  We propose a new treatment of the dynamics of a periodically time-dependent
Liouvillian by mapping it onto a time-independent problem and give a systematic
expansion for its effective Liouvillian. In the case of a two-level system, the
lowest order contribution is equivalent to the well-known rotating wave
approximation. We extend the formalism to a pair of coupled two-level systems.
For this pair, we find two Rabi frequencies and we can give parameter regimes
where the leading order of the expansion is suppressed and higher orders become
important. These results might help to investigate the interaction of tunneling
systems in mixed crystals by providing a tool for the analysis of echo
experiments.
