2024/12/15 by Alessia Nota, Nota, Alessia, Dominik Alex Nowak +3 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Atomic and Subatomic Physics Research #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2412.11134
openalex publication_date 2024/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the magnetic Lorentz gas proposed by Bobylev et al. [4], which describes a point particle moving in a random distribution of hard-disk obstacles in ℝ2 under the influence of a constant magnetic field perpendicular to the plane. We show that, in the coupled low-density and diffusion limit, when the intensity of the magnetic field is smaller than (8π)/(3), the non-Markovian effects induced by the magnetic field become sufficiently weak. Consequently, the particle's probability distribution converges to the solution of the heat equation with a diffusion coefficient dependent on the magnetic field and given by the Green-Kubo formula. This formula is derived from the generator of the generalized Boltzmann process associated with the generalized Boltzmann equation, as predicted in [4].