Spectral regularity and defects for the Kohmoto model

TL;DR

This paper investigates the spectral properties of the Kohmoto model, including Sturmian Hamiltonians and the Kohmoto butterfly, providing spectral estimates and analyzing defects caused by impurities at rational rotations.

Contribution

It introduces new spectral estimates for the Kohmoto model using Farey numbers and characterizes spectral defects due to impurities, extending understanding similar to the Almost-Mathieu operator.

Findings

Spectral estimates derived using Farey numbers.

Identification of impurities causing spectral defects.

Comparison with Almost-Mathieu operator results.

Abstract

We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we determine the impurities at rational rotations leading to the spectral defects in the Kohmoto butterfly. Our results are similar to the ones obtained for the Almost-Mathieu operator and the associated Hofstadter butterfly.