Exact density-functional potentials for time-dependent quasiparticles

We calculate the exact Kohn-Sham potential that describes, within time-dependent density-functional theory, the propagation of an electron quasiparticle wave packet of nonzero crystal momentum added to a ground-state model semiconductor. The potential is observed to have a highly nonlocal functional dependence on the charge density, in both space and time, giving rise to features entirely lacking in local or adiabatic approximations. The dependence of the nonequilibrium part of the Kohn-Sham electric field on the local current and charge density is identified as a key element of the correct Kohn-Sham functional.