Anderson localization for the almost Mathieu operator in the exponential regime

作者：Liu Wencai^*; Yuan Xiaoping

来源：Journal of Spectral Theory, 2015, 5(1): 89-112.

DOI：10.4171/JST/92

• Anderson localization
• almost Mathieu operator

For the almost Mathieu operator
(H(lambda,alpha,theta)u )(n) = u(n+1) + u(n-1) + 2 lambda cos 2 pi(theta + n alpha)u(n),
Jitomirskaya conjectures that for a.e. theta, H-lambda,H-alpha,H-theta satisfies Anderson localization if vertical bar lambda vertical bar > e(beta). Avila and Jitomirskaya verify this for vertical bar lambda vertical bar > e(16/9 beta). In the present paper, we extend their result to regime vertical bar lambda vertical bar > e(3/2 beta).

• 出版日期2015
• 单位复旦大学