Frenkel exciton population dynamics of an excitonic dimer is studied by comparing results from a quantum master equation (QME) involving rates from second-order perturbative treatment with respect to the excitonic coupling with 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 cumulant expansion. The coupling of electronic transitions to bath modes is modeled either as overdamped oscillators for description of thermal bath components or as underdamped oscillators to account for intramolecular vibrations. Cases of initial nonequilibrium and equilibrium vibrations are discussed. In 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, also this approach can 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.
A theoretical model for linear and nonlinear spectroscopy of plexcitons
Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences（中国科学院化学研究所，不稳定和稳定物质结构化学国家重点实验室，北京分子科学国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Environmental Control Extends Beyond Quantum Dephasing in Exciton Energy Transfer
Ningbo University（宁波大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；Hangzhou Dianzi University（杭州电子科技大学）；University of Toronto（多伦多大学）；Rosalind Franklin Institute（罗莎琳德·富兰克林研究所）；University of Oxford（牛津大学）
