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(B1) Proof: for an integer power g(x) = xk we have the known formula (readily proven by induction) [ A,Bk] =∑ k r=1Br−1[A,B ]Bk−r, which is equivalent to the expression in Eq

General relation We prove the following general statement: for an analytic function (at some domain) g, operators A andB we have [A,g (B)] = lim s→0 g(B +s[A,B ]) −g(B) s

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Quasi-integrable systems are slow to thermalize but may be good scramblers

quant-ph · 2019-09-04 · conditional · novelty 6.0

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.

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  • Quasi-integrable systems are slow to thermalize but may be good scramblers quant-ph · 2019-09-04 · conditional · none · ref 7

    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.