On the spectrum of critical almost Mathieu operators in the rational case

TL;DR

This paper introduces a new formula and tighter bounds for the spectrum measure of critical almost Mathieu operators with rational frequencies, advancing understanding of their spectral properties.

Contribution

It presents a novel Chambers-type formula and improved spectral measure bounds for critical almost Mathieu operators at rational frequencies.

Findings

Derived a new Chambers-type formula.

Proved sharper upper bounds on spectrum measure.

Enhanced understanding of spectral properties at rational frequencies.

Abstract

We derive a new Chambers-type formula and prove sharper upper bounds on the measure of the spectrum of critical almost Mathieu operators with rational frequencies.