Author(s)

Chunhui Zhang, Zhanwu Bai^*

Department of Mathematics and Physics, North China Electric Power University, Baoding, China.

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.

Diffusion Coefficient, Periodic Potential, Brownian Motion

Zhang, C. and Bai, Z. (2021) A Simple Model for the Calculation of Diffusion Coefficient in a Periodic Potential. Journal of Modern Physics, 12, 91-98. doi: 10.4236/jmp.2021.122009.