Specific features of threshold diffusion in a tilted periodic potential. Simple model and analytical results in the underdamped regime
The specific features of Brownian motion in periodic tilted potential (PTP) are analyzed in the low damping limit (LDL), near the region of locked-to-running transition, with the use of the simple model of thin reflective barriers. This model allows for a fairly accurate analytical description of transport properties of the particle in the LDL. Derived formulas reproduce the numerical results obtained for PTP, in particular: strongly non-exponential (proved to be of Lévy-type) distribution of jump lengths, the dependence of this distribution on the external force, the force dependence of the lifetime of the running state, etc.