Sensitivity to perturbations in a quantum chaotic billiard.

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.