Threshold diffusion in a tilted washboard potential

We characterize the locked-to-running transition of a Brownian particle in a tilted washboard potential by looking at its transport properties in the vicinity of the transition threshold. At low temperatures the (normal) spat ial diffusion of the particle is enhanced as a consequence of the unlocking mechanism; in the overdamped regime an analytic expression is obtained tha t relates the particle diffusion constant to its mobility; in the underdamp ed regime an unusually large diffusion constant is revealed through numeric al simulation. The latter regime is analyzed in terms of multiple jump stat istics.