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Quantum-Chaotic Evolution Reproduced from Effective Integrable Trajectories.

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Integrable approximations accurately model chaotic quantum systems, outperforming chaotic trajectories even in chaotic regions. This method reveals limitations in chaotic trajectory propagation over time.

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • Chaotic periodic systems present challenges for accurate quantum mechanical modeling.
  • Semiclassical approximations are often used to bridge classical and quantum descriptions.

Purpose of the Study:

  • To construct classically integrable approximants for chaotic periodic systems.
  • To compare the accuracy of integrable versus chaotic semiclassical approximations for quantum systems.
  • To investigate the breakdown of chaotic trajectory propagation in certain time regimes.

Main Methods:

  • Application of the Baker-Hausdorff-Campbell formula to construct integrable approximants.
  • Comparison of evolving wave density and autocorrelation functions.
  • Utilizing semiclassical approximations based on both chaotic and integrable trajectories.

Main Results:

  • Integrable approximants successfully model chaotic quantum systems.
  • Integrable trajectory approximations provide superior accuracy compared to chaotic ones, even for initial states in chaotic regions.
  • Quantum oscillations are well reproduced by the integrable approach.
  • Breakdown of chaotic trajectory propagation is observed in extended time regimes.

Conclusions:

  • Classically integrable approximants offer a robust method for studying chaotic quantum systems.
  • The Baker-Hausdorff-Campbell formula is effective for generating these accurate approximations.
  • Integrable approximations provide a more reliable description of quantum dynamics than chaotic ones in many scenarios.