关于霍尔效应的量子理论
On The Quantum Theory of Hall Effect
摘要：
我们讨论了一个基于半经典Schroedinger-Chern-Simons作用量的经典和整数量子霍尔效应模型，其中欧姆方程作为运动方程。在典型的量子霍尔条件下，经典的陈-西蒙斯作用量部分的量子化导致量子化的霍尔电导率。我们进一步表明，经典的霍尔效应是由一个理论所描述的量子霍尔效应理论的经典极限。该模型还解释了边缘电流在样本边界上的偏好和范围。
英文摘要：
We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical Chern-Simons-part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall-effect is described by a theory which arises as the classical limit of a theory of quantum Hall-effect. The model explains also the preference and the domain of the edge currents on the boundary of samples.
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