A Kohn-Sham system at zero temperature

Details A Kohn-Sham system at zero temperature A Kohn-Sham system at zero temperature

2008-01-17

arxiv.org/abs/0801.2693v1

J. Phys. A: Math. Theor. 41 385304 (2008)

Physics

Mathematical Physics

27 pages

Scientific paper

10.1088/1751-8113/41/38/385304

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.

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