In research area B a top-down approach is pursued. Here we will investigate what novel effects arise from the interplay and the competition between the unitary dynamics of an interacting many-body system and the coupling to reservoir(s) and/or time-periodic drives. In these complex systems typically not all degrees of freedom can be controlled precisely; the complexity leads, however, to new exciting collective phenomena, such as phase transitions.

Stationary states of open systems offer potential advantages such as robustness to perturbations and thus are of interest for the generation of exotic and otherwise fragile many-body states. In contrast to condensed matter systems, reservoir interactions in quantum optics can very often be considered as being Markovian, which allows for a better understanding of the underlying physics and thus offers large potential for their exploitation in reservoir engineering.