  We propose a time-dependent many-body approach to study the short-time
dynamics of correlated electrons in quantum transport through nanoscale systems
contacted to metallic leads. This approach is based on the time-propagation of
the Kadanoff-Baym equations for the nonequilibrium many-body Green's function
of open and interacting systems out of equilibrium. An important feature of the
method is that it takes full account of electronic correlations and embedding
effects in the presence of time-dependent external fields, while at the same
time satisfying the charge conservation law. The method further extends the
Meir-Wingreen formula to the time domain for initially correlated states. We
study the electron dynamics of a correlated quantum wire attached to
two-dimensional leads exposed to a sudden switch-on of a bias voltage using
conserving many-body approximations at Hartree-Fock, second Born and GW level.
We obtain detailed results for the transient currents, dipole moments, spectral
functions, charging times, and the many-body screening of the quantum wire as
well as for the time-dependent density pattern in the leads, and we show how
the time-dependence of these observables provides a wealth of information on
the level structure of the quantum wire out of equilibrium. For moderate
interaction strenghts the 2B and GW results are in excellent agreement at all
times. We find that many-body effects beyond the Hartree-Fock approximation
have a large effect on the qualitative behavior of the system and lead to a
bias dependent gap closing and quasiparticle broadening, shortening of the
transient times and washing out of the step features in the current-voltage
curves.
