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Extra 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

Sample text

F = moe9 . 5 9 Fig. 17. 34, and 9. indicator of the self-trapping transition, the transition being evidenced by an actual jump discontinuity in the effective mass, and the onset of the transition being marked by the parameter values at which such jumps first appear. The effective mass obtained with the GL method is shown in Fig. 17. As anticipated, for finite J the ratio mef 1 /mo remains near unity up to a finite value of the coupling coefficient and then grows rapidly. This growth is rapid but continuous, and in the real physical system we expect this to be the behavior for any J .

By the Merrifield, Toyozawa, or GL method) is the wedge or tongue-shaped region within which the dependence of the variational energy on J, g, and r;, is not smooth. ·· ··... ··. Q L---~--~--~--~--~ 0 2 4 J 6 8 10 Fig. 14. Phase diagram. 90. 66. 69. energy states at high /'i, (1/'i,l > /'i,*) are small-polaron-like. The traditional self-trapping transition associated with the notion of a discrete jump in the polaron effective mass corresponds to the limit /'i,* __... , to the point at which the large polaron region /'i, E ( -/'i,*, +/'i,*) is squeezed out of existence.

L ·········-······' I I I \ \ \ [-.. . ---· ! o .. . __ 5 10 __,_, 15 Fig. 19. ". Panel a), a~=o plotted on a logarithmic scale for g == 1, 3, 4, and 5 obtained with the GL method. 38. Panel b), sample curves showing some quasi-exponential shape functions. ) shape of (69), we show in Fig. 19a unnormalized exciton amplitudes a~=O from weak to strong coupling at a large fixed value of J; this scans across the far right of the phase diagram from bottom to top, showing the characteristic contraction of the exciton profile with increasing g.

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