Continuum theory of single-file diffusion in terms of label variable

摘要

The problem of one-dimensional diffusion is studied for Brownian particles with short-range repulsive interaction. The adoption of the continuous label variable as the spatial coordinate, inspired by the Lagrangian description in fluid mechanics, is shown to be effective in correct prediction of the anomalous diffusion, in which the mean square displacement of the particle grows in proportion to √t. The method is also applicable to the cases in which an externalfield is present. This suggests potential usefulness of the label variable formulation in describing the slow dynamics of glassy systems.