Hannover 2010 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 2: Atomic Systems in External Fields I
A 2.2: Vortrag
Montag, 8. März 2010, 14:15–14:30, F 107
Effective potentials in a density functional theory via local force equations — •Michael Ruggenthaler1,2 and Dieter Bauer1 — 1Institut für Physik, Universität Rostock, 18057 Rostock — 2Max-Planck-Institut für Kernphysik, 69117 Heidelberg
Time-dependent density functional theory reformulates usual wave-function-based time-dependent quantum mechanics in terms of the simple one-particle density alone [1]. The basis of a time-dependent Kohn-Sham (KS) scheme, i.e., mapping the interacting many-body problem uniquely to an auxiliary system of fictitious noninteracting particles, was given in the van Leeuwen theorem [2]. However, the van Leeuwen theorem does merely prove the uniqueness of an effective KS potential. The existence of such a potential, given via the local force balance equation of quantum mechanics, was not further investigated. We find conditions for the existence of an effective potential and prove its existence under certain restrictions [3]. Further, by expressing the interacting wave-function in terms of the noninteracting KS wave-function we find differential equations for the local Hartree-exchange and the local correlation potential [4]. Under certain assumptions we give explicit expressions for both potentials and compare the local Hartree-exchange-only approximation with the exact-exchange approximation.
[1]E.Runge and E.K.U.Gross, Phys.Rev.Lett. 52, 997 (1984)
[2]R.Van Leeuwen, Phys.Rev.Lett. 82, 3863 (1999)
[3]M.Ruggenthaler,M.Penz,D.Bauer, J.Phys.A 42, 425207 (2009)
[4]M.Ruggenthaler and D.Bauer, Phys.Rev.A 80, 052502 (2009)