18-22 Pavel Exner and Andrii Khrabustovskyi
Gap control by singular Schr\"odinger operators in a periodically structured metamaterial (455K, pdf) Feb 21, 18
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Abstract. We consider a family $\{\mathcal{H}_ arepsilon\}_{ arepsilon}$ of $arepsilon\mathbb{Z}^n$-periodic Schr\"odinger operators with $\delta'$-interactions supported on a lattice of closed compact surfaces; within a minimal period cell one has $m\in\N$ surfaces. We show that in the limit when $arepsilon o 0$ and the interactions strengths are appropriately scaled, $\mathcal{H}_ arepsilon$ 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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