Theoretical and numerical study on the fluctuation of the potential energy landscape

The diffusion of a Brownian particle exploring a meta-stable potential energy landscape with fluctuations is studied theoretically and numerically. The inverse harmonic part of the potential is replaced by a Gaussian approximated curve in the neighborhood of the saddle point and a new type of Monte-Carlo simulation algorithm is presented to simulate the random fluctuations of the potential energy. The probability of successful barrier surmounting and terminal arrival was calculated and compared with previous results. It is shown that, the replacement we have made is reasonable for the study of diffusion, which is primarily affected by the fluctuation of the barrier height, while other variations have little influence on the diffusion process. The Gaussian permutation and random Gaussian algorithms proposed here are expected to bring new ideas to the research of more complex problems.