Diffusion of the random Lorentz process in a magnetic field

2024/11/06 by Christopher Lutsko, Lutsko, Christopher, Bálint Tóth +1 · 2 citations
Physics and Astronomy · #60F17 #60K35 #82C22 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Mechanics and Applications #Radioactive Decay and Measurement Techniques #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2411.03984

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, 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.

Cited by

• Random Flights and Anomalous Diffusion: A Non-Markovian Take on Lorentz Processes
• Improved geometric and recollision estimates for the invariance principle of the random Lorentz gas

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