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Pavel Exner and Andrii Khrabustovskyi
On the spectrum of narrow Neumann waveguide with periodically distributed $\delta'$ traps
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.