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Computing Quantum Mean Values in the Deep Chaotic Regime.

Gabriel M Lando1,2, Olivier Giraud1,3,4, Denis Ullmo1

  • 1<a href="https://ror.org/03xjwb503">Université Paris-Saclay</a>, CNRS, LPTMS, 91405 Orsay, France.

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This study introduces a novel approach for quantum simulations in chaotic systems. It achieves high accuracy where standard semiclassical methods fail, improving quantum chaos understanding.

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Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Computational physics

Background:

  • Studying quantum operator time evolution is challenging in regimes with small Planck's constant (ℏ) and strong classical chaos.
  • Purely quantum calculations become computationally infeasible as ℏ approaches zero.
  • Existing semiclassical methods face conceptual and practical issues in deep chaotic regimes.

Purpose of the Study:

  • To address conceptual problems in semiclassical methods for quantum chaotic systems.
  • To gain a deeper understanding of interference contributions to quantum operator mean values.
  • To develop more accurate and efficient methods for quantum simulations.

Main Methods:

  • Implementation of a novel approach to address conceptual challenges in semiclassical methods.
  • Analysis of the time evolution of mean values of quantum operators.
  • Comparison with a standard semiclassical method (Herman-Kluk propagator).

Main Results:

  • The new approach provides unprecedented accuracy in the deep chaotic regime.
  • Standard semiclassical methods, like the Herman-Kluk propagator, yield only numerical noise in this regime.
  • The study clarifies the origin of interference contributions to operator mean values.

Conclusions:

  • The developed approach offers a significant improvement for quantum simulations of systems with chaotic classical limits.
  • This work enables the development of more efficient and accurate computational methods.
  • It deepens the fundamental understanding of quantum chaos and semiclassical approximations.