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

在这个项目中，我们在非简并的电荷密度波（CDW）模型的框架下，估计了从第一激发态的弛豫态（禁闭孤子和反孤子）到基态的无辐射跃迁的几率，主要问题是如何把决定非绝热跃迁程度的声子模考虑进去。在第一年中，我们只处理了孤子和反孤子的相对坐标，发现得到的概率很小，所以选择不够。通过详细的分析，我们澄清了其原因是缺乏长波声子，这是非常密切相关的有关转变。因此，我们在第二年解决了如何包含如此多模式的问题。作为第一种方法，我们添加了孤立子周围局部变形的幅度作为第二模式。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查第一年的预测。结果，概率急剧增加，对于某个参数集给出约8.6 ns的寿命。(Cf：在单坐标处理的情况下约为12 ms）接下来，我们包括余弦型模式，而不是局部模式。这样的模式从k= 0开始以递增的顺序添加。幸运的是，具有不同波数的模式几乎可以独立地处理。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，我们在200个站点的系统中将模式数量从1增加到40。结果，概率几乎在25的数量处达到饱和。最后，我们得到了110 ps的寿命值，这与半经典方法的结果80 ps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.