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Quantum-classical correspondence in perturbed chaotic systems.

Giuliano Benenti1, Giulio Casati

  • 1International Center for the Study of Dynamical Systems, Università degli Studi dell'InsubriaIstituto Nazionale per la Fisica della Materia, Unità di Como, Via Valleggio 11, 22100 Como, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 22, 2002
PubMed
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Quantum decay in chaotic systems mirrors classical decay above a critical perturbation. This quantum-classical correspondence explains the observed independence of decay rates from perturbation strength.

Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • Fidelity decay in quantum systems is a key indicator of quantum-classical correspondence.
  • Understanding this behavior is crucial for fields ranging from quantum computing to statistical mechanics.

Purpose of the Study:

  • To investigate the behavior of fidelity in classically chaotic quantum systems.
  • To identify the conditions under which quantum decay processes align with classical predictions.

Main Methods:

  • Analysis of fidelity decay in a model of a classically chaotic quantum system.
  • Theoretical examination of the influence of perturbation strength on decay rates.

Main Results:

  • A critical perturbation value was identified, above which quantum decay (exponential or power law) matches classical decay.

Related Experiment Videos

  • The decay rate's independence from perturbation strength, previously noted in literature, is shown to be a result of quantum-classical correspondence.

    • Conclusions:

    • Quantum-classical correspondence governs fidelity decay in chaotic systems.
    • The identified critical perturbation threshold provides a framework for understanding the transition from quantum to classical decay regimes.