This study investigates the diffusive motion of a Brownian particle in a 1D periodic potential. The reactive flux theory for finite barriers and memory friction is developed to calculate the escape rate in the spatial...This study investigates the diffusive motion of a Brownian particle in a 1D periodic potential. The reactive flux theory for finite barriers and memory friction is developed to calculate the escape rate in the spatial diffusion regime. The diffusion coefficient is obtained in terms of the jump-model. The theoretical results agree well with the Langevin simulation results. The method can be generalized to other colored noises with Gaussian distribution.展开更多
Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where...Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where the internal noise is a Gaussian white noise, and the basic cell of the periodic potential is composed of a parabolic potential linked with a harmonic potential. When the particles cross the joint point of the potential, a time coarse-graining scheme is used to obtain a simple analytical expression of the probability distribution. The particles drift and diffuse from the first barrier to the second barrier, the passing probability over the second barrier corresponding to the escape rate becomes decrease serves as the long-jump probability. The theoretical result is confirmed by numerical simulation results. The approach can be extended to color noise case.展开更多
文摘This study investigates the diffusive motion of a Brownian particle in a 1D periodic potential. The reactive flux theory for finite barriers and memory friction is developed to calculate the escape rate in the spatial diffusion regime. The diffusion coefficient is obtained in terms of the jump-model. The theoretical results agree well with the Langevin simulation results. The method can be generalized to other colored noises with Gaussian distribution.
文摘Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where the internal noise is a Gaussian white noise, and the basic cell of the periodic potential is composed of a parabolic potential linked with a harmonic potential. When the particles cross the joint point of the potential, a time coarse-graining scheme is used to obtain a simple analytical expression of the probability distribution. The particles drift and diffuse from the first barrier to the second barrier, the passing probability over the second barrier corresponding to the escape rate becomes decrease serves as the long-jump probability. The theoretical result is confirmed by numerical simulation results. The approach can be extended to color noise case.
