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of the localized phonon wave packets related to β$_{n}$ ( t ) be- comes faster J is increased from 0 . 5 to 1 . 0 as shown in Fig. 8. 

As for the ˜ D Ansatz, an increase in the width of the phonon dispersion W will substantially deepen the phonon dissipative effect on the exciton amplitude ψ$_{n}$ ( t ), and as a result the exciton coherence quickly vanishes from the case of W = 0 . 8. (cf. Fig. 6b and 6c). W is also one main factor which determines the velocity of the phonon wave packets for both types of phonon dis- 

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placements λ$_{n}$ ( t ) and β$_{n}$ ( t ). Fig. 7c shows that when W is small, most of λ$_{n}$ ( t ) will be localized on the n = 0 site. As the phonon band width incr eases, λ$_{n}$ ( t ) will form two traveling wave packets with op posite directions and propagate to the entire chain as sho wn in Fig. 7b. 

The dynamics of β$_{n}$ ( t ) is more c omplex. As shown in Figs. 7b and 7c, the phonon displac ements described by parameter λ$_{n}$ ( t ) propagate from t he n = 0 site to the rest of the aggregate. But the same is not true for β$_{n}$ ( t ). Most of β$_{n}$ ( t ) will stay localized o n the site of exciton 

<img src='content_image/398290.jpg'>

