  We provide a comprehensive study of the energy transfer phenomenon --
populating a given energy level -- in 3- and 4-level quantum systems coupled to
two thermal baths. In particular, we examine the effects of an external
periodic driving and the coherence induced by the baths on the efficiency of
the energy transfer. We consider the Floquet-Lindblad and the Floquet-Redfield
scenarios, which both are in the Born-Markov, weak-coupling regime but differ
in the treatment of the secular approximation, and for the latter, we develop
an appropriate Floquet-type master equation by employing a partial secular
approximation. Throughout the whole analysis we keep Lamb-shift corrections in
the master equations. We observe that, especially in the Floquet-Redfield
scenario, the driving field can enhance the energy transfer efficiency compared
to the nondriven scenario. In addition, unlike degenerate systems where
Lamb-shift corrections do not contribute significantly on the energy transfer,
in the Redfield and the Floquet-Redfield scenarios these corrections have
nonnegligible effects.
