周期场时间导数Ornstein-Uhlenbeck噪声Fokker-Planck方程的小参数展开求解

The small parameter expansion solution to Fokker-Planck equation for Brownian motion in a periodic potential with internal time derivative Ornstein-Uhlenbeck noise

通过引入变量,周期场中内部时间导数Ornstein-Uhlenbeck噪声驱动的布朗运动可用高维Fokker-Planck方程来描述.上述系统不能直接应用通常的小参数展开和势谷中心展开近似求解.用一种变通的小参数展开方法近似求解了系统的Fokker-Planck方程,结果适用于小势垒高度、中等关联时间和较大的相空间区域,近似解析解可获得系统的改进.

By introducing suitable variables, the Brownian particles＇ motion in a periodic potential with internal time derivative Ornstein-Uhlenbeck noise can be described by a high-dimensional Fokker-Planck equation. The equation can not be solved by the usual small parameter expansion method and potential valley expansion method. An alternative small parameter expansion method is proposed to deal with the equation, and the result is applicable for small potential barrier height, intermediate correlation time and in a larger phase space domain, the approximation can be improved systematically.