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

Abstract

In this paper, we study the non-self dual extended Harper's model with Liouvillean frequency. By establishing quantitative reducibility results together with the averaging method, we prove that the lengths of spectral gaps decay exponentially.

arXiv commentA revised version with 1 figure

References in corpus (7)

• A Nonperturbative Eliasson's Reducibility Theorem
• The absolutely continuous spectrum of the almost Mathieu operator
• Asymptotics of spectral gaps of quasi-periodic Schrödinger operators
• Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies
• Spectral Gaps of Almost Mathieu Operator in Exponential Regime
• Central spectral gaps of the almost Mathieu operator
• Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency

Cited by in corpus (1)

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