Exact local distribution of the absolutely continuous spectral measure

Abstract

It is well-established that the spectral measure for one-frequency Schrödinger operators with Diophantine frequencies exhibits optimal $1/2$-Hölder continuity within the absolutely continuous spectrum. This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified Hölder continuity of the spectral measure at subcritical energies.

49 pages