Periodic quantum graphs with predefined spectral gaps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017088" target="_blank" >RIV/62690094:18470/20:50017088 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1751-8121/aba98b" target="_blank" >https://doi.org/10.1088/1751-8121/aba98b</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/aba98b" target="_blank" >10.1088/1751-8121/aba98b</a>

Result language
angličtina
Original language name
Periodic quantum graphs with predefined spectral gaps
Original language description
Let Gamma be an arbitrary Z(n)-periodic metric graph, which does not coincide with a line. We consider the Hamiltonian H-epsilon on Gamma with the action -epsilon(-1)d(2)/dx(2) on its edges; here epsilon > 0 is a small parameter. Let m is an element of N. We show that under a proper choice of vertex conditions the spectrum sigma(H-epsilon) of H-epsilon has at least m gaps as e is small enough. We demonstrate that the asymptotic behavior of these gaps and the asymptotic behavior of the botto m of sigma(H-epsilon) as epsilon -> 0 can be completely controlled through a suitable choice of coupling constants standing in those vertex conditions. We also show howto ensure for fixed (small enough) e the precise coincidence of the left endpoints of the first m spectral gaps with predefined numbers.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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