Particle transport in space-periodic potentials in underdamped systems

We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data and the new simulation results we show that the underdamped motion of particles in space-periodic potentials can be considered as overdamped motion in the velocity space in the effective double-well potential. Simple analytic expressions for the particle mobility and diffusion coefficient are derived with the use of the presented model. These accurately match numerical simulation results.