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

Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems

This paper establishes that in translation-covariant quasiperiodic systems, the infrared scaling of long-wavelength charge fluctuations is fundamentally governed by the irrationality measure of the system's frequencies, which dictates how efficiently the hull charge profile's weight is transferred to the infrared, thereby distinguishing the behavior of algebraic irrationals from exceptionally well-approximable transcendental numbers.

Junmo Jeon, Shiro Sakai2026-09-11

🔢 mathematics

Spectral properties of Random Matrices

This paper establishes the theoretical foundations of random matrix theory by utilizing the Stieltjes transform and Dyson equation methods to prove optimal convergence to the Marchenko-Pastur distribution, eigenvalue rigidity, and universal local laws for an interpolating random matrix model.

Anastasis Kafetzopoulos2026-09-11

🔢 mathematics

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

This paper establishes a generalized KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length that accommodates both classical smooth and highly irregular perturbations, yielding new spectral results such as purely absolutely continuous spectrum and $1/2$ -Hölder continuity of the integrated density of states for associated quasiperiodic Schrödinger operators.

Xueyin Wang, Jiangong You2026-09-11

🔢 mathematics

The Quantum Composition Paradox

This paper investigates the "Quantum Composition Paradox," demonstrating that while certain unitary operations (specifically phase-dressed permutations) allow probability laws to be consistently composed across time, most quantum sequences fail to maintain this genealogy after internal restarts, a phenomenon the author links to a new framework for quantum music theory where predicting musical transitions is proven to be PromiseBQP-complete.

Jacob Biamonte2026-09-11

🔢 mathematics

Diffeomorphism Invariance of the Favre-Filtered Compressible Navier--Stokes System under Spacetime Dilation

This paper proves that the Favre-filtered compressible Navier–Stokes system with subgrid-scale closure terms is diffeomorphism-invariant under spacetime dilation, demonstrating that the equations in scaled coordinates are obtained via a smooth diffeomorphism that preserves the solution set and establishes a canonical isomorphism between the solution spaces for all dilation parameters.

Yuanya Li2026-09-11

🔢 mathematics

Fourier decay of Gaussian multiplicative chaos and boundary geometry

This paper introduces a new approach to determine the Fourier dimension and decay rates of Gaussian multiplicative chaos on tori and bounded sets, demonstrating how boundary geometry and multifractal concentration jointly govern these properties and providing a simplified proof of the Garban-Vargas conjecture in the circle setting.

Marcu-Antone Orsoni, William Verreault2026-09-11

🔢 mathematics

Moduli spaces of geometric functorial field theories

This paper develops a framework for computing moduli spaces of geometric functorial field theories by defining Cartesian realizations of geometric structures as equivariant simplicial presheaves, thereby presenting these moduli spaces as mapping spaces between such presheaves.

Jacek Kenig, Dmitri Pavlov2026-09-11

🔢 mathematics

Mathematical inverse problem for the world data inference of the parton distribution functions of the proton

This paper proposes a novel, model-bias-free methodology for extracting proton parton distribution functions by reformulating the global analysis of deep inelastic scattering data as a linear tensor reconstruction inverse problem, thereby replacing traditional parameter fitting with the direct solution of coupled linear integral equations derived from perturbative QCD.

Henri Hänninen2026-09-11

🌀 nonlinear sciences

Block regularisation of the logarithm central problem

This paper proves that the logarithm central force problem in $\mathbb{R}^2$ , where the logarithm serves as the gravitational potential, is block regularizable, allowing its flow to be continuously extended over the singularity at the origin through appropriate re-parametrization.

Archishman Saha, Cristina Stoica2026-09-10

🔢 mathematics

Legendre Transformation under Micro Canonical Ensemble

This paper leverages the dimensionless nature and symmetry of the Legendre transformation to derive characteristic functions, partition functions, and thermodynamic formulas for various statistical ensembles, thereby clarifying the fundamental interrelations between the microcanonical ensemble and other ensembles.

Jingxu Wu, Chenjia Li, Zhenzhou Lei, Tuerdi Wumaier, Congyu Li, Yan Wang, Zekun Wang2026-09-10

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