The Edge of Quantum Chaos

Details The Edge of Quantum Chaos The Edge of Quantum Chaos

2002-06-04

arxiv.org/abs/cond-mat/0206039v2

Phys. Rev. Lett. 89, 214101 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, revised version in press PRL

Scientific paper

10.1103/PhysRevLett.89.214101

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with $[1+(q-1) (t/\tau)^2]^{1/(1-q)}$ (with the nonextensive entropic index $q$ and $\tau$ depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.

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