Anderson localization for multi-frequency quasi-periodic Jacobi operators

Zhen Zhang; Xiong Li

doi:10.3934/dcds.2022128

Article Contents

2022, Volume 42, Issue 12: 5869-5891. Doi: 10.3934/dcds.2022128

This issue Previous Article Generic properties of geodesic flows on analytic hypersurfaces of Euclidean space Next Article Upper and lower $ L^2 $-decay bounds for a class of derivative nonlinear Schrödinger equations

Anderson localization for multi-frequency quasi-periodic Jacobi operators

Zhen Zhang^1, and
Xiong Li^1, ,

1.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

^*Corresponding author: Xiong Li
^*Corresponding author: Xiong Li

Received: March 2022

Early access: September 7, 2022

Published online: September 7, 2022

Partially supported by the NSFC (11971059)..

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Abstract

In this paper, we are concerned with the quasi-periodic Jacobi operators with large potentials on $ \mathbb{T}^d $ ($ d \geq 1 $) and establish the positivity and continuity of the Lyapunov exponent by combining the large deviation theorem with the avalanche principle. Moreover, we show that Anderson localization takes place for almost all Diophantine frequencies when the coupling is sufficiently large.

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Mathematics Subject Classification: Primary: 81Q10; Secondary: 47A25.

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