On the spectrum of narrow Neumann waveguide with periodically distributed δ' traps

2014/05/06 by Pavel Exner, Exner, Pavel, Andrii Khrabustovskyi +1
Mathematics · Physics and Astronomy · #35J10 #35P05 #35P20 #81Q37 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.AP #math.MP #math.SP #msc:35J10 #msc:35P05 #msc:35P20 #msc:81Q37

paper · pdf · doi:10.48550/arxiv.1405.1367

14 pages

arxiv created 2014/05/06 · arxiv updated 2014/05/07

Abstract

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

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