Best mean-field for condensates
Abstract
The Gross-Pitaevskii equation assumes that all (identical) bosons of a condensate reside in a single one-particle function. Here, we raise the question whether it always provides the best mean-field ansatz for condensates, leading to the lowest mean-field ground state energy. To this end, we derive a mean-field approach allowing for bosons to reside in several different one-particle functions. The number of bosons in each of these functions is a variational parameter minimizing the energy. The energy and one-particle functions at these optimal numbers can be determined directly. A numerical example is presented demonstrating that the mean-field energy of trapped bosons can be below that provided by the Gross-Pitaevskii equation. Implications are discussed.
Cite
@article{arxiv.cond-mat/0310697,
title = {Best mean-field for condensates},
author = {L. S. Cederbaum and A. I. Streltsov},
journal= {arXiv preprint arXiv:cond-mat/0310697},
year = {2007}
}
Comments
(11 pages, 2 figures). Physics Letters A Article in Press