Bose-Einstein Condensation of Dilute Gases in Traps

TL;DR

This paper provides a rigorous proof of Bose-Einstein condensation in dilute trapped gases of bosons, demonstrating the phenomenon in a realistic physical setting through the Gross-Pitaevskii limit analysis.

Contribution

It offers the first rigorous proof of Bose-Einstein condensation for dilute trapped gases in the Gross-Pitaevskii limit, connecting microscopic interactions to macroscopic quantum phenomena.

Findings

Proves Bose-Einstein condensation occurs in dilute trapped gases

Establishes the Gross-Pitaevskii limit as a valid framework

Links microscopic interactions to macroscopic condensate behavior

Abstract

The ground state of a gas of Bosons confined in an external trap potential and interacting via repulsive two-body forces has recently been shown to exhibit complete Bose-Einstein condensation in the dilute limit, yielding for the first time a rigorous proof of this phenomenon in a physically realistic setting. We give here an account of this work about the Gross-Pitaevskii limit where the particle number $N$ goes to infinity with $Na$ fixed, where $a$ is the scattering length of the interparticle interaction, measured in units of the trap size.