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Central Spectral Gaps of the Almost Mathieu Operator

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Title: Central Spectral Gaps of the Almost Mathieu Operator
Authors: Krasovsky, I
Item Type: Journal Article
Abstract: We consider the spectrum of the almost Mathieu operator Hα with frequency α and in the case of the critical coupling. Let an irrational α be such that |α − pn/qn| < cq−κ n , where pn/qn, n = 1, 2, . . . are the convergents to α, and c, κ are positive absolute constants, κ < 56. Assuming certain conditions on the parity of the coefficients of the continued fraction of α, we show that the central gaps of Hpn/qn , n = 1, 2, . . . , are inherited as spectral gaps of Hα of length at least c 0 q −κ/2 n , c 0 > 0.
Issue Date: 20-Oct-2016
Date of Acceptance: 8-Sep-2016
URI: http://hdl.handle.net/10044/1/39992
DOI: https://dx.doi.org/10.1007/s00220-016-2774-9
ISSN: 1432-0916
Publisher: Springer Verlag
Start Page: 419
End Page: 439
Journal / Book Title: Communications in Mathematical Physics
Volume: 351
Issue: 1
Copyright Statement: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: The Leverhulme Trust
Funder's Grant Number: RF-2015-243 Krasovsky
Keywords: Science & Technology
Physical Sciences
Physics, Mathematical
Physics
SCHRODINGER-OPERATORS
HARPER EQUATION
CANTOR SPECTRUM
BETHE-ANSATZ
0105 Mathematical Physics
0206 Quantum Physics
0101 Pure Mathematics
Mathematical Physics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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