摘要： We have studied the quantum diffusion in an octagonal quasiperiodic tiling. Paticular attention is paid to the analysis of long-time behavior of the autocorrelation function C(t) and the relationship between diffusion and fractal dimensions of energy spectrum. For the pure hopping model, numerical calculations show that C(t)～t^-1 , which corresponds to the case of periodic systems. For the combined model, in which the contribution of site potentials is considered, C(t)～t^-δ with 0＜δ≤1. The scaling factor δ is related to Hamiltonian parameters and the type of site where electron is initially located. Moreover, we find a crossover from δ=1 to 0＜δ＜1 with increasing site potentials.

Abstract: We have studied the quantum diffusion in an octagonal quasiperiodic tiling. Paticular attention is paid to the analysis of long-time behavior of the autocorrelation function C(t) and the relationship between diffusion and fractal dimensions of energy spectrum. For the pure hopping model, numerical calculations show that C(t) ～t^-1 , which corresponds to the case of periodic systems. For the combined model, in which the contribution of site potentials is considered, C(t) ～t^-$\delta$ with 0＜$\delta$≤1. The scaling factor $\delta$ is related to Hamiltonian parameters and the type of site where electron is initially located. Moreover, we find a crossover from $\delta$=1 to 0＜$\delta$＜1 with increasing site potentials.

中图分类号:  (Quasicrystals)

• 61.44.Br

66.30.Dn (Theory of diffusion and ionic conduction in solids) 71.23.Ft (Quasicrystals)