3366 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 spectral triples for one- and two-qubit states to define Connes spectral distances, which are then used to propose new measures for quantum discord and coherence, revealing geometric structures such as the Pythagorean theorem in specific two-qubit cases.
This paper presents a minimal port-Hamiltonian formulation for interacting particle systems to analyze their stability and mean-field limits, while simultaneously issuing an erratum that corrects a previous claim regarding trajectory compactness by providing a counterexample for repulsive interactions and a revised proof for Hamiltonian gradient convergence.
This paper proves that the infinite system-size free energy of quantum -spin glasses in a transverse magnetic field converges to that of the quantum random energy model as , achieved by combining non-commutative analytical techniques with the geometry of extreme negative deviations in classical -spin glasses.
This paper classifies and analyzes exactly solvable one-dimensional complex Schrödinger operators related to the Gauss hypergeometric equation, organizing them into three geometric families (spherical, hyperbolic, and deSitterian) to compute their spectra and Green functions while establishing transmutation identities and linking them to symmetric manifolds.
This paper introduces spectral Barron spaces within the framework of quantum harmonic analysis, establishes their fundamental properties such as completeness and continuous embeddings, and applies these results to prove the existence and uniqueness of solutions for a Schrödinger-type equation.
This paper introduces a novel mechanism called exceptional-bound (EB) band engineering that enables system-size-controlled topological transitions in non-Hermitian systems through unique critical scaling near exceptional points, distinct from the non-Hermitian skin effect and applicable to diverse experimental platforms.
This paper introduces the instrumental group algebra (IGA) as a Banach algebra framework for sequential quantum measurements, demonstrating that the time-dependent Kraus-operator density (KOD) evolves via a classical Kolmogorov equation and that combining instruments corresponds to convolution within the IGA, thereby providing a unified mathematical structure for observables that cannot be measured by orthogonal projections.
This paper investigates the Cauchy problem for a nonlinear damped Schrödinger equation involving the Riemann zeta function, establishing the uniqueness of distributional solutions, proving the existence of global solutions via regularization and compactness arguments, and demonstrating that solutions in the one-dimensional case vanish in finite time.
This paper establishes the theoretical framework for solving axial symmetric Navier-Stokes equations in a cylindrical topology by constructing a complete basis of harmonic 1-forms comprising Beltrami, anti-Beltrami, and closed components, thereby reducing the problem to a hierarchy of quadratic relations suitable for future optimization via Physics-Informed Neural Networks.
This paper clarifies the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces used in Cartan Neural Networks by proving that only Kähler spaces support Gibbs distributions, explicitly characterizing their generalized temperature spaces via adjoint orbits, and demonstrating the equivalence between various information and thermodynamical geometries while establishing the covariance of these distributions under the full symmetry group.