Transport properties under the influence of finite friction

Using the Langevin Monte Carlo method, the influence of friction on the directed motion of a Brownian particle driven by an external noise source is investigated. The results show that the existence and change of the environment friction influence the establishment and development of the steady motion of a Brownian particle derived by non-equilibrium fluctuation. The most probable correlation time, which corresponds to the maximum current, is inversely proportional to the friction coefficient. The abnormal transition of the current with different friction appears because of the coupling between the effective ratchet potential and coloured noise intensity.