朗道能级系统中导引中心的作用与机械角动量和赝轨道角动量
Role of guiding center in Landau level system and mechanical and pseudo orbital angular momenta
摘要：
在朗道能级系统中，除了著名的正则角动量和力学角动量外，还有一个有趣但不太常见的量，称为赝轨道角动量。伪OAM可以看作是规范OAM的规范不变扩展，它在形式上是规范不变的，在一定的规范下退化为规范OAM。由于伪OAM和机械OAM都是规范不变的，因此不可能仅从规范原理来判断它们中的哪一个优于另一个。然而，这两种OAM具有完全不同的物理含义。机械OAM显示出明显的可观测性和明确的对应关系与经典OAM的回旋运动。另一方面，我们证明了朗道问题中的标准正则OAM以及伪OAM是关键取决于坐标系原点的选择的概念。我们试图揭示伪OAM和机械OAM之间的关系，以及它们的可观测性，特别注意在朗道问题中的引导中心算子的作用。
英文摘要：
There is an interesting but not so popular quantity called pseudo orbital angular momentum (OAM) in the Landau-level system, besides the well-known canonical and mechanical OAMs. The pseudo OAM can be regarded as a gauge-invariant extension of the canonical OAM, which is formally gauge invariant and reduces to the canonical OAM in a certain gauge. Since both of the pseudo OAM and the mechanical OAM are gauge invariant, it is impossible to judge which of those is superior to the other solely from the gauge principle. However, these two OAMs have totally different physical meanings. The mechanical OAM shows manifest observability and clear correspondence with the classical OAM of the cyclotron motion. On the other hand, we demonstrate that the standard canonical OAM as well as the pseudo OAM in the Landau problem are the concepts which crucially depend on the choice of the origin of the coordinate system. We try to reveal the relation between the pseudo OAM and the mechanical OAM as well as their observability by paying special attention to the role of guiding-center operator in the Landau problem.
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