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Quantum breaking time scaling in superdiffusive dynamics.

A Iomin1, G M Zaslavsky

  • 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA. phr92ai@physics.technion.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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The breaking time of quantum-classical correspondence depends on kinetics and stickiness. For the quantum kicked rotor, superdiffusive dynamics lead to a specific scaling of this breaking time.

Area of Science:

  • Quantum dynamics
  • Classical mechanics
  • Statistical physics

Background:

  • Quantum-classical correspondence describes how quantum systems approach classical behavior.
  • Stickiness in dynamical systems refers to regions where trajectories remain for extended periods.
  • The quantum kicked rotor is a model system for studying quantum chaos.

Purpose of the Study:

  • To investigate the breaking time of quantum-classical correspondence in the quantum kicked rotor model.
  • To determine how kinetics and stickiness influence this breaking time.
  • To analyze the scaling laws governing the breaking time.

Main Methods:

  • Numerical simulations of the quantum kicked rotor dynamics.
  • Analysis of sticky dynamics within hierarchical island structures.

Related Experiment Videos

  • Examination of superdiffusive transport regimes.

    • Main Results:

    • The breaking time scales with the quantum parameter (Planck's over 2pi) as tau approximately (1/Planck's over 2pi)(1/mu) for superdiffusive dynamics (mu>1).
    • This scaling is linked to the accelerator mode within the hierarchical set of islands.
    • Other scaling behaviors and transitions to logarithmic dependence are discussed.

    Conclusions:

    • The breaking time of quantum-classical correspondence is sensitive to the nature of stickiness and kinetics.
    • Superdiffusive dynamics significantly impact the breaking time scaling in the quantum kicked rotor.
    • Understanding these scaling laws is crucial for characterizing quantum chaos and its classical limit.