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The Quantum-Classical Transition in Nonlinear Dynamical Systems

Salman Habib·Kurt Jacobs·Hideo Mabuchi·Robert Ryne·Kosuke Shizume·Bala Sundaram
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Abstract

Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.

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Salman Habib, Kurt Jacobs, Hideo Mabuchi, Robert Ryne, Kosuke Shizume, Bala Sundaram. 2000-10-26. The Quantum-Classical Transition in Nonlinear Dynamical Systems. https://doi.org/10.1103/physrevlett.88.040402

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