Quantum monodromy and its generalizations and molecular manifestations

Quantum monodromy is a non-trivial qualitative characteristic of certain non-regular lattices formed by the joint eigenvalue spectrum of mutually commuting operators. The latter are typically the Hamiltonian (energy) and the momentum operator(s) which label the eigenstates of the system. We give a b...

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Bibliographic Details
Published inMolecular physics Vol. 104; no. 16-17; pp. 2595 - 2615
Main Authors Sadovskií, D. A., Zhilinskií, B. I.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.01.2006
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Summary:Quantum monodromy is a non-trivial qualitative characteristic of certain non-regular lattices formed by the joint eigenvalue spectrum of mutually commuting operators. The latter are typically the Hamiltonian (energy) and the momentum operator(s) which label the eigenstates of the system. We give a brief review of known quantum systems with monodromy, which include such fundamental systems as the hydrogen atom in external fields, Fermi resonant vibrations of the CO 2 molecule, and non-rigid triatomic molecules. We emphasize the correspondence between the classical Hamiltonian monodromy and its quantum analogue and discuss possible generalizations of this characteristic in classical integrable Hamiltonian dynamical systems and their quantum counterparts.
ISSN:0026-8976
1362-3028
DOI:10.1080/00268970600673363