A geometric approximation of delta-interactions by Neumann Laplacians

0547649 - ÚJF 2022 RIV GB eng J - Journal Article
Khrabustovskyi, Andrii - Post, O.
A geometric approximation of delta-interactions by Neumann Laplacians.
Journal of Physics A-Mathematical and Theoretical. Roč. 54, č. 46 (2021), č. článku 465201. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA ČR(CZ) GA21-07129S
Institutional support: RVO:61389005
Keywords : Delta-interaction * singularly perturbed domains * Neumann Laplacian * norm resolvent convergence * operator estimates * spectral convergence
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.331, year: 2021
Method of publishing: Limited access
https://doi.org/10.1088/1751-8121/ac2d52

We demonstrate how to approximate one-dimensional Schrodinger operators with delta-interaction by a Neumann Laplacian on a narrow waveguide-like domain. Namely, we consider a domain consisting of a straight strip and a small protuberance with 'room-and-passage' geometry. We show that in the limit when the perpendicular size of the strip tends to zero, and the room and the passage are appropriately scaled, the Neumann Laplacian on this domain converges in generalised norm resolvent sense to the above singular Schrodinger operator. Also we prove Hausdorff convergence of the spectra. In both cases estimates on the rate of convergence are derived.
Permanent Link: http://hdl.handle.net/11104/0323842