Functional dependence of the exact time-dependent Kohn-Sham potential for quantum transport

We present methods for determining exact steady-state and time-dependent Kohn-Sham potentials from known charge and current densities. Applying these methods to cases of a single electron added to the conduction band of a model semiconductor, we calculate the exact Kohn-Sham potentials and discuss their meaning in the context of describing quantum transport. We show that the inclusion of a longitudinal Kohn-Sham vector potential is quite unavoidable in describing steady-state current-carrying systems, whereas the addition of an electron in a wavepacket state necessitates, inter alia, the appearance of an exchange-correlation electric field. We also present our findings on the functional dependence of the exact Kohn-Sham scalar and vector potentials on the charge and current density.