Universal few-body physics in a harmonic trap

Simon Tölle; Hans-Werner Hammer; Bernard Ch. Metsch

doi:10.1016/j.crhy.2010.11.011

Universal few-body physics in a harmonic trap
[Universalité du problème à petit nombre de corps dans un piège harmonique]

Simon Tölle ¹ ; Hans-Werner Hammer ¹ ; Bernard Ch. Metsch ¹

¹ Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany

Comptes Rendus. Physique, Few body problem, Volume 12 (2011) no. 1, pp. 59-70.

Résumé
Abstract

Les systèmes à petit nombre de corps avec des interactions à courte portée résonnantes présentent des propriétés universelles indépendantes des détails de leur structure et de leurs potentiels d'interaction aux petites distances. Dans des systèmes à trois corps, ces propriétés incluent l'existence d'un spectre géométrique d'états d'Efimov à trois corps et une invariance d'échelle discrète. Des propriétés universelles similaires apparaissent dans des systèmes à quatre corps et peut-être aussi dans des systèmes à davantage de corps. Nous construisons une théorie effective pour des systèmes à petit nombre de corps dans un piège harmonique et nous étudions les modifications de la physique universelle des systèmes à trois et quatre corps dues au potentiel de piégeage. En particulier, nous nous concentrons sur les systèmes où le phénomène d'Efimov peut apparaître, et nous examinons la dépendance du spectre à quatre corps en les paramètres ajustables expérimentalement.

Few-body systems with resonant short-range interactions display universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry. Similar universal properties appear in 4-body and possibly higher-body systems as well. We set up an effective theory for few-body systems in a harmonic trap and study the modification of universal physics for 3- and 4-particle systems in external confinement. In particular, we focus on systems where the Efimov effect can occur and investigate the dependence of the 4-body spectrum on the experimental tuning parameters.

Publié le : 2011-01-01

DOI : 10.1016/j.crhy.2010.11.011

Keywords: Universality, Effective theory, External confinement
Mots-clés : Universalité, Théorie effective, Confinement extérieur

Affiliations des auteurs :

Simon Tölle ¹ ; Hans-Werner Hammer ¹ ; Bernard Ch. Metsch ¹

¹ Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany

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Simon Tölle; Hans-Werner Hammer; Bernard Ch. Metsch. Universal few-body physics in a harmonic trap. Comptes Rendus. Physique, Few body problem, Volume 12 (2011) no. 1, pp. 59-70. doi : 10.1016/j.crhy.2010.11.011. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.11.011/

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