3383 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 introduces a family of generalized fidelities rooted in the Riemannian geometry of the Bures-Wasserstein manifold that unifies and extends standard quantum fidelities and Rényi divergences while establishing their key invariance properties, matrix characterizations, and Uhlmann-like theorems.
This paper investigates the rich dynamical structure of higher-order -th -family equations by proposing and computationally verifying conjectures regarding the existence of distinct -independent and -dependent peakon and pseudo-peakon solutions, thereby generalizing previous results and outlining future directions for rigorous proof and physical application.
This paper introduces a novel grading approach to simplify and systematize the construction of polynomial Poisson algebras associated with commutants in Lie algebra enveloping algebras, demonstrating its utility through detailed analyses of reduction chains and the classification of centralizers for classical series .
This paper investigates the spectral properties of the scalar Laplacian on -dimensional warped product manifolds with compact cross-sections, specifically analyzing both compact and non-compact cases with finite-volume cusps to derive the resolvent, scattering matrix, and heat kernel, while demonstrating that the asymptotics of the regularized heat trace involve global coefficients expressed via the zeta function of the cross-sectional manifold.
This paper develops a semiclassical technique to compute the form factors of composite branch-point twist operators in the 1+1 dimensional quantum sinh-Gordon model on multi-sheeted Riemann surfaces, addressing the challenge of identifying exact bootstrap solutions with specific local fields to facilitate the calculation of entanglement entropies.
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.