Semiclassical analysis of the largest gap of quasi - periodic Schrödinger operators .
نویسنده
چکیده
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.
منابع مشابه
ar X iv : 0 81 2 . 50 38 v 1 [ m at h . SP ] 3 0 D ec 2 00 8 SEMICLASSICAL ANALYSIS OF SCHRÖDINGER OPERATORS WITH MAGNETIC WELLS
We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schrödinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the individual eigenvalues for operators on closed manifolds and existence of gaps in intervals close to the bottom of the spectrum of periodic operators.
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