A Kohn-Sham system at zero temperature

Loading...
Thumbnail Image
Date
2008
Volume
1293
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Link to publishers version
Abstract

An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain $W^1,2$-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.

Description
Keywords
Kohn-Sham systems, Schrödinger-Poisson systems, non-linear operators, density operator, zero temperature, Fermi-Dirac distribution
Citation
Cornean, H., Hoke, K., Neidhardt, H., Racec, P. N., & Rehberg, J. (2008). A Kohn-Sham system at zero temperature (Vol. 1293). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Collections
License
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.