Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model

Understand

The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time.

• Lately, this question gained increased interest due to the proposal to probe chaotic dynamics and scrambling using out-of-time-order correlators.
• In this work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time reversal in a semiclassical approach.
• We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows to identify a Lyapunov exponent $\lambda_L$.