Anderson localization for the completely resonant phases

摘要

For the almost Mathieu operator (HA,,,eu)(n) = u(n + 1) + u(n 1) -I- 2A cos 27r(0 na)u(n), Avila and Jitomirskaya conjecture that for every phase 0 ERA{0 ER120-FaZE7L}, HA,a,(9 satisfies Anderson localization if IAI > e2)5. In the present paper, we verify the conjecture for jAl > JO. (C) 2014 Elsevier Inc. All rights reserved.