1605 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 utilizes the path integral formalism and an approximation for the centrifugal term to derive the energy spectrum and wave functions for a linear combination of Yukawa and four-parameter diatomic potentials, subsequently using these results to calculate the system's partition function and thermodynamic properties.
This paper systematically unifies different notions of higher Hilbert spaces and their associated module categories by introducing -dagger categories and -Hermitian 2-vector spaces, where varying subgroups recover distinct operator algebra structures like , , and -algebras, while also proposing criteria for positivity and an inductive framework for arbitrary dimensions.
This paper presents numerical simulations of static equilibrium configurations for a flat hyperelastic body embedded in a curved surface of revolution, demonstrating how the interplay between curvature-induced restorative forces and gravitational potential can create a "levitation" phenomenon where the body's deformation forces perfectly cancel gravitational pull.
This paper establishes the well-posedness of Kohn-Sham Density Functional Theory models for two-dimensional materials encapsulated between conducting electrodes, where the resulting short-ranged Yukawa-type Coulomb interaction allows for rigorous analysis of both periodic and quasi-periodic systems.
This paper establishes a singularity theorem that replaces the classical Hawking–Penrose focusing hypothesis with a condition on asymptotic volume growth, proving past timelike geodesic incompleteness under the strong energy condition for both smooth spacetimes and non-smooth Lorentzian length spaces.
This paper provides direct proofs of determinantal formulas for connected -point functions and KP integrability in hermitian matrix models, while also deriving new explicit formulas for affine coordinates and establishing duality for specific models.
This paper develops and numerically solves a dislocation pile-up model to predict how residual stress gradients in thin films evolve based on the film's thickness-to-width ratio and initial stress distribution, revealing that equilibrium requires a mixed population of dislocations with both positive and negative Burgers vectors.
This paper presents an exact solution to the relativistic finite-difference equation for the three-dimensional ring-shaped Quesne oscillator potential, deriving discrete energy spectra and wavefunctions expressed via continuous dual Hahn and Jacobi polynomials while establishing an SU(1,1) dynamical symmetry group for an algebraic determination of the spectrum.
This chapter reviews mathematical results concerning the high-frequency eigenmodes of the Laplacian on chaotic systems, providing a detailed proof of the Quantum Ergodicity theorem for manifolds with boundary and discussing the Quantum Unique Ergodicity conjecture alongside recent progress on constraints and delocalization of semiclassical measures.
This paper presents the comprehensive theory of graphical functions in even dimensions greater than or equal to four, offering detailed reviews of their properties and full proofs to facilitate the calculation of Feynman periods and renormalization constants in high-loop quantum field theories.