Singular spectrum for radial trees

Jonathan Breuer*, Rupert L. Frank

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that, generically (in the sense of Baire), radial trees have purely singular continuous spectrum.

Original languageAmerican English
Pages (from-to)929-945
Number of pages17
JournalReviews in Mathematical Physics
Volume21
Issue number7
DOIs
StatePublished - Aug 2009
Externally publishedYes

Bibliographical note

Funding Information:
We are grateful to Barry Simon for useful discussions. RF appreciates the warm hospitality of Caltech, where part of this work has been done, and acknowledges support through DAAD grant D/06/49117.

Keywords

  • Quantum graphs
  • Reflectionless property.
  • Schr̈odinger operators
  • Singular spectrum
  • Trees

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