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Related Experiment Videos

Phase space localization and matrix element distributions in systems with mixed classical phase space.

B Mehlig1, K Müller, B Eckhardt

  • 1Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, United Kingdom.

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

Quantum distributions of matrix elements mirror classical dynamics in mixed phase spaces. Deviations from ergodicity, like particle trapping, are quantitatively reflected in quantum properties, offering insights into system behavior.

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Statistical physics

Background:

  • Investigating quantum-classical correspondence in systems with mixed phase space.
  • Understanding the behavior of diagonal matrix elements for smooth observables.

Purpose of the Study:

  • To analyze quantum distributions of diagonal matrix elements in systems with mixed classical phase space.
  • To connect quantum properties to classical dynamics, particularly deviations from ergodicity.

Main Methods:

  • Comparing quantum distributions with classical trajectory segments of Heisenberg time length.
  • Analyzing non-Gaussian wings in distributions and linking them to classical phase space structures.

Main Results:

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  • Quantum distributions closely match classical distributions derived from Heisenberg-time trajectory segments.
  • Non-Gaussian features in quantum distributions correlate with classical trapping and transport barriers.
  • Classical deviations from ergodicity are quantitatively mirrored in quantum matrix elements.

    • Conclusions:

    • The study establishes a quantitative link between classical phase space structure and quantum matrix elements.
    • Classical trapping and transport barriers significantly influence quantum distributions.
    • Findings provide insights into quantum-classical correspondence and phenomena like quantum scars.