Dynamics of few-body quantum systems and chaos

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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.