H\"older continuity of the integrated density of states for Extended Harper's Model with Liouville frequency

TL;DR

This paper proves that the integrated density of states for the extended Harper's model with Liouville frequency is 1/2-Hölder continuous, and demonstrates the spectrum's Carleson homogeneity, advancing understanding of spectral properties in quasi-periodic models.

Contribution

It establishes the Hölder continuity of the IDS for a non-self-dual extended Harper's model with Liouville frequency, extending previous results to a broader class of models.

Findings

IDS is 1/2-Hölder continuous for the model.

Spectrum exhibits Carleson homogeneity.

Results apply to non-self-dual extended Harper's models 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.