Inhomogeneous friction leading to current in periodic system

We study the diffusion process of a Brownian particle moving in a one-dimensional ratchet with space-dependent friction that is subjected to an external source. The equation of motion for a particle involves a multiplicative fluctuation, a nonlinear friction and an external driving force or a Gaussian white noise. The average position of the particle is simulated numerically in terms of the Langevin Monte Carlo method and discussed by means of the adiabatic approximation and the effective potential. The influence of coordinate-dependent friction on the average position and the direction of current of the particle is investigated. The results show that a net drift can be produced in the presence of both a coordinate-dependent friction and an external fluctuation, even when the ratchet potential and the temporal force are completely symmetrical.