Condensate fluctuations in the dilute Bose gas

TL;DR

This paper investigates particle number fluctuations in a dilute Bose-Einstein condensate using a grand canonical ensemble approach, introducing a method beyond mean-field approximation to estimate fluctuations.

Contribution

It presents a novel method for evaluating condensate fluctuations beyond mean-field theory and proposes a formula linking canonical and grand canonical fluctuations.

Findings

Mean-field approximation fails for the single-mode Hamiltonian.

The Hartree Hamiltonian allows estimation of fluctuations with a numerical factor.

A new hypothesis relates canonical and grand canonical fluctuations.

Abstract

The fluctuations of a number of particles in the Bose-Einstein condensate are studied in the grand canonical ensemble with an effective single-mode Hamiltonian, which is derived from an assumption that the mode corresponding to the Bose-Einstein condensate does not asymptotically correlate with other modes. The fluctuations are evaluated in the dilute limit with a proposed simple method, which is beyond the mean-field approximation. The accuracy of the latter is estimated; it is shown that the mean-field scheme does not work for the single-mode Hamiltonian, while for the Hartree Hamiltonian it allows us to estimate the condensate fluctuations up to a numerical factor. As a hypothesis, a formula is proposed that relates the fluctuations in the canonical ensemble with that of the grand canonical one.