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Distributions of transition matrix elements in classically mixed quantum systems.

D Boosé1, J Main

  • 1Laboratoire de Physique Théorique, Université Louis Pasteur, F-67084 Strasbourg, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study analyzes how mixed phase space affects transition matrix elements. Findings show classical averages and Fourier transforms accurately predict these quantum properties, aiding in understanding complex systems.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Atomic physics

Background:

  • Understanding the statistical properties of quantum systems is crucial.
  • Transition matrix elements are key to describing quantum transitions.
  • Mixed phase space dynamics present unique challenges in theoretical analysis.

Purpose of the Study:

  • To quantitatively assess the contribution of mixed phase space to the mean and variance of transition matrix elements.
  • To establish a connection between classical dynamics and quantum statistical properties.
  • To validate theoretical predictions with numerical computations.

Main Methods:

  • Analysis of diagonal and nondiagonal transition matrix elements.
  • Decomposition of mean and variance based on classical phase space properties.

Related Experiment Videos

  • Utilizing ergodic trajectories and stable periodic orbits for classical averages and Fourier transforms.

    • Main Results:

    • The mean of diagonal transition matrix elements is accurately represented by weighted classical averages along ergodic and periodic orbits.
    • The variance of nondiagonal transition matrix elements is well reproduced by weighted Fourier transforms of classical autocorrelation functions.
    • Numerical computations for a hydrogen atom in a strong magnetic field confirm these findings.

    Conclusions:

    • Mixed phase space contributions to quantum statistical properties can be effectively described using classical dynamical concepts.
    • The developed method provides a powerful tool for analyzing complex quantum systems.
    • This work bridges the gap between classical and quantum descriptions in the realm of statistical properties.