Random walk on percolation under an external field

Random walk on percolation under an external field has been investigated by using statistical analysis and Monte Carlo simulation. The mean square displacement 〈R2〉 as a function of time t was obtained. There exist some steps in the log〈R2〉–logt plot. The defect in the percolation plays the part of the trap for the walker. Each step corresponds to a type of trap. The height of the steps indicates the mean square displacement before the walker enters the trap and the width of the step expresses the trapping time spent in the trap. The calculated height and width by the probability theory are in agreement with simulation results quite well.