On the classical and quantum integrability of systems of resonant oscillators

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• 作者：Massimo Marino
• 关键词：integrable systems ; resonant harmonic oscillators ; noncommutative integrability ; quantization
• 刊名：Regular and Chaotic Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：22
• 期：1
• 页码：1-17
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Dynamical Systems and Ergodic Theory;
• 出版者：Pleiades Publishing
• ISSN：1468-4845
• 卷排序：22

文摘

We study in this paper systems of harmonic oscillators with resonant frequencies. For these systems we present general procedures for the construction of sets of functionally independent constants of motion, which can be used for the definition of generalized actionangle variables, in accordance with the general description of degenerate integrable systems which was presented by Nekhoroshev in a seminal paper in 1972. We then apply to these classical integrable systems the procedure of quantization which has been proposed to the author by Nekhoroshev during his last years of activity at Milan University. This procedure is based on the construction of linear operators by means of the symmetrization of the classical constants of motion mentioned above.