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

Abstract

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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Cited by in corpus (5)

• On the nature of Bose-Einstein condensation in disordered systems
• Large Deviation Principle for Non-Interacting Boson Random Point Processes
• Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approach
• Thermodynamics of inhomogenous imperfect quantum gases in harmonic traps
• On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model