Quantum Ergodicity and Chaos
The purpose of this contribution is to discuss how the classical concepts of ergodicity and chaos can be introduced into quantum theory. The scheme presented here treats quantum systems with no classical properties at all, thus it deals with analogs rather than generalizations of the classical notions, and there is no semiclassical limit as a guide. However, it turns out that the structure is quite similar to the classical one, though essentially non-commutative. It deals primarily with finite quantum systems with Hamiltonian dynamics, where the information about the system comes from repeated observations of a subsystem. A typical example is provided by the vibrational motion of a small molecule, where the system is probed through the resonant interaction of a laser beam with one of the normal modes (the ‘active mode’)1. The anharmonic coupling of the modes creates a ‘mode mixing’ and the resulting dynamics may eventually allow us to probe the whole interacting system.
KeywordsInformation Rate Springer Lecture Note Quantum Chaos Phase Space Point Completely Positive
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