Long memory effects in excitonic systems dynamics: Spectral relations and excitation transport

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.