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.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics