3210 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 constructs explicit generators for the Cartan centralisers of rank-three Lie algebras , , and , analyzes the inclusion relations of their associated polynomial Poisson algebras, and utilizes these structures to derive algebraic superintegrable systems for specific reduction chains.
This paper presents a multi-variable quantum algorithm that efficiently computes the gradient of a logarithm-determinant and the pseudo-inverse of sparse operators with super-linear convergence, offering significant speedups over classical methods for applications in statistical physics, quantum field theory, and kernel-based quantum machine learning.
This paper provides a complete characterization of the ground state manifold of the flat band interacting Hamiltonian for magic angle twisted bilayer graphene, proving that it consists precisely of the linear span of ferromagnetic Slater determinants.
This paper proposes a method to quantify the Gibbs measure of disordered crystals up to the melting point by demonstrating that the crystal lattice can be uniquely reconstructed from the statistics of Voronoi cells, specifically utilizing four persistent facets that survive thermal fluctuations as a fundamental signature of the solid phase.
This paper introduces a surface observable in nonabelian four-dimensional theory with a cosmological term to generate new 2-knot invariants and, via BV pushforward, induces electric observables in nonabelian Yang-Mills theory that realize 't Hooft operators, with applications also discussed for self-dual Yang-Mills theory.
This paper introduces the synchronization zeta function for pairs of self-maps on topological spaces, deriving explicit growth formulas for synchronization points on compact Abelian groups, establishing Gauss congruences and asymptotic behaviors under rationality assumptions, and exploring connections to topological entropy.
This paper establishes the stability of thermal equilibrium states in infinite fermionic lattice systems under extensive perturbations by demonstrating that exponential decay of correlations and local indistinguishability in the unperturbed state lead to stretched-exponential decay in the perturbed state, utilizing Quantum Belief Propagation and Lieb-Robinson bounds to close the cycle of implications between correlation decay, local perturbation principles, and local indistinguishability.
This paper utilizes the Gross-Pitaevskii equation to analyze the wave dynamics of superfluid dam breaks in Bose-Einstein condensates, revealing that perturbative regimes produce quantum undular bores with Airy-function profiles analogous to double rainbows and Alexander's dark band, while non-perturbative regimes can generate self-induced sonic event horizons.
This paper provides a global-in-time justification of the Marchioro-Pulvirenti vortex-wave system as the inviscid limit of the two-dimensional Navier-Stokes equations for initial data comprising a point vortex and a smooth background, by establishing quantitative convergence estimates for both the regular and concentrated vorticity components on any prescribed finite time interval.
This paper introduces a finite-plane diagnostic using Cauchy kernels and Pick matrices to probe Hermitian matrix models, demonstrating how "dressed saddles" impose transverse constraints on moment-space loci and enable the reconstruction of filling-fraction manifolds through enhanced spectral susceptibilities, thereby clarifying how local consistency conditions constrain low moments prior to global equilibrium selection.