Moscow International School of Physics 2022

Out-of-time ordered correlation functions (OTOCs) are widely used as a diagnostic of quantum chaos and allow one to estimate the quantum Lyapunov exponent, which reproduces classical Lyapunov exponent in the semiclassical limit. However, in most cases, OTOCs and quantum Lyapunov exponent are calculated numerically. We consider nonlinear vector mechanics with a broken $O(N)$ symmetry, which exhibits a chaotic behavior in classical case, and analytically calculate the quantum Lyapunov exponent summing the ladder diagrams in the large-$N$ limit. Furthermore, we explicitly show that in the high-temperature limit, quantum exponent reproduces the classical one.