Effects of asymmetry of potential on stochastic Stokes' drift

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