Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime
Mathematical Physics
2015-06-19 v1 Quantum Gases
math.MP
Abstract
We study the problem of dimension reduction for the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate confined in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a strong interaction regime, we have to analyze two combined singular limits: a semi-classical limit in the transport direction and the strong partial confinement limit in the transversal direction. We prove that both limits commute together and we provide convergence rates. The by-products of this work are approximated models in reduced dimension for the GPE, with a priori estimates of the approximation errors.
Cite
@article{arxiv.1403.2884,
title = {Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime},
author = {Weizhu Bao and Loic Le Treust and Florian Mehats},
journal= {arXiv preprint arXiv:1403.2884},
year = {2015}
}