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Related Experiment Videos

Breaking time reversal in a simple smooth chaotic system.

Steven Tomsovic1, Denis Ullmo, Tatsuro Nagano

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

Researchers explored breaking time reversal symmetry in quantum chaotic systems. They found a coupled quartic oscillator system exhibiting Gaussian unitary ensemble statistics, demonstrating strong symmetry breaking with minimal chaos regularization.

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Area of Science:

  • Quantum Chaos
  • Random Matrix Theory
  • Semiclassical Systems

Background:

  • Eigensolution statistics in random matrix theory critically depend on time reversal symmetry.
  • The Bohigas-Giannoni-Schmit conjecture extends this principle to quantum systems with chaotic classical analogs.
  • Previous numerical studies on symmetry breaking predominantly used billiards or maps, with limited exploration in smooth systems.

Purpose of the Study:

  • To investigate methods for breaking time reversal invariance in continuous-time systems with smooth potentials.
  • To identify a parameter regime where symmetry breaking is significant but does not regularize chaotic dynamics.

Main Methods:

  • Studied a system of two coupled quartic oscillators.
  • Analyzed energy level statistics and phase space dynamics.

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  • Investigated the interplay between symmetry breaking and chaotic behavior.

    • Main Results:

    • The coupled quartic oscillator system's energy level statistics closely matched the Gaussian unitary ensemble.
    • This indicates a strong breaking of time reversal symmetry.
    • The system exhibited only a minor proportion of regular motion, preserving chaotic characteristics.

    Conclusions:

    • Successfully demonstrated a smooth, continuous-time system that breaks time reversal symmetry.
    • The findings support the application of random matrix theory predictions to quantum chaotic systems.
    • This system serves as a valuable model for studying symmetry breaking effects in quantum chaos.