Propagator and mean-square displacement in single-file systems

Abstract

It is shown that the propagator in single-file systems may quite generally be deduced from the propagator in the corresponding unrestricted case. Irrespective of its structure in the unrestricted case, the propagator of single-file systems in the long-time limit approaches a Gaussian distribution. It is found that the exponent of the time dependence of the mean-square displacement is reduced by a factor of two, compared with the unrestricted case. Examples for different models of particle propagation are considered and compared with literature data. For one model the theoretical result is compared with a molecular dynamics simulation.