We study a system of charged, noninteracting classical particles moving in a Poisson distri- bution of hard-disk scatterers in two dimensions, under the effect of a magnetic field perpen- dicular 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.
Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit / Nota, A; Saffirio, C; Simonella, S. - In: ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. - ISSN 0246-0203. - (2022).
Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit
Simonella S
2022
Abstract
We study a system of charged, noninteracting classical particles moving in a Poisson distri- bution of hard-disk scatterers in two dimensions, under the effect of a magnetic field perpen- dicular 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.File | Dimensione | Formato | |
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