| Budget Amount *help |
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥2,700,000 (Direct Cost: ¥2,700,000)
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| Research Abstract |
In this project we have estimated the probability of the non-radiative transition from the relaxed state (confined soliton and antisoliton) in the first excited state to the ground state, in the framework of a non-degenerate charge-density-wave(CDW) model.
All through this project, the main problem has been how to incorporate modes of phonons which are ruling the degree of non-adiabatic transitions. In the first year, we only treated the relative coordinate between the soliton and the antisoliton to find that the obtained probability was very small and so the selection was not enough. By detailed analysis, we clarified that the reason was the lack of long-wave phonons which are very closely related to the concerned transition. Therefore we tackled with the problem of how to include such many modes, in the second year.
As the first method, we have added the amplitude of a deformation localized around the solitons as the second mode. Here the deformation is prepared to consist mainly of the modes close to k=0. Thus the purpose of this method is to check the prediction in the first year. As a result, the probability drastically increases to give the life time of about 8.6 ns for a certain parameter set. (Cf : it was about 12 ms in the case of one-coordinate treatment)
Next, we have included cosine-type modes, instead of the localized mode. Such modes are added from the k=o one in increasing order. Fortunately, modes with different wave numbers can be treated almost independently. Thus, their contributions become additive without any interference with each other. In this situation, we have increased the number of modes from 1 to 40 in the system with 200 sites. As a result, the probability almost reaches to saturation at the number of 25. Finally, we have obtained the value of 110 ps as the life time, which is consistent with the result by the semi-classical method, namely, 80 ps.
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