Exciton line shapes and migration with stochastic exciton lattice coupling

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Abstract
In a recent article, Sumi [J. Chem. Phys. 67, 2943 (1977)] has discussed the optical line shape of an exciton interacting with phonons using a Gaussian Markov process for this interaction. By assuming that the correlation time of the process is nonzero, he was able to explore various limits of (motional) narrowing of the line. His analysis used a dynamic coherent potential approximation (CPA) in order to calculate the line shape. In the present paper, we derive these results in closed analytic form, without the CPA, by using standard analysis. Since our results agree with Sumi very closely, the present approach provides a simple way of understanding the underlying physics. In addition, we show how the exciton density of states enters in a simple way, and compare the hemicircular and the Lorentzian forms for this density of states.

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