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Wavelet statistical complexity analysis of the classical limit. (English) Zbl 1098.81777

Summary: We introduce the notion of wavelet statistical complexity (WSC) and investigate the classical limit of the non-linear dynamics of two interacting harmonic oscillators. It is shown that a rather special relationship between entropy and chaos ensues that, using the WSC tool, sheds some light on the intricacies of the classical-quantum transition. The associated transition region is seen to consists of two sub-zones, each with quite different properties. In one of them, a solid-gas like (smooth) transition seems to take place.

MSC:

81Q50 Quantum chaos
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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