$\delta'$-interaction as a limit of a thin Neumann waveguide with transversal window
Spectral Theory
2018-08-17 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We consider a waveguide-like domain consisting of two thin straight tubular domains connected through a tiny window. The perpendicular size of this waveguide is of order . Under the assumption that the window is appropriately scaled we prove that the Neumann Laplacian on this domain converges in (a kind of) norm resolvent sense as to a one-dimensional Schr\"odinger operator corresponding to a -interaction of a non-negative strength. We estimate the rate of this convergence, also we prove the convergence of spectra.
Keywords
Cite
@article{arxiv.1808.05402,
title = {$\delta'$-interaction as a limit of a thin Neumann waveguide with transversal window},
author = {Giuseppe Cardone and Andrii Khrabustovskyi},
journal= {arXiv preprint arXiv:1808.05402},
year = {2018}
}
Comments
26 pages, 2 figures