Mechanism for the appearance of a high-efficiency Brownian motor with fluctuating potential

A version of a Brownian motor (system generating a unidirectional motion of a Brownian particle in an asymmetric fluctuating potential) is considered for the case where the potential consists of an asymmetric periodic component undergoing random shifts by a half-period $L$ with a certain frequency and the potential of an external force $F$. The high efficiency of such a motor (ratio of the useful work against the load force $F$ to the energy imparted to the particle due to the potential shifts) is due to a high and narrow barrier, as well as to a smooth arbitrarily shaped potential relief repeated with an energy shift on both half-periods $L$. Simple analytic expressions are obtained for the flux and efficiency as functions of the load force over a wide frequency range.