Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions

Details Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions

2004-07-02

arxiv.org/abs/cond-mat/0407065v1

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

We study two-body correlations for $N$ identical bosons by use of the hyperspherical adiabatic expansion method. We use the zero-range interaction and derive a transcendental equation determining the key ingredient of the hyperradial potential. The necessary renormalization is for both repulsive and attractive interactions achieved with an effective range expansion of the two-body phase-shifts. Our solutions including correlations provide the properties of Bose-Einstein condensates exemplified by stability conditions as established by mean-field Gross-Pitaevskii calculations. The many-body Efimov states are unavoidable for large scattering lengths.

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