Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional

TL;DR

This paper rigorously proves that the Gross-Pitaevskii energy functional accurately describes the ground state energy and density of dilute Bose gases with positive interactions in external traps, confirming its theoretical validity.

Contribution

It provides the first rigorous proof of the asymptotic exactness of the Gross-Pitaevskii functional for dilute Bose gases with positive interactions.

Findings

Gross-Pitaevskii functional accurately predicts ground state energy

Validation of the functional for particle density in dilute gases

First rigorous proof of this approximation's validity

Abstract

The ground state properties of interacting Bose gases in external potentials, as considered in recent experiments, are usually described by means of the Gross-Pitaevskii energy functional. We present here the first proof of the asymptotic exactness of this approximation for the ground state energy and particle density of a dilute Bose gas with a positive interaction.