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Journal of Computational Physics

A two-parameter continuation algorithm using radial basis function collocation method for rotating Bose-Einstein condensates

ShihYin-Tzer, TsaiChih-Ching

Published Nov 1, 2013• 0 citations
Publisher

Abstract

We present an efficient numerical algorithm to observe the dynamical formation of vortex lattice of a rotating trapped Bose-Einstein condensate (BEC) via solving a two-dimensional Gross-Pitaevskii ...
DOI
10.5555/2743134.2743261

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We study the dynamics of rotating two-component Bose-Einstein condensates(BECs) toward vortex lattice formation by numerically solving the two-dimensional Gross-Pitaevskii equations.The dynamics are similar to that of single-component BEC, and the whole changes of physical quantities in two cases are qualitatively similar.However, there are some differences between two cases.First, the characteristic time toward vortex entering depends on the inter-component interaction.The time toward vortex entering becomes shorter with increasing the inter-component interaction.Second, the angular momenta exchange between two components with keeping the total angular momentum.
We study a radial basis function collocation method (RBFCM) to discretize a coupled nonlinear Schr o¨\ddot{o}o¨ dinger equation (CNLSE) that governs a two dimensional rotating Bose-Einstein condensate (BEC) with an angular momentum rotation term. We exploit a RBFCM-continuation method (RBFCM-CM) to trace the solution curve of the CNLSE. We compare the performance of the RBFCM-CM with the FEM-CM. We observe that the RBFCM-CM is very robust in a coarse grid for resolving the ground state solution with many vortices when the angular momentum rotation is close to the limit. Numerical results demonstrate the efficiency and accuracy of the RBFCM-CM for computing the superfluid density of the ground level of the BEC.
We describe multi-parameter continuation methods combined with spectral collocation methods for computing numerical solutions of rotating two-component Bose–Einstein condensates (BECs), which are governed by the Gross–Pitaevskii equations (GPEs). Various types of orthogonal polynomials are used as the basis functions for the trial function space. A novel multi-parameter/multiscale continuation algorithm is proposed for computing the solutions of the governing GPEs, where the chemical potential of each component and angular velocity are treated as the continuation parameters simultaneously. The proposed algorithm can effectively compute numerical solutions with abundant physical phenomena. Numerical results on rotating two-component BECs are reported.