Geodesic
Gap control by singular Schrödinger operators in a periodically structured metamaterial
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 3, pp. 270-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a family $\{\mathcal{H}^\varepsilon\}_{\varepsilon>0}$ of $\varepsilon\mathbb{Z}^n$-periodic Schrödinger operators with $\delta'$-interactions supported on a lattice of closed compact surfaces; within a minimum period cell one has $m\in\mathbb{N}$ surfaces. We show that in the limit when $\varepsilon\to 0$ and the interactions strengths are appropriately scaled, $\mathcal{H}^\varepsilon$ has at most $m$ gaps within finite intervals, and moreover, the limiting behavior of the first $m$ gaps can be completely controlled through a suitable choice of those surfaces and of the interactions strengths. 
@article{JMAG_2018_14_3_a1,
     author = {Pavel Exner and Andrii Khrabustovskyi},
     title = {Gap control by singular {Schr\"odinger} operators in a periodically structured metamaterial},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {270--285},
     year = {2018},
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     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2018_14_3_a1/}
}
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Pavel Exner; Andrii Khrabustovskyi. Gap control by singular Schrödinger operators in a periodically structured metamaterial. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 3, pp. 270-285. http://geodesic.mathdoc.fr/item/JMAG_2018_14_3_a1/

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