有限Hall系统的扩展边缘态
Extended Edge States in Finite Hall Systems
摘要：
研究了线性尺寸为L的有限宏观二维系统中电子在磁场中的随机薛定谔算符的边缘态。y方向是L-周期的，在x方向上，电子被两个平滑增加的平行边界势限制。我们证明了，以大概率，在第一个频谱间隙的散装哈密顿量的能量范围内，频谱的完整的哈密顿量只包括两套本征能的本征函数有平均速度这是严格的正/负，一致的系统的大小。我们的结果给出了一个定义明确的意义的概念的边缘状态的有限圆柱有两个边界，并扩展了以前的研究只有一个边界的系统。
英文摘要：
We study edge states of a random Schroedinger operator for an electron submitted to a magnetic field in a finite macroscopic two dimensional system of linear dimensions equal to L. The y direction is L-periodic and in the x direction the electron is confined by two smoothly increasing parallel boundary potentials. We prove that, with large probability, for an energy range in the first spectral gap of the bulk Hamiltonian, the spectrum of the full Hamiltonian consists only on two sets of eigenenergies whose eigenfuntions have average velocities which are strictly positive/negative, uniformly with respect to the size of the system. Our result gives a well defined meaning to the notion of edge states for a finite cylinder with two boundaries, and extends previous studies on systems with only one boundary.
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