Quantum-Classical Correspondence via Liouville Dynamics: I. Integrable Systems and the Chaotic Spectral Decomposition

Details Quantum-Classical Correspondence via Liouville Dynamics: I. Integrable Systems and the Chaotic Spectral Decomposition Quantum-Classical Correspondence via Liouville Dynamics: I. Integrable Systems and the Chaotic Spectral Decomposition

1996-08-15

arxiv.org/abs/chao-dyn/9608013v1

Nonlinear Sciences

Chaotic Dynamics

38 pages, revtex, first of two papers

Scientific paper

10.1103/PhysRevA.55.27

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liouville spectral decomposition, developed herein. General approaches to the construction of these Liouville eigenfunctions and classical spectral projectors in quantum and classical mechanics are discussed and are employed to construct Liouville eigenfunctions for classically chaotic systems. Correspondence for systems whose classical analogs are chaotic is discussed, based on this decomposition, in the following paper.

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