Anomalous and nonanomalous behaviors of single-file dynamics

We study the dynamics of a tagged particle that undergoes single-file diffusion in an environment of point Brownian particles. Specifically, we examine the effect of the particle density on the well-known anomalous sub-diffusion behavior of the tagged particle. We compare two single-file systems; the first maintains a fixed average particle density and the second experiences a dilution with time. Both our analytical predictions and computational results, that study the time evolution of the mean square displacement per particle for both systems, show that the behavior of the tagged particle transforms from anomalous sub-diffusive (if the average particle density is kept fixed) to normal if a reduction in the average particle density takes place during the diffusion. Our computational results are based on a discrete Monte-Carlo technique that captures perfectly the dynamics of the continuum formulation of single-file systems.