3366 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 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.
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.
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.
This paper demonstrates through a counting argument that translation symmetry enforces long-range entanglement in mixed states, specifically showing that the strong-to-weak spontaneous symmetry breaking fixed point cannot be represented as a mixture of short-range entangled states despite the existence of symmetric short-range entangled eigenstates.