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Quantum-classical transition in nonlinear dynamical systems.

Salman Habib1, Kurt Jacobs, Hideo Mabuchi

  • 1T-8, Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters
|January 22, 2002
PubMed
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Classical approximations to quantum mechanics can violate density matrix properties. This research classifies dynamical systems to predict when decoherence fails to induce the quantum-classical transition, even if the Wigner function becomes positive.

Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Quantum-classical transition

Background:

  • Classical evolutions can approximate quantum mechanics but may violate density matrix properties.
  • Understanding the quantum-classical transition is crucial for quantum technologies.

Purpose of the Study:

  • To classify dynamical systems based on classical-quantum correspondence.
  • To identify conditions under which environmental interaction (decoherence) fails to induce the quantum-classical transition.

Main Methods:

  • Analyzing violations of positive semidefiniteness in the density matrix.
  • Classifying dynamical systems using classical-quantum correspondence.
  • Examining the late-time behavior of the Wigner function.

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Main Results:

  • A classification of dynamical systems based on classical-quantum correspondence is proposed.
  • Decoherence can be unsuccessful in inducing the quantum-classical transition under certain conditions.
  • The Wigner function can become positive at late times without a corresponding approach to classical dynamics.

Conclusions:

  • The study provides insights into the limitations of classical approximations in quantum mechanics.
  • Key issues for experiments studying the quantum-classical transition are highlighted.
  • The findings are relevant for understanding and controlling quantum systems.