The main quantity that controls excitation relaxation and transport in molecular systems is the environment-induced fluctuation correlation function. Commonly used models assume the exponentially decaying correlation function, characterized by a given characteristic time, which allows us to define the Markovian conditions and, hence, allows us to use rate equations for excitation dynamics. A long memory fractional correlation function is studied in this paper as an alternative model. Such a function has an infinite characteristic decay time, and thus, system decay to equilibrium becomes poorly defined. Consequently, it becomes impossible to define the Markovian regime. By assuming the weak system–bath coupling regime, we apply the non-Markovian equations of motion to describe the equilibration process in an excitonic molecular aggregate. The long memory model causes a weaker decay of coherent components in excitonic system relaxation dynamics. Nevertheless, the short time dynamics, which is important in optical spectroscopy, depends on the short time interval of the fluctuation correlation function. Excitation relaxation in this window appears to be well described by non-Markovian approaches.

中文翻译：

---

激子系统动力学中的长记忆效应：光谱关系和激发传输。

控制分子系统中激发弛豫和传输的主要量是环境诱导的波动相关函数。常用的模型假定指数衰减的相关函数具有给定的特征时间，这使我们能够定义马尔可夫条件，从而使我们能够将速率方程用于激励动力学。作为替代模型，本文研究了长记忆分数相关函数。这样的函数具有无限的特征衰减时间，因此，系统衰减到平衡的定义变得很困难。因此，不可能定义马尔可夫政权。通过假设弱系统-浴耦合机制，我们应用非马尔可夫运动方程来描述激子分子聚集体中的平衡过程。长记忆模型在激子系统弛豫动力学中导致相干分量的减弱。然而，在光谱学中很重要的短时间动力学取决于波动相关函数的短时间间隔。非马尔可夫方法似乎很好地描述了该窗口中的激励松弛。