Tansport Of Büttiker-Landauer Ratchet And Coupled Brownian Ratchet

This paper discusses the coherence and the diffusion of Büttiker-Landauer ratchet andtwo-particle coupled Brownian ratchet model in detail. It includes the following two parts:First, by analyzing the model of Büttiker-Landauer and get its expressions of speedand diffusion coefficient. We find some new interesting characteristics:a. When the temperature of the cold reservoir is low, the diffusion increases with thetemperature difference growing. At the same time, diffusion efficient increases with theburden growing, but Pe shows nonmonotonic behavior.b. When the temperature of the cold reservoir is high,the diffusion shows monotonicbehavior with the temperature difference growing, but doe not show the maximum.Besides, it increases with burden growing. But when the temperature of the cold reservoiris low, the diffusion is still growing with the burden growing, but Pe is no longermonotonic.Second, we derive an overdamped Langevin equation of two-particle coupled ratchetand get its expression of speed and diffusion. We discuss the speed and diffusion changewith additional force, and interparticle separation and so on under the strong couplinglimit and under-coupling conditions. We find:a. Under the strong coupling limit, due to different noise strength, speed as thefunction of four curves may be divided into three parts. When noise strength issmall,diffusion as the function of tilt shows giant diffusion. With the noise strengthgrowing, the maximum slowly moves to the right. When it passes the critical point, itdeclines slowly.b. Under the finite coupling strength, when the coupling strength is small, diffusionas the function of equilibrium interparticle separation, its top does not oscillate. But whenthe coupling strength is growing, its top stars to oscillate. We guess there is a criticalcoupling point.