Proof of Bose-Einstein Condensation for Dilute Trapped Gases

TL;DR

This paper provides the first rigorous proof that dilute trapped bosonic gases exhibit Bose-Einstein condensation into the ground state, confirming experimental observations through a theoretical framework based on the Schrödinger equation.

Contribution

It establishes a rigorous mathematical proof of Bose-Einstein condensation in a realistic continuum model for dilute trapped gases, linking microscopic interactions to macroscopic quantum phenomena.

Findings

Proof of 100% BEC into the Gross-Pitaevskii ground state

First rigorous demonstration in a continuum model

Validates experimental observations theoretically

Abstract

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schroedinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.