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We study the properties of wave functions and the wave-packet dynamics inquasiperiodic tight-binding models in one, two, and three dimensions. The atomsin the one-dimensional quasiperiodic chains are coupled by weak and strongbonds aligned according to the Fibonacci sequence. The associated d-dimensionalquasiperiodic tilings are constructed from the direct product of d such chains,which yields either the hypercubic tiling or the labyrinth tiling. Thisapproach allows us to consider rather large systems numerically. We show thatthe wave functions of the system are multifractal and that their properties canbe related to the structure of the system in the regime of strong quasiperiodicmodulation by a renormalization group (RG) approach. We also study the dynamicsof wave packets to get information about the electronic transport properties.In particular, we investigate the scaling behaviour of the return probabilityof the wave packet with time. Applying again the RG approach we show that inthe regime of strong quasiperiodic modulation the return probability isgoverned by the underlying quasiperiodic structure. Further, we also discusslower bounds for the scaling exponent of the width of the wave packet andpropose a modified lower bound for the absolute continuous regime.

Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings