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Exact local distribution of the absolutely continuous spectral measure

Mathematical Physics 2024-07-15 v1 Dynamical Systems math.MP Spectral Theory

Abstract

It is well-established that the spectral measure for one-frequency Schr\"odinger operators with Diophantine frequencies exhibits optimal 1/21/2-H\"older 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 H\"older continuity of the spectral measure at subcritical energies.

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Cite

@article{arxiv.2407.09278,
  title  = {Exact local distribution of the absolutely continuous spectral measure},
  author = {Xianzhe Li and Jiangong You and Qi Zhou},
  journal= {arXiv preprint arXiv:2407.09278},
  year   = {2024}
}

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49 pages