2619 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 that the expected spectral measures of self-adjoint operators on infinite unimodular weighted graphs satisfy a logarithmic Hölder regularity estimate under natural geometric conditions, extending the classical Craig–Simon theorem beyond Euclidean lattices to diverse settings including group algebras, random operators, and quasi-transitive graphs.
This study reveals that while attractive interactions mediated by shell restructuring enable the formation of bound pairs, chains, and hexagonal clusters of bimerons and hopfions in chiral magnet thin films with a conical background, these systems ultimately fail to crystallize into stable lattices due to the progressive invasion of conical spiral or CF-1 phases into inter-soliton regions.
This paper establishes that multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium equations are the necessary and sufficient conditions for a magnetic field and metric to be stationary points of magnetic energy under constraints on pressure, relative helicity, and magnetic flux, while also introducing a new gauge condition, proving the gauge invariance of relative helicity, and identifying a sufficient condition for energy minimization in single-region cases.
This paper establishes an upper bound on the ground state energy of a dilute two-dimensional Fermi gas with repulsive short-range interactions, deriving a two-dimensional analogue of the Huang–Yang formula that captures the first three terms of the asymptotic expansion for small density and scattering length.
This paper investigates a nonlinear heat transfer equation in one, two, and three spatial dimensions by classifying its symmetries with respect to the thermal conductivity function, deriving recursion operators and infinite symmetry hierarchies for the one-dimensional case, and constructing exact solutions for all dimensions.
This paper utilizes the Kac-Rice formalism to derive the finite-size eigenvalue and eigenvector distributions for a Gaussian ensemble interpolating between non-Hermitian classes A and AI, revealing that while bulk and fixed-parameter edge behaviors follow standard laws, a specific scaling of the interpolation parameter uncovers a new universal transitional regime in the edge eigenvalue density.
This paper establishes that the category of -twisted representations of a conformal net with a discrete group action naturally forms a -crossed balanced -tensor category, thereby extending Müger's earlier results on -crossed braided tensor categories to the setting of not necessarily rational nets using localized endomorphisms.
This paper investigates the asymptotic behavior of complex - symbols, demonstrating that when their parameters scale according to the dihedral angles of a hyperideal hyperbolic tetrahedron, the symbols relate to the tetrahedron's volume and Gram matrix determinant, with potential implications for the complex Liouville string in specific cases.
This paper presents an exactly solvable five-parametric fermionic three-site Swanson-like model that elucidates the unitary evolution toward a triple exceptional point (EP3), explicitly characterizing the degeneracy and its unitary-accessible vicinity while distinguishing the true singularity from a nearby avoided false energy-level crossing.
This paper extends constructive quantum field theory techniques to analyze both ordinary and scalar cumulants of a simple matrix model in the bounded rank regime, providing results valid for arbitrarily large positive coupling through the application of a variational approach.