Zero measure spectrum for the almost Mathieu operator |
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Authors: | Y Last |
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Institution: | (1) Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel |
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Abstract: | We study the almost Mathieu operator: (H
, ,
u)(n)=u(n+1)+u(n-1)+ cos (2n+)u(n), onl
2
(Z), and show that for all ,, and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely |4–2|. In particular, for ||=2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and ||=2) we show that the Hausdorff dimension of the spectrum is smaller than or equal to 1/2.Work partially supported by the GIF |
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Keywords: | |
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