Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential.

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F<F_{c} the late-time and intermediate-time diffusive regimes are indistinguishable. Explicit asymptotic regimes for the MSD curves are identified at all time scales.