We study the onset of dissipation in an externally driven small system, coupled to an
environment. More specifically, we focus on the interplay between Zener dynamics (induced
by the driving source), and the interaction with the environment, which gives rise to both
dephasing and relaxation. We first consider a toy model, consisting of an externally driven
two-level system coupled to various tupes of environments. We demonstrate the onset of
dephasing, manifested as a decay of interference terms. In addition, we derive an effective …