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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Generalized Langevin equation revisited: Mechanical random force and self-consistent structure
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Generalized Langevin equation revisited: Mechanical random force and self-consistent structure

机译：重述广义Langevin方程：机械随机力和自洽结构

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摘要

The generalized Langevin equation (GLE) is considered with emphasis put on a mechanical random force F (t), whose time evolution is not natural due to the presence of a projection operator in a propagator. We first derive the GLE for a set of dynamical variables A of interest not by formal manipulation of the operator identity as is usually done, but by expressing the random force in terms of natural trajectory in the phase space. Based on this new derivation we observe two structural characteristics, (1) a linear functional interdependence between F(t) and A(t) and (2) a self-consistent structure (SCS) inherent in the GLE. The SCS gives an iterative procedure to determine F(t) and its time correlation function, i.e. a memory function K(t), once we have numerical data for A(t) supplied by computer experiments. This method generates F (t) and a memory function K(t), nicely for an exactly solvable many-body system after several iterations. Some merits of using the SCS are further discussed in connection with numerical methods to calculate the autocorrelation function of A(t).
机译：考虑广义朗格文方程（GLE），重点放在机械随机力F（t）上，由于传播子中存在投影算子，其时间演化不自然。首先，我们不是通过通常对操作员身份的正式操纵来得出感兴趣的一组动态变量A的GLE，而是通过根据相空间中的自然轨迹来表达随机力。基于这一新的推论，我们观察到两个结构特征：（1）F（t）和A（t）之间的线性功能相互依赖关系;（2）GLE中固有的自洽结构（SCS）。一旦获得了由计算机实验提供的A（t）的数值数据，SCS就会给出确定F（t）及其时间相关函数（即存储函数K（t））的迭代过程。此方法生成F（t）和存储函数K（t），非常适合经过多次迭代后可精确求解的多体系统。结合数值方法来计算A（t）的自相关函数，进一步讨论了使用SCS的优点。

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