2548 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 integrable aspects of a generalized non-linear fluid equation relevant to optical fibers and plasmas by deriving diverse solitary wave solutions, performing bifurcation and stability analyses, and validating the findings through computational simulations to establish a robust framework for understanding energy propagation in anisotropic dispersive media.
This paper presents a constructive algorithm for obtaining a Kraus decomposition of completely positive operators on infinite-dimensional Hilbert spaces by iteratively generating operators with increasing zero entries, thereby ensuring strong-operator convergence and improving upon standard nonconstructive proofs through practical process tomography.
This paper investigates the extra structure on categories of topological defects in reflection positive topological field theories, demonstrating that in two dimensions, the associated bicategory of defects naturally forms an -dagger bicategory which, under reflection positivity, acquires structure closely related to 3-Hilbert spaces.
This paper establishes a Landis-type unique continuation theorem at infinity for solutions to the Schrödinger equation with radially growing potentials, proving that solutions decaying faster than an explicitly computable threshold must vanish identically.
This paper analytically demonstrates that the conformal dimensions of fields in the Ising model coupled to two-dimensional causal dynamical triangulations align with those on a fixed lattice, contrasting with Liouville gravity predictions by utilizing lattice methods and an adapted Duplantier-Sheffield framework.
This paper establishes operator-norm bounds and essential self-adjointness for discrete Hodge Laplacians on weighted flag simplicial complexes without requiring geometric completeness or curvature assumptions, demonstrating that the bound is sharp for unweighted -regular bipartite graphs while providing exact norms for standard periodic lattices via Floquet–Bloch analysis.
This paper employs the gauge PDE approach and introduces a novel concept of -boundary to systematically construct a recursive boundary calculus that derives explicit equations, including higher-order conformal Yang-Mills and obstruction equations, for gauge fields on asymptotically AdS spaces by treating the boundary-defining function as a dynamical field.
This paper establishes that for any odd dimension , the spherically symmetric Yang-Mills equations in dimensions possess exactly three smooth self-similar solutions, two of which admit closed-form expressions, suggesting a rigid and simple landscape for high-dimensional blowup scenarios.
This paper proves general cases of the Hall-Ho heat flow conjecture for random matrices, demonstrating that the empirical measure of the zeros of the heat-flow-evolved characteristic polynomial of a complex Ginibre matrix converges almost surely to the semicircle law.
This paper derives and validates exact, reflectionless transparent boundary conditions for the spatially discrete Schrödinger equation in 1D lattices by utilizing Laplace transforms to obtain Bessel-function-based Dirichlet-to-Neumann maps, which are shown to be consistent with the continuum limit and effectively eliminate spurious backscattering in numerical simulations.