  The quantum average energy decay and the purity decay are studied for a
system particle as a function of the number of constituents of a discrete bath
model. The system particle is subjected to two distinct physical situations:
the harmonic oscillator (HO) and the Morse potential. The environment (bath) is
composed by a {\it finite} number N of uncoupled HOs, characterizing the
structured bath, which in the limit $N\to\infty$ is assumed to have an ohmic,
sub-ohmic or super-ohmic spectral density. For very low values of N the mean
energy and purity remain constant in time but starts to decay for intermediate
values (10<N<20), where two distinct time regimes are observed: two exponential
decays for relatively short times and a power-law decay for larger times. In
this interval of N decoherence occurs for short times and a non-Markovian
dynamics is expected for larger times. When $N$ increases, energy and coherence
decay very fast and a Markovian dynamics is expected to occur. Wave packet
dynamics is used to determine the evolution of the particle inside the system
potentials.
