2010, Racec, Roxana, Wulf, Ulrich, Racec, Paul Nicolae

We analyze a quantum dot strongly coupled to the conducting leads via quantum point contacts - Fano regime of transport - and report a variety of resonant states which demonstrate the dominance of the interacting resonances in the scattering process in a low confining potential. There are resonant states similar to the eigenstates of the isolated dot, whose widths increase with increasing the coupling strength to the environment, and hybrid resonant states. The last ones are approximatively obtained as a linear combination of eigenstates with the same parity in the lateral direction, and the corresponding resonances show the phenomena of resonance trapping or level repulsion. The existence of the hybrid modes suggests that the open quantum dot behaves in the Fano regime like an artificial molecule quantum point contacts

2008, Cornean, Horia, Hoke, Kurt, Neidhardt, Hagen, Racec, Paul Nicolae, Rehberg, Joachim

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.