Memory Effects and Memory Functions in Surface Diffusion

Abstract

We consider the diffusive dynamics of particles in various model systems with strong interactions. We study the temporal dependence of the single-particle velocity autocorrelation function o(t), and its corresponding memory function. We find o(t) to decay non-exponentially and in most cases follow a power-law o(t) t- x at intermediate times i, while at long times there is a crossover to an exponential decay. We characterize the possible values of the decay exponent x, and show that x correlates with interaction and ordering effects. In many cases, the memory function follows behavior similar to that of o(t). These results suggest that o(t) can be used to obtain information about the ordering of the system and about the nature of predominant interactions between adparticles using experimental techniques such as scanning tunneling microscopy, in which o(t) can be measured in terms of discrete adparticle displacements. Finally, our studies suggest that the decay of velocity correlations in collective diffusion is qualitatively similar to the case of tracer diffusion.