Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
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DOI：
10.1063/1.4921234
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发表时间：
2015-05-21
影响因子：
4.4
通讯作者：
Althorpe, Stuart C.
中科院分区：
文献类型：
--
作者：
Hele, Timothy J. H.;Willatt, Michael J.;Althorpe, Stuart C.
最近，我们通过对“经典维格纳”近似的推导做一个简单的改变，得到了一个量子玻尔兹曼守恒的经典动力学。在这里，我们表明，这种“松原动力学”的进一步近似产生了两个流行的启发式方法治疗量子玻尔兹曼时间相关函数：质心分子动力学（CMD）和环聚合物分子动力学（RPMD）。我们表明，CMD是一个平均场近似松原动力学，通过丢弃（经典）的质心周围的波动，和RPMD是丢弃一个长期的结果，在松原Liouvillian移动这些波动的频率。这些发现与以前的数值结果是一致的，并给出明确的公式，CMD和RPMD遗漏的条款。(C)2015 AIP Publishing LLC.
We recently obtained a quantum-Boltzmann-conserving classical dynamics by making a single change to the derivation of the "Classical Wigner" approximation. Here, we show that the further approximation of this "Matsubara dynamics" gives rise to two popular heuristic methods for treating quantum Boltzmann time-correlation functions: centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD). We show that CMD is a mean-field approximation to Matsubara dynamics, obtained by discarding (classical) fluctuations around the centroid, and that RPMD is the result of discarding a term in the Matsubara Liouvillian which shifts the frequencies of these fluctuations. These findings are consistent with previous numerical results and give explicit formulae for the terms that CMD and RPMD leave out. (C) 2015 AIP Publishing LLC.