  We have developed a method based on the embedded Kadanoff-Baym equations to
study the time evolution of open and inhomogeneous systems. The equation of
motion for the Green's function on the Keldysh contour is solved using
different conserving many-body approximations for the self-energy. Our
formulation incorporates basic conservation laws, such as particle
conservation, and includes both initial correlations and initial embedding
effects, without restrictions on the time-dependence of the external driving
field. We present results for the time-dependent density, current and dipole
moment for a correlated tight binding chain connected to one-dimensional
non-interacting leads exposed to DC and AC biases of various forms. We find
that the self-consistent 2B and GW approximations are in extremely good
agreement with each other at all times, for the long-range interactions that we
consider. In the DC case we show that the oscillations in the transients can be
understood from interchain and lead-chain transitions in the system and find
that the dominant frequency corresponds to the HOMO-LUMO transition of the
central wire. For AC biases with odd inversion symmetry odd harmonics to high
harmonic order in the driving frequency are observed in the dipole moment,
whereas for asymmetric applied bias also even harmonics have considerable
intensity. In both cases we find that the HOMO-LUMO transition strongly mixes
with the harmonics leading to harmonic peaks with enhanced intensity at the
HOMO-LUMO transition energy.
