Some Spectrum Property of Periodic Coupling AMO Operator

TL;DR

This paper investigates the spectral properties of the periodic coupling Aubry-Andre model, establishing conditions for absolutely continuous and singular continuous spectra, and demonstrating the continuity of the Lyapunov exponent.

Contribution

It introduces new conditions for the spectral types of the periodic coupling AMO model and proves the Lyapunov exponent's continuity with respect to the coupling.

Findings

Existence of an interval with purely absolutely continuous spectrum

Conditions under which the spectrum becomes singular continuous

Continuity of the Lyapunov exponent relative to the periodic coupling

Abstract

We study spectrum of the periodic coupling AMO model. Meantime there establish the continuity of Lyapunov exponent about the the periodic coupling of AMO model. Through the dynamical method can find a interval the AMO model only have absolutely continuous spectrum. At the same time, some condition make the periodic coupling of AMO model is singular continuous.