  We formulate an effective-description framework for the dynamics of open
quantum systems by extending the time-coarse-graining formalism to open
systems. Our coarse-graining procedure efficiently removes high-frequency
processes which are responsible for coherences between lower- and
upper-manifold states and are irrelevant when considering only low-energy
dynamics. We investigate the regime of validity of the resulting coarse-grained
master equation by applying it to multi-level atoms driven by far-detuned
lasers. Except for such high-frequency coherences, we find good agreement
between the exact and coarse-grained dynamics unless the driving lasers are too
strong or the initial high-frequency coherences are sizable.
