CAJ | 학술논문

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.
연구일개주기수격타라적보진도、수도효응화능량양자기대치.연구발현,수착타격강도λ적증가,경전상공간결구종규칙적궤도도출현도재도완전혼돈.당삼수취위α=π/2,λ=3.0시,이상공간적은정고정점처적주기궤도대응적상간태작위초시태적보진도최고,이차수시간정주기성변화；이규칙구역대응적상간태작위초시태적보진도정불규칙적변화；이혼돈구역대응적상간태작위초시태적보진도유흔대폭도적하강.당삼수취위α=1.0,λ=2.0시,상공간중량개도중심대응적상간태가이상호수천,수천주기수혼돈적삼투대폭도축단.경전상공간중규칙구역화혼돈구역적상간태대응적능량양자기대치수시간적변화표현출준주기성,단시유불동적표현형식.
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.