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Related Experiment Videos

Phase space localization of chaotic eigenstates: violating ergodicity.

A Lakshminarayan1, N R Cerruti, S Tomsovic

  • 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 explores quantum chaos using level velocities and eigenfunction intensities to understand phase space localization. Findings reveal how classical structures in chaotic systems influence quantum behavior and deviations from ergodicity.

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Exploring phase space localization of chaotic eigenstates via parametric variation.

Physical review. E, Statistical, nonlinear, and soft matter physics·2001

Area of Science:

  • Quantum Chaos
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Exploring phase space localization in quantized nonintegrable systems is crucial.
  • Deviations from ergodicity due to quantum effects are important for understanding typical observables.

Purpose of the Study:

  • To investigate the correlation between level velocities and eigenfunction intensities.
  • To use this correlation as a measure of deviations from ergodicity in quantum chaotic systems.
  • To study correlations in simple, chaotic dynamical systems using the bakers map and standard map.

Main Methods:

  • Analyzing correlations between level velocities and eigenfunction intensities.
  • Utilizing the bakers map and standard map as model systems.
  • Developing a semiclassical theory based on periodic orbit sums.

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Main Results:

  • Identified correlations as a new method for exploring phase space localization.
  • Observed that behaviors are dominated by classical structures like short periodic orbits and homoclinic excursions.
  • Highlighted eigenfunction features violating ergodicity through perturbation-dependent correlations.
  • Semiclassical theory successfully reproduced quantum localization features, showing superexponential cutoff of correlations.

Conclusions:

  • The correlation between level velocities and eigenfunction intensities offers a novel approach to quantum chaos.
  • Classical structures significantly influence quantum localization and ergodicity in these systems.
  • Semiclassical theory provides a robust framework for understanding these quantum phenomena.