14-36 Pavel Exner and Andrii Khrabustovskyi

On the spectrum of narrow Neumann waveguide with periodically distributed $\delta'$ traps (233K, pdf) May 7, 14

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Abstract. We analyze a family of singular Schr\"odinger operators describing a Neumann waveguide with a periodic array of singular traps of a $\delta'$ type. We show that in the limit when perpendicular size of the guide tends to zero and the $\delta'$ interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.

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