1668 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 utilizes the Schwarz and Jensen inequalities to derive and analyze generalized uncertainty relations for multiple non-commuting observables, demonstrating how these relations can be equivalently expressed through quantum Pearson correlation coefficients to characterize state-dependent correlations.
This paper introduces a quasi-orthogonal geometric framework for stabilizer codes that relaxes strict orthogonality constraints to enable more flexible and resource-efficient designs, demonstrating significant improvements in logical error rates and code performance under depolarizing noise compared to traditional orthogonal counterparts.
This paper provides a concise didactical introduction to quantum graphs as Schrödinger Hamiltonians on metric graphs, focusing on their role in quantum chaos and spectral theory while summarizing seminal results and recent developments in periodic orbit theory.
This paper introduces generalised (bi-)Hamiltonian structures for evolutionary partial differential equations, characterising their hydrodynamic type via geometric data and establishing their association with (bi-)flat F-manifolds and compatibility with principal hierarchies.
This paper presents a variationally consistent mesoscopic extension of Cosserat elasticity that treats torsion and curvature as independent distributed defect measures, utilizing a Palatini-type approach to unify defect kinematics, configurational forces, and microstructural evolution through a geometric framework grounded in material invariance and Bianchi identities.
This paper establishes a direct link between flat connections and higher complex structures by analyzing -parabolic connections with rank-at-most-1 curvature, demonstrating how infinitesimal gauge transformations of the line subbundle realize infinitesimal higher diffeomorphisms and connecting these constructions to Toda integrable systems.
This paper identifies a distinct class of non-eigenstates where the lower bounds of both product and sum uncertainty relations vanish due to zero correlation, thereby revealing a dual nature of the uncertainty principle as both a lower bound on standard deviations and an upper bound on the correlation function.
This paper mathematically justifies the physical view of the Toda lattice at thermal equilibrium as a dense collection of soliton-like quasiparticles by rigorously defining their locations, approximating local charges and currents, and proving an asymptotic scattering relation based on the spectral properties of the system's random Lax matrix.
This paper classifies positive traces on the Coulomb branch algebras of specific three-dimensional and four-dimensional gauge theories, focusing on quantizations of type Kleinian singularities and algebras associated with pure and gauge theories.
This paper establishes that shock formation in general first-order strictly hyperbolic systems in one spatial dimension is locally self-similar and universal, mirroring the behavior of the inviscid Burgers' equation, and derives an analytical formula for this universal solution.