具有无界随机变量的随机Landau Hamilton算子的离域化
Delocalization for Random Landau Hamiltonians with Unbounded Random Variables
摘要：
本文证明了在振幅无界的电势随机扰动下Landau哈密顿量的定域/离域跃迁的存在性。特别是，当随机势开启时，朗道能隙的存在概率为1，能隙闭合，局部态填满。在离域区有最小的输运速率。要做到这一点，我们利用霍尔电导的先验量子化和扩展最近的Wegner估计的情况下，无界的随机变量。
英文摘要：
In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the random potential is turned on, the gaps close, filling up partly with localized states. A minimal rate of transport is exhibited in the region of delocalization. To do so, we exploit the a priori quantization of the Hall conductance and extend recent Wegner estimates to the case of unbounded random variables.
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