  We consider a simple microscopic model where the open-system dynamics of a
qubit, despite being Markovian, shows features which are typically associated
to the presence of memory effects. Namely, a non monotonic behavior both in the
population and in the coherence evolution arises due to the presence of
non-secular contributions, which break the phase covariance of the Lindbladian
(semigroup) dynamics. We also show by an explicit construction how such a
non-monotonic behaviour can be reproduced by a phase covariant evolution, but
only at the price of inserting some state-dependent memory effects.
