周期受击陀螺的保真度隧道效应及能量量子期待值

Fidelity,Tunneling,and Quantum Expectation Value of Energy for a Periodically Kicked Free Top

研究一个周期受击陀螺的保真度、隧道效应和能量量子期待值.研究发现,随着打击强度λ的增加,经典相空间结构从规则的轨道到出现岛再到完全混沌.当参数取为α=π/2,λ=3.0时,以相空间的稳定固定点处的周期轨道对应的相干态作为初始态的保真度最高,而且随时间呈周期性变化;以规则区域对应的相干态作为初始态的保真度呈不规则的变化;以混沌区域对应的相干态作为初始态的保真度有很大幅度的下降.当参数取为α=1.0,λ=2.0时,相空间中两个岛中心对应的相干态可以相互遂穿,隧穿周期随混沌的渗透大幅度缩短.经典相空间中规则区域和混沌区域的相干态对应的能量量子期待值随时间的变化表现出准周期性,但是有不同的表现形式.

This paper studies fidelity,tunneling,and the quantum expectation value of energy for a periodically kicked free top. The study found that,with the strengthλincreased the classical phase space portraits transform from the regular track to island and finally complete chaotic. When α=π/2,λ=3. 0,fidelity that the initial coherent state corresponds to the fixed point is the highest and presents regular periodic change. Fidelity that the initial coherent state corresponds to regular track presents irregular change. Fidelity that the initial coherent state corresponds to chaos reduces drastically. When α=1. 0,λ=2. 0,two coherent states that correspond to the centre of two islands can mutually tunnel each other, the period of tunneling will be greatly reduced when chaos set in. Quantum expectation values of energy for regular and chaotic region are quasi-periodic,but the manifestations are different.