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

被引：51
|
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.
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页码：1397 / 1412
页数：16
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