Deriving the Gross-Pitaevskii equation
Abstract
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is macroscopically described by the Gross-Pitaevskii equation. On the microscopic level, the dynamics of Bose gases are described by the -body Schr\"odinger equation. We review our article [BdS12] in which we construct a class of initial data in Fock space which are energetically close to the ground state and prove that their evolution approximately follows the Gross-Pitaevskii equation. The key idea is to model two-particle correlations with a Bogoliubov transformation.
Cite
@article{arxiv.1404.4568,
title = {Deriving the Gross-Pitaevskii equation},
author = {Niels Benedikter},
journal= {arXiv preprint arXiv:1404.4568},
year = {2014}
}
Comments
5 pages; contribution to the proceedings of QMath12