Mixed spectral types for the one frequency discrete quasi-periodic Schr\"odinger operator

Shiwen Zhang

Mixed spectral types for the one frequency discrete quasi-periodic Schr\"odinger operator

Spectral Theory 2015-08-17 v2 Mathematical Physics Dynamical Systems math.MP

Authors: Shiwen Zhang

Abstract

We consider a family of one frequency discrete analytic quasi-periodic Schr\"odinger operators which appear in [Bjer]. We show that this family provides an example of coexistence of absolutely continuous and point spectrum for some parameters as well as coexistence of absolutely continuous and singular continuous spectrum for some other parameters.

Keywords

discrete quasi-periodic Schrödinger operator mixed spectral types absolutely continuous spectrum point spectrum singular continuous spectrum one frequency

Cite

@article{arxiv.1508.02787,
  title  = {Mixed spectral types for the one frequency discrete quasi-periodic Schr\"odinger operator},
  author = {Shiwen Zhang},
  journal= {arXiv preprint arXiv:1508.02787},
  year   = {2015}
}

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