Solving the Kadanoff-Baym equations for inhomogenous systems: Application to atoms and molecules

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.