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
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 (, 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
0105 Mathematical Physics
0206 Quantum Physics
0101 Pure Mathematics
Mathematical Physics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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