  We study the quantum diffusion in quasiperiodic tight-binding models in one,
two, and three dimensions. First, we investigate a class of one-dimensional
quasiperiodic chains, in which the atoms are coupled by weak and strong bonds
aligned according to the metallic-mean sequences. The associated generalized
labyrinth tilings in d dimensions are then constructed from the direct product
of d such chains, which allows us to consider rather large systems numerically.
The electronic transport is studied by computing the scaling behavior of the
mean-square displacement of the wave packets with respect to the time. The
results reveal the occurrence of anomalous diffusion in these systems. By
extending a renormalization group approach, originally proposed for the
golden-mean chain, we show also for the silver-mean chain as well as for the
higher-dimensional labyrinth tilings that in the regime of strong quasiperiodic
modulation the wave-packet dynamics are governed by the underlying
quasiperiodic structure.

Mesoscale and Nanoscale Physics