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Loschmidt echo for a chaotic oscillator.

A Iomin1

  • 1Department of Physics, Technion, Haifa, 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2004
PubMed
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The study reveals that the quantum stability of chaotic nonlinear oscillators, measured by the Loschmidt echo, decays exponentially due to classical Lyapunov exponents. This quantum-classical connection in chaotic dynamics is observed over specific time scales.

Area of Science:

  • * Nonlinear dynamics and quantum chaos.
  • * Statistical mechanics and quantum measurement.

Background:

  • * Understanding quantum stability in chaotic systems is crucial for quantum information and computation.
  • * The semiclassical approximation bridges quantum mechanics and classical mechanics for complex systems.

Purpose of the Study:

  • * To investigate the semiclassical dynamics of a nonlinear oscillator exhibiting chaotic behavior.
  • * To quantify quantum stability using the Loschmidt echo under time-dependent perturbations.
  • * To determine the classical origins of quantum instability in chaotic systems.

Main Methods:

  • * Calculation of the Loschmidt echo in the semiclassical approximation.
  • * Analysis of time-dependent variations in a nonlinear oscillator model.

Related Experiment Videos

  • * Application of Lyapunov exponent theory to quantum dynamics.

    • Main Results:

    • * Demonstrated exponential decay of the Loschmidt echo, indicating quantum instability.
    • * Established a direct link between the Loschmidt echo decay and the classical Lyapunov exponent.
    • * Showcased the purely classical nature of this observed quantum decay.
    • * Identified a power-law relationship for the Lyapunov regime concerning the semiclassical parameter.

    Conclusions:

    • * Quantum instability in chaotic nonlinear oscillators under perturbation is fundamentally classical.
    • * The Loschmidt echo serves as a sensitive probe for quantum-classical correspondence in chaotic systems.
    • * Semiclassical analysis provides valuable insights into the dynamics of quantum chaos.