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1 October 2017 Sharp phase transitions for the almost Mathieu operator
Artur Avila, Jiangong You, Qi Zhou
Duke Math. J. 166(14): 2697-2718 (1 October 2017). DOI: 10.1215/00127094-2017-0013

Abstract

It is known that the spectral type of the almost Mathieu operator (AMO) depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency. We study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place, which solves Jitomirskaya’s conjecture. Together with a previous work by Avila, this gives the sharp description of phase transitions for the AMO for the a.e. phase.

Citation

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Artur Avila. Jiangong You. Qi Zhou. "Sharp phase transitions for the almost Mathieu operator." Duke Math. J. 166 (14) 2697 - 2718, 1 October 2017. https://doi.org/10.1215/00127094-2017-0013

Information

Received: 18 December 2015; Revised: 25 February 2017; Published: 1 October 2017
First available in Project Euclid: 26 May 2017

zbMATH: 06803180
MathSciNet: MR3707287
Digital Object Identifier: 10.1215/00127094-2017-0013

Subjects:
Primary: 47B36
Secondary: 37C55, 39A70, 47B39, 81Q10

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 14 • 1 October 2017
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