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 demonstrates that in the large-party limit of topological entanglement entropy for Chern-Simons theory on torus link complements, non-Abelian contributions are suppressed, leaving an upper bound of determined solely by Abelian anyons, a result explicitly quantified for the SU(2) case.
This paper establishes a rigorous, algorithmic perturbative framework that creates a two-way correspondence between a continuous nonlinear Helmholtz system with high-contrast inclusions and a discrete nonlinear capacitance matrix, enabling the expansion of resonant frequencies and fields in powers of the contrast parameter to characterize solitons and symmetry-breaking bifurcations.
This paper derives an explicit, closed-form expression for the parametric number covariance of complex Ginibre matrices in symmetry class A, demonstrating its universality across various non-Hermitian ensembles and establishing a connection between these spectral correlations and the distribution of eigenvector non-orthogonality factors.
This paper presents a gauge-invariant generalization of the Proca equation by introducing an additional vector field, extending the results to the Yang-Mills-Proca equations to achieve non-Abelian gauge symmetry.
This paper extends the discrete slot decomposition framework of the Box-Ball System to a continuous setting by mapping piecewise constant functions to point configurations of solitons and demonstrating that, under specific product measure conditions with weights, this decomposition yields a Poisson process.
This paper extends the geometric electromagnetic particle-in-cell framework (GEMPICX) to solve quasineutral hybrid Vlasov-Maxwell equations with drift-kinetic electrons and fully kinetic ions by deriving a discrete action principle, employing a structure-preserving finite difference method on dual grids, and validating the resulting numerical model through dispersion relation analysis.
This paper presents a convergent binary tree expansion solution to Polchinski's equation for the Wilsonian effective action in fermionic field theories, establishing its validity through novel combinatorial estimates under conditions of finite determinant and decay constants for the fermionic covariance.
This paper presents a digital signal processing framework that adapts finite-impulse-response (FIR) filter design methods to optimize the beam pattern of the 32-m Ghana Radio Astronomy Observatory telescope, successfully suppressing sidelobes and cross-polar leakage to enhance its polarimetric precision and suitability for high-dynamic-range radio astronomy applications.
This paper establishes a Central Limit Theorem and Sanov's principle for the fluctuations of a Mixture of Experts generated by quantum neural networks trained via gradient flow, demonstrating that these fluctuations satisfy a linear transport equation while the network converges to a limit function governed by the neural tangent kernel.
This paper rigorously analyzes the geometric structures of pseudo-sonic curves in two-dimensional self-similar solutions of the Euler equations for potential flow, proving that these curves are necessarily circular arcs under specific conditions and establishing regularity for shock reflection-diffraction problems with non-uniform incoming flows.