Dynamics of few-body quantum systems and chaos

少体量子系统动力学和混沌

基本信息

批准号：
10640366
负责人：
TODA Mikito
金额：
$ 2.43万
依托单位：
Nara Women's University (2001)Kyoto University (1998-2000)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2001
项目状态：
已结题

项目摘要

The purpose of this project is to study dynamical behavior of few-body quantum systems from classical-quantum point of view. In particular, dynamical processes of chemical reactions and mesoscopic phenomena are among the most interesting. In our study, we pay attention to the following three points. Firstly, we study how the properties of the networks of nonlinear resonances (Arnold webs) affect dynamical behavior. Secondly, we investigate how stable manifolds and unstable manifolds intersect in high-dimensional phase space. Thirdly, we study how symmetry of the systems lead to the difference between classical and quantum systems.The results of our study show the following. First, in the study of vibrationally highly excited molecules, we obtain some clues in utilizing the Arnold web in manipulating molecular systems by external laser fields. In particular, we find that non-ergodicity of the intramolecular vibrational-energy redistribution (IVR) plays an important role. Second, we obtain a method to compute stable and unstable manifolds by generalizing the Lie perturbation. Third, we find that the method of the molecular permutation group, which is used in the conventional study of the deformation of molecules, is insufficient for the investigation of large deformations involving chaotic behavior.For future development of our study, the following directions are among the most important. First, we need a method to design laser fields to increase the efficiency of reaction processes. In particular, in order to increase the effects which result from the combination of nonlinear resonances and laser fields, general methods to design laser fields utilizing the Arnold web are necessary. Second, semiclassical formulation based on stable and unstable manifolds is necessary to analyze quantum-classical correspondence. Third, we need a method to find how subgroups of the molecular permutation groups correspond to the Arnold web.

该项目的目的是从经典量词的角度研究几个体量子系统的动态行为。特别是，化学反应和介绍现象的动态过程是最有趣的。在我们的研究中，我们注意以下三点。首先，我们研究非线性共振网络（Arnold Web）的特性如何影响动态行为。其次，我们研究了高维相空间中稳定的歧管和不稳定的歧管如何相交。第三，我们研究系统的对称性如何导致经典系统和量子系统之间的差异。我们研究的结果显示了以下内容。首先，在振动高度激发的分子的研究中，我们获得了一些线索，用于利用Arnold Web通过外部激光场来操纵分子系统。特别是，我们发现分子内振动 - 能源重新分布（IVR）的非连通性起着重要作用。其次，我们通过概括谎言扰动来获取一种计算稳定和不稳定的歧管的方法。第三，我们发现，用于分子变形的常规研究中使用的分子置换基团的方法不足以研究涉及混沌行为的大变形。对于我们的研究的未来发展，以下方向是最重要的。首先，我们需要一种设计激光场来提高反应过程效率的方法。特别是，为了增加非线性共振和激光场的组合所产生的效果，必须使用Arnold Web设计激光场的一般方法。其次，基于稳定和不稳定的歧管的半古典公式对于分析量子古典对应是必要的。第三，我们需要一种方法来查找分子置换基组的亚组与阿诺德韦克斯的相对应。