  We study the steady-state dynamics of the Hubbard model driven
out-of-equilibrium by a constant electric field and coupled to a dissipative
heat bath. For very strong field, we find a dimensional reduction: the system
behaves as an equilibrium Hubbard model in lower dimensions. We derive
steady-state equations for the dynamical mean field theory in the presence of
dissipation. We discuss how the electric field induced dimensional crossover
affects the momentum resolved and integrated spectral functions, the energy
distribution function, as well as the steady current in the non-linear regime.
