Anderson localization for the almost Mathieu operator in the exponential regime

Wencai Liu; Xiaoping Yuan

doi:10.4171/jst/92

JournalsjstVol. 5, No. 1pp. 89–112

Anderson localization for the almost Mathieu operator in the exponential regime

Wencai Liu
Fudan University, Shanghai, China
Xiaoping Yuan
Fudan University, Shanghai, China

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Abstract

For the almost Mathieu operator

(H_{λ, α, θ} u)_{n} = u_{n + 1} + u_{n - 1} + 2 λ cos 2 π (θ + n α) u_{n},

Avila and Jitomirskaya verify this for $∣ λ ∣ > e^{\frac{16}{9} β}$ . In the present paper, we extend their result to the regime $∣ λ ∣ > e^{\frac{3}{2} β}$ .

Cite this article

Wencai Liu, Xiaoping Yuan, Anderson localization for the almost Mathieu operator in the exponential regime. J. Spectr. Theory 5 (2015), no. 1, pp. 89–112

DOI 10.4171/JST/92