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 establishes a unified contact Tulczyjew formalism on skew algebroids that intrinsically explains dissipative dynamics through a modified morphism and extends this framework to both continuous Euler-Lagrange-Herglotz equations and discrete contact variational integrators.
This paper resolves a problem posed by A. Agrachev regarding the minimum number of traversals required for a circle in to admit a deformation with a nondegenerate Frenet frame, revealing that the answer depends on the chosen topology and introducing decorated turn data to characterize accessibility via constant or time-dependent controls across various dimensions.
This paper introduces a weighted least action principle for the geometric optics limit of Maxwell equations that determines the complete bundle of Fresnel rays connecting two planes based on intensity measurements, thereby enabling the reconstruction of electromagnetic wave phases through reciprocity.
This paper reviews random matrix theory approaches to chaotic wave scattering and transport in open systems, emphasizing universal statistics and non-perturbative methods derived from effective non-Hermitian Hamiltonians to describe scattering matrices, time delays, and resonance phenomena.
This paper proposes a method to discriminate between different topological classes of many-body quantum states by expressing strange correlators as Kirkwood-Dirac quasiprobabilities, thereby establishing a quantum topology witness achievable through interferometric protocols involving sudden quench transformations.
This paper constructs a new three-spectral-parameter Yang-Baxter equation for the chiral Potts model by extending the unification of solvable edge and vertex models, thereby generalizing Onsager's star-triangle relation to account for the higher-genus curve structure and the specific interaction terms of symmetric systems.
This paper proposes a unified representation-level framework for equilibrium quantum many-body theory that characterizes different methods as encoders mapping admissible states to specific variables, thereby clarifying the conditions for exact reconstruction and unifying concepts like functionals, kernels, and quantum embedding through the analysis of state fibers and task-relevant information.
This paper develops the fundamental formulae of hyperspherical trigonometry in multidimensional Euclidean space using vector products to derive addition formulae for elliptic functions with two distinct moduli, and applies these results to establish a connection between the multidimensional Euler top and the Double Elliptic model.
This paper demonstrates that the time evolution of weakly interacting fermions in a cold gas, when viewed as perturbations of the Fermi ball, is effectively governed by a discrete quantum Boltzmann collision operator for the momentum distribution under conditions of small coupling and appropriate initial data.
This paper extends the rigorous derivation of quantum Boltzmann equations near a Bose-Einstein condensate by employing Bogoliubov rotations and Weyl transformations to derive renormalized Hartree-Fock-Bogoliubov equations, thereby significantly improving error bounds and extending the time of validity to .