2669 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 investigates the probability distribution of stabilizer Rényi entropies for Haar-random quantum states, revealing that the density of non-stabilizerness exhibits Van Hove-like singularities, specifically a logarithmic divergence at -magic states for single qubits, which disappears in higher dimensions and is linked to the partial incompatibility of quantum measurements.
This paper investigates the spectral properties of Sturm-Liouville problems on graphs with Robin-Kirchhoff boundary conditions by analyzing eigenvalue asymptotics and establishing a method to recover the Robin coefficients from the graph's structure and a subset of eigenvalues.
This paper introduces the concept of "Painlevé solitons" as waves resulting from the interaction between Painlevé waves and solitons, and explicitly constructs extended Painlevé II and IV solitons for the KdV and Boussinesq equations using a novel symmetry decomposition method aided by nonlocal residual symmetries.
This paper presents a quantum framework, based on an entropy penalisation method, that efficiently extracts viscosity solutions to nonlinear Hamilton-Jacobi equations with convex Hamiltonians by reformulating them into linear dynamics suitable for quantum simulation, thereby overcoming the typical obstacles of nonlinearity and long-time evolution in quantum PDE algorithms.
This paper analyzes the inelastic collapse of four one-dimensional particles by introducing a piecewise projective -to- mapping that enables the rigorous discovery of new stable periodic and quasi-periodic orbits, extending known results on collision orders and stability bounds for the system.
This paper resolves the extension of the Glazman–Harel–Zelesko theorem for planar site percolation under a countability hypothesis on end-equivalence classes while constructing a counterexample to the Benjamini–Schramm conjecture by demonstrating that planar graphs with minimum degree at least 7 can exhibit a uniqueness threshold strictly below .
This paper establishes a general substitution principle for self-avoiding walks on infinite cubic graphs, demonstrating that replacing vertices with symmetric three-port gadgets creates a functional relationship between the connective constants of the original and transformed graphs while preserving critical exponents, thereby enabling the exact calculation of connective constants for new infinite families of graphs.
This paper presents a comprehensive computational and experimental study of matrix permanents across various ensembles, utilizing GPU acceleration to verify distributional properties (such as Gaussian, -stable, and lognormal behaviors) for random matrices and to derive universal scaling laws for permanents along geodesics on the unitary group.
This paper extends Frenkel's integral formula for traces of operators to the operators themselves, establishing a generalized formula applicable to bounded self-adjoint positive operators and compact positive operators within the -Schatten class.
This paper investigates phase transitions, non-extremality (reconstruction), and Markov entropy rates for the mixed spin- Ising model on a Cayley tree of order three by analyzing the stability of a high-dimensional dynamical system, applying spectral reconstruction tests consistent with the Kesten–Stigum condition, and deriving closed-form entropy rate expressions for arbitrary spin .