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arXiv · 1910.12983

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

Alessia Nota·Chiara Saffirio·Sergio Simonella
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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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Alessia Nota, Chiara Saffirio, Sergio Simonella. 2019-10-28. Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit. https://arxiv.org/abs/1910.12983

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