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arXiv 1209.3287cond-mat.mes-hallnlin.CD
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量子线中双电子系统的量子混沌与经典混沌

Quantum and classical chaos of a two-electron system in a quantum wire

Shumpei Masuda, Shin-ichi Sawada, Yasushi Shimizu

摘要:

研究了两个无自旋粒子在库仑排斥或吸引相互作用下的经典和量子动力学。这种相互作用导致了经典力学中的不规则动力学,这反映了系统在能级统计中的量子特性(量子混沌的特征)。我们调查特别密切的经典和量子混沌之间的对应关系。目前的经典动力学具有某些标度性质,而量子动力学则没有。然而,我们证明了能级统计意味着即使在量子系统中也存在相应的标度性质。我们引入了一种新的最大李雅普诺夫指数来代替普通的最大李雅普诺夫指数(MLE),它被证明是当前经典系统混沌不规则性的合适度量。结果表明,表征量子系统能级统计的Brody参数的能量依赖性与新的极大似然估计的能量依赖性趋势一致。

英文摘要:

We study classical and quantum dynamics of two spinless particles confined in a quantum wire with repulsive or attractive Coulomb interaction. The interaction induces irregular dynamics in classical mechanics, which reflects on the quantum properties of the system in the energy level statistics (the signatures of quantum chaos). We investigate especially closer correspondence between the classical and quantum chaos. The present classical dynamics has some scaling property, which the quantum counterpart does not have. However, we demonstrate that the energy level statistics implies the existence of the corresponding scaling property even in the quantum system. Instead of ordinary maximum Lyapunov exponent (MLE), we introduce a novel kind of MLE, which is shown to be suitable measure of chaotic irregularity for the present classical system. We show that tendency of the energy dependence of the Brody parameter, which characterizes the energy level statistics in the quantum system, is consistent with that of the novel kind of MLE.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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