Metal-insulator transition for the almost Mathieu operator

• 成果类型: Article
• 署名作者: Jitomirskaya, SY
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121066
• 发表日期: 1999
• 页码: 1159-1175
• 关键词: periodic schrodinger-operators; singular continuous-spectrum; tight-binding model; ABSOLUTELY CONTINUOUS-SPECTRUM; anderson localization; jacobi matrices; point spectrum; equation; absence; PROOF

摘要

We prove that for Diophantine omega and almost every theta, the almost Mathieu operator, (H(omega,lambda,theta)Psi)(n) = Psi(n + 1) + Psi(n - 1) + lambda cos 2 pi(wn + theta)Psi(n), exhibits localization for lambda > 2 and purely absolutely continuous spectrum for lambda < 2. This completes the proof of (a correct version of) the Aubry-Andre conjecture.