1515 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 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.
This paper introduces a classical Heun observable as the most general bilinear combination of two observables satisfying classical Askey-Wilson relations, demonstrating that its associated Hamiltonian dynamics are governed by quartic differential equations and elliptic functions, thereby providing an algebraic mechanism that links classical Leonard pairs to elliptic solvability.
This paper generalizes the theory of finitely correlated states to disordered systems driven by ergodic topological dynamics, demonstrating that a specific disordered AKLT state exhibits a closed bulk spectral gap, almost surely exponentially decaying correlations, and a time-reversal invariant Tasaki index of $-1$.
This paper provides an equivalent characterization of the previously unknown constant in the leading order term of the lattice Yang-Mills free energy by adjusting boundary conditions, thereby enabling its explicit computation.