Spectral and diffusive properties of silver-mean quasicrystals in one, two, and three dimensions

Abstract

Spectral properties and anomalous diffusion in the silver-mean (octonacci) quasicrystals in d=1,2,3 are investigated using numerical simulations of the return probability C(t) and the width of the wave packet w(t) for various values of the hopping strength v. In all dimensions we find C(t)~t^(-delta), with results suggesting a crossover from delta1 to delta=1 when v is varied in d=2,3, which is compatible with the change of the spectral measure from singular continuous to absolute continuous; and we find w(t)~t^beta with 0beta(v)1 corresponding to anomalous diffusion. Results strongly suggest that beta(v) is independent of d. The scaling of the inverse participation ratio suggests that states remain delocalized even for very small hopping amplitude v. A study of the dynamics of energy-filtered wave packets in large three-dimensional quasiperiodic structures furthermore reveals that wave packets composed of eigenstates from an interval around the band edge diffuse faster than those composed of eigenstates from an interval of the band-center states: while the former diffuse anomalously, the latter appear to diffuse slower than any power law.