Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula

TL;DR

This paper reviews rigorous mathematical results confirming that the Gross-Pitaevskii energy functional accurately describes the ground state energy of dilute Bose gases in traps, in both 2D and 3D.

Contribution

It provides a rigorous proof of the asymptotic exactness of the Gross-Pitaevskii formula for the ground state energy of dilute Bose gases.

Findings

Gross-Pitaevskii energy functional is asymptotically exact for 2D and 3D dilute Bose gases.

Rigorous mathematical validation of the Gross-Pitaevskii approximation.

Clarification of the approximation's validity in recent experimental contexts.

Abstract

Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the Gross-Pitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two- and three-dimensional case.