  We provide sufficient conditions such that the time evolution of a mesoscopic
tight-binding open system with a local Hartree-Fock non-linearity converges to
a self-consistent non-equilibrium steady state, which is independent of the
initial condition from the "small sample". We also show that the steady charge
current intensities are given by Landauer-B\"uttiker-like formulas, and make
the connection with the case of weakly self-interacting many-body systems.
