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Bose Gases Near Resonance: renormalized interactions in a condensate

We study the interplay between few- and many-body physics in Bose gases near resonance. The effect of condensates on the two-body running coupling constant is investigated via imposing a boundary condition on a self-consistent renormalization flow equation. Bose gases are found to become nearly fermionized when the chemical potential as a function of scattering lengths reaches a maximum and the atomic condensates lose meta-stability. The maximum and accompanied insta- bility are illustrated as a precursor of the sign change of g_2, the renormalized two-body interaction between condensed atoms from effectively repulsive to effectively attractive when approaching res- onance even though the scattering length is still positive. This occurs when dimers, under the influence of condensates, emerge at zero energy in the atomic gases at a finite positive scattering length.