Convergence rate of dimension reduction in Bose-Einstein condensates

TL;DR

This paper investigates how the three-dimensional Gross-Pitaevskii equation for Bose-Einstein condensates can be simplified to lower dimensions, providing convergence rates and identifying regimes where reduction is not feasible.

Contribution

It offers new asymptotic and numerical results on the convergence rates of dimension reduction for the 3D GPE in various trapping regimes.

Findings

Convergence rates for ground state and dynamics in disk-shaped condensates.

Convergence rates for ground state and dynamics in cigar-shaped condensates.

Identification of parameter regimes where 3D GPE cannot be reduced.

Abstract

In this paper, we study dimension reduction of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) modelling Bose-Einstein condensation under different limiting interaction and trapping frequencies parameter regimes. Convergence rates for the dimension reduction of 3D ground state and dynamics of the GPE in the case of disk-shaped condensation and cigar-shaped condensation are reported based on our asymptotic and numerical results. In addition, the parameter regimes in which the 3D GPE cannot be reduced to lower dimensions are identified.