Abstract
We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrödinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Hölder continuity near almost reducible energies (an essential support of absolutely continuous spectrum). For non-perturbatively small potentials (and for the almost Mathieu operator with subcritical coupling), our results apply for all energies.
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Communicated by B. Simon
This work was supported in part by NSF, grant DMS-0601081, and BSF, grant 2006483. This research was partially conducted during the period A.A. served as a Clay Research Fellow.
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Avila, A., Jitomirskaya, S. Hölder Continuity of Absolutely Continuous Spectral Measures for One-Frequency Schrödinger Operators. Commun. Math. Phys. 301, 563–581 (2011). https://doi.org/10.1007/s00220-010-1147-z
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DOI: https://doi.org/10.1007/s00220-010-1147-z