Resonances for perturbations of a semiclassical periodic Schrödinger operator

Frédéric Klopp Départment de Mathématique Université de Paris-Sud Centre d'Orsay, U.R.A. 760 C.N.R.S.

TBD mathscidoc:1701.332819

Arkiv for Matematik, 32, (2), 323-371, 1993.4
In the semi-classical regime we study the resonances of the operator$P$_{$t$}=$h$^{2}Δ+$V$+$t$·δ$V$in some small neighborhood of the first spectral band of$P$_{0}. Here$V$is a periodic potential, δ$V$a compactly supported potential and$t$a small coupling constant. We construct a meromorphic multivalued continuation of the resolvent of$P$_{$t$}, and define the resonances to be the poles of this continuation. We compute these resonances and study the way they turn into eigenvalues when$t$crosses a certain threshold.
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@inproceedings{frédéric1993resonances,
  title={Resonances for perturbations of a semiclassical periodic Schrödinger operator},
  author={Frédéric Klopp},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203543782969628},
  booktitle={Arkiv for Matematik},
  volume={32},
  number={2},
  pages={323-371},
  year={1993},
}
Frédéric Klopp. Resonances for perturbations of a semiclassical periodic Schrödinger operator. 1993. Vol. 32. In Arkiv for Matematik. pp.323-371. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203543782969628.
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