Overlap of exact and Gross-Pitaevskii wavefunctions in Bose-Einstein condensates of dilute gases

TL;DR

This paper investigates the overlap between the Gross-Pitaevskii wavefunction and the exact ground state in Bose-Einstein condensates, revealing that the overlap can be less than one or even zero despite identical energies and densities.

Contribution

It demonstrates that the Gross-Pitaevskii wavefunction does not necessarily have a high overlap with the exact ground state, challenging assumptions about their similarity.

Findings

Overlap is always less than one

Overlap can vanish despite identical energies

Implications for understanding Bose-Einstein condensates

Abstract

It has been proven theoretically for bosons with two-body repulsive interaction potentials in the dilute limit that the Gross-Pitaevskii equation provides the exact energy and density per particle as does the basic many-particle Schroedinger equation [Lieb and Seiringer, Phys. Rev. Lett. 88, 170409 (2002)]. Here, we investigate the overlap of the Gross-Pitaevskii and exact ground state wavefunctions. It is found that this overlap is always smaller than unity and may even vanish in spite of the fact that both wavefunctions provide the same energy and density per particle. Consequences are discussed.