A Kohn--Sham system at zero temperature
Please always quote using this URN:urn:nbn:de:0296-matheon-5600
- 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.
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| Author: | Horia Cornean, Kurt Hoke, Hagen Neidhardt, Paul Racec, Joachim Rehberg |
|---|---|
| URN: | urn:nbn:de:0296-matheon-5600 |
| Referee: | Alexander Mielke |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2009/11/02 |
| Release Date: | 2009/11/02 |
| Preprint Number: | 554 |
