Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation
Mean dimension of shifts of finite type and of generalized inverse limits
August 2020, 40(8): 4777-4800. doi: 10.3934/dcds.2020201
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,,
Department of Mathematics, Nanjing University, Nanjing 210093, China
Department of Mathematics, University of California, Irvine, CA 92612, USA
* Corresponding author: Xin Zhao
Received July 2019 Revised January 2020 Published May 2020
Fund Project: The first author is supported by NSFC grant (11671192). The second author is supported by China Scholarship Council (No. 201906190072) and NSFC grant (11571327)
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.
Keywords: Sharp upper bounds, homogeneous spectrum, spectral gaps, extended Harper's model, non-critical region.
Mathematics Subject Classification: Primary: 81Q10; Secondary: 47B39.
Citation: Xu Xu, Xin Zhao. Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 4777-4800. doi: 10.3934/dcds.2020201
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Figure 1. parameter partition
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