Investigation on the directed transport efficiency of feedback-control ratchet
Authors: Fan Li-Ming  , L&uuml; Ming-Tao  , Huang Ren-Zhong  , Gao Tian-Fu  , Zheng Zhi-Gang  ,   College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China;,   College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
Published: December 2020

Brownian motion in the environment of the thermal fluctuations is a long-study issue in nonequilibrium statistical physics. In recent years, the directed transport properties of Brownian ratchets attract the widespread attention of scholars. When a ratchet system possesses the spatio-temporal symmetry-breaking feature, the directed transport can be produced. Although the breakthrough progress in the directed transport of the Brownian ratchet has been made, the energy conversion efficiency of feedback ratchet is not clear. Therefore, the center-of-mass mean velocity and the energy conversion efficiency of coupled ratchet under the influences of the time asymmetry of external force and the spatial asymmetry of external potential are discussed in detail.
The overdamped coupled Brownian particles are investigated. Nevertheless, the optimized control of the coupled ratchet is the important for directed transport. Therefore, the closed-loop control which depends on the state of the system is adopted. The dynamic behavior of coupled particles can be described by the overdamped Langevin equation, and the equation is numerically solved by using the stochastic Runge-Kutta algorithm. Some properties of the directed transport can be obtained through this method, such as the center-of-mass mean velocity, the energy conversion efficiency, etc. It is interesting to find that the center-of-mass mean velocity can reach a maximum as the amplitude of external force increases. However, the mean velocity can show the quasi-periodic oscillations with the increase of the period of external force for different values of the spatial asymmetry of external potential. In addition, it can be found that the feedback ratchet needs strong noise to make the directed transport of the ratchet reach the maximum as the coupled strength increases. On the other hand, the energy conversion efficiencies of the feedback ratchet can achieve their corresponding maximum values with the increase of the amplitude of external force for different values of the time asymmetry, and the maximum increases as the time asymmetry increases. However, the efficiency can also show the quasi-periodic oscillations with the increase of the period of the external force for different values of the spatial asymmetry of external potential. Moreover, the energy conversion efficiency can achieve the maximum as the noise strength increases, but the maximum of the efficiency will decrease with the increase of coupling strength. From the discussion above, the optimal values of the time asymmetry, the spatial asymmetry, the period of the external force and the noise strength can promote the directed transport of the feedback coupled Brownian ratchet. These conclusions can provide some guidance in the enhancement of the energy conversion efficiency of a nanomachine.