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By modeling the interaction of a system with an environment through a renewalapproach, we demonstrate that completely positive non-Markovian dynamics maydevelop some unexplored non-standard statistical properties. The renewalapproach is defined by a set of disruptive events, consisting in the action ofa completely positive superoperator over the system density matrix. The randomtime intervals between events are described by an arbitrary waiting-timedistribution. We show that, in contrast to the Markovian case, if one performsa system-preparation (measurement) at an arbitrary time, the subsequentevolution of the density matrix evolution is modified. The non-stationarycharacter refers to the absence of an asymptotic master equation even when thepreparation is performed at arbitrary long times. In spite of this property, wedemonstrate that operator expectation values and operators correlations havethe same dynamical structure, establishing the validity of a non-stationaryquantum regression hypothesis. The non-stationary property of the dynamic isalso analyzed through the response of the system to an external weakperturbation.

Non-Markovian non-stationary completely positive open quantum system dynamics