Quantum singular complete integrability

  title={Quantum singular complete integrability},
  author={Thierry Paul and Laurent Stolovitch},
  journal={arXiv: Mathematical Physics},
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… Expand
2 Citations
Normalization in Banach scale Lie algebras via mould calculus and applications
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  • A. Anikin
  • Physics, Computer Science
  • Asymptot. Anal.
  • 2017


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