Non-monotonicity in the quantum-classical transition: Chaos induced by quantum effects

Abstract

The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\hslash$ is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective $\hslash$ is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is non-monotonic in $\hslash$.

4 pages; presentation modified significantly to demonstrate that quantum effects are indeed responsible for the `anomalous' chaos. 2 figures added

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• Chaos in Continuously Monitored Quantum Systems: An Optimal Path Approach
• Quantum measurement with chaotic apparatus
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• Comment on "Non-monotonicity in the Quantum-Classical Transition: Chaos Induced by Quantum Effects"
• Experimental signatures of the quantum-classical transition in a nanomechanical oscillator modeled as a damped driven double-well problem
• Chaos in circuit QED: decoherence, localization, and nonclassicality
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• Photon waiting time distributions: a keyhole into dissipative quantum chaos
• Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation