  In this work, we present a multiple-scale perturbation technique suitable for
the study of open quantum systems, which is easy to implement and in few
iterative steps allows us to find excellent approximate solutions. For any
time-local quantum master equation, whether markovian or non-markovian, in
Lindblad form or not, we give a general procedure to construct analytical
approximations to the corresponding dynamical map and, consequently, to the
temporal evolution of the density matrix. As a simple illustrative example of
the implementation of the method, we study an atom-cavity system described by a
dissipative Jaynes-Cummings model. Performing a multiple-scale analysis we
obtain approximate analytical expressions for the strong and weak coupling
regimes that allow us to identify characteristic time scales in the state of
the physical system.
