| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
|
|
|---|---|---|
| Page(s) | 256 - 268 | |
| DOI | https://doi.org/10.1051/mmnp/20105411 | |
| Published online | 12 May 2010 | |
Semiclassical Analysis of the Largest Gap of Quasi-Periodic Schrödinger Operators
Department of Mathematics, Rice University, Houston, TX
77005, USA
1 E-mail: helge.krueger@rice.edu
In this note, I wish to describe the first order semiclassical approximation to the spectrum of one frequency quasi-periodic operators. In the case of a sampling function with two critical points, the spectrum exhibits two gaps in the leading order approximation. Furthermore, I will give an example of a two frequency quasi-periodic operator, which has no gaps in the leading order of the semiclassical approximation.
Mathematics Subject Classification: 47B36 / 47A55
Key words: gaps in the spectrum / Schrödinger operators / semiclassical analysis
© EDP Sciences, 2010
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