Anomalous quantum diffusion in two- and three-dimensional generalized Rauzy tilings

Abstract We compute the quantum diffusion of electron wavepackets in two- and three-dimensional quasiperiodic structures: the generalized Rauzy tilings. The algorithm allows us to treat systems of more than one million sites, and to consider energy-filtered wavepackets. We show that the anomalous diffusion exponent, β , depends on the energy, and that the propagation is almost ballistic at band edges ( β ≃1). This study is completed by exact diagonalizations of small clusters. The results strongly suggest that band-edge eigenstates are extended, which is consistent with their ballistic propagation.