In this paper, we consider the momentum operator of a quantum particle directed along the displacement of two of its neighbors. A modified open-path path integral molecular dynamics is presented to sample the distribution of this directional momentum distribution, where we derive and use a new estimator for this distribution. Variationally enhanced sampling is used to obtain this distribution for an example molecule, malonaldehyde, in the very low temperature regime where deep tunneling happens. We find no secondary feature in the directional momentum distribution and that its absence is due to quantum entanglement through a further study of the reduced density matrix.

中文翻译：

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深隧道效应中的量子动量分布和量子纠缠。

在本文中，我们考虑了沿两个相邻粒子的位移定向的量子粒子的动量算符。提出了一种改进的开放路径路径积分分子动力学，以采样该方向动量分布的分布，在此我们导出并使用一种新的估计器进行该分布。在发生深隧道效应的极低温条件下，使用变异增强的采样来获得示例分子丙二醛的这种分布。我们没有发现方向动量分布中的任何次要特征，并且它的缺乏是由于通过对密度矩阵的进一步研究而引起的量子纠缠。