Exact solution of the three-boson problem at vanishing energy

Christophe Mora (1) , Alexander O. Gogolin (2, 3) , Reinhold Egger (3)

1 LPA - Laboratoire Pierre Aigrain
2 Department of Mathematics [Imperial College London]
3 Insitut fur Theoretische Physik I

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.

Domaines: Gaz Quantiques [cond-mat.quant-gas]

Christophe Mora, Alexander O. Gogolin, Reinhold Egger. Exact solution of the three-boson problem at vanishing energy. C. R. Physique, 2011, 12, pp.27-38. ⟨10.1016/j.crhy.2010.11.002⟩. ⟨hal-00659647⟩