  We calculate the exact Kohn-Sham potential that describes, within
time-dependent density-functional theory, the propagation of an electron
quasiparticle wavepacket of non-zero 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 non-equilibrium 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.
