Theory of non-Markovian exciton transport in a one dimensional lattice

Abstract

We consider non-Markovian exciton transport in a one dimensional system with nearest neighbor interactions. Kubo's stochastic Liouville equation (SLE) is used to derive a set of coupled equations of motion which are exact for a Poisson bath and which also should give a fairly accurate long time description for a Gaussian bath. The SLE is especially suitable for this problem since both cumulunt expansion and projection operator techniques encounter difficulties when the system is quantum mechanical, the stochastic off-diagonal coupling is strong, and the relaxation is non-Markovian. To elucidate the role of correlations in space and time, we consider two different models: (a) Both diagonal and off-diagonal fluctuations arise from the same bath. (b) All the fluctuations arise from uncorrelated baths. We find that model (a) always gives coherent exciton transport even at long times if the mean off-diagonal coupling J is nonzero. Model (b) gives diffusive behavior at long times, but the diffusion constant is very different in the non-Markovian limit from the prediction of Markovian or weak-coupling theories. In the Markovian limit, the expressions for the mean square displacement agree exactly with those of Haken and co-workers and of Grover and Silbey. Some interesting new features of non-Markovian transport are discussed.