A theoretical‐computational procedure, recently proposed for modelling Vibrational Energy Relaxation (VER) processes of a molecule (Quantum Center, QC) embedded in a complex atomic‐molecular system, is extended and applied for analyzing in detail the features of the QC density matrix (DM) temporal evolution. The results, obtained using aqueous azide ion as a case study, show the total lack of coherence in the DM, when the system is prepared to be initially in a pure vibrational eigenstate. This finding is fully in line with the statistical interpretation of the process typically adopted also in the experimental studies where the relaxation processes are all described within the typical schemes of chemical kinetics. Consistently, when the initial vibrational state corresponds to an eigenstate mixture, although initially coherent, the DM relaxes to a fully incoherent condition with a mean lifetime related to the one of the diagonal elements relaxation. These specific DM features turn out to be essentially governed by the thermal equilibrium condition of the atomic‐molecular classical coordinates which drive the ensemble of the quantum‐trajectories toward the observed statistical regime. Finally, from the analysis of a single long timescale quantum vibrational trajectory it also clearly emerges its ergodic behaviour.

中文翻译：

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关于软凝聚态分子系统中量子振动轨迹的统计体系、相干性与不相干性以及遍历性

最近提出的一种理论计算程序，用于模拟嵌入复杂原子分子系统中的分子（量子中心，QC）的振动能量弛豫（VER）过程，该程序被扩展并应用于详细分析 QC 密度矩阵的特征（DM）时间演化。使用含水叠氮化物离子作为案例研究获得的结果表明，当系统最初准备处于纯振动本征态时，DM 完全缺乏相干性。这一发现完全符合实验研究中通常采用的过程的统计解释，其中弛豫过程都是在化学动力学的典型方案中描述的。一致地，当初始振动状态对应于本征态混合时，尽管最初是相干的，但 DM 弛豫到完全非相干条件，其平均寿命与对角元素弛豫之一相关。这些特定的 DM 特征本质上是由原子分子经典坐标的热平衡条件控制的，它驱动量子轨迹的整体朝着观察到的统计状态发展。最后，通过对单个长时间尺度量子振动轨迹的分析，它也清楚地显现出其遍历行为。