Quantum instability and Ehrenfest time for an inverted harmonic oscillator  

作　　者：Shangyun Wang Songbai Chen Jiliang Jing 

机构地区：[1]College of Physics and Electronic Engineering,Hengyang Normal University,Hengyang 421002,China [2]Department of Physics,Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education,Synergetic Innovation Center for Quantum Effects and Applications,Hunan Normal University,Changsha 410081,China [3]Center for Gravitation and Cosmology,College of Physical Science and Technology,Yangzhou University,Yangzhou 225009,China

出　　处：《Communications in Theoretical Physics》2025年第1期35-40,共6页理论物理通讯(英文版)

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12275078,11875026,12035005,2020YFC2201400;the innovative research group of Hunan Province under Grant No.2024JJ1006。

摘　　要：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 visualize the quantum wave packets during exponential growth of the OTOCs.Our results show that quantum instability exists at arbitrary orbits in the IHO system,and the Ehrenfest time in the IHO system depends not only on the photon number of the initial system but also on the central positions of the initial states in phase space.

关 键 词：out-of-time order correlators inverted harmonic oscillator quantum instability Ehrenfest time 

分 类 号：O413[理学—理论物理]