Memory effects on energy transport in substitutionally disordered molecular crystals

Abstract

Abstract In this paper we consider the manifestations of coherence effects in electronic energy transport (EET) between randomly distributed donors. We have extended previous theoretical schemes for EET in an impurity band to incorporate a finite memory time for the EET. The short-time behaviour of the mean square displacement of the excitation. [ x 2 ( t )], and the initial-site survival probability, P 0 ( t ), exhibit two distinct transport regimes: (i) A coherent regime at ultrashort times, where [ x 2 ( t )] ∝ t 2 , and (ii) a partially coherent regime, which is characterized by [ x 2 ( t )] ∝ t 10/μ , where μ is the order of the multipolar transition rate, which is intermediate between coherent and conventional diffusive behaviour. Coherence effects also result in the retardation of the short-time decay of P 0 ( t ). The short-time partially coherent transport regime may be amenable to experimental interrogation by utilizing sub-ps and fs laser excitation. On the time scale exceeding the memory time, the conventional dispersive diffusive behaviour and the subsequent onset of classical diffusion for EET are recovered.