  In this paper, we report results for the wave packet dynamics in a class of
quasiperiodic chains consisting of two types of weakly coupled clusters. The
dynamics are studied by means of the return probability and the mean square
displacement. The wave packets show anomalous diffusion in a stepwise process
of fast expansion followed by time intervals of confined wave packet width.
Applying perturbation theory, where the coupling parameter v is treated as
perturbation, the properties of the eigenstates of the system are investigated
and related to the structure of the chains. The results show the appearance of
non-localized states only in sufficiently high orders of the perturbation
expansions. Further, we compare these results to the exact solutions obtained
by numerical diagonalization. This shows that eigenstates spread across the
entire chain for v>0, while in the limit v->0 ergodicity is broken and
eigenstates only spread across clusters of the same type, in contradistinction
to trivial localization for v=0. Caused by this ergodicity breaking, the wave
packet dynamics change significantly in the presence of an impurity offering
the possibility to control its long-term dynamics.
