Temperature-Frequency Controlling the Characteristics of a Pulsating Brownian Ratchet with Slightly Fluctuating Potential Energy

Abstract

Within the approximation of slight fluctuations of the nanoparticle potential energy, we developed a method for calculating the characteristics of a Brownian ratchet (a complex nonlinear system capable of extracting useful work from unbiased nonequilibrium fluctuations). The method is suitable for studying the mechanisms and modes of functioning of artificial nanomotors. Unlike the effort-consuming obtaining and applying for this studying the Green's functions of the coordinate representation which describe diffusion in the stationary component of the potential, the proposed method operates with the Fourier representation of both the control and desired functions. That allows calculating the Green's functions as inverse matrices in the space of Fourier harmonics and finding the average velocity of a Brownian ratchet with an arbitrary spatial and temporal dependence of the potential energy. To illustrate the method, an analysis has been performed of the functioning of a ratchet in which the directional motion of nanoparticles arises due to small stochastic fluctuations of an asymmetric sawtooth potential profile with an arbitrary barrier-heightto- thermal-energy ratio. It is shown that, with a harmonic coordinate dependence of these fluctuations, a change in the direction and intensity of the ratchet effect is controlled not only by tuning the magnitude of their phase shift relative to the sawtooth potential (the fact revealed before in the high-temperature approximation), but also by changing the temperature and the frequency of fluctuations. The nontrivial dependencies of the ratchet velocity on the geometric, frequency, and energy parameters of the system are obtained by numerical implementing the proposed calculation method.