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Exploring phase space localization of chaotic eigenstates via parametric variation.

N R Cerruti1, A Lakshminarayan, J H Lefebvre

  • 1Department of Physics, Washington State University, Pullman, WA 99164-2814, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 17, 2001
PubMed
Summary

This study enhances a phase space localization measure for chaotic systems. It reveals strong correlations in stadium billiards, aligning with semiclassical theories and extending previous findings.

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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Phase space dynamics

Background:

  • A novel correlation measure was previously introduced to probe phase space localization of eigenstates.
  • This measure correlates level velocities with overlap intensities between eigenstates and a localized state.

Purpose of the Study:

  • To further develop the theoretical basis of the correlation measure.
  • To extend previous findings on the stadium billiard to full phase space.
  • To investigate the dependence on Planck's constant and validate against semiclassical theory.

Main Methods:

  • Correlation analysis of eigenstates.
  • Application to the stadium billiard model.
  • Investigation of Planck's over 2pi dependence.

Related Experiment Videos

  • Comparison with semiclassical theory based on homoclinic orbits.

    • Main Results:

    • Strong correlations were observed in the stadium billiard, contradicting random matrix theory predictions for chaotic systems.
    • The study extends these observations to the full phase space.
    • The measure's dependence on Planck's over 2pi was analyzed.
    • Agreement was demonstrated between the measure and semiclassical theory.

    Conclusions:

    • The enhanced correlation measure provides a sensitive tool for probing phase space localization in chaotic systems.
    • The findings support the validity of the measure and its connection to underlying semiclassical dynamics.
    • This work deepens the understanding of quantum chaos and localization phenomena.