Spectral behavior of quasi periodic potentials

@article{Sarnak1982SpectralBO,
  title={Spectral behavior of quasi periodic potentials},
  author={P. Sarnak},
  journal={Communications in Mathematical Physics},
  year={1982},
  volume={84},
  pages={377-401}
}
  • P. Sarnak
  • Published 1982
  • Mathematics
  • Communications in Mathematical Physics
  • Spectral properties of Schrödinger operators of the typeHɛ=−Δ+ɛV, where Δ is the Laplacian,V a quasiperiodic potential and ɛ a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small ɛ a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as ɛ is increased. 
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