Integrability and nonintegrability of quantum systems: Quantum integrability and dynamical symmetry
WM Zhang, JM Yuan, SJ Wang - Physical Review A, 1989 - APS
WM Zhang, JM Yuan, SJ Wang
Physical Review A, 1989•APSIn 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 …
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 …
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.
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