Abstract We use out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for an inverted harmonic oscillator (IHO). For initial states located in the stable manifolds of the IHO we find that the corresponding OTOC exhibits identical evolutionary characteristics to the saddle point before the Ehrenfest time. For initial states located in the unstable manifolds, the OTOCs still grow exponentially but the time to maintain exponential growth is related to the center position of its wave packet in phase space. Moreover, we use the Husimi Q function to visualiz...
