QUANTUM DIFFUSION IN TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS

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.