Moment analysis for localization in random Schrodinger operators

• 成果类型: Article
• 署名作者: Aizenman, M; Elgart, A; Naboko, S; Schenker, JH; Stolz, G
• 署名单位: Princeton University; Stanford University; Saint Petersburg State University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Alabama System; University of Alabama Birmingham; Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0463-y
• 发表日期: 2006
• 页码: 343-413
• 关键词: quantized hall conductance; anderson localization; unique continuation; large disorder; edge states; perturbations; absence; inequalities; diffusion; spectrum

摘要

We study localization effects of disorder on the spectral and dynamical properties of Schrodinger 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-L-1 estimate concerning the boundary-value distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theory.