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Letters in Mathematical Physics

, Volume 82, Issue 1, pp 25–37 | Cite as

On the Dense Point and Absolutely Continuous Spectrum for Hamiltonians with Concentric δ Shells

  • Pavel Exner
  • Martin Fraas
Article

Abstract

We consider Schrödinger operators in dimension ν ≥ 2 with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum covers a half line determined by the appropriate one-dimensional comparison operator; it is dense pure point in the gaps of the latter. If the interaction is nontrivial and radially periodic, there are infinitely many absolutely continuous bands; in contrast to the regular case the lengths of the p.p. segments interlacing with the bands tend asymptotically to a positive constant in the high-energy limit.

Mathematics Subject Classification (2000)

35J10 35P99 81Q10 

Keywords

Schrödinger operator singular interaction concentric spheres spectral properties 

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Nuclear Physics InstituteCzech Academy of SciencesŘež near PragueCzech Republic
  2. 2.Doppler InstituteCzech Technical UniversityPragueCzech Republic

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