Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum singular complete integrability   We consider some perturbations of a family of pairwise commuting linear
quantum Hamiltonians on the torus with possibly dense pure point spectra. We
prove that the Rayleigh-Schr{\"o}dinger perturbation series converge near each
unperturbed eigenvalue under the form of a convergent quantum Birkhoff normal
form. Moreover the family is jointly diagonalised by a common unitary operator
explicitly constructed by a Newton type algorithm. This leads to the fact that
the spectra of the family remain pure point. The results are uniform in the
Planck constant near $\hbar= 0$. The unperturbed frequencies satisfy a small
divisors condition %(Bruno type condition (including the Diophantine case) and
we explicitly estimate how this condition can be released when the family tends
to the unperturbed one.

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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph