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

Thomas Guérin (1) , David S. Dean (1)

1 LOMA - Laboratoire Ondes et Matière d'Aquitaine

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Thomas Guérin, David S. Dean. Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential. Physical Review E , 2017, 95 (1), pp.012109 (1-7). ⟨10.1103/PhysRevE.95.012109⟩. ⟨hal-01452850⟩