Reversal of the motion direction of a Brownian ratchet induced by the curvature reversal of the ratchet potential

Abstract

Brownian motion of a particle in a stationary potential profile of universal symmetry is considered, the drift of which occurs due to dichotomous fluctuations of that profile with the coordinate dependence of the fluctuations described by either symmetric or antisymmetric periodic functions. Unlike existing models of ratchet systems, the asymmetry of the system under consideration is introduced by means of fluctuations due to a shift in the positions of their symmetry axes or symmetry centers relative to the stationary profile. In the high-temperature approximation, analytical relations are obtained for the frequency dependence of the ratchet average velocity, which implies the existence of the ratchet effect when two spatial harmonics of the fluctuating potential are taken into account. The temperature dependences of the average velocity have been calculated in the adiabatic mode of the motion. It is shown that the reversal of the curvature of the stationary component of the potential profile under spatially symmetric fluctuations can lead to a reversal of the motion direction. The dependences of the average velocity on the fluctuation frequency, the shift of the symmetry axes of the stationary and fluctuating components of the potential energy, as well as on the ratio of the amplitudes of these components to the thermal energy have been analysed. Optimal motion modes of the ratchet system under consideration have been revealed.