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

Abstract

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.

References in corpus (5)

• Radii in weakly-bound light halo nuclei
• Two-body correlations in N-body boson systems
• Correlated N-boson systems for arbitrary scattering length
• Binding Energies and Scattering Observables in the ^3He^4He_2 Atomic System
• Structure of boson systems beyond the mean-field

Cited by in corpus (5)

• Universal few-body physics and cluster formation
• N-body Efimov states of trapped bosons
• Bose atoms in a trap: a variational Monte Carlo formulation for the universal behavior at the Van der Waals length scale
• Universality in Ultra-Cold Few- and Many-Boson Systems
• Correlations in many-body systems with the Stochastic Variational Method