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 introduces a fractional generalization of Tsallis entropy using the -Caputo operator to derive a closed series representation involving the -Gamma function, demonstrating that the standard entropy is recovered as the fractional order approaches one and analyzing the parameter domains where the resulting entropy remains non-negative.
This paper investigates the Dirac operator on a finite warped cylinder with a gauge field by characterizing the APS boundary spectrum, demonstrating the vanishing of the APS index in the invertible constant-gauge case, and introducing a regularized self-adjoint boundary condition that ensures continuity across spectral crossings to enable a consistent spectral flow analysis within the Maslov framework.
This study proposes and validates through a mathematical stability analysis and experimental data that dryout inception in two-phase CO2 annular flow within microchannels is triggered by liquid-vapour interface instability, identifying a critical vapour quality threshold () that governs this phenomenon.
This paper reorganizes exact density-functional theory into two parallel variational hierarchies rooted in Lieb's interacting and exact ensemble noninteracting formulations, clarifying their relationship to the Kohn-Sham construction and unifying concepts like fractional particle numbers and derivative discontinuities within a single framework.
This paper applies deformation quantization to an oscillator system with second-class constraints in a deformed fermionic phase space by utilizing the Dirac bracket to define the star product, subsequently deriving the system's energy levels, Wigner functions, and deformation-induced entanglement entropy.
This paper identifies three explicit families of non-degradable and non-PPT states that possess a single-letter formula for one-way distillable entanglement by introducing weakened degradability conditions, establishing stability for orthogonally flagged mixtures, and proposing a generalized spin-alignment principle for entropy minimization.
This paper demonstrates that for the -fold symmetric one-harmonic polynomial conformal map, the first spectral instability of the mixed Hessian of the dispersionless Toda -function occurs at the analytic threshold rather than the later geometric threshold where univalence is lost, characterized by a single logarithmically diverging eigenvalue and a bounded remainder spectrum.
This paper establishes a unified variational framework for the inverse Kohn-Sham problem by identifying the fixed-density constrained search as a natural anchor, thereby demonstrating that diverse existing inversion methods are equivalent realizations of the same underlying optimization structure that differ primarily in how they treat state equations and density constraints.
This paper investigates perturbations of relative cubic Dirac operators for basic classical Lie superalgebras within the colour quantum Weil algebra framework, yielding three distinct classes of invariants: semisimple orbits characterizing atypicality, a unified cohomology theory combining Dirac and Duflo–Serganova cohomologies, and a Chern-type invariant derived from a Weil-covariant differential.
This paper derives an explicit expression for the joint correlation measure between eigenvalues and singular values in bi-unitarily invariant complex random matrix ensembles, providing closed formulas that simplify significantly for polynomial and Pólya ensembles.