Dimension reduction for anisotropic Bose–Einstein condensates in the strong interaction regime

Weizhu Bao, Loïc Le Treust, Florian Méhats
2015 Nonlinearity  
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.
more » ... 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.
doi:10.1088/0951-7715/28/3/755 fatcat:4tnlsqrebbhotmvqmfadnl5qrq