  We derive dynamical equations for a driven, dissipative quantum system in
which the environment- induced relaxation rate is comparable to the Rabi
frequency, avoiding assumptions on the frequency dependence of the
environmental coupling. When the environmental coupling varies significantly on
the scale of the Rabi frequency, secular or rotating wave approximations break
down. Our approach avoids these approximations, yielding dynamical, periodic
steady-states. This is important for the qualitative and quantitative
description of the interaction between driven quantum dots and their phonon
environment. The theory agrees well with recent experiments, describing the
transition from asymmetric unsaturated resonances at weak driving to population
inversion at strong driving.
