On the spectrum of narrow Neumann waveguide with periodically   distributed $\delta'$ traps
  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. 
Pavel Exner, Andrii Khrabustovskyi
math.SP math-ph math.AP math.MP