On the Spectrum of a Bent Chain Graph

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F08%3A04146924" target="_blank" >RIV/68407700:21340/08:04146924 - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/08:00314243
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On the Spectrum of a Bent Chain Graph
Original language description
We study Schrödinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by ?-couplings with a parameter alpha in R. If the graph is 'straight', i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever ? not equal 0. We consider a 'bending' deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling ? and the 'bending angle' as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.
Czech name
O spektru ohnutého řetězového grafu
Czech description
Vyšetřujeme spektrum řetězového grafu "ohnutého" v vybrané smyčce a odvozujeme chování vlastních hodnot v lakunách a rezonancí systému.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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