Dry Ten Martini problem for non self-dual extended Harper's model

TL;DR

This paper proves the dry Ten Martini problem for the extended Harper's model, establishing that the spectrum is a Cantor set with all gaps open in the non self-dual case for Diophantine frequencies.

Contribution

It provides the first proof of the dry Ten Martini problem for the non self-dual extended Harper's model, confirming the Cantor spectrum with all gaps open.

Findings

Spectrum is a Cantor set with all gaps open

Validates the dry Ten Martini problem in the non self-dual case

Applicable for Diophantine frequencies

Abstract

In this paper we prove the dry version of the Ten Martini problem: Cantor spectrum with all gaps open, for the extended Harper's model in the non self-dual region for Diophantine frequencies.