We study the temperature-dependent dephasing rate of excitons in chains of chromophores, accounting for scattering on static disorder as well as acoustic phonons in the host matrix. From this we find a powerlaw temperature dependence of the absorption line width, in excellent quantitative agreement with experiments on dye aggregates. We also propose a relation between the line width and the exciton coherence length imposed by the phonons. The results indicate that the much debated steep rise of the fluorescence lifetime of pseudo-isocyanine aggregates above 40 K results from the fact that this coherence length drops below the localization length imposed by static disorder.
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