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On the absence of absolutely continuous spectra for Schrodinger operators on radial tree graphs
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SYSNO ASEP 0357921 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the absence of absolutely continuous spectra for Schrodinger operators on radial tree graphs Author(s) Exner, Pavel (UJF-V) RID, ORCID, SAI
Lipovský, Jiří (UJF-V)Source Title Journal of Mathematical Physics. - : AIP Publishing - ISSN 0022-2488
Roč. 51, č. 12 (2010), 122107/1-122107/19Number of pages 19 s. Language eng - English Country US - United States Keywords QUANTUM GRAPHS ; METRIC TREES Subject RIV BA - General Mathematics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000285768900007 DOI 10.1063/1.3526963 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2011
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