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arXiv · 1401.3371

Spectra for semiclassical operators with periodic bicharacteristics in dimension two

Michael A. Hall·Michael Hitrik·Johannes Sjoestrand
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Abstract

We study the distribution of eigenvalues for selfadjoint $h$--pseudodifferential operators in dimension two, arising as perturbations of selfadjoint operators with a periodic classical flow. When the strength $\varepsilon$ of the perturbation is $\ll h$, the spectrum displays a cluster structure, and assuming that $\varepsilon \gg h^2$ (or sometimes $\gg h^{N_0}$, for $N_0 >1$ large), we obtain a complete asymptotic description of the individual eigenvalues inside subclusters, corresponding to the regular values of the leading symbol of the perturbation, averaged along the flow.

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Michael A. Hall, Michael Hitrik, Johannes Sjoestrand. 2014-01-14. Spectra for semiclassical operators with periodic bicharacteristics in dimension two. https://arxiv.org/abs/1401.3371

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