Analytical determination of multitime correlation functions in quantum chaotic systems

The time-dependence of multipoint observable correlation functions are essential quantities in analysis and simulation of quantum dynamics. Open quantum systems approaches utilize two-point correlations to describe the influence of an environment on a system of interest, and in studies of chaotic quantum system, the out-of-time-ordered correlator (OTOC) is used to probe chaoticity of dynamics. In this work we analytically derive the time dependence of multipoint observable correlation functions in quantum systems from a random matrix theoretic approach, with the highest-order function of interest being the OTOC. We find in each case that dynamical contributions are related to a simple function, related to the Fourier transform of coarse-grained wave functions. We compare the predicted dynamics to exact numerical experiments in a spin chain for various physical observables. We comment on implications toward the emergence of Markovianity and quantum regression in closed quantum systems, as well as relate our results to known bounds on chaotic dynamics.