Memory Effects

We consider the characterization of quantum dynamical maps that describe the reduced dynamics of open quantum systems and embody the quantum counterpart of a classical stochastic evolution. The distinction of classical stochastic processes in Markovian and non-Markovian provides a natural reference, so that we discuss the enforcement of this perspective in the quantum setting. We especially highlight an approach to compare the different dynamics based on the analysis of the information exchange between system and environment. We address insofar these characterizations of the dynamics can be introduced with reference to the quantum dynamical map itself or to the associated evolution equations. We are thus lead to consider the notion of divisible map, as well as of time-local and memory-kernel master equations. We illustrate these concepts by means of several examples.