From level dynamics, we show that when two levels come to an avoided level crossing, violent fluctuations of the corresponding eigenstates are similar to a two level process: rapid mixing of the two eigenstates. This can be checked sensitively by the expectation values of a smooth observable and its derivative with respect to the strength parameter of perturbation. In Husimi distribution, the mixing can be viewed as that the two eigenstates exchange parts of their distributions in a simple way.

中文翻译：

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通过两级动力学方法来研究本能态在避免平交路口周围的波动

从水平动力学来看，我们表明，当两个水平达到避免的水平交叉时，相应本征态的剧烈波动类似于两个水平过程：两个本征态的快速混合。可以通过平滑可观察到的期望值及其对摄动强度参数的导数来灵敏地检查这一点。在Husimi分布中，可以将混合视为两个本征态以简单的方式交换其分布的一部分。