Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency

Abstract

In this paper, we study the non-self-dual extended Harper's model with a Liouville frequency. Based on the work of \cite{SY}, we show that the integrated density of states (IDS for short) of the model is $\frac{1}{2}$-H$\ddot{\text{o}}$lder continuous. As an application, we also obtain the Carleson homogeneity of the spectrum.

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References in corpus (8)

• The absolutely continuous spectrum of the almost Mathieu operator
• Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators
• Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies
• Homogeneity of the spectrum for quasi-periodic Schrödinger operators
• Hölder Continuity of the Spectral Measures for One-Dimensional Schrödinger Operator in Exponential Regime
• Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
• Exponential decay of the size of spectral gaps for quasiperiodic Schrödinger operators
• Exponential Decay of the lengths of Spectral Gaps for Extended Harper's Model with Liouvillean Frequency

Cited by in corpus (1)

• Exponential Decay of the lengths of Spectral Gaps for Extended Harper's Model with Liouvillean Frequency