Аннотация
We study the properties of wave functions and the wave-packet dynamics in
quasiperiodic tight-binding models in one, two, and three dimensions. The atoms
in the one-dimensional quasiperiodic chains are coupled by weak and strong
bonds aligned according to the Fibonacci sequence. The associated d-dimensional
quasiperiodic tilings are constructed from the direct product of d such chains,
which yields either the hypercubic tiling or the labyrinth tiling. This
approach allows us to consider rather large systems numerically. We show that
the wave functions of the system are multifractal and that their properties can
be related to the structure of the system in the regime of strong quasiperiodic
modulation by a renormalization group approach. We also study the dynamics of
wave packets in order to get information about the electronic transport
properties. In particular, we investigate the scaling behavior of the return
probability of the wave packet with time. Applying again the RG approach we
show that in the regime of strong quasiperiodic modulation the return
probability is governed by the underlying quasiperiodic structure. Further, we
also discuss lower bounds for the scaling exponent of the width of the wave
packet and propose a modified lower bound for the absolute continuous regime.
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