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arXiv · 0705.1502

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

Ludovic Pricoupenko·Yvan Castin
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Abstract

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.

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Ludovic Pricoupenko, Yvan Castin. 2007-09-26. Three fermions in a box at the unitary limit: universality in a lattice model. https://doi.org/10.1088/1751-8113/40/43/003

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