Abstract
In most realistic situations a quantum system is never perfectly isolated and has to be considered as an open quantum system: it is coupled to an environment that induces decoherence and dissipation. These phenomena can not be described within the standard Schroedinger unitary evolution. In my talk I provide a basic introduction to Markovian semigroups stressing the very concept of complete positivity which plays a key role in modern quantum information theory being a mathematical representation of a quantum channel. However, quantum systems cannot always be described within a Markovian semigroup, which requires a large separation of system and environment time scales. I discuss basic concepts of non-Markovian evolution which are illustrated with simple physical models. Finally, I discuss a natural connection to quantum stochastic processes and the property of Markovianity and classicality.
