光滑Hamilton系统的经典分岔与纠缠
Classical bifurcations and entanglement in smooth Hamiltonian system
摘要：
研究了两个耦合四次振子的纠缠。结果表明，对于一般的混沌本征态，用冯诺伊曼熵度量的纠缠随经典混沌参数的增加而增加.我们考虑某些孤立的周期轨道，其分叉序列影响一类量子本征态，称为通道局域态。对于这些状态，纠缠是一个局部最小值附近的干草叉分叉，但是一个局部最大值附近的反干草叉分叉。我们把这些结果的背景下，可能存在的纠缠措施和传统的本地化措施，已在量子混沌和其他地方进行了大量的研究之间的密切联系。我们还指出了一个有趣的近简并，出现在某些状态的约化密度矩阵的频谱作为本地化和对称性的相互作用。
英文摘要：
We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near a anti-pitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization that have been much studied in quantum chaos and elsewhere. We also point to an interesting near-degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay of localization and symmetry.
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