Moment analysis for localization in random Schrödinger operators
Moment analysis for localization in random Schrödinger operators
复制标题
随机薛定谔算子定位的矩分析
DOI：
10.1007/s00222-005-0463-y
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发表时间：
2003
影响因子：
3.1
通讯作者：
G. Stolz
中科院分区：
文献类型：
--
作者：
M. Aizenman;A. Elgart;S. Naboko;J. Schenker;G. Stolz
我们研究了无序对具有随机势的薛定谔算符的谱和动力学性质的局域化效应。新的结果包括跃迁幅度和相关投影核的指数衰减界，包括平均值。这些是通过分析预解剂的分数矩而得到的，由于无序的共振扩散效应，分数矩是有限的。到目前为止，阻碍这种方法推广到连续统的主要困难可以追溯到与局部势项有关的Lifshitz-Krein谱移位上缺乏统一的界限。这里通过使用关于最大耗散算子预解的边值分布的弱L1估计，结合相对紧性理论的标准工具来避免这一困难。
We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonance-diffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. The difficulty is avoided here through the use of a weak-L1 estimate concerning the boundary-value distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theory.