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

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.

References in corpus (5)

• Numerical Solution of the Gross-Pitaevskii Equation for Bose-Einstein Condensation
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• The Mathematics of the Bose Gas and its Condensation
• Convergence rate of dimension reduction in Bose-Einstein condensates

Cited by in corpus (2)

• Vortices in Bose-Einstein condensates with $\mathcal{P}\mathcal{T}$-symmetric gain and loss
• Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions