Accuracy of the coherent potential approximation for a one-dimensional Frenkel exciton system with a Gaussian distribution of fluctuations in the optical transition frequency

We investigate the accuracy of the coherent potential approximation (CPA) for a one-dimensional Frenkel exciton system with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the optical transition frequency. The CPA values of the integrated density of states and the inverse localization length are shown to be in excellent agreement with the results of mode-counting studies carried out on arrays of 107–108 sites. We also consider the asymptotic behavior of the inverse localization length and show that it can be approximated by the reciprocal of the decay length of an eigenstate localized about a single, strongly perturbed site in an otherwise perfect lattice.