Bounds on the density of states for Schrodinger operators

• 成果类型: Article
• 署名作者: Bourgain, Jean; Klein, Abel
• 署名单位: Institute for Advanced Study - USA; University of California System; University of California Irvine
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0440-1
• 发表日期: 2013
• 页码: 41-72
• 关键词: integrated density; continuity; localization

摘要

We establish bounds on the density of states measure for Schrodinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a density of states outer-measure that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-Holder continuity for this density of states outer-measure in one, two, and three dimensions for Schrodinger operators, and in any dimension for discrete Schrodinger operators.