Spectra for semiclassical operators with periodic bicharacteristics in\n dimension two

2014/01/14 by Michael Hall, Hall, Michael A., Michael Hitrik +3
Computer Science · Materials Science · Mathematics · #35P20 #35Q40 #35S05 #37J35 #37J45 #58J40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Quasicrystal Structures and Properties #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1401.3371

openalex publication_date 2014/01/14 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study the distribution of eigenvalues for selfadjoint\nh--pseudodifferential operators in dimension two, arising as perturbations of\nselfadjoint operators with a periodic classical flow. When the strength\n\ε of the perturbation is \≪ h, the spectrum displays a cluster\nstructure, and assuming that \ε \≫ h² (or sometimes \≫ h^N₀,\nfor N₀ >1 large), we obtain a complete asymptotic description of the\nindividual eigenvalues inside subclusters, corresponding to the regular values\nof the leading symbol of the perturbation, averaged along the flow.\n

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