  We investigate the dynamics of a two-dimensional Hubbard model in a static
electric field in order to identify the conditions to reach a non-equilibrium
stationary state. For a generic electric field, the convergence to a stationary
state requires the coupling to a thermostating bath absorbing the work done by
the external force. Following the real-time dynamics of the system, we show
that a non-equilibrium stationary state is reached for essentially any value of
the coupling to the bath. We map out a phase diagram in terms of dissipation
and electric field strengths and identify the dissipation values in which
steady current is largest for a given field.
