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 establishes the future global-in-time existence and uniqueness of small perturbations for both Maxwell-Jüttner equilibria and vacuum solutions of the massless Boltzmann equation on decelerating FLRW spacetimes with topology, covering hard ball interactions for all expansion rates and vacuum stability for .
This paper introduces a novel eigenvalue technique to solve the adjoint Fokker-Planck equation for the probability distribution of inflationary e-folds, revealing a previously overlooked power-law intermediate regime in quantum diffusion and characterizing how constant drift potentials qualitatively alter the distribution's peak and tail behavior in narrow- versus broad-well limits.
This paper establishes that while smooth observables in the spherical ensemble exhibit standard Gaussian free field fluctuations, logarithmic Green singularities decouple in high dimensions to produce an explicit white-noise limit, yielding precise asymptotics for logarithmic potentials and characteristic polynomials governed by chordal geometry.
This paper integrates Reimann's spectral typicality theorem with Interval Quantum Mechanics to demonstrate that quantum parcels representing finite-precision epistemic knowledge thermalize and concentrate around microcanonical values at late times, while preserving exact separations between conserved quantities even after fuzzy measurements.
This paper establishes a direct superintegrable realization of the Laguerre–Heun algebra by identifying it as the quadratic symmetry algebra of the two-dimensional Smorodinsky–Winternitz II system, which is separable in both Cartesian and parabolic coordinates.
This paper demonstrates that axisymmetric Willmore surfaces can be described by a first-order ordinary differential equation derived from two independent first integrals, thereby providing a convenient classification scheme for such surfaces.
This paper establishes a precise framework for distinguishing between energy-independent Wilson holonomies and energy-dependent spectral monodromies in spin-orbit rings, demonstrating how this separation enables the mapping of spin-orbit Hamiltonians to effective gauge connections to derive exact spectral quantization and transport properties in systems like graphene and Rashba-Dresselhaus rings.
This paper analyzes the coupled Riemann problem for compressible Euler equations with a stationary heat-flux discontinuity, demonstrating that non-uniqueness arises in Lax weak entropy solutions and establishing the existence and structure of unique admissible solutions under specific smallness conditions on the heat flux jump while identifying cases where no such solutions exist.
This paper revisits Jean-Marie Souriau's geometric quantization of the relativistic electron by proving key theorems to establish necessary symplectic and contact structures, ultimately deriving the Dirac equation, spin current conservation, and a systematic Kaluza-Klein-based construction of C, P, and T symmetries.
This heuristic paper extends the Laplace-Beltrami formalism, previously used to model gravitational wave energy from coalescing compact binaries, to a broader analysis of the Einstein field equations across zeroth, first, and second-order differential terms to evaluate its practicality and limitations in describing various general relativistic systems.