Quantum chaos without false positives

Abstract

Out-of-time-order correlators are widely used as an indicator of quantum chaos, but give false-positive quantum Lyapunov exponents for integrable systems with isolated saddle points. We propose an alternative indicator that fixes this drawback and retains all advantages of out-of-time-order correlators. In particular, the new indicator correctly predicts the average Lyapunov exponent and the Ehrenfest time in the semiclassical limit, can be calculated analytically using the replica trick, and satisfies the bound on chaos.

arXiv comment7 pages, 5 figures. v2: minor corrections

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• D-commuting SYK model: building quantum chaos from integrable blocks
• Dependence of Krylov complexity on the initial operator and state
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Unveiling Novel Insights in Quantum Dynamics through Extended Sachdev-Ye-Kitaev Model