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

TL;DR

This paper analyzes a mean-field boson gas in weak harmonic traps, revealing a phase transition characterized by boson condensation and localization phenomena, aligning with experimental observations of Bose-Einstein Condensation.

Contribution

It introduces a rigorous analysis of phase transition and localization in mean-field interacting bosons within weak harmonic traps using boson random point fields methods.

Findings

Identification of two distinct phases based on chemical potential.

Demonstration of boson condensation and localization at the transition.

Alignment of theoretical results with experimental Bose-Einstein Condensation observations.

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.