On an Exchange Interaction Model for Quantum Transport: The Schrödinger–Poisson

On an Exchange Interaction Model for Quantum Transport: The Schrödinger–Poisson–Slater System

Published:2003-10 Issue:10 Volume:13 Page:1397-1412
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Bokanowski Olivier¹,López José L.²,Soler Juan²

Affiliation:

1. Lab. Jacques Louis Lions (Paris 6), UFR Mathématique B.P. 7012, Université Paris 7, 16 rue Clisson, 75013 Paris, France

2. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202503002969

Reference19 articles.

1. Accuracy of mean field approximations for atoms and molecules

2. Local Density Approximations for the Energy of a Periodic Coulomb Model

3. LOCAL APPROXIMATION FOR THE HARTREE–FOCK EXCHANGE POTENTIAL: A DEFORMATION APPROACH

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