  We report results of numerical simulations of wave-packet dynamics in a class
of chains consisting of two types of weakly coupled clusters arranged in a
quasiperiodic sequence. Properties of eigenstates are investigated using
perturbation theory of degenerate levels in the coupling strength v and by
numerical diagonalization. Results show that wave packets anomalously diffuse
via a two-step process of rapid and slow expansions, which persist for any v>0.
An elementary analysis of the degenerate perturbation expansion reveals that
non-localized states may appear only in a sufficiently high order of
perturbation theory, which is simply related to the combinatorial properties of
the sequences. Numerical diagonalization furthermore shows that eigenstates
ergodically spread across the entire chain for v>0, while in the limit as v->0
ergodicity is broken and eigenstates spread only across clusters of the same
type, in contradistinction with trivial localization at v=0. An investigation
of the effects of a single-site perturbation on wave-packet dynamics shows
that, by changing the position or strength of such an impurity, it is possible
to control the long-time wave-packet dynamics. By adding a single impurity it
is possible to induce wave-packet localization on individual subchains as well
as on the whole chain.
