  The dynamics of a single quantum state embedded in one or several
(quasi-)continua is one of the most studied phenomena in quantum mechanics. In
this work we investigate its discrete analogue and consider short and long time
dynamics based on numerical and analytical solutions of the Schr\"odinger
equation. In addition to derivation of explicit conditions for initial
exponential decay, it is shown that a recent model of this class [Phys. Rev. A
95, 053821, (2017)], describing a qubit coupled to a phonon reservoir with
energy dependent coupling parameters is identical to a qubit interacting with a
finite number of parallel regularly spaced band of states via constant
couplings. As a consequence, the characteristic near periodic initial state
revivals can be viewed as a transition of probability between different
continua via the reviving initial state. Furthermore, the observation of
polynomial decay of the reviving peaks is present in any system with constant
and sufficiently strong coupling.
