Completely Positive Markovian Quantum Dynamics in the Weak-Coupling Limit

We obtain new types of 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 new type of 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, like a new Quantum version of the celebrated Fermi's Golden Rule and some recently proposed entangling projections.