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Interaction and multiscale mechanics

Radial basis function collocation method for a rotating Bose-Einstein condensation with vortex lattices

Yin-Tzer Shih, C.C. Tsai, K.T. Chen

Published Jun 25, 2012• 1 citation
Publisher

Abstract

We study a radial basis function collocation method (RBFCM) to discretize a coupled nonlinear Schr $\ddot{o}$ 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.

DOI
10.12989/imm.2012.5.2.131

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In this thesis, we study a continuation algorithm to trace the solution of two dimensional coupled nonlinear Schr‥odinger equations (CNLSE) that governs rotating Bose-Einstein condensates (BEC) around z-axis. We discretize CNLSE by Galerkin finite element method and prove the existence of the finite element method solution. The numerical tests depict the robust of the continuation algorithm for tracing the solution of the CNLSE. The numerical superfluid densities appear similarly as in [18], and this algorithm is quite practicable for describing the votex lattices in fast rotating BEC.
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We study efficient continuation methods for computing the ground state solution of quasi-2D rotating dipolar Bose-Einstein condensates (BECs). First, the highly accurate spectral collocation method is used to discretize the governing Gross-Pitaevskii equation (GPE). Then, we modify the two-level continuation scheme for 3D dipolar BECs described in Jeng et al. (2014) to develop a single-parameter continuation method for quasi-2D rotating dipolar BECs, where the chemical potential is treated as the continuation parameter. Further, by adding the ratio of dipolar interaction strength to contact interaction strength as the second continuation parameter, we propose an efficient two-parameter continuation method which can effectively show the change of the ground-state vortex structures as the dipolar interaction strength gradually increases. Moreover, we also study linear stability analysis for the GPE. Sample numerical results on quasi-2D rotating dipolar BECs are reported.
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