On the spectrum of multi-frequency quasiperiodic Schrodinger operators with large coupling

• 成果类型: Article
• 署名作者: Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
• 署名单位: University of Toronto; Yale University; University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00872-7
• 发表日期: 2019
• 页码: 603-701
• 关键词: density-of-states; anderson localization; continuity; shifts

摘要

We study multi-frequency quasiperiodic Schrodinger operators on Z. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location that we establish non-perturbatively in the regime of positive Lyapunov exponent.