On the spectrum of narrow Neumann waveguide with periodically distributed $\delta'$ traps
Spectral Theory
2014-05-07 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We analyze a family of singular Schr\"odinger operators describing a Neumann waveguide with a periodic array of singular traps of a type. We show that in the limit when perpendicular size of the guide tends to zero and the interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.
Keywords
Cite
@article{arxiv.1405.1367,
title = {On the spectrum of narrow Neumann waveguide with periodically distributed $\delta'$ traps},
author = {Pavel Exner and Andrii Khrabustovskyi},
journal= {arXiv preprint arXiv:1405.1367},
year = {2014}
}
Comments
14 pages