  We introduce a versatile method to compute electronic steady state properties
of strongly correlated extended quantum systems out of equilibrium. The
approach is based on dynamical mean-field theory (DMFT), in which the original
system is mapped onto an auxiliary non-equilibrium impurity problem imbedded in
a Markovian environment. The steady state Green's function of the auxiliary
system is solved by full diagonalization of the corresponding Lindblad
equation. The approach can be regarded as the nontrivial extension of the
exact-diagonalization based DMFT to the non-equilibrium case. As a first
application, we consider an interacting Hubbard layer attached to two metallic
leads and present results for the steady-state current and the non-equilibrium
density of states.
