关于系统绝热近似

根据算符的微分性质和分部积分法分别讨论了绝热近似下的形式消去公式,然后用迭代法得出快变量的表达式,继而用一个非线性随机微分系统为例子来说明迭代法的原理和应用方法,最后利用直接求解法处理在乘法噪声驱动下的线性随机微分系统,得到了其绝热近似下的快变量表达式.

On the Systematic Adiabatic Approximation

The formal elimination formula has been obtained in accordance with the differential properties of operators and the partial integration, regspectively. An expression for the fast variable has been derived with the iteration method. The linear stochastic differential system driven by multiplicative noise is dealt with by the direct solving method. Detailed calculation of the statistical properties of zt has been made and the scope of application of the direct solving method as well as the essence of the systematic adiabatic approximation are given. It is concluded that the systematic adiabatic approximation is a generalization of the traditional a-diabatic approximation and it provides a concise approach to solving non-autonomous and stochastic systems and some autonomous systems that cannot be solved by the traditional one. With adiabatic approximation, the adiabatic and non-adiabatic contributions can be easily separated. Systematic adiabatic approximation can always be used as long as non-adiabatic contribution is not great enough to exert any effect on the accuracy desired.