On an Exchange Interaction Model for Quantum Transport: The Schrödinger–Poisson–Slater System
- 1 October 2003
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 13 (10) , 1397-1412
- https://doi.org/10.1142/s0218202503002969
Abstract
We study a mixed-state Schrödinger–Poisson–Slater system (SPSS). This system combines the nonlinear and nonlocal Coulomb interaction with a local potential nonlinearity 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 are analyzed in ℝ3 with L2 or H1 initial data. Stationary solutions and conservation laws are also analyzed by using a variational approach due to E. Lieb.Keywords
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