  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.
