  We have implemented time-propagation of the non-equilibrium Green function
for atoms and molecules, by solving the Kadanoff-Baym equations within a
conserving self-energy approximation. We here demonstrate the usefulnes of
time-propagation for calculating spectral functions and for describing the
correlated electron dynamics in a non-perturbative electric field. We also
demonstrate the use of time-propagation as a method for calculating
charge-neutral excitation energies, equivalent to highly advanced solutions of
the Bethe-Salpeter equation.
