2563 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 investigates the topological dynamics of pullback maps on full shifts over groups, establishing a sharp dichotomy between equicontinuity and cofinite sensitivity based on the periodicity of group elements under the inducing endomorphism, while also characterizing measure-theoretic properties like Bernoulli preservation and strong mixing.
This paper proposes a high-accuracy semi-analytical method based on cylindrical harmonic expansions and Graf's addition theorem to solve the two-dimensional electromagnetic wave scattering problem for arbitrary ensembles of parallel circular cylinders, enabling numerically verified solutions with controlled precision even for densely packed subwavelength configurations.
This paper constructs non-smooth, finite-time blowup Leray-Hopf solutions to the incompressible Navier-Stokes equations on a periodic 3D torus driven by turbulent fluctuations, while demonstrating that the mean value of such weak solutions corresponds to a smooth solution.
This paper utilizes the representation theory of Cherednik algebras to derive various generalizations of integrable spin Calogero-Moser systems with non-symmetric potential singularities, originally introduced by Chalykh, Goncharenko, and Veselov in 1999.
This paper proposes and analyzes generalized MICZ-Kepler systems on three-dimensional spheres and two-sheet hyperboloids, deriving their energy spectra and wave functions to demonstrate that these systems are minimally superintegrable.
This paper constructs a partially integrable Kuramoto model on a random graph of specific network motifs and demonstrates its partial integration by deriving conserved quantities and an operator-theoretic Watanabe-Strogatz transformation using Koopman theory, Magnus expansion, and the Baker-Campbell-Hausdorff formula.
This paper establishes the finite-band universality and exterior asymptotics of high-order Heun operators by deriving a determinant representation for their spectral polynomials, proving that the weak limits of their roots depend solely on the leading coefficient, and providing explicit Picard–Fuchs equations and a mother-body conjecture for the resulting spectral measures.
This paper proposes a robust optical design and tolerancing framework that utilizes autodiff-based Hessian spectral analysis to reveal performance degradation mechanisms, derive a scalar robustness metric, and generate deterministic tolerance budgets, thereby replacing costly Monte Carlo sampling with efficient eigenmode decomposition.
This paper resolves the two-boost problem for the rotating Kepler problem by extending Lagrangian Rabinowitz Floer homology to a broader class of settings and successfully computing the corresponding homology despite the challenges posed by the non-compactness of the energy hypersurface near collision and infinity.
This paper establishes refined spectral asymptotics for the curl operator on a closed Riemannian 3-manifold by deriving explicit formulae for the first six global and local Weyl coefficients, proving the holomorphy of the eta function in the half-plane , and improving Bär's counting function remainder to under specific geodesic flow assumptions.