For a weakly noise-driven integrable quantum system, the OTOC grows at the classical Lyapunov rate (scaling as epsilon^{1/3}) in the semiclassical limit, but quantum effects suppress the Lyapunov regime at low quantum numbers or very weak perturbations.
In Fig- ure 3 we show the evolution of the OTOC in Eq
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Quasi-integrable systems are slow to thermalize but may be good scramblers
For a weakly noise-driven integrable quantum system, the OTOC grows at the classical Lyapunov rate (scaling as epsilon^{1/3}) in the semiclassical limit, but quantum effects suppress the Lyapunov regime at low quantum numbers or very weak perturbations.