Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps

Details Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps

2008-07-22

arxiv.org/abs/0807.3530v1

Physics

Mathematical Physics

Scientific paper

10.1063/1.3072911

A model of the mean-field interacting boson gas trapped by a weak harmonic potential is considered by the \textit{boson random point fields} methods. We prove that in the Weak Harmonic Trap (WHT) limit there are two phases distinguished by the boson condensation and by a different behaviour of the local particle density. For chemical potentials less than a certain critical value, the resulting Random Point Field (RPF) coincides with the usual boson RPF, which corresponds to a non-interacting (ideal) boson gas. For the chemical potentials greater than the critical value, the boson RPF describes a divergent (local) density, which is due to \textit{localization} of the macroscopic number of condensed particles. Notice that it is this kind of transition that observed in experiments producing the Bose-Einstein Condensation in traps.

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