Stability of the non-critical spectral properties I: arithmetic absolute continuity of the integrated density of states

TL;DR

This paper proves the absolute continuity of the integrated density of states for certain perturbations of the almost Mathieu operator, under specific arithmetic conditions on frequency, contributing to spectral theory in mathematical physics.

Contribution

It establishes the absolute continuity of the integrated density of states for a class of non-critical almost Mathieu operators with analytic perturbations, under arithmetic conditions.

Findings

Proves absolute continuity of the integrated density of states.

Applies to frequency-independent analytic perturbations.

Operates under specific arithmetic conditions on frequency.

Abstract

We prove absolute continuity of the integrated density of states for frequency-independent analytic perturbations of the non-critical almost Mathieu operator under arithmetic conditions on frequency.