Nonadiabatic corrections to the velocity of a Brownian motor with a complex potential profile

A number of laws have been established that govern the motion of a Brownian particle in a periodic potential profile for the adiabatically fast (with the time τ₀) and adiabatically slow variations in its shape. The average velocity of a particle has been calculated including a nonadiabatic contribution depending on τ₀ and the characteristic times of the system, which are determined by the characteristic features of the potential profile. It has been shown that the nonadiabatic correction to the velocity is proportional to τ₀² for a smooth potential profile and to τ₀ for a hopping movement in a potential containing barriers and wells, and this correction limits the large values of the rectification factor of motion for a high-performance motor operation mode.