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.

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🔢 math-ph

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🔢 math-ph

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🔢 math-ph

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🔢 math-ph

Lissajous coherent states via projection

This paper constructs stationary coherent states concentrated on Lissajous figures for isotropic and anisotropic harmonic oscillators by projecting products of ordinary coherent states onto degenerate subspaces, thereby clarifying phase singularities, linking probability current laminar flow to quantum interference, and providing a rigorous definition of vortex states that resolves to known SU(2) coherent states in the isotropic limit.

Errico J. Russo, James Schneeloch, Edwin E. Hach, Richard J. Birrittella, Wanda Vargas, Christopher C. Gerry2026-03-03🔢 math-ph

Unbounded length minimal synchronizing words for quantum channels over qutrits

This paper extends previous findings on qutrit quantum channels by demonstrating the existence of channels with arbitrarily long minimal synchronizing words, thereby contrasting with the bounds suggested by Černý's conjecture for finite automata.

Bjørn Kjos-Hanssen, Swarnalakshmi Lakshmanan2026-03-03🔢 math-ph

Solutions to autonomous partial difference equations via the third and sixth Painlevé equations and the Garnier system in two variables

This paper demonstrates that integrable autonomous partial difference equations admit special solutions governed by non-autonomous ordinary difference equations derived from the Bäcklund transformations of the third and sixth Painlevé equations and the Garnier system in two variables.

Nobutaka Nakazono2026-03-03🌀 nlin

Multipartite parity bounds and total correlation

This paper establishes that the expectation of multipartite observables formed from sums of local self-adjoint contractions exceeds the product state threshold only when accompanied by a quantifiable amount of total correlation, a relationship derived from the parity structure of the observable's square and bounded by pairwise defect weights.

James Tian2026-03-03🔢 math-ph

Color symmetry in the Potts spin glass at high temperature

This paper demonstrates that color symmetry is preserved at high temperatures in the Potts spin glass model with three or more colors using the second moment method, while also proving that unbalanced configurations are exponentially rare for the two-color case at all temperatures due to gauge symmetry.

Heejune Kim2026-03-03🔢 math-ph

A Leibniz rule of distributional pairing and hyperforce sum rule

This paper reformulates and generalizes the equilibrium hyperforce sum rule and the BBGKY hierarchy for both Euclidean and periodic systems by demonstrating that they can be derived from the Leibniz rule applied to the pairing of tempered distributions and Schwartz functions.

Takashi Maruyama, Tatsuki Seto, Viktor Zaverkin, Henrik Christiansen2026-03-03🔢 math-ph

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