white holes that yields a finite-dimensional Hilbert space and bounded entropy, thereby resolving evaporation divergences through a stable cold remnant and establishing a consistent semiclassical link between quantum gravity and cosmology.

S. Jalalzadeh, R. Jalalzadeh, H. Moradpour2026-03-31⚛️ gr-qc

Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion

This paper demonstrates that a 1D periodic network of slowly time-modulated interfaces can generate effective time-dependent bulk wave properties and high-order dispersive effects through homogenization, while preserving reciprocity and exhibiting k-gaps under periodic modulation.

Michaël Darche, Raphaël Assier, Sébastien Guenneau, Bruno Lombard, Marie Touboul2026-03-31🔢 math-ph

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