Abstract. Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has led to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This conclusion is supported by an analytical argument for short times and numerical evidence at later times.

PACS number: 05.45.Mt

Print publication: Issue 43 (27 October 2006)
Received 17 June 2006, in final form 22 August 2006
Published 11 October 2006