Diffusion dynamics in sierpinski gasket and pentagonal lattice

Abstract

Monte Carlo and exact enumeration method were applied to the random walk problems on Sierpinski gasket and pentagonal lattice. The mean square displacement $R^2(t)$ was calculated by the two methods and the probability of returning to the origin by exact enumeration method. The calculated values of the anomalous-diffusion exponent ($d_w=2.32\pm0.012$) and the spectral dimension ($d_s=1.65\pm0.0066$) in the gasket fractal are in good agreement with the theoretical values. The diffusion exponent of the pentagonal lattice is found to be identical to the space dimension.