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.

Edge Universality for Inhomogeneous Random Matrices II: Markov Chain Comparison and Critical Statistics

This paper extends edge universality results for inhomogeneous random matrices to subcritical and critical sparsity regimes by establishing new Markov chain comparison conditions that link universal edge statistics to the comparability of underlying variance-profile Markov chains, thereby enabling the analysis of diverse models like random band and Hankel matrices beyond classical random matrix theory.

Dang-Zheng Liu, Guangyi Zou2026-04-23🔢 math-ph

On integrable by Euler planar differential systems

This paper discusses the theory of integrable planar differential systems by examining the foundational work presented in Euler's classical textbooks, *Institutiones Calculi Differentialis* and *Institutiones Calculi Integralis*.

A. V. Tsiganov2026-04-23🌀 nlin

Direct construction of scalar quantum fields by L{é}vy fields -- nontrivial exact Wightman fields in a wider field with a relaxed Gårding-Wightman Axioms-

This paper presents a construction of exact relativistic scalar quantum fields in arbitrary space-time dimensions using Lévy random fields and stochastic calculus, initially satisfying a relaxed version of the Gårding-Wightman axioms where field operators are symmetric, and subsequently demonstrating how to derive non-trivial exact Wightman fields that fully satisfy all axioms by restricting to appropriate subspaces of the physical Hilbert space.

Sergio Albeverio, Suji Kawasaki, Yumi Yahagi, Minoru W. Yoshida2026-04-23🔢 math-ph

Generalised Langevin Dynamics: Significance and Limitations of the Projection Operator Formalism

This paper rigorously analyzes the mathematical foundations of the Mori-Zwanzig projection operator formalism, demonstrating that while Mori's generalized Langevin equation is well-posed via semigroup theory and Volterra equations, Zwanzig's formulation faces unresolved existence issues for unbounded perturbations, and clarifying that the resulting memory term is fundamentally a coupling mechanism that can vanish under specific spectral projections rather than necessarily representing temporal memory.

Christoph Widder, Tanja Schilling2026-04-23🔢 math-ph

Native quantum games from interacting discrete-time quantum walks

This paper introduces a framework for "native" quantum games where strategic interaction and Nash equilibria emerge intrinsically from the unitary dynamics of coupled discrete-time quantum walks, demonstrating that stable strategy profiles arise specifically from interaction-induced interference rather than external mathematical imposition.

Rashid Ahmad2026-04-23🔢 math-ph

Superintegrable 2D systems in magnetic fields with a parabolic type integral

This paper investigates two-dimensional superintegrable systems with quadratic integrals of motion in magnetic fields by analyzing cases with parabolic-type integrals and concludes that, on the Euclidean plane, the only such system is the one characterized by a constant magnetic field and a constant electrostatic potential.

Tatiana Ekelchik, Antonella Marchesiello2026-04-23🔢 math-ph

Macroscopic loops in the random loop model on sparse random graphs

This paper establishes the existence of macroscopic loops in the random loop model with crosses and bars on sparse random graphs by developing a deterministic drift method that yields averaged lower bounds for macroscopic loop probabilities when edge density exceeds a specific threshold, with these results strengthened to pointwise bounds for integer loop weights via trace representation.

Andreas Klippel2026-04-23🔢 math-ph

A semiclassical approach to spectral estimates for random Landau Schrodinger operators

This paper establishes semiclassical Wegner and Minami estimates for random Landau Schrödinger operators on $L^2(\mathbb{R}^2)$ with bounded random potentials by employing semiclassical pseudodifferential calculus and the Grushin method to reduce the problem to an effective Hamiltonian on $L^2(\mathbb{R})$ .

D. Borthwick, S. Eswarathasan, P. D. Hislop2026-04-23🔢 math-ph

The Tentacles Landscape

This paper rigorously proves that the basins of attraction for identical oscillators on a ring coupled by any smooth, strictly increasing odd function exhibit an "octopus-like" geometry with volume scaling as $e^{-kq^2}$ and concentrated in filamentary tentacles, thereby validating the conjecture previously supported only by unreliable high-dimensional simulations.

Pablo Groisman2026-04-23🔢 math-ph

The Ising Model on a Two-Community Stochastic Block Model

This paper provides a complete characterization of the phase diagram for the Ising model on a two-community stochastic block model, detailing the almost sure uniqueness/non-uniqueness phase transition, the convergence of magnetization to specific Dirac mixtures in the supercritical regime, and the distinct fluctuation behaviors (Gaussian vs. non-Gaussian) in the subcritical and critical regions.

Alessandra Bianchi, Vanessa Jacquier, Matteo Sfragara2026-04-23🔢 math-ph

← Previous Next →