Stochastic Brownian motors with small potential energy fluctuations

Abstract

We suggest a new approach to description of driven diffusive systems in which fluctuations of nano-particle potential energy, being a source of directed motion, are considered as small. The base of the approach is the method of the Green’s functions, which allow writing analytical expressions for the sought-for average nano-particle velocity. These expressions are essentially simplified under the assumption of high temperatures. Within this high-temperature approximation, we consider a system (Brownian motor) with small harmonic oscillations of the particle potential energy of a saw-tooth shape. The obtained representation for the average motor velocity is the product of two functions. One of them depends on the fluctuation frequency and the other includes geometrical parameters of the system (that is of the steady and perturbing potential profiles). It is shown that the frequency dependence of the average velocity is a nonmonotonic function with the maximum position determining by the inverse characteristic diffusion time. In its turn, the average motor velocity as a function of the asymmetry parameter of the nonfluctuating component of the potential profile and the phase shift of the fluctuating one is sign-changing. This result means that there exists a possibility to govern the direction of the motor motion by the phase shift of harmonic oscillations relative to a fixed saw-tooth potential component. The intervals of both the phase shift and the asymmetry parameter values, in which the particle can move to the right or to the left, are diagrammed. The regularities obtained are of great importance to choose the values of parameters which provide effective regimes of Brownian motors operation.