A Kohn--Sham system at zero temperature
- Cornean, Horia
- Hoke, Kurt
- Neidhardt, Hagen
- Racec, Paul N.
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 34L40 34L30 47H05 81V70
- Kohn-Sham systems, Schrödinger-Poisson systems, non-linear operators, density operator, zero temperature, Fermi-Dirac distribution
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.
- J. Phys. A, 41 (2008) pp. 385304/1--385304/21.