Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
复制标题
随机哈密顿量的一级扰动下的奇异连续谱和定位
DOI：
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
T. Wolff
中科院分区：
文献类型：
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作者：
B. Simon;T. Wolff
我们考虑自伴算子A和向量φ上的自伴一阶投影P，它对A是循环的。根据谱测度dμAφ，我们给出了A+λP对A有空的奇异连续谱或只有点谱的充要条件。λ.我们将这些结果应用于一维和多维Anderson模型中的局部化问题。
We consider a selfadjoint operator, A, and a selfadjoint rank-one projection, P, onto a vector, φ, which is cyclic for A. In terms of the spectral measure dμAφ, we give necessary and sufficient conditions for A + λ P to have empty singular continuous spectrum or to have only point spectrum for a.e. λ. We apply these results to questions of localization in the one- and multi-dimensional Anderson models.