Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators

Details Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators

2009-12-16

arxiv.org/abs/0912.3246v1

Mathematics

Dynamical Systems

16 pages

Scientific paper

We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrodinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Holder 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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