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The transport of electronic excitation energy has been the subject of experimental and theoretical investigations since the sixties of the last century or even before. For example, it was assumed that the electronic energy transport between traps in molecular crystals occurred via the host molecules. Another example is the energy transport in light harvesting systems: after absorption of light the energy is transformed to a Frenkel exciton which is transported to the special pair in which the chemical part of the transformation of light to chemical energy occurs. Soon the question arouse whether the exciton is transported incoherently or coherently, i.e. via a hopping process or coherently in a wavelike manner. Both limiting cases have been modeled. The first model which successfully allowed to described the two limiting cases and the whole range in between used transfer integrals for the electronic transport. The influence of the vibrational degrees of freedom was taken into account by allowing for fluctuations of the electronic excitation energies and of the transfer integrals. The fluctuations were described by a Gaussian stochastic process with white noise. For this model the fluctuation averaged equation of motion for the excitonic density operator was derived without further approximations and solved in simple cases exactly. The model was used to describe exciton transport, optical absorption as well as electron and spin resonance absorption. The extension of the model to allow for dichotomic colored noise was performed in the early nineties. Also in this case, exact equations of motion for the density operator and correlation functions have been obtained and been solved for the case of dimers. If time allows, the connection with procedures using Green’s functions methods (Silbey at al.) and the Nakajima-Zwanzig generalized master equation (Kenkre et al.) will be shortly discussed.
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