Perturbations of selfadjoint operators with periodic classical flow

2003/03/03 by Johannes Sjoestrand, Sjoestrand, Johannes · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.AP #math.SP #msc:32A25 #msc:34M99 #msc:35P20 #msc:35Q40 #msc:37G99

paper · pdf · doi:10.48550/arxiv.math/0303023

arxiv created 2003/03/03 · arxiv updated 2009/11/30

Abstract

We consider non-selfadjoint perturbations of a self-adjoint h-pseudodifferential operator in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength ε of the perturbation satisfies h^δ₀ <ε≤ ε₀ for some δ₀∈ ]0,1/2[ and a sufficiently small ε₀>0. We get a complete asymptotic description of all eigenvalues in certain rectangles [-1/C,1/C]+iε[F₀-1/C,F₀+1/C]. In particular we are able to treat the case when ε>0 is small but independent of h.

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• Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2
• Diophantine tori and spectral asymptotics for non-selfadjoint operators

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