  We consider the motion of an underdamped Brownian particle in a tilted
periodic potential in a wide temperature range. Based on the previous data [1]
and the new simulation results we show that the underdamped motion of particles
in space-periodic potentials can be considered as the overdamped motion in the
velocity space in the effective double-well potential. Simple analytic
expressions for the particle mobility and diffusion coefficient have been
derived with the use of the presented model. The results of analytical
computations match well with numerical simulation data.
