Three Routes to the Friction Matrix and Their Application to the Coarse-Graining of Atomic Lattices
Three Routes to the Friction Matrix and Their Application to the Coarse-Graining of Atomic Lattices
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DOI：
10.1002/mats.201100014
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发表时间：
2011-08-25
影响因子：
1.4
通讯作者：
Succi, Sauro
中科院分区：
文献类型：
--
作者：
Kauzlaric, David;Espanol, Pep;Succi, Sauro
在原子动力学的粗粒度（CG）描述中，摩擦矩阵的计算是一个至关重要的问题，以便正确地解释原子动力学的任何简化表示所固有的耗散效应。在CG的Mori-Zwanzig投影算子方法中，摩擦矩阵的定义有几种可能性，这取决于所使用的投影仪。本文讨论了其中两个投影仪（Mori投影仪和Zwanzig投影仪）的连接，并分析了它们各自的优点和局限性。此外，还介绍了Mori框架中摩擦矩阵的三种不同计算方法，并沿着讨论了它们之间的联系。通过在石墨烯晶格中的CG质量斑点变量的中心的例子，它示出，即使这三种方法是从理论的角度来看是等效的，它们可能会有很大的不同，在计算机模拟的目的，在实际实施方面。在给定的例子中，这是原子晶格的代表，事实证明，速度-速度相关函数的线性回归，灵感来自爱因斯坦-赫尔方方法，是最不容易出错的光学模式的干扰。
The calculation of the friction matrix in the coarse-grained (CG) description of an atomistic system is a crucial issue, in order to properly account for the dissipative effects inherent to any reduced representation of the atomistic dynamics. Within the Mori-Zwanzig projection operator approach to CG, there are several possibilities for the definition of the friction matrix, depending on the projector that is being used. In this paper, the connection of two of these projectors (Mori's and Zwanzig's) is discussed and the corresponding merits and limitations are analysed. Moreover, three different ways of computing the friction matrix in the Mori's framework are presented, along with a discussion of their mutual connections. By the example of CG centre of mass blob variables in the graphene lattice, it is shown that, even though the three approaches are equivalent from a theoretical viewpoint, they may differ considerably in terms of practical implementation for computer simulation purposes. In the given example, which is representative for atomic lattices, it turns out that a linear regression of the velocity-velocity correlation function, inspired by the Einstein-Helfand approach, is the least error-prone against disturbances from optical modes.