Spectral gap for quantum graphs and their edge connectivity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F13%3A00398984" target="_blank" >RIV/61389005:_____/13:00398984 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1088/1751-8113/46/27/275309" target="_blank" >http://dx.doi.org/10.1088/1751-8113/46/27/275309</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8113/46/27/275309" target="_blank" >10.1088/1751-8113/46/27/275309</a>

Result language
angličtina
Original language name
Spectral gap for quantum graphs and their edge connectivity
Original language description
The spectral gap for Laplace operators on metric graphs and the relation between the graph's edge connectivity is investigated, in particular what happens to the gap if an edge is added to (or deleted from) a graph. It is shown that, in contrast to discrete graphs, the connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding sufficiently large edges as well as cutting away sufficiently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
—

Project
<a href="/en/project/GAP203%2F11%2F0701" target="_blank" >GAP203/11/0701: Guided Quantum Dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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