Repeated pumping of quantum systems

We consider a closed quantum system on a finite-dimensional Hilbert space. This system is repeatedly brought into contact with another closed system, from which it can either absorb energy or to which it can transfer energy. We study the dynamics of the full system and how this depends on various model parameters, e.g., on the strength of the coupling between the two systems and the time between the repeated contacts. For this purpose, we introduce a statistical approach to characterize the discrete-time statistics, which is determined by the contact between the two closed systems. This provides a sequence of probabilities for the time-evolved states of the system. In particular, we analyze the asymptotic probability (return probability) for a certain state of the system returning to itself. Moreover, we investigate the discrete-time correlation functions of the system to uncover a few salient topological features of the long-time dynamics.