Effects of Asymmetry of Potential on Stochastic Stokes’ Drift

The directed motion of Brownian particles is generated by a travelling asymmetric potential. The asymptotic behaviour of probability density of the particles at long time is a solitary wave. The Brownian particles can do work against an external opposing force with high efficiency. The analytical expressions of the solitary wave and the efficiency of the Brownian particles are obtained. The average velocity and the efficiency of the particles depends strongly on the travelling speed and the asymmetry of the potential.