Spectral structure of Anderson type Hamiltonians
Spectral structure of Anderson type Hamiltonians
复制标题
安德森型哈密顿量的谱结构
DOI：
10.1007/s002220000076
复制
发表时间：
2000
影响因子：
3.1
通讯作者：
Y. Last
中科院分区：
文献类型：
--
作者：
V. Jaksic;Y. Last
本文研究形式为？Hω=H0+∑λω(N)δn的自伴算子，其中δn是一族正交化向量，λω(N)‘S是具有绝对连续概率分布的独立分布的随机变量。我们证明了一个一般的结构定理，即对于每一对(n，m)，如果对应于向量δn和δm的循环子空间不是完全正交的，则Hω对这些子空间的限制是酉等价的(概率为1)。这对这类算子的谱理论有一定的影响。特别地，我们证明了Anderson型哈密顿量的“行为良好”的绝对连续谱一定是纯的，并用它证明了在某些具体情况下绝对连续谱的纯洁性。
Abstract.We study self adjoint operators of the form¶Hω = H0 + ∑λω(n) δn,¶where the δn’s are a family of orthonormal vectors and the λω(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 δn and δm are not completely orthogonal, then the restrictions of Hω 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.