  We present a first-principles derivation of the Markovian semi-group master
equation without invoking the rotating wave approximation (RWA). Instead we use
a time coarse-graining approach which leaves us with a free timescale
parameter, which we can optimize. Comparing this approach to the standard
RWA-based Markovian master equation, we find that significantly better
agreement is possible using the coarse-graining approach, for a three-level
model coupled to a bath of oscillators, whose exact dynamics we can solve for
at zero temperature. The model has the important feature that the RWA has a
non-trivial effect on the dynamics of the populations. We show that the two
different master equations can exhibit strong qualitative differences for the
population of the energy eigenstates even for such a simple model. The
RWA-based master equation misses an important feature which the coarse-graining
based scheme does not. By optimizing the coarse-graining timescale the latter
scheme can be made to approach the exact solution much more closely than the
RWA-based master equation.

Quantum Physics