Quantification and control of non-Markovian evolution in finite quantum systems via feedback

We consider the unitary time evolution of continuous quantum-mechanical systems confined to a cavity in contact with a finite bath of variable size. We define a measure relating to (non-)Markovianity which parallels the standard one for the case of integrable Lindbladian dynamics but has the advantage of being numerically tractable also for large many-particle systems. The relevant time scales are identified which characterize non-Markovian transient behavior, boundary-scattering-induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable parameters such as the bath size and the strength of the system-bath coupling.