08-14 Horia Cornean, Kurt Hoke, Hagen Neidhardt, Paul N. Racec, Joachim Rehberg

A Kohn-Sham system at zero temperature (335K, pdf) Jan 17, 08

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

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 Schr\"odinger 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.

Files: 08-14.src( 08-14.keywords , preprint.pdf.mm )