Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model

Xu Xu; Xin Zhao

doi:10.3934/dcds.2020201

Article Contents

2020, Volume 40, Issue 8: 4777-4800. Doi: 10.3934/dcds.2020201

This issue Previous Article Mean dimension of shifts of finite type and of generalized inverse limits Next Article Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation

Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model

Xu Xu^1, and
Xin Zhao^1,2, ,

1.
Department of Mathematics, Nanjing University, Nanjing 210093, China
2.
Department of Mathematics, University of California, Irvine, CA 92612, USA

^* Corresponding author: Xin Zhao
^* Corresponding author: Xin Zhao

Received: June 30, 2019

Revised: December 31, 2019

Published: May 2020

The first author is supported by NSFC grant (11671192). The second author is supported by China Scholarship Council (No. 201906190072) and NSFC grant (11571327)

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Abstract

For non-critical extended Harper's model with Diophantine frequency, we establish the exponential decay of the upper bounds on the spectral gaps and prove the spectrum is homogeneous. Especially we give a relationship between the decaying rate and Lyapunov exponent in non-self-dual region.

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Mathematics Subject Classification: Primary: 81Q10; Secondary: 47B39.

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