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arXiv · 1802.07522

Gap control by singular Schr\"odinger operators in a periodically structured metamaterial

Pavel Exner·Andrii Khrabustovskyi
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Abstract

We consider a family $\{\mathcal{H}^\varepsilon\}_{\varepsilon>0}$ of $\varepsilon\mathbb{Z}^n$-periodic Schr\"odinger operators with $\delta'$-interactions supported on a lattice of closed compact surfaces; within a minimal 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.

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BibTeXRIS

Pavel Exner, Andrii Khrabustovskyi. 2018-02-21. Gap control by singular Schr\"odinger operators in a periodically structured metamaterial. https://doi.org/10.15407/mag14.03.270

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