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Ehrenfest times for classically chaotic systems.

P G Silvestrov1, C W J Beenakker

  • 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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The semiclassical WKB approximation accurately describes quantum wave packet spreading in chaotic systems. This approximation breaks down at a later time scale (tau) than previously thought, offering new insights into quantum chaos.

Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Statistical physics

Background:

  • Understanding quantum wave packet spreading is crucial for quantum mechanics.
  • The semiclassical WKB approximation is a key tool for studying quantum systems.
  • Previous studies suggested limitations on the applicability of semiclassical methods in chaotic systems.

Purpose of the Study:

  • To investigate the quantum-mechanical spreading of a Gaussian wave packet using the semiclassical WKB approximation.
  • To determine the time scale at which the WKB approximation breaks down in chaotic systems.
  • To compare this breakdown time scale with previously considered Ehrenfest times.

Main Methods:

  • Application of the semiclassical WKB approximation developed by Berry and Balazs.

Related Experiment Videos

  • Analysis of wave packet dynamics in a one-dimensional chaotic system.
  • Derivation of the time scale (tau) for the breakdown of the WKB approximation.

    • Main Results:

    • The WKB approximation provides a description of quantum wave packet spreading.
    • The time scale (tau) for the breakdown of the WKB approximation in chaotic systems is found to be larger than previously considered Ehrenfest times.
    • In one dimension, tau is determined by the Lyapunov exponent (lambda) and a typical classical action (A).

    Conclusions:

    • The semiclassical WKB approximation remains valid for longer durations in chaotic systems than previously assumed.
    • The breakdown of the WKB approximation is linked to the system's Lyapunov exponent and classical action.
    • This research refines our understanding of the interplay between quantum mechanics and chaos.