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- W4295949187 abstract "We consider a family of quantum graphs ${(Gamma,mathcal{A}_varepsilon)}_{varepsilon>0}$, where $Gamma$ is a $mathbb{Z}^n$-periodic metric graph and the periodic Hamiltonian $mathcal{A}_varepsilon$ is defined by the operation $-varepsilon^{-1} {mathrm{d} ^2over mathrm{d} x^2}$ on the edges of $Gamma$ and either $delta'$-type conditions or the Kirchhoff conditions at its vertices. Here $varepsilon>0$ is a small parameter. We show that the spectrum of $mathcal{A}_varepsilon$ has at least $m$ gaps as $varepsilonto 0$ ($minmathbb{N}$ is a predefined number), moreover the location of these gaps can be nicely controlled via a suitable choice of the geometry of $Gamma$ and of coupling constants involved in $delta'$-type conditions." @default.
- W4295949187 created "2022-09-16" @default.
- W4295949187 creator A5078471617 @default.
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- W4295949187 date "2015-02-16" @default.
- W4295949187 modified "2023-09-24" @default.
- W4295949187 title "Gaps in the spectrum of a periodic quantum graph with periodically distributed $delta'$-type interactions" @default.
- W4295949187 doi "https://doi.org/10.48550/arxiv.1502.04664" @default.
- W4295949187 hasPublicationYear "2015" @default.
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