Quantum diffusion in two-dimensional octagonal quasicrystals

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-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.