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April 2012 Persistence of gaps in the spectrum of certain almost periodic operators
Norbert Riedel
Adv. Theor. Math. Phys. 16(2): 693-712 (April 2012).

Abstract

It is shown that for any irrational rotation number and any admissible gap labelling number the almost Mathieu operator (also known as Harper’s operator) has a gap in its spectrum with that labelling number. This answers the strong version of the so-called "Ten Martini Problem". When specialized to the particular case where the coupling constant is equal to one, it follows that the "Hofstadter butterfly" has for any quantum Hall conductance the exact number of components prescribed by the recursive scheme to build this fractal structure.

Citation

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Norbert Riedel. "Persistence of gaps in the spectrum of certain almost periodic operators." Adv. Theor. Math. Phys. 16 (2) 693 - 712, April 2012.

Information

Published: April 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1269.81227
MathSciNet: MR3019414

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 2 • April 2012
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