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.

🌀 nonlinear sciences

Two-dimensional nonlinear Schrödinger equations with potential and dispersion given by arbitrary functions: Reductions and exact solutions

This paper investigates a generalized two-dimensional nonlinear Schrödinger equation with arbitrary potential and dispersion functions, deriving various dimensional reductions and presenting numerous new exact solutions through methods like functional separation of variables and structural analogy to serve as benchmarks for numerical and analytical verification.

Andrei D. Polyanin2026-03-03

🔢 mathematics

Finding Graph Isomorphisms in Heated Spaces in Almost No Time

This paper introduces a novel, verified algorithm that leverages spectral graph theory and vertex curvatures to efficiently and accurately determine graph isomorphism in polynomial time, successfully resolving challenging instances that defeat classical spectral techniques.

Sara Najem, Amer E. Mouawad2026-03-03

🔢 mathematics

Complete asymptotics in the formation of quiescent big bang singularities

This paper unifies three major categories of mathematical results on quiescent big bang singularities by demonstrating that solutions satisfying recent general conditions for big bang formation indeed induce well-defined initial data on the singularity, thereby bridging the gap between stable formation proofs and geometric data construction.

Andrés Franco-Grisales, Hans Ringström2026-03-03

🔢 mathematics

Convergent Twist Deformations

This paper establishes a functorial framework ensuring the convergence, continuity, and holomorphic dependence of Drinfeld's Universal Deformation Formula on spaces of analytic vectors by matching series order with equicontinuity conditions, thereby affirmatively resolving Giaquinto and Zhang's question regarding the existence of strict versions for their explicit twists.

Chiara Esposito, Michael Heins, Stefan Waldmann2026-03-03

🔢 mathematics

Dynamic Level Sets

This paper introduces and analyzes the novel mathematical concept of "dynamic level sets," which arises from a 2012 Turing incomputability study and relies on the Principle of Self-Modifiability to explain how physical reconfiguration via incomputable processes can generate computational behaviors distinct from standard dynamical systems and probabilistic Turing machines.

Michael Stephen Fiske2026-03-03

🔢 mathematics

Remling's Theorem for vector-valued discrete Schrodinger operators

This paper extends Remling's Theorem to vector-valued discrete Schrödinger operators by demonstrating that the $\omega$ -limit points of their matrix potentials are reflectionless on the absolutely continuous spectrum with full multiplicity under the shift map.

Keshav Raj Acharya2026-03-03

🔢 mathematics

Hankel Determinant for a Perturbed Laguerre Weight with Pole Singularities and Generalized Painlevé III' Equation

This paper investigates the Hankel determinant associated with a perturbed Laguerre weight featuring pole singularities of order up to two, deriving a system of difference equations for recurrence coefficients and establishing coupled partial differential equations that reduce to generalized Painlevé III' equations, while also extending the analysis to higher-order pole perturbations.

Shulin Lyu, Yuanfei Lyu2026-03-03

🔢 mathematics

Axiomatic Foundation of Quantum-Inspired Distance Metrics

This paper establishes a rigorous axiomatic framework that identifies the Fubini-Study metric as the unique canonical distance on projective Hilbert spaces and unifies various quantum information measures through principles of invariance, sensitivity, and contextuality.

Maryam Bagherian2026-03-03

🔢 mathematics

Generalized Bopp shift, Darboux Canonicalization, and the Kinematical Inequivalence of NCQM and QM

This paper demonstrates that while generalized Bopp shifts and Darboux canonicalizations provide linear transformations between noncommutative and ordinary quantum mechanical operators, they do not establish unitary equivalence between the two theories because they correspond to distinct irreducible representations of the underlying nilpotent Lie group $G_{\hbox{\tiny{NC}}}$ that cannot be mapped to one another.

S. Hasibul Hassan Chowdhury2026-03-03

🔢 mathematics

Nonlocal convolution type functionals and related Orlicz spaces

This paper introduces and analyzes the fundamental properties of Banach and separable Orlicz-type spaces defined by nonlocal convolution integral functionals, including the characterization of their duals and illustrative examples.

Denis Borisov, Andrey Piatnitski2026-03-03

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