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

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.