二维耦合定向输运模型研究

A two-dimensional coupled directed transport model

建立了外部驱动力及噪声作用下的二维耦合定向输运模型,其中的一个维度上为周期性分段棘齿势,另一垂直维度上为周期性对称非棘齿势,外部驱动力及噪声加在周期对称非棘齿势方向上,而棘齿势方向不加任何驱动,采用非平衡统计及非线性动力学理论研究了过阻尼情况下耦合系统在两个维度上的输运性质.结果显示,棘齿势与非棘齿势方向均可产生定向输运,其中棘齿势方向的系统平均速度对耦合强度、噪声强度、驱动力强度及粒子数目均有明显的依赖性,合适的耦合强度、噪声强度、驱动力强度或粒子数目下均可产生最大输运速度.而非棘齿势方向的系统平均速度受非棘齿势势垒高度影响显著,但随耦合强度、驱动力强度、驱动力初相位差及粒子数目的变化均出现波动现象,表现出平均速度对这些参量的依赖性较弱.

Under the effect of external driving force and noise, a directed transport model for coupled particles in a twodimensional potential is established. Here, a one-dimensional potential is taken as the periodic piecewise ratchet potential,and the other one is taken as the periodic symmetric non-ratchet potential to which the external periodic driving force and noise are applied. According to the nonequilibrium statistical theory and the nonlinear dynamics, the transport characters of the coupled system in the overdamped case are researched and discussed. Numerical results show that an obvious directed transport can appear both in the ratchet potential and in the non-ratchet potential case. But,the average velocities of the coupled system in the two potentials have completely different dependence on the system parameters. In the case of ratchet potential, the average velocity is strongly dependent on the coupling intensity, noise intensity, the driving strength, and the particle population; the average velocity can reach the maximum at appropriate coupling intensity, noise intensity, the driving strength or the particle population. Otherwise, in the case of non-ratchet potential, the average velocity is strongly dependent on the barrier height for the non-ratchet potential, but fluctuates as the coupling intensity, the driving strength, the driving initial phase difference or the particle population varies. This shows that the average velocity of the coupled system in the non-ratchet potential has weak dependence on system parameters, including the coupling intensity, the driving strength, the driving initial phase difference and the particle population.