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Title: A Kohn-Sham system at zero temperature
Authors: Cornean, HoriaHoke, KurtNeidhardt, HagenRacec, Paul NicolaeRehberg, Joachim
Issue Date: 2008
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1293, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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.
Keywords: Kohn-Sham systems; Schrödinger-Poisson systems; non-linear operators; density operator; zero temperature; Fermi-Dirac distribution
DDC: 510
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.
Appears in Collections:Mathematik



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