  Excitonic transport in static disordered one dimensional systems is studied
in the presence of thermal fluctuations that are described by the
Haken-Strobl-Reineker model. For short times, non-diffusive behavior is
observed that can be characterized as the free-particle dynamics in the
Anderson localized system. Over longer time scales, the environment-induced
dephasing is sufficient to overcome the Anderson localization caused by the
disorder and allow for transport to occur which is always seen to be diffusive.
In the limiting regimes of weak and strong dephasing quantum master equations
are developed, and their respective scaling relations imply the existence of a
maximum in the diffusion constant as a function of the dephasing rate that is
confirmed numerically. In the weak dephasing regime, it is demonstrated that
the diffusion constant is proportional to the square of the localization length
which leads to a significant enhancement of the transport rate over the
classical prediction. Finally, the influence of noise and disorder on the
absorption spectrum is presented and its relationship to the transport
properties is discussed.
