Schmitt, MarkusSels, DriesKehrein, StefanPolkovnikov, Anatoli2019-06-062019-06-062019-04-08Markus Schmitt, Dries Sels, Stefan Kehrein, Anatoli Polkovnikov. 2019. "Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model." Physical review B: Condensed matter and materials physics, Volume 99, Issue 13, pp. 134301 - 134301 (10). https://doi.org/10.1103/PhysRevB.99.1343011098-0121https://hdl.handle.net/2144/35952The 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 λ_L. In particular, we find that λ_L is twice the Lyapunov exponent of the semiclassical equations of motion. This behavior is attributed to the growth of an out-of-time-order double commutator that resembles an out-of-time-order correlator.10 p.en-USPhysical sciencesChemical sciencesFluids & plasmasArticle10.1103/PhysRevB.99.1343010000-0002-5549-7400 (Polkovnikov, Anatoli)343671