Quantum Dynamics of Soliton-Pair Creation in Quasi-One-Dimensional Halogen-Bridged metal Complexes

在这个项目中，我们在一个非简并电荷密度波(CDW)模型的框架下，估计了从第一激发态的弛豫态(约束孤子和反孤子)到基态的非辐射跃迁的几率。在整个项目中，主要的问题是如何结合决定非绝热跃迁程度的声子模。在第一年，我们只处理孤子和反孤子之间的相对坐标，发现得到的概率很小，因此选择不够。通过详细的分析，我们澄清了原因是缺少与所关注的跃迁密切相关的长波声子。因此，我们在第二年解决了如何包含这么多个模的问题。作为第一种方法，我们添加了局域在孤子周围的形变的幅度作为第二模。这里，变形准备主要由接近k=0的模式组成。因此，这种方法的目的是检验第一年的预测。结果，对于特定的参数集，概率急剧增加，给出了大约8.6 ns的寿命。(cf：在单坐标处理的情况下大约是12ms)接下来，我们包括了余弦型模式，而不是局域型模式。这样的模式以递增的顺序从k=0开始相加。幸运的是，不同波数的模式几乎可以独立处理。因此，它们的贡献是相加的，彼此没有任何干扰。在这种情况下，我们已将拥有200个站点的系统中的模式数量从1个增加到40个。结果是，概率在25时几乎达到饱和。最后，我们得到了寿命为110ps的数值，这与用半经典方法得到的80ps的结果是一致的。

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.