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

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 analyse two combined singular limits: a semiclassical 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.