On the absence of absolutely continuous spectra for Schrodinger operators on radial tree graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F10%3A00357921" target="_blank" >RIV/61389005:_____/10:00357921 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On the absence of absolutely continuous spectra for Schrodinger operators on radial tree graphs

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

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Volume of the periodical

51

Issue of the periodical within the volume

12

Country of publishing house

US - UNITED STATES

Number of pages

19

Pages from-to

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UT code for WoS article

000285768900007

EID of the result in the Scopus database

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