Theoretical Study on Properties and Dynamics of Molecules in Highly Exited Vibrational States.

本文根据作者发展的相空间半经典力学，导出了诸如高激发分子振动态等混沌系统态密度的一般表达式。在稳定但不可积的系统中，态密度引起共振型量子条件，这与混沌分子（如乙炔）的实验光谱学的理解和分配高度相关。我还设计了一种计算相对较大的多原子分子作用变量的非常实用的方法。作为对作用变量的近似，定义了一个准作用变量，使得它是频率的连续函数。准作用变量具有有意义的扩展，在混沌区域中给出连续谱。通过对拟作用变量的数值检验，发现了由于相空间中两个流形的接触而产生的不稳定性谱，以及保守混沌系统能量传递过程中夹带机制的模拟。

A general expression of the density of states for chaotic systems such as a highly excited molecular vibrational state has been derived in terms of a phase-space semiclassical mechanics developed by the present author. In stable but nonintegrable systems, the density of states gives rise to a resonance type quantum condition, which is highly relevant to the understanding and assignment of the experimental spectroscopy for chaotic molecules, such as acetylene.I have also devised a very practical method of calculating the action variables for relatively large polyatomic molecules. As an approximation to the action variables, a quasi-action variables has been defined so that it is a continuous function of the frequency. The quasi-action variable has a meaningful extension giving continuous spectra in a chaotic region. Through the numerical examination of the quasi-action variables, I have found out an intermittency spectrum due to the contact of two manifolds in phase space, and also an analogue of the entrainment mechanism in energy transfer processes of conservative chaotic systems.