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Related Experiment Videos

Classical diffusion and quantum level velocities: systematic deviations from random matrix theory.

A Lakshminarayan1, N R Cerruti, S Tomsovic

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

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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We link quantum chaotic system energy level behavior to classical diffusion using semiclassical analysis. Deviations from random matrix theory reveal connections to classical time correlations in chaotic systems.

Area of Science:

  • Quantum Chaos
  • Statistical Mechanics
  • Semiclassical Analysis

Background:

  • Quantized chaotic systems exhibit complex energy level dynamics.
  • Random matrix theory (RMT) often describes these systems, assuming eigenvalue-eigenvector independence.
  • Classical diffusion coefficients characterize chaotic system dynamics.

Purpose of the Study:

  • To investigate the relationship between quasienergy level velocities and classical diffusion coefficients in quantized chaotic systems.
  • To explore deviations from RMT and connect them to classical time correlations.
  • To analyze the impact of mixed phase-space dynamics on level velocity variance.

Main Methods:

  • Detailed semiclassical analysis of quasienergy level velocities.
  • Calculation and comparison of level velocity variance with classical diffusion coefficients.

Related Experiment Videos

  • Study of the standard map as a model system.

    • Main Results:

    • Systematic deviations from RMT predictions were observed and linked to higher-order classical time correlations.
    • The oscillatory behavior of the diffusion coefficient in the standard map was mirrored in the level velocity variance.
    • A transition in scaling properties of the variance was identified, correlating with the classical transition to chaos.

    Conclusions:

    • Semiclassical analysis provides a bridge between quantum level dynamics and classical transport properties.
    • Higher-order classical correlations are crucial for understanding deviations from RMT in quantized chaotic systems.
    • The study highlights the intimate connection between quantum and classical chaos, even in mixed phase-space regimes.