Gap Control by Singular Schrödinger Operators in a Periodically Structured Metamaterial
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...
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| Date: | 2018 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2018
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/jm14-0270e |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | 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.
Mathematics Subject Classification: 35P05, 35P20, 35J10, 35B27 |
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