非线性非势系统的Fokker-Planck方程的非定态解

TIME-DEPENDENT SOLUTION OF THE FOKKER-PLANCK EQUATION OF NONLINEAR NONPOTENTIAL SYSTEMS

本文应用Green函数的Ω展开理论,讨论了弱噪声极限下非线性非势系统的Fokker-Planck方程的非定态解,并讨论了系统从不稳定点出发到稳定态的弛豫过程中的维数约化和标度关系。

The time-dependent problem of Fokker-Planck equation of the nonlinear systems without detailed balance is solved in the weak noise limit by using the Ω-expansion of the Green function. We further reveal the possibility of the dimension reduction and some scaling relations in the relaxation of the system from the unstable state to the stable state.