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

在这个项目中，我们估计了在非简并电荷密度波（CDW）模型的框架下，从第一激发态的松弛态（受限孤子和反孤子）到基态的非辐射跃迁的概率。在整个项目中，主要的问题是如何将控制非绝热跃迁程度的声子模式结合起来。在第一年，我们只对孤子和反孤子的相对坐标进行了处理，发现得到的概率很小，因此选择不够。通过详细的分析，我们明确了原因是缺乏与相关跃迁密切相关的长波声子。所以我们在第二年就解决了如何包含这么多模式的问题。作为第一种方法，我们在孤子周围加入了局部变形的振幅作为第二种模态。在这里，变形主要由接近k=0的模态组成。因此，这种方法的目的是在第一年检查预测。结果，概率急剧增加，给出一个特定参数集的寿命约8.6 ns。（Cf：在单坐标处理的情况下大约是12ms）接下来，我们加入了余弦型模式，而不是局域模式。这些模态从k= 0开始按递增顺序添加。幸运的是，具有不同波数的模态几乎可以独立处理。因此，它们的贡献是相加的，彼此之间没有任何干扰。在这种情况下，我们将200个站点的系统中的模式数量从1增加到40。因此，在数量为25时，概率几乎达到饱和。最后，我们得到了110 ps的寿命值，与半经典方法得到的80 ps的寿命值一致。

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.