Nota, Alessia and Saffirio, Chiara and Simonella, Sergio. (2021) Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit. Preprints Fachbereich Mathematik, 2021 (03).
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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. [BMHH, BMHH1, BHPH]. In this model, Boltzmann's chaos fails, and the kinetic equation includes non-Markovian terms. The ideas of [G69] can be however adapted to prove convergence of the process with memory.
Faculties and Departments: | 12 Special Collections > Preprints Fachbereich Mathematik 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Mathematical Physics (Saffirio) |
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UniBasel Contributors: | Saffirio, Chiara |
Item Type: | Preprint |
Publisher: | Universität Basel |
Language: | English |
edoc DOI: | |
Last Modified: | 01 Feb 2021 19:28 |
Deposited On: | 01 Feb 2021 19:28 |
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