On the self-consistent Landauer-B\"uttiker formalism

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.