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.

🔬 applied physics

A Systematic Benchmark of Physics-Informed Neural Network Architectures for the Stiff Poisson-Nernst-Planck System: Adaptive LossWeighting and Multi-Scale Resolution

This paper presents a systematic, data-free benchmark of eleven Physics-Informed Neural Network architectures for the stiff Poisson-Nernst-Planck system, demonstrating that the Balanced Residual Decay Rate (BRDR) strategy offers an optimal balance between accuracy and computational efficiency compared to other methods, while providing an open-source implementation for future research.

David Pankaczy, Conrard Giresse Tetsassi Feugmo2026-06-04

🔢 mathematics

Spectrum of the Maxwell Equations for a Flat Interface between Non-Homogeneous Dispersive Media in 2D and 3D

This paper characterizes the spectrum of time-harmonic Maxwell equations for a flat interface separating two half-spaces filled with non-homogeneous, dispersive media by analyzing fundamental solutions and applying Floquet theory to distinguish between radiation modes away from and along the interface.

Tomáš Dohnal, Michael Plum, Karl M. Schmidt, Ian Wood2026-06-04

⚛️ high-energy theory

Multi-entropy in random tensor networks

This paper investigates Rényi multi-entropies in random tensor networks, proving that for $n=2$ these quantities are determined by minimal multiway cuts while demonstrating that this minimal cut conjecture generally fails for integer $n>2$ .

Miao Hu, Simon Lin, Ion Nechita2026-06-04

🔢 mathematics

A Thomson-type variational principle for diffusion coefficients

This paper introduces a new Thomson-type variational principle that characterizes the diffusion coefficient of reversible interacting particle systems as the supremum of a functional, offering a more natural framework for deriving lower bounds compared to the standard infimum formulation, and demonstrates its application to a kinetically constrained lattice gas.

Assaf Shapira2026-06-04

🔢 mathematics

On the Conicality of Causally Simple, Future Cohesive Spacetimes

This paper demonstrates that while neither homotopy to Minkowski space nor global hyperbolicity alone ensures conicality, causally simple, future cohesive spacetimes of dimension $1+N$ ( $N \geq 2$ )—including TIP spacetimes representing an observer's timelike past—do satisfy this property, thereby validating the conjecture for a physically relevant class of spacetimes.

Claudio F. Paganini2026-06-04

🔢 mathematics

Maximal Minimal Spacing for Random Points

This paper derives exact distributional identities and asymptotic behavior for the maximal minimal spacing between $M+1$ points selected from $N+1$ random points on a line by reformulating the problem as a threshold-resetting random walk, where the optimal spacing probability corresponds to the likelihood of completing at least $M$ reset cycles within $N$ steps.

Fabio Deelan Cunden, Noemi Cuppone, Giovanni Gramegna, Pierpaolo Vivo2026-06-04

🌀 nonlinear sciences

Novel periodic solutions and rogue waves of the defocusing scalar and coupled Ablowitz-Ladik systems on a nonzero background

This paper employs Hirota's bilinear method to derive novel time-periodic solutions, regular breathers, and rogue waves for both scalar and coupled defocusing Ablowitz-Ladik systems on a nonzero background, while also establishing the correspondence between Hirota's parameters and inverse scattering spectral parameters.

Francesco Coppini, Barbara Prinari2026-06-04

🔬 physics

The General Solutions of Linear ODE and Riccati Equation

This paper presents the general solutions for variable-coefficient linear ODEs and Riccati equations by utilizing convergent and reversible integral series E(X) and F(X), which serve as generalized forms of the exponential function.

Yimin Yan2026-06-03

⚛️ general relativity

Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints

This paper investigates apparent bifurcation phenomena, specifically the existence of multiple solutions with quadratic folds, in the conformal formulations of the Einstein constraint equations by applying modern bifurcation theory and numerical homotopy methods using the AUTO software to verify these findings.

M. Holst, V. Kungurtsev2026-06-03

🔢 mathematics

Central Limit Theorem for tensor products of free variables

This paper establishes a central limit theorem for tensor products of free variables, demonstrating that the limiting distribution is the semi-circle law for centered variables and a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws for non-centered variables.

Cécilia Lancien, Patrick Oliveira Santos, Pierre Youssef2026-06-03

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