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–Büttiker-like formulas, and make the connection with the case of weakly self-interacting many-body systems. This is joint work with Giovanna Marcelli (https://arxiv.org/abs/2309.01564). [Il seminario si svolgerà all'interno delle attività del progetto PRIN 2022AKRC5P "Interacting Quantum Systems: Topological Phenomena and Effective Theories" finanziato dall’Unione europea – Next Generation EU.]