Universal quantum localizing transition of a partial barrier in a chaotic sea.
Universal quantum localizing transition of a partial barrier in a chaotic sea.
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DOI：
10.1103/physrevlett.109.234101
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发表时间：
2012-06
影响因子：
8.6
通讯作者：
Matthias Michler;A. Bäcker;R. Ketzmerick;H. Stöckmann;S. Tomsovic
中科院分区：
文献类型：
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作者：
Matthias Michler;A. Bäcker;R. Ketzmerick;H. Stöckmann;S. Tomsovic
一般的二维哈密顿系统在其混沌相空间中具有限制经典输运的部分势垒。从量子力学的角度来看，如果普朗克常数h比经典的通量h>；>；Φ大，那么输运就会被抑制，从而使波包和波态局域化。相比之下，H<；<；Φ的经典运输是被模仿的。设计具有可控通量Φ的孤立部分势垒的量子映射是研究这种形式的量子局域化到模拟经典输运的转变的关键。我们观察到量子输运遵循一条普适的跃迁曲线，它是预期标度参数Φ/h的函数。我们发现这条曲线对称于Φ/h=1，宽度为2个数量级的Φ/h，并且没有量子化的台阶。我们建立了局部耦合的相关性，改进了以往依赖全局耦合的随机矩阵模型。结果表明，唯象的2×2模型对跃迁曲线给出了精确的解析描述。
Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically, the transport is suppressed if Planck's constant h is large compared to the classical flux, h>>Φ, such that wave packets and states are localized. In contrast, classical transport is mimicked for h<<Φ. Designing a quantum map with an isolated partial barrier of controllable flux Φ is the key to investigating the transition from this form of quantum localization to mimicking classical transport. It is observed that quantum transport follows a universal transition curve as a function of the expected scaling parameter Φ/h. We find this curve to be symmetric to Φ/h=1, having a width of 2 orders of magnitude in Φ/h, and exhibiting no quantized steps. We establish the relevance of local coupling, improving on previous random matrix models relying on global coupling. It turns out that a phenomenological 2×2 model gives an accurate analytical description of the transition curve.