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 establishes the existence and uniqueness of harmonic balls on Liouville quantum gravity surfaces via the Hele-Shaw flow obstacle problem, characterizes their geometric properties as distinct from Lipschitz and metric balls with Jordan curve boundaries, and conjectures their role as the scaling limit of internal diffusion limited aggregation on random planar maps.
This paper establishes a shape theorem demonstrating that internal diffusion limited aggregation and the divisible sandpile on mated-CRT maps converge to an LQG harmonic ball, a limit object previously constructed by the authors.
This paper establishes a simplified bijection between finite-dimensional graded irreducible representations of Lie colour algebras and Lie superalgebras by iteratively applying the loop module construction to cyclic groups of prime order, while demonstrating that Lie colour algebras retain distinct representation theory through applications to quantum mechanics and specific algebraic structures.
This paper establishes that random walks on a broad class of deterministic tilings in arbitrary dimensions, including Delaunay triangulations and sphere packings, converge to Brownian motion modulo time parameterization under mild regularity conditions, while also providing quantitative convergence bounds for finite volume schemes and a simplified proof for the two-dimensional case.
This paper investigates the Type D asymmetric simple exclusion process (ASEP) through both probabilistic stochastic fusion and algebraic crystal base methods, revealing that unlike the Type A case, these two approaches yield distinct generator matrices and thus demonstrate that the established equivalence between stochastic fusion and ground state transformations does not generalize to all finite-dimensional simple Lie algebras.
This paper investigates a non-factorizable spherical analogue of the linear quantum harmonic oscillator, specifically computing its spectrum and partition function in the critical two-dimensional case due to its potential relevance to chiral models in 2D quantum field theory.
This paper proposes the Fiedler Gradient Iterative Attack (FGIA) algorithm, which leverages Laplacian spectral perturbation and Fiedler vector gradients to efficiently identify and remove critical edges, thereby maximizing the degradation of network synchronization while preserving global connectivity.
This paper serves as a comprehensive introduction to measure theory, integration, and function spaces, bridging basic motivations from discrete probability with standard theoretical developments and concluding with advanced applications in both discrete and continuous probability.
This paper investigates the Dirac oscillator in one, two, and three spatial dimensions, demonstrating that its ladder operators realize specific -graded colour Lie superalgebras linked to parastatistics, which provide a powerful framework for analyzing the system's eigenspaces.
This paper establishes a comprehensive framework for non-asymptotic efficient entanglement manipulation by analyzing the properties of computational one-shot distillable entanglement and cost under various operations, deriving continuity bounds and separations from information-theoretic measures, and ultimately formulating a "Second Law of Efficient Entanglement Manipulation."