Anomalies in non-Markovian quantum dynamics

The non-Markovian dynamics of general finite dimensional open quantum systems is studied. In the framework of the continuous time quantum random walk inverse power law tailed distributions of the waiting times between two consecutive interactions with the external environment are considered. Hindered time evolution appears over long time scales if the distribution of the long waiting times increases up to the critical decay 1/t. More generally, arbitrarily slow relaxations to the asymptotic configurations are found in the scenario of dynamical maps of a qudit. Similar features characterize the time evolution of the entanglement of X states.