Nonequilibrium Green Functions Simulations on the Next Level: Theoretical Advances and Applications to Finite Lattice Systems

This thesis is devoted to the description of correlated finite lattice systems under nonequilibrium conditions. In this context, the lack of small parameters in the corresponding standard many-body equations makes it difficult to construct suitable approximations for theoretical tools, which renders the computation of relevant observables numerically costly and impractical. At the same time, rigorous predictions for the ultrafast dynamics in correlated lattices are highly valuable for the understanding of many state-of-the-art experiments. The nonequilibrium Green functions (NEGF) technique is particularly well-suited to meet the challenging demands that come with the description of the nontrivial interplay between quantum correlations and nonequilibrium effects in excited lattice systems. However, in order to apply the approach on a practically relevant scale, several methodological improvements come to be indispensable. The present thesis contains these theoretical advances of the NEGF method, alongside with—thus accessible—applications to ultracold atoms in optical lattices and excited finite graphene nanostructures