Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain.
Faraday Discuss. 2010;144:301-22; discussion 323-45, 467-81. doi: 10.1039/b902479b.
An operational procedure is presented to compute explicitly the different terms in the generalized Langevin equation (GLE) for a few relevant variables obtained within Mori-Zwanzig formalism. The procedure amounts to introducing an artificial controlled parameter which can be tuned in such a way that the so-called projected dynamics becomes explicit and the GLE reduces to a Markovian equation. The projected dynamics can be realised in practice by introducing constraints, and it is shown that the Green-Kubo formulae computed with these dynamics do not suffer from the plateau problem. The methodology is illustrated in the example of star polymer molecules in a melt using their center of mass as relevant variables. Through this example, we show that not only the effective potentials, but also the friction forces and the noise play a very important role in the dynamics.
提出了一种操作程序，用于根据 Mori-Zwanzig 形式主义获得的几个相关变量，明确计算广义朗之万方程（GLE）中的不同项。该程序包括引入一个人工控制参数，该参数可以进行调整，以使所谓的投影动力学变得显式，并且 GLE 简化为马尔可夫方程。通过引入约束，可以在实际中实现投影动力学，并且表明，使用这些动力学计算的格林-库珀公式不会受到平台问题的影响。该方法在使用质心作为相关变量的熔体中的星形聚合物分子的示例中进行了说明。通过这个例子，我们表明，不仅有效势，而且摩擦力和噪声在动力学中起着非常重要的作用。
