Truncated Levy walk of a nanocluster bound weakly to an atomically flat surface: Crossover from superdiffusion to normal diffusion

We have demonstrated that the fast stick-slip diffusion of a nanocluster bound weakly to an atomically flat surface such as graphite is a truncated Levy walk. To do this, a 2 mus molecular dynamics simulation was performed using a finite two-dimensional Frenkel-Kontolova-type model with Langevin-thermostats. We found that the statistics of jump durations obey a power-law distribution truncated at similar to ns and that the exponent gamma of a mean-square displacement (similar tot(gamma)) becomes 1 only for tgreater than or similar tons. Short (200 ns) simulations cannot correctly show the crossover from superdiffusion (gamma>1) to normal-diffusion (gamma=1).