Completely positive Markovian quantum dynamics in the weak-coupling limit

Abstract

We obtain exponential decay laws for solutions of density-matrix master equations in the weak-coupling limit: after comparing with results already present in the literature and developing the necessary techniques, we study the crucial aspect of complete positivity under fairly general conditions. We propose a time average that guarantees complete positivity and approximates, in Markovian fashion, the exact dynamics for a plethora of physical applications, no matter which are the spectral properties of the subsystem, or its dimensions. We shall comment on some interesting examples, such as a quantum version of the celebrated Fermi's ``golden rule'' and some recently proposed entangling projections.