On contact interactions as limits of short-range potentials

Abstract

We reconsider the norm resolvent limit of $-\Delta + V_\ell$ with $V_\ell$ tending to a point interaction in three dimensions. We are mainly interested in potentials $V_\ell$ modelling short range interactions of cold atomic gases. In order to ensure stability the interaction $V_\ell$ is required to have a strong repulsive core, such that $\lim_{\ell \to 0} \int V_\ell >0$. This situation is not covered in the previous literature.

Key words: Contact interaction, Birman-Schwinger principle, Schr¨odinger operator.

Full Text

Article Information

Title	On contact interactions as limits of short-range potentials
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 364-375
MathSciNet	MR3156301
zbMATH	1313.81009
Milestones	Received 22/05/2013
Copyright	The Author(s) 2013 (CC BY-SA)

Authors Information

Gerhard Braunlich
Mathematical Institute, University of Tu}bingen, Auf der Morgenstelle 10, 72076 Tubingen, Germany

Christian Hainzl
Mathematical Institute, University of Tubingen, Auf der Morgenstelle 10, 72076 Tubingen, Germany

Robert Seiringer
Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria

Citation Example

Gerhard Bräunlich, Christian Hainzl, and Robert Seiringer, On contact interactions as limits of short-range potentials, Methods Funct. Anal. Topology 19 (2013), no. 4, 364-375.

BibTex

@article {MFAT699,
    AUTHOR = {Bräunlich, Gerhard and Hainzl, Christian and Seiringer, Robert},
     TITLE = {On contact interactions as limits of short-range potentials},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {364-375},
      ISSN = {1029-3531},
  MRNUMBER = {MR3156301},
 ZBLNUMBER = {1313.81009},
       URL = {http://mfat.imath.kiev.ua/article/?id=699},
}