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Semiclassical Analysis of the Largest Gap of Quasi-PeriodicSchrödinger Operators

Published online by Cambridge University Press:  12 May 2010

H. Krüger
H. Krüger*
Affiliation:
Department of Mathematics, Rice University, Houston, TX 77005, USA
*
1 E-mail: helge.krueger@rice.edu
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Abstract

In this note, I wish to describe the first order semiclassical approximation to thespectrum of one frequency quasi-periodic operators. In the case of a sampling functionwith two critical points, the spectrum exhibits two gaps in the leading orderapproximation. Furthermore, I will give an example of a two frequency quasi-periodicoperator, which has no gaps in the leading order of the semiclassical approximation.

Keywords

gaps in the spectrumSchrödinger operatorssemiclassical analysis
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 256 - 268
Copyright
© EDP Sciences, 2010

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