Seminarium KMMF "Teoria Dwoistości"

In this talk, I will discuss recent results on the long-time dynamics of strongly interacting many-body quantum systems, focusing on two settings: local random quantum circuits and the unitary time evolution of closed quantum systems. For random quantum circuits, I will show that the circuit complexity of states and unitaries saturates after exponential time and undergoes recurrence after double-exponential time (in the system size). For unitary dynamics of closed quantum systems, I will present a doubly exponential upper bound on recurrence times and give examples of Hamiltonians and states that saturate this bound.