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.

Entropic Collapse and Extreme First-Passage Times in Discrete Ballistic Transport

This paper investigates extreme first-passage statistics of random walkers on discrete hierarchical networks, identifying a unique class of non-classical distributions characterized by a strict lower time bound in source-trap-dominated geometries and explaining the mechanism of "entropic collapse" that destroys this scaling in bulk-dominated structures, thereby establishing a geometry-encoding function to diagnose network hierarchy.

Bhargav R. Karamched2026-05-15🔢 math-ph

How opinions shape epidemics: a graphon-based kinetic approach

This paper proposes a graphon-based kinetic framework that models the coupled dynamics of opinion formation, physical contact patterns, and disease transmission to reveal how shaping population opinions can effectively control epidemic spread.

Abu Safyan Ali, Elisa Calzola, Giacomo Dimarco, Lorenzo Pareschi, Thomas Rey2026-05-15🔢 math-ph

Nonlinear Multiphysics Modeling of Batch Digester Discharge Dynamics with Rheology-Driven Hydraulic Transport and Drainability Coupling

This paper presents a nonlinear dynamic model and a robust Sliding Mode Control strategy to regulate discharge flow in industrial batch digesters by accounting for evolving slurry rheology, consistency-dependent hydraulic resistance, and complex drainability phenomena.

José M. Campos-Salazar2026-05-15🔢 math-ph

Integral representation of time-harmonic solutions to Maxwell's equations with fast numerical convergence

This paper constructs integral representations for time-harmonic solutions to Maxwell's equations and Helmholtz-type equations that utilize assignable distributions to enable exponentially fast numerical convergence via trapezoidal rules, facilitating the approximation of complex wave phenomena such as constructive interference in icosahedral structures.

Kalpesh Jaykar, Richard D. James2026-05-15🔬 physics.optics

Geometric construction of superintegrable Poisson projection chains via Poisson centralizers

This paper introduces a geometric framework for constructing superintegrable systems by utilizing Poisson centralizers within the Lie-Poisson algebra of a complex semisimple Lie algebra, demonstrating how chains of reductive subgroups and their invariant subalgebras generate superintegrable Poisson projection chains with explicitly computed dimensions and symplectic structures.

Kai Jiang, Guorui Ma, Ian Marquette, Junze Zhang, Yao-Zhong Zhang2026-05-15🔢 math-ph

Topics in Gaussian Wiener chaos expansion

These lecture notes for the 44th Finnish Summer School on Probability and Statistics provide an introduction to finite-dimensional Wiener chaos decomposition, the construction of Gaussian fields on the torus (including white noise and the Gaussian free field), and applications to the $\Phi^4$ model, while explicitly excluding topics such as stochastic integration, stochastic PDEs, and Malliavin calculus.

Nils Berglund2026-05-15🔢 math-ph

Lower bound on the mixing time of $p$ -spin glasses

The paper demonstrates that Glauber dynamics for $p$ -spin glasses exhibit exponentially slow mixing at inverse temperatures exceeding a constant times $\ln(p)/p$ for large $p$ , a result established by analyzing the energy landscape via Gaussian decompositions to prove a bottleneck bound.

Anouar Kouraich, Simone Warzel2026-05-15🔢 math-ph

Weakly nonlinear analysis of Hopf bifurcations in the elastohydrodynamics of Cosserat rods

This paper derives a Stuart-Landau amplitude equation via weakly nonlinear analysis to analytically describe the supercritical Hopf bifurcation and the resulting stable limit-cycle oscillations of a Cosserat rod in a viscous fluid under a terminal follower force.

Mohamed Warda2026-05-15🔢 math-ph

On the catastrophe time of fluids under the action of a gravitational field

This paper investigates Burgers-type fluid dynamics under gravitational fields by deriving perturbative expressions for the catastrophe time in both Newtonian and Schwarzschild spacetimes, demonstrating that the validity of the expansion is governed by a specific dimensionless parameter rather than local gravitational acceleration alone.

D. Astesiano, G. Ortenzi, M. L. Ruggiero2026-05-15🔢 math-ph

Noether symmetries and conservation laws of a class of time-dependent multidimensional nonlinear wave equations

This paper derives conservation laws for time-dependent damped nonlinear multidimensional wave equations using Noether's theorem, identifying that while arbitrary damping and nonlinearity yield Euclidean symmetries producing linear and angular momentum conservation, specific forms of these terms enlarge the symmetry algebra to a subalgebra of the conformal group, resulting in additional conserved quantities.

F. Güngör, C. Özemir2026-05-15🔢 math-ph

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