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Published January 28, 2002 | public
Journal Article Open

Quantum-Classical Transition in Nonlinear Dynamical Systems


Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the 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.

Additional Information

©2002 The American Physical Society Received 31 October 2000; revised 6 August 2001; published 8 January 2002 The authors acknowledge helpful discussions with Tanmoy Bhattacharya, Doron Cohen, and Andrew Doherty. The work of B. S. was supported by the National Science Foundation and a grant from the City University of New York. Large-scale numerical simulations were carried out at the Advanced Computing Laboratory (ACL), LANL, and at the National Energy Research Scientific Computing Center (NERSC), LBNL.


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