Quantum dynamics through the looking glass

Quantum dynamics of Many-Body Systems has been the subject of a great num- ber of theoretical and experimental studies in the past decade. Initially most of the attention has been focusing on traditional characterizations of the dynamics in terms of the time dependence of observables and correlation functions. Un- fortunately most of the systems are quite boring in this respect. This happens because of thermalization: waiting sufficiently long after kicking the system out of equilibrium all local measurements will just make the state of the system ap- pear a mundane equilibrium thermal state. But can this apparent thermal state be really thermal ? In order to address this question one has to look at quan- tum dynamics literally ”through the looking glass”, exploring the strange world of entanglement structures, multipartite entanglement, scrambling of quantum information and out-of-time-order correlation functions. I will introduce the audience pedagogically to these topics and discuss recent advances in charac- terizing dynamics in terms of the structure of quantum many-body states.