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Related Experiment Videos

Sensitivity to perturbations in a quantum chaotic billiard.

Diego A Wisniacki1, Eduardo G Vergini, Horacio M Pastawski

  • 1Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429 Buenos Aires, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

The Loschmidt echo (LE) quantifies a system

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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Dynamical systems

Background:

  • The Loschmidt echo (LE) assesses a quantum system's fidelity after time-reversal.
  • Classical chaos theory predicts exponential decay for LE in chaotic systems.
  • This prediction relies on the Fermi's golden rule (FGR), limiting its applicability.

Purpose of the Study:

  • To investigate the validity of LE decay conjectures beyond the Fermi's golden rule regime.
  • To explore the crossover between decay rates in a non-FGR regime.
  • To test theoretical predictions in a paradigmatic chaotic system.

Main Methods:

  • Utilizing the Bunimovich stadium billiard as a model for a fully chaotic system.
  • Applying perturbations in a regime where FGR is not applicable.
  • Analyzing the Loschmidt echo decay dynamics under these conditions.

Main Results:

  • Observed a crossover in LE decay from the density of states width (Gamma) to the Lyapunov exponent.
  • Demonstrated that LE decay conjectures hold true even when FGR is invalid.
  • Challenged the established analytic interpretation of LE decay mechanisms.

Conclusions:

  • The conjectures on Loschmidt echo decay in chaotic systems are robust and extend beyond FGR validity.
  • The study provides crucial insights into quantum chaos and fidelity decay.
  • Findings necessitate a re-evaluation of the theoretical underpinnings of LE in non-perturbative regimes.

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