A MATHEMATICAL-ANALYSIS OF QUANTUM TRANSPORT IN 3-DIMENSIONAL CRYSTALS

被引：6

作者：

DEGOND, P

MARKOWICH, PA

机构：

[1] ECOLE POLYTECH,CTR MATH APPL,F-91128 PALAISEAU,FRANCE

[2] VIENNA TECH UNIV,INST ANGEW & NUMER MATH,A-1040 VIENNA,AUSTRIA

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 1991年 / 160卷

关键词：

D O I：

10.1007/BF01764126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an existence and uniqueness result for a quantum transport model in three dimensional crystals. The model consists of a quantum transport (Wigner) equation posed on the phase space consisting of a discrete position variable and a <<continuous>> wave vector, which is restricted to a bounded domain in R3 (first Brillouin zone of the crystal). The potential is modeled self-consistently by a discrete Poisson equation (Coulomb interaction). Also we investigate the limits of solutions of this model as the grid spacing tends to zero and show that they converge to the solution of a quantum transport model posed on the <<fully continuous>> phase space. The transport model derived by this limiting procedure treats the band diagram of the crystal in a semi-classical way and the potential energy term quantum mechanically.

引用

页码：171 / 191

页数：21