On contact interactions as limits of short-range potentials
type: Item
instance of: scholarly article
zbMATH Open document ID: 1313.81009
author: Gerhard Bräunlich
author: C. Hainzl
author: R. Seiringer
publication date: 2014-08-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.3805
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 6333564
zbMATH Keywords: contact interaction
zbMATH Keywords: short-range potential
zbMATH Keywords: scattering length
MaRDI profile type: Publication
arXiv ID: 1305.3805
arXiv classification: math-ph
arXiv classification: math.FA
arXiv classification: math.MP
arXiv classification: math.SP
title: On contact interactions as limits of short-range potentials
published in: Methods of Functional Analysis and Topology
review text: The physical applications of Hamiltonians of point interactions defined as extensions of operators require a correct choice of the extension. In particular, in models of cold atomic gases the choice is based on approximation by short-range potentials \(V_l\) with the range \(l\) converging to zero, as \(l\to 0\), while the scattering length tends to a finite limit. The paper provides a rigorous implementation of the above idea. The interaction \(V_l\) is required to have a strong repusive core. An important ingredient is a formula for the scattering length obtained by \textit{C. Hainzl} and \textit{R. Seiringer} [Lett. Math. Phys. 84, No. 2-3, 99--107 (2008; Zbl 1164.81006)].
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6333564