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Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction

Published online by Cambridge University Press:  28 May 2015

Weizhu Bao  and
Yongyong Cai
Weizhu Bao*
Affiliation:
Department of Mathematics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117543
Yongyong Cai*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 117543
*
Corresponding author. Email: bao@math.nus.edu.sg
Corresponding author. Email: caiyongyong@nus.edu.sg
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Abstract

In this paper, we prove existence and uniqueness results for the ground states of the coupled Gross-Pitaevskii equations for describing two-component Bose-Einstein condensates with an internal atomic Josephson junction, and obtain the limiting behavior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented, for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported, to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomena of the ground sates in the problem.

Keywords

35Q5549J4565N0665N1265Z0581-08Bose-Einstein condensatecoupled Gross-Pitaevskii equationstwo-componentground statenormalized gradient flowinternal atomic Josephson junctionenergy
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 1 , February 2011 , pp. 49 - 81
Copyright
Copyright © Global-Science Press 2011

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