Work

Diffusion of the random Lorentz process in a magnetic field

Year: 2025

Type: article

Abstract: Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method established by the authors [Lutsko and Tóth, Commun. Math. Phys. 379, 589–632 (2020)], we show that this “magnetic Lorentz gas” satisfies an invariance principle in an intermediate scaling limit. That is, we apply the low-density (Boltzmann–Grad) limit and simultaneously take the limit as time goes to infinity, then prove convergence of the rescaled trajectory to a Brownian motion in this limit.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0255890

Authors: Christopher Lutsko, Bálint Toth

Institutions: University of Houston, HUN-REN Alfréd Rényi Institute of Mathematics, University of Bristol

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Engineering and Physical Sciences Research Council, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap

Awards: G3439360318, Random Walks and Quantum Spin Systems, G8885059494