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On the absence of absolutely continuous spectra for Schrodinger operators on radial tree graphs
- 1.0357921 - ÚJF 2011 RIV US eng J - Journal Article
Exner, Pavel - Lipovský, Jiří
On the absence of absolutely continuous spectra for Schrodinger operators on radial tree graphs.
Journal of Mathematical Physics. Roč. 51, č. 12 (2010), 122107/1-122107/19. ISSN 0022-2488. E-ISSN 1089-7658
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : QUANTUM GRAPHS * METRIC TREES
Subject RIV: BA - General Mathematics
Impact factor: 1.291, year: 2010
The subject of the paper is Schrodinger operators on tree graphs which are radial, having the branching number b(n) at all the vertices at the distance t(n) from the root. We consider a family of coupling conditions at the vertices characterized by (b(n) - 1)(2) + 4 real parameters. We prove that if the graph is sparse so that there is a subsequence of {t(n+1) - t(n)} growing to infinity, in the absence of the potential the absolutely continuous spectrum is empty for a large subset of these vertex couplings, but on the the other hand, there are cases when the spectrum of such a Schrodinger operator can be purely absolutely continuous.
Permanent Link: http://hdl.handle.net/11104/0196088
Number of the records: 1