分子激发振动的非线性结构与性质：李代数的研究

The complicated and strange structure of molecular highly excitation is studied by the Lie algebraic coset method. It includes: the properties of the semiclassical trajectories of molecular highly excited vibration, the energy transfer among the various modes, the properties of normal and local modes, their differences and the possible associated chaos. Meanwhile, we emphasize on the global topological properties of vibrational dynamics in the phase space. Besides, we also study the 1,2 shift due to the highly excited bending motion, the assignment of highly excited vibrational states and the quantization of chaotic systems. These works include the dynamical analysis of chaotic motion by the Lyapunov exponents, the existence and physical significances of the approximate constants of motion, the elucidation of the vibrational potential curves close to the dissociation, the properties of periodic orbits and the relaxation of vibrational excitation by the H function. All these results enrich much our understanding of molecular vibration and molecular spectroscopy.

本项目旨在探索具有强烈非线性效应的分子高激发振动态的半经典结构与性质，包括分形与混沌。研究的重点在激发态相空间中的整形体拓扑性质。研究的手段是李代数的陪集表示方法。此研究与分子内键间能量的传递有关，从而与化学反应紧密相关。如乙炔的C－H键的高激发弯曲振动会导致键的1，2位移。此外，高激发振动的归属，亦是研究的内容。