Spectral structure of Anderson type Hamiltonians

• 成果类型: Article
• 署名作者: Jaksic, V; Last, Y
• 署名单位: University of Ottawa; Hebrew University of Jerusalem; California Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220000076
• 发表日期: 2000
• 页码: 561-577
• 关键词: LOCALIZATION; disorder

摘要

We study self adjoint operators of the form H-omega = H-0 + Sigma lambda(omega)(n) [delta(n), .] delta(n), where the delta(n),'s are a family of orthonormal vectors and the lambda(omega)(n)'s are independently distributed random variables with absolutely continuous probability distributions. We prove a general structural theorem saying that for each pair (n, m), if the cyclic subspaces corresponding to the vectors delta(n) and delta(m) are not completely orthogonal, then the restrictions of H-omega to these subspaces are unitarily equivalent (with probability one). This has some consequences for the spectral theory of such operators. In particular, we show that well behaved absolutely continuous spectrum of Anderson type Hamiltonians must be pure, and use this to prove the purity of absolutely continuous spectrum in some concrete cases.