Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees

Publikationstyp
Journal Article
Date Issued
2013-07-12
Sprache
English
Author(s)
Exner, Pavel  
Seifert, Christian  orcid-logo
Stollmann, Peter  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/9949
Journal
Annales Henri Poincaré  
Volume
15
Issue
6
Start Page
1109
End Page
1121
Citation
Annales Henri Poincare 15 (6): 1109-1121 (2014)
Publisher DOI
10.1007/s00023-013-0274-4
Scopus ID
2-s2.0-84901193662
Publisher
Springer International Publishing AG
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.
DDC Class
510: Mathematik