The dynamical characteristics of one-dimensional molecular aggregate with the randomness in exciton hopping is considered. We show that the randomness of the distribution of signs of the exciton hopping of the aggregate dramatically changes the dynamical characteristics. In the homogeneous case, the dynamical characteristics of the molecular aggregate manifest narrow lines at edges of the band of Frenkel excitons of the aggregate. On the other hand, we show that the considered randomness yields nonzero contributions to the dynamical characteristics of all excitons of the band.

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