In open quantum system dynamics, rich information about the major energy relaxation channels and corresponding relaxation rates can be elucidated by monitoring the vibrational energy flow among individual bath modes. However, such calculations often become tremendously difficult as the complexity of the subsystem–bath coupling increases. In this paper, we attempt to make this task feasible by using a mixed quantum–classical method, the Poisson-bracket mapping equation with non-Hamiltonian modification (PBME-nH) [H. W. Kim and Y. M. Rhee, J. Chem. Phys. 140, 184106 (2014)]. For a quantum subsystem bilinearly coupled to harmonic bath modes, we derive an expression for the mode energy in terms of the classical positions and momenta of the nuclei, while keeping consistency with the energy of the quantum subsystem. The accuracy of the resulting expression is then benchmarked against a numerically exact method by using relatively simple models. Although our expression predicts a qualitatively correct dissipation rate for a range of situations, cases involving a strong vibronic resonance are quite challenging. This is attributed to the inherent lack of quantum back reaction in PBME-nH, which becomes significant when the subsystem strongly interacts with a small number of bath modes. A rigorous treatment of such an effect will be crucial for developing quantitative simulation methods that can handle generic subsystem–bath coupling.

中文翻译：

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通过混合量子经典模拟来监测开放量子系统中的耗散振动能流。

在开放量子系统动力学中，可以通过监视各个浴池模式之间的振动能量流来阐明有关主要能量弛豫通道和相应弛豫率的丰富信息。但是，随着子系统-浴耦合的复杂性增加，这种计算通常变得非常困难。在本文中，我们试图通过使用混合量子经典方法，具有非哈密顿量修正的Poisson-bracket映射方程（PBME-nH）[HW Kim和YM Rhee，J。Chem。物理 140，184106（2014）]。对于双线性耦合至谐波浴模的量子子系统，我们在保持与量子子系统能量一致性的同时，根据原子核的经典位置和动量推导了模式能量的表达式。然后，通过使用相对简单的模型，以数值精确的方法为基准对结果表达式的准确性进行基准测试。尽管我们的表达式预测了一系列情况在质量上正确的耗散率，但是涉及强振动共振的情况却颇具挑战性。这归因于PBME-nH中固有的量子逆反应的缺乏，当子系统与少量浸浴模式强烈相互作用时，这将变得尤为重要。