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

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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Official URL: https://edoc.unibas.ch/81504/

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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 > Kinetische Theorie (Saffirio)
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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