Semi‐classical limits in a crystal with a Coulombian self‐consistent potential: Effective mass theorems

Article type: Research Article

Authors: Bechouche, Philippe

Affiliations: Laboratoire J.A. Dieudonné, URM 6621 du CNRS, Université de Nice, Parc Valrose, F‐06108 Nice, France

Abstract: We study the semi‐classical limit of the dynamics of electrons in a crystal under the influence of a self‐consistent Coulombian potential. To do this, we introduce two small parameters: \varepsilon, the typical length of the crystal, and h, the macroscopic Planck constant. When \varepsilon and h tend to zero, under special conditions, the electrons distribution limit follows a Vlasov equation where the electrons mass is replaced by an effective mass.

Journal: Asymptotic Analysis, vol. 19, no. 2, pp. 95-116, 1999