Three fermions in a box at the unitary limit: universality in a lattice model

Ludovic Pricoupenko (1) , Yvan Castin (2)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 LKB (Lhomond) - Laboratoire Kastler Brossel

We consider three fermions with two spin components interacting on a lattice model with an infinite scattering length. Low lying eigenenergies in a cubic box with periodic boundary conditions, and for a zero total momentum, are calculated numerically for decreasing values of the lattice period. The results are compared to the predictions of the zero range Bethe-Peierls model in continuous space, where the interaction is replaced by contact conditions. The numerical computation, combined with analytical arguments, shows the absence of negative energy solution, and a rapid convergence of the lattice model towards the Bethe-Peierls model for a vanishing lattice period. This establishes for this system the universality of the zero interaction range limit.

Mots clés: unitarity; lattice model; fermions; three-body problem

Domaines: Autre [cond-mat.other]

Ludovic Pricoupenko, Yvan Castin. Three fermions in a box at the unitary limit: universality in a lattice model. Journal of Physics A General Physics (1968-1972), 2007, pp.12863. ⟨hal-00145589v2⟩