2 results
Search Results
Now showing 1 - 2 of 2
- ItemA Kohn-Sham system at zero temperature(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Cornean, Horia; Hoke, Kurt; Neidhardt, Hagen; Racec, Paul Nicolae; Rehberg, JoachimAn 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.
- ItemAnalyticity for some operator functions from statistical quantum mechanics : dedicated to Günter Albinus(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hoke, Kurt; Kaiser, Hans-Christoph; Rehberg, Joachim; Albinus, GünterFor rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain factorizes over the space of essentially bounded functions.