论文标题
非绝热状态中热平均计算的多级蒙特卡洛路径积分分子动力学
Multi-level Monte Carlo path integral molecular dynamics for thermal average calculation in the nonadiabatic regime
论文作者
论文摘要
使用路径积分方法，可以通过在扩展配置空间上的环聚合物表示近似多电状态量子系统中的热平均值，在该空间中，额外的自由度与每个珠的表面索引相关。这项工作的主要目标是提出一种更有效的采样算法，以计算此类热平均值。我们根据表面索引的构型重新重新重新重新制定扩展的环聚合物近似，并通过引入适当的参考度量，重新制作被重塑为两个功能扩展期望的比率。通过定量估计亚估计器，并最大程度地估算采样平均值的总方差，我们提出了一种多级蒙特卡洛路径积分分子动力学方法（MLMC-PIMD），以实现计算成本和准确性的最佳平衡。
With the path integral approach, the thermal average in a multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are associated with the surface index of each bead. The primary goal of this work is to propose a more efficient sampling algorithm for the calculation of such thermal averages. We reformulate the extended ring polymer approximation according to the configurations of the surface indexes, and by introducing a proper reference measure, the reformulation is recast as a ratio of two expectations of function expansions. By quantitatively estimating the sub-estimators, and minimizing the total variance of the sampled average, we propose a multi-level Monte Carlo path integral molecular dynamics method (MLMC-PIMD) to achieve an optimal balance of computational cost and accuracy.
