Exact local distribution of the absolutely continuous spectral measure

2024/07/12 by Li, Xianzhe, You, Jiangong, Zhou, Qi · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2407.09278

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.

Cited by

• Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
• Hölder continuity and Fourier asymptotics of spectral measures for 1D Schrödinger operators under exponentially decaying perturbations

Related

• Hölder continuity and Fourier asymptotics of spectral measures for 1D Schrödinger operators under exponentially decaying perturbations
• Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operators
• The absolutely continuous spectrum of the almost Mathieu operator
• Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators
• The absolutely continuous spectrum of finitely differentiable quasi-periodic Schrödinger operators