Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit
| Autor: | Nota, Alessia, Saffirio, Chiara, Simonella, Sergio |
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| Přispěvatelé: | Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila] (DISIM), Università degli Studi dell'Aquila = University of L'Aquila (UNIVAQ), Department of Mathematics [Basel], University of Basel (Unibas), Centre National de la Recherche Scientifique (CNRS), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila] (DISIM), Università degli Studi dell'Aquila (UNIVAQ), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Generalized Boltzmann equation Lorentz gas Low-density limit Magnetic field Memory terms Non-Markovian process low-density limit Probability (math.PR) FOS: Physical sciences magnetic field Mathematical Physics (math-ph) generalized Boltzmann equation non- Markovian process Mathematics - Analysis of PDEs memory terms FOS: Mathematics Statistics Probability and Uncertainty [MATH]Mathematics [math] Mathematical Physics Mathematics - Probability Analysis of PDEs (math.AP) |
| Zdroj: | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, 58 (2), pp.1228-1243 Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), In press |
| ISSN: | 0246-0203 1778-7017 |
| Popis: | 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. Comment: 18 pages, 6 figures. Minor modifications |
| Databáze: | OpenAIRE |
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