By K. Lindenberg, Y. Zhao, D. W. Brown (auth.), Pedro L. Garrido, Joacquín Marro (eds.)
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Additional info for Fourth Granada Lectures in Computational Physics: Proceedings of the 4th Granada Seminar on Computational Physics Held at Granada, Spain, 9–14 September 1996
This behavior is explored further in the next subsection. 3 Energy Bands and Effective Mass We have seen that the structure of polaron energy bands at general parameter values is strongly influenced by the limiting behaviors at small g and small J. At zero coupling, the free exciton energy band enters the one-phonon continuum at r;,c, such that the energies of the joint ground states of the exciton-phonon system are given by (22), E(r;,)- E(O) = 2J[1- cos(r;,)] =1 (62) with r;,c given by the relation (21).
An indication of the improvement, not only for the case just discussed but for other cases as well, can be seen in Fig. 4. 8 Fig. 4. 0, g = 1, 2, 3 as computed by the GL method (solid lines) and the Toyozawa method (dashed lines). 95 to allow all curves to be compared in a single illustration. K = r;,j1r. Confirmation of the polaron structure just described is obtained by looking at the exciton and phonon amplitude surfaces for another set of parameter values in this regime, namely, J = 9 and g = 5.
Above the self-trapping transition the energy band is nearly sinusoidal and strongly narrowed, suggesting a small polaron form; however, non-trivial finite-J corrections remain. 0 and various values of g. Figure 16 shows the dependence of the polaron bandwidth on g for J's ranging from 2 (see Fig. 4) to 9 (see Fig. 15). Consistent with the discus- 40 K. Lindenberg, Y. W. 2 ·-. 9 \ 0 0 2 g '· 3 4 5 Fig. 16. Polaron bandwidths E(r;, = 'll')- E(r;, = 0) as computed by the GL method vs. 0. sion above, the bandwidth is near unity up to a finite ]-dependent value of g, then it drops rather quickly as the band narrows through the "selftrapping-transition" region, and the continued narrowing beyond that can not be resolved on the scale of this figure.