On an exchange interaction model for quantum transport:: The Schrodinger-Poisson-Slater system

被引：54

作者：

Bokanowski, O ^{[1
]}

López, JL

Soler, J

机构：

[1] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, E-18071 Granada, Spain

[2] Univ Paris 07, Lab Jacques Louis Lions Paris 6, UFR Math, F-75013 Paris, France

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2003年 / 13卷 / 10期

关键词：

exchange interaction; Slater approach; mixed-state Schrodinger-Poisson system; Strichartz estimates; minimal energy solution;

D O I：

10.1142/S0218202503002969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a mixed-state Schrodinger-Poisson-Slater system (SPSS). This system combines the nonlinear and nonlocal Coulomb interaction with a local potential nonlineaxity known as the "Slater exchange term" which models a fermionic effect. The origin of the model is explained and related models are also proposed. Existence, uniqueness and regularity of local-in-time and global solutions axe analyzed in R-3 with L-2 or H-1 initial data. Stationary solutions and conservation laws are also analyzed by using a variational approach due to E. Lieb.

引用

页码：1397 / 1412

页数：16

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