Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations

Abstract

We present a study of general symmetry properties of a Brownian ratchet model. The study is based both on constructing chains of symmetry transformations reflecting explicit and hidden symmetries of the average ratchet velocity as a functional of the spatially periodic potential energy of a nanoparticle and on taking into account the symmetry types of periodic functions that are components of the potential energy of an additive-multiplicative form. A ratchet with a sawtooth stationary potential profile, dichotomously perturbed by a spatially harmonic signal, is investigated. Conclusions are made on both the possibility of occurrence of the ratchet effect and its direction for given values of the asymmetry parameter of the sawtooth profile, phase shifts of the control component, and frequencies of temporal fluctuations. These conclusions have been obtained only on the basis of symmetry transformations; that demonstrates the predictive value of the approach presented. The results of the symmetry analysis are confirmed by numerical simulation of the functioning of a ratchet with dichotomous stochastic spatially periodic fluctuations of the nanoparticle potential energy.