Spectral and Diffusive Properties of Silver-Mean Quasicrystals in 1,2, and 3 Dimensions

TL;DR

This paper investigates spectral properties and anomalous diffusion in silver-mean quasicrystals across 1, 2, and 3 dimensions, revealing a crossover in spectral measure and consistent anomalous diffusion behavior.

Contribution

It provides a comprehensive numerical analysis of spectral and diffusive properties in silver-mean quasicrystals in multiple dimensions, highlighting the independence of diffusion exponent from dimension.

Findings

Crossover from singular continuous to absolute continuous spectral measure with varying hopping strength.

Anomalous diffusion characterized by a diffusion exponent eta(v) between 0 and 1.

States remain delocalized even at very small hopping amplitudes.

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)\sim 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)\sim 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 hopping amplitude v. A study of the dynamics of initially localized wavepackets in large three-dimensional quasiperiodic structures furthermore reveals that wavepackets 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.