2619 papers
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.
This paper demonstrates that, unlike their bosonic counterparts which vanish, static fermionic tidal Love numbers are non-zero for non-extremal Reissner-Nordström black holes, highlighting a universal distinction in how black holes respond to fermionic versus bosonic tidal perturbations.
This paper investigates the spectral properties of generators for non-local Dirichlet forms on ultrametric path spaces of Bratteli diagrams and establishes a cohomological Dirichlet principle guaranteeing unique energy-minimizing representatives for cohomology classes when the parameter exceeds a sharp bound determined by the diagram's structure and the measure-theoretic entropy of the associated Gibbs measure.
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.
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.
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.
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.
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.
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 model, while explicitly excluding topics such as stochastic integration, stochastic PDEs, and Malliavin calculus.
The paper demonstrates that Glauber dynamics for -spin glasses exhibit exponentially slow mixing at inverse temperatures exceeding a constant times for large , a result established by analyzing the energy landscape via Gaussian decompositions to prove a bottleneck bound.
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.