The self-consistent Mori approach to transport in exciton-phonon systems

In earlier calculations of exciton transport in exciton-phonon systems diffusivity in general has been achieved by means of semi-phenomenological elements. The present investigation aims at giving an ab initio derivation of the diffusion function, involving only intrinsic characteristics of the model. Using a projection operator technique we have studied a one-dimensional molecular crystal model with site-diagonal coupling to a phonon bath of acoustic type. The relevant memory kernels in the transport equations have been evaluated in a consistent perturbative treatment up to second order in the exciton-phonon interaction for two different kinds of local excitation. The evolution of the second moment of the exciton probability density helps us to discuss coherent (M(2) similar to t(2)) and diffusive (M(2) similar to t) transport. The time dependence of these memory functions displays an oscillatory short-time decay in the case of a broad exciton band, which results in diffusive transport. In the high-temperature limit the diffusion constant is found to decrease with increasing temperature with the power law D similar to 1/T. In the opposite case of a small excitonic band the decay remains incomplete and the time dependence of the second moment is governed by the t(2)-law typical of coherent transport processes. Since this is a rigorous second-order result, the vanishing of the second-order term may serve as a check for any non-perturbative calculation of the diffusion constant in this case.