Abstract
Abstract We used out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for the inverted harmonic oscillator (IHO). For the initial states located in the stable manifolds of IHO, we find that the corresponding OTOC exhibits identical evolutionary characteristics as the saddle point before the Ehrenfest time. For the 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 the phase space. Moreover, we use the Husimi Q function to visualize the quantum wave packets during the OTOC’s exponential growth. Our results show that the quantum instability exists at arbitrary orbits in the IHO system, and the Ehrenfest time in the IHO system depends not only on the initial system photon number, but also on the central positions of the initial states in the phase space.
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