  We simulate the dynamics of a single-electron source, modeled as a quantum
dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead,
in time-dependent density functional theory. Based on this system, we develop a
time-nonlocal exchange-correlation potential by exploiting analogies with
quantum-transport theory. The time non-locality manifests itself in a dynamical
potential step. We explicitly link the time evolution of the dynamical step to
physical relaxation time scales of the electron dynamics. Finally, we discuss
prospects for simulations of larger mesoscopic systems.
