论文标题
真正的量子混乱和量子状态之间的物理距离
Genuine Quantum Chaos and Physical Distance Between Quantum States
论文作者
论文摘要
我们表明，尽管量子动力学是线性的，但仍存在真正的量子混乱。通过在两个量子状态之间引入物理距离来揭示这一点。在定性上与量子状态的现有距离有所不同，例如，fubini研究距离，两个相互正交量子状态之间的物理距离可能很小。结果，在随之而来的量子动力学演化过程中，两个量子状态最初非常接近物理距离，它们可以彼此差异。我们能够使用物理距离来定义量子Lyaponov指数和量子混乱。后者导致经典庞加莱段的量子类似物，该部分绘制了量子动力学是规则的区域以及量子动力学混乱的区域。三个不同的系统，即踢转子，三个位点的玻色 - 哈伯德模型和Spin-1/2 XXZ模型，用于说明我们的结果。
We show that there is genuine quantum chaos despite that quantum dynamics is linear. This is revealed by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for example, the Fubini-Study distance, the physical distance between two mutually orthogonal quantum states can be very small. As a result, two quantum states, which are initially very close by physical distance, can diverge from each other during the ensuing quantum dynamical evolution. We are able to use physical distance to define quantum Lyaponov exponent and quantum chaos measure. The latter leads to quantum analogue of the classical Poincaré section, which maps out the regions where quantum dynamics is regular and the regions where quantum dynamics is chaotic. Three different systems, kicked rotor, three-site Bose-Hubbard model, and spin-1/2 XXZ model, are used to illustrate our results.
