Time scales for the observation of diffusion in very small systems

We consider the time scales for the observation of diffusion in small cluster systems. Molecular-dynamics calculations are performed to investigate the long-time behavior of the velocity autocorrelation function for the finite system. It is found that the resulting power spectrum exhibits liquidlike behavior over frequencies larger than those corresponding to large-amplitude motion across the boundaries of the cluster. The results are consistent with an interpretation of the cluster as a finite mixing system exhibiting decay of correlations and zero diffusion constant. The decay to zero diffusion constant as approaches zero occurs in a nearly singular fashion.