Anderson localization for 2 D discrete Schrödinger operator with random vector potential
Anderson localization for 2 D discrete Schrödinger operator with random vector potential
复制标题
具有随机向量势的二维离散薛定谔算子的安德森定位
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
S. Nakamura
中科院分区：
文献类型：
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作者：
F. Klopp;S. Nakamura
本文证明了具有一类随机矢量势而无标量势的二维离散薛定谔算子在谱底附近的安德森局部化。主要引理是Lifshitz尾和Wegner估计的积分态密度。然后，安德森局部化，即，通过标准多尺度论证证明了特征函数呈指数下降的纯点谱。
We prove the Anderson localization near the bottom of the spectrum for two dimensional discrete Schrödinger operators with a class of random vector potentials and no scalar potentials. Main lemmas are the Lifshitz tail and the Wegner estimate on the integrated density of states. Then, the Anderson localization, i.e., the pure point spectrum with exponentially decreasing eigenfunctions, is proved by the standard multiscale argument.