Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational invariant tori, phase space tunneling, and spectra for
  non-selfadjoint operators in dimension 2   We study spectral asymptotics and resolvent bounds for non-selfadjoint
perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2,
assuming that the classical flow of the unperturbed part is completely
integrable. Spectral contributions coming from rational invariant Lagrangian
tori are analyzed. Estimating the tunnel effect between strongly irrational
(Diophantine) and rational tori, we obtain an accurate description of the
spectrum in a suitable window in the complex spectral plane, provided that the
strength of the non-selfadjoint perturbation $\gg h$ (or sometimes $\gg h^2$)
is not too large.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom