  We study a driven two-state system interacting with a structured environment.
We introduce the non-Markovian master equation ruling the system dynamics, and
we derive its analytic solution for general reservoir spectra. We compare the
non-Markovian dynamics of the Bloch vector for two classes of reservoir
spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the
analytic conditions for complete positivity with and without the secular
approximation. Interestingly, the complete positivity conditions have a
transparent physical interpretation in terms of the characteristic timescales
of phase diffusion and relaxation processes.
