Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees

@article{Exner2014AbsenceOA,
  title={Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees},
  author={P. Exner and C. Seifert and P. Stollmann},
  journal={Annales Henri Poincar{\'e}},
  year={2014},
  volume={15},
  pages={1109-1121}
}
  • P. Exner, C. Seifert, P. Stollmann
  • Published 2014
  • Mathematics
  • Annales Henri Poincaré
  • In this paper, we prove that the existence of absolutely continuous spectrum of the Kirchhoff Laplacian on a radial metric tree graph together with a finite complexity of the geometry of the tree implies that the tree is in fact eventually periodic. This complements the results by Breuer and Frank in (Rev Math Phys 21(7):929–945, 2009) in the discrete case as well as for sparse trees in the metric case. 
    Quantum Graphs on Radially Symmetric Antitrees
    5

    References

    Publications referenced by this paper.