Exact solution of the three-boson problem at vanishing energy

Christophe Mora; Alexander O. Gogolin; Reinhold Egger

doi:10.1016/j.crhy.2010.11.002

Exact solution of the three-boson problem at vanishing energy
[Solution exacte du problème à trois corps à énergie nulle]

Christophe Mora ¹ ; Alexander O. Gogolin ² ; Reinhold Egger ³

¹ Laboratoire Pierre-Aigrain, ENS, Université Denis-Diderot 7 – CNRS, 24, rue Lhomond, 75005 Paris, France
² Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
³ Institut für Theoretische Physik, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany

Comptes Rendus. Physique, Volume 12 (2011) no. 1, pp. 27-38.

Résumé
Abstract

Les interactions résonantes à deux corps entre trois bosons identiques sont modélisées par une approche de portée nulle. Une phase, paramètre sans dimension, caractérise la condition aux limites à trois corps tandis que la longueur de diffusion entre dans la condition aux limites de Bethe–Peierls. Le modèle est résolu exactement à énergie nulle pour toute valeur de la longueur de diffusion, positive ou négative. Une expression analytique pour le taux de recombinaison à trois corps vers le dimère universel peu profond est extraite de cette solution.

A zero-range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe–Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.

Publié le : 2011-01-01

DOI : 10.1016/j.crhy.2010.11.002

Keywords: Few-body problem, Three-body recombination, Efimov effect
Mot clés : Problème à quelques corps, Recombinaison à trois corps, Phénomène d'Efimov

Affiliations des auteurs :

Christophe Mora ¹ ; Alexander O. Gogolin ² ; Reinhold Egger ³

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Christophe Mora; Alexander O. Gogolin; Reinhold Egger. Exact solution of the three-boson problem at vanishing energy. Comptes Rendus. Physique, Volume 12 (2011) no. 1, pp. 27-38. doi : 10.1016/j.crhy.2010.11.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.11.002/

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