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

被引：1

作者：

Nota, Alessia ^{[1
]}

Saffirio, Chiara ^{[2
]}

Simonella, Sergio ^{[3
]}

机构：

[1] Univ Aquila, Dipartimento Ingn & Sci Informaz & Matemat, Via Vetoio, I-67100 LAquila, Italy

[2] Univ Basel, Dept Math & Informat, Spiegelgasse 1, CH-4051 Basel, Switzerland

[3] Ecole Normale Super, UMR CNRS 5669, CNRS & UMPA, 46 allee Italie, F-69364 Lyon, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2022年 / 58卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

Lorentz gas; Magnetic field; Generalized Boltzmann equation; Low-density limit; Non-Markovian process; Memory terms; EQUATION; GAS; DERIVATION;

D O I：

10.1214/21-AIHP1181

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (Phys. Rev. Lett. 75 (1995) 2, J. Stat. Phys. 87 (1997) 1205???1228, J. Stat. Phys. 102 (2001) 1133???1150). In this model, Boltzmann???s chaos fails, and the kinetic equation includes non-Markovian terms. The ideas of (Phys. Rev. 185 (1969) 308???322) can be however adapted to prove convergence of the process with memory.

引用

页码：1228 / 1243

页数：16

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