Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

Wei Min Zhang, Da Hsuan Feng, Jian Min Yuan

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31 Citations (Scopus)


Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerh, the quantum phase space is a 2M-dimensional topological space, where M is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (scrG) is the maximal stability subgroup of a fixed state in gerh. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of quantum chaos via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

Original languageEnglish
Pages (from-to)7125-7150
Number of pages26
JournalPhysical Review A
Issue number12
Publication statusPublished - 1990 Jan 1

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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