Coherent Transport And Giant Diffusion In Periodic Potential

There are various stochastic dynamic systems in many scientific fields. Recently, it has become a hot focus to investigate the stochastic systems by means of theory and experiment. In this paper, we studied the phenomenon of stochastic resonance in overdamped periodic potential, and the massive damped motion of Brownian particles in tilted periodic potential,by using the numerical simulation algorithms. Three aspects are included in this paper.First, the phenomenon of stochastic resonance, occurring in periodic potential, driven only by time periodic external force, is studied. Results show that power-spectrum is sensitively affected by the noise intensity. With the moderate noise intensity, the peak value of power-spectrum attains a maximum. It proves the present of stochastic resonance in periodic potential.Second,the phenomenon of coherent transport, in the massive damped tilted periodic potential, is studied.(1) We studied the effects of the friction coefficientηon the Péclet number .It is found that the average velocity and effective diffusion coefficient are decreasing functions of the friction coefficient, in the case of the same particle. However, the decreasing of the average velocity is slower than the effective diffusion coefficient. Thus, their ratio (Péclet number) becomes higher. And higher the Péclet number more coherent is transport. (2)We studied phenomenon of coherent transport when friction coefficient is also periodic(sinusoidal). Results show that the Péclet number is strongly increased, when the friction coefficient has the same period, but shifted in phase, comparing with the periodic potential. This is because the particles easily escape over the barriers and the diffusion of the particles is weakened, with the periodic friction coefficient. And the system attains the much higher coherence. (3) We studied the effects of the periodic noise modulation on the Péclet number .Result shown that the phase shift between the symmetric potential and the periodic noise modulation enhances the coherence of the system.Third, a noise-induced directed transport is necessarily accompanied by diffusive spreading. We studied the diffusive spreading in the massive damped tilted periodic potential. Results show that D D0tains a maximum at Fc which is the critical threshold of tilted force. Unlike over damped case, the maximum of at D D0at F is the decreasing function of the friction coefficient cη. However, the value of Fc where D D0 attains a maximum is the increasing function ofη.