Frenkel exciton population dynamics of an excitonic dimer is studied by comparing the results from a quantum master equation involving rates from second-order perturbative treatment with respect to the excitonic coupling with the non-perturbative results from “Hierarchical Equations of Motion” (HEOM). By formulating generic Liouville-space expressions for the rates, we can choose to evaluate them either via HEOM propagations or by applying the cumulant expansion. The coupling of electronic transitions to bath modes is modeled either as overdamped oscillators for the description of thermal bath components or as underdamped oscillators to account for intramolecular vibrations. Cases of initial nonequilibrium and equilibrium vibrations are discussed. In the case of HEOM, initial equilibration enters via a polaron transformation. Pointing out the differences between the nonequilibrium and equilibrium approach in the context of the projection operator formalism, we identify a further description, where the transfer dynamics is driven only by fluctuations without involvement of dissipation. Despite this approximation, this approach can also yield meaningful results in certain parameter regimes. While for the chosen model, HEOM has no technical advantage for evaluation of the rate expressions compared to cumulant expansion, there are situations where only evaluation with HEOM is applicable. For instance, a separation of reference and interaction Hamiltonian via a polaron transformation to account for the interplay between Coulomb coupling and vibrational oscillations of the bath at the level of a second-order treatment can be adjusted for a treatment with HEOM.

中文翻译：

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激子传递使用从“运动分层方程”中提取的速率

激子二聚体的Frenkel激子种群动力学是通过比较量子主方程的结果而得出的，该方程涉及二阶微扰处理的速率与激子耦合之间的关系，以及“运动层次方程”（HEOM）的非微扰结果。通过为费率制定通用的Liouville空间表达式，我们可以选择通过HEOM传播或通过累积累积量对其进行评估。电子跃迁与熔池模式的耦合被建模为用于描述热熔池组件的过阻尼振荡器，或用于考虑分子内振动的欠阻尼振荡器。讨论了初始非平衡和平衡振动的情况。在HEOM的情况下，初始平衡通过极化子转换进入。指出了在投影算子形式主义背景下非均衡和均衡方法之间的差异，我们确定了进一步的描述，其中转移动力学仅由波动驱动，而没有耗散。尽管有这种近似，但这种方法在某些参数范围内也可以产生有意义的结果。尽管对于所选模型，HEOM与累积量扩展相比在评估速率表达式方面没有技术优势，但在某些情况下，仅适用于使用HEOM进行评估。例如，可以通过极化子变换将参考和相互作用的哈密顿量分开，以解决库仑耦合和二阶处理水平下的镀液振动振荡之间的相互作用，从而适用于HEOM处理。