Cooper C D, Child M S
The University of Oxford, Physical and Theoretical Chemistry Department, South Parks Road, Oxford, UK.
Phys Chem Chem Phys. 2005 Jul 21;7(14):2731-9. doi: 10.1039/b502772c. Epub 2005 Jun 9.
The Xiao-Kellman catastrophe map, for the classification of classical periodic orbits of the standard 2:1 Fermi resonance Hamiltonian is extended to species with finite vibrational angular momentum. The influence of the classical periodic orbit structure on different organizations of the quantum mechanical eigenvalues, in the four regions of the map, is strikingly demonstrated. The quantum eigenvalue lattices in angular momentum and energy space show dislocations attributable to a topological effect, termed quantum monodromy. Analogues with quantum monodromy in quasi-linear molecules and LiCN/LiNC isomerisation are demonstrated.
用于标准2:1费米共振哈密顿量经典周期轨道分类的肖-凯尔曼突变图被扩展到具有有限振动角动量的物种。该图四个区域中经典周期轨道结构对量子力学本征值不同组织形式的影响得到了显著证明。角动量和能量空间中的量子本征值晶格显示出由一种称为量子单值性的拓扑效应引起的位错。文中展示了准线性分子中的量子单值性类似物以及LiCN/LiNC异构化情况。
