Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit

2019/10/28 by Alessia Nota, Nota, Alessia, Chiara Saffirio +3 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics and Entropy

paper · doi:10.48550/arxiv.1910.12983

openalex publication_date 2019/10/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We study a system of charged, noninteracting classical particles moving in a Poisson distribution of hard-disk scatterers in two dimensions, under the effect of a magnetic field perpendicular to the plane. We prove that, in the low-density (Boltzmann-Grad) limit, the particle distribution evolves according to a generalized linear Boltzmann equation, previously derived and solved by Bobylev et al. [4, 5, 6]. In this model, Boltzmann's chaos fails, and the kinetic equation includes non-Markovian terms. The ideas of [13] can be however adapted to prove convergence of the process with memory.

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• 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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