Peierls' substitution for low lying spectral energy windows

@article{Cornean2017PeierlsSF,
  title={Peierls' substitution for low lying spectral energy windows},
  author={Horia D. Cornean and Bernard Helffer and Radu Purice},
  journal={Journal of Spectral Theory},
  year={2017}
}
We consider a $2d$ magnetic Schrodinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `Landau type' structure of spectral islands at the bottom of the spectrum, under the hypothesis that the lowest Bloch eigenvalue of the unperturbed operator remained simple on the whole Brillouin zone, even though its range may overlap with the range of the second eigenvalue. We also assumed that the first Bloch… 

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  • A. Drouot
  • Physics, Mathematics
    Pure and Applied Analysis
  • 2019
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