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gaps in the spectrum

Mathematical Modelling of Natural Phenomena (1)

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Semiclassical Analysis of the Largest Gap of Quasi-PeriodicSchrödinger Operators
H. Krüger
Journal:

Mathematical Modelling of Natural Phenomena / Volume 5 / Issue 4 / 2010

Published online by Cambridge University Press:

12 May 2010, pp. 256-268

Print publication:

2010
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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.