Narrow Results

A number of results connecting quantum and classical Markov semigroups, as well as their dilations is reported. The method presented here is based on the analysis of the structure of the semigroup generator. In particular, measure-valued processes appear as a combination of classical reduction and classical dilation of a given quantum Markov semigroup.

Quantum Markov semigroups have been used as a predominant model of open quantum dynamics where the system interacts with the environment. Thus, the main dynamics is submitted to perturbations which change the nature of its mathematical structure. This paper explores a class of perturbations which do not change the invariant elements of the main dynamics, which we call adiabatic perturbations. This is typically the case when the environment evolves according to a slower time scale than that of the system dynamics. As an illustration, we study a class of interacting limit behaviour leading to adiabatic perturbations of the main dynamics. Finally, we study the connection between adiabatic perturbations and the phenomenon of quantum decoherence.