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arXiv · 0801.2693

A Kohn-Sham system at zero temperature

Horia Cornean·Kurt Hoke·Hagen Neidhardt·Paul N. Racec·Joachim Rehberg
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Abstract

An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor {nano}structures 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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Horia Cornean, Kurt Hoke, Hagen Neidhardt, Paul N. Racec, Joachim Rehberg. 2008-01-17. A Kohn-Sham system at zero temperature. https://doi.org/10.1088/1751-8113/41/38/385304

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