Spectral and diffusive properties of silver-mean quasicrystals in one, two, and three dimensions
- Cerovski, V.Z.
- Schreiber, M.
- Grimm, U.
DOIAbstract
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 delta<1 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 0<beta(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 hoppin...
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