Out-of-time ordered correlator for a chaotic many-body quantum system

Using the parametric representation of a chaotic many-body quantum system derived earlier, we calculate explicitly the large-time dependence and asymptotic value of the out-of-time correlator (OTOC) of that system. The dependence on time t is determined by Δ t / ℏ . Here Δ is the energy correlation width within which the Bohigas–Giannoni–Schmit conjecture applies. We conjecture that Δ is universally related to the leading Ljapunov coefficient of the corresponding classical system by Δ = ℏ λ max . Then the large-time behavior of OTOC is given by the dimensionless parameter λ max t .