  The evolution of two, non-interacting two-level atoms immersed in a weakly
coupled bath can be described by a refined, time coarse grained Markovian
evolution, still preserving complete positivity. We find that this improved
reduced dynamics is able to entangle the two atoms even when their internal
frequencies are unequal, an effect which appears impossible in the standard
weak coupling limit approach. We study in detail this phenomenon for an
environment made of quantum fields.
