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

Weizhu Bao (1) , Loïc Le Treust (2, 3) , Florian Méhats (2, 3)

1 Department of Mathematics [Singapore]
2 IPSO - Invariant Preserving SOlvers
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Gross-Pitaevskii equation; dimension reduction; semi-classical limit; averaging; Asymptotic Analysis; highly oscillatory equations; nonlinear Schrödinger equations

Domaines: Gaz Quantiques [cond-mat.quant-gas]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Weizhu Bao, Loïc Le Treust, Florian Méhats. Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime. Nonlinearity, 2015, 28 (3), pp.755-772. ⟨10.1088/0951-7715/28/3/755⟩. ⟨hal-00959084⟩