Integrability and nonintegrability of quantum systems: Quantum integrability and dynamical symmetry

Wei Min Zhang, Da Hsuan Feng, Jian Min Yuan, Shun Jin Wang

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)

Abstract

In this paper we discuss the concepts of quantum integrability and nonintegrability. Based on the concept of a complete set of commuting observables and the Hilbert-space structure of a quantum system, the definitions are given for the quantum-dynamical degrees of freedom and quantum phase space from which the quantum integrability is defined. A criterion for quantum integrability then emerges; the system is integrable if it possesses dynamical symmetry. Breaking of dynamical symmetry is connected with the nonintegrability of systems and thus is the inherent mechanism of chaotic motion. A number of examples are discussed.

Original languageEnglish
Pages (from-to)438-447
Number of pages10
JournalPhysical Review A
Volume40
Issue number1
DOIs
Publication statusPublished - 1989 Jan 1

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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