Volume 1, Issue 1
Ground States of Two-Component Bose-Einstein Condensates with an Internal Atomic Josephson Junction

Weizhu Bao & Yongyong Cai

East Asian J. Appl. Math., 1 (2011), pp. 49-81.

Published online: 2018-02

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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

Bose-Einstein condensate, coupled Gross-Pitaevskii equations, two-component, ground state, normalized gradient flow, internal atomic Josephson junction, energy.

  • AMS Subject Headings

35Q55, 49J45, 65N06, 65N12, 65Z05, 81-08

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-49, author = {}, title = {Ground States of Two-Component Bose-Einstein Condensates with an Internal Atomic Josephson Junction}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {1}, pages = {49--81}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.190310.170510a}, url = {http://global-sci.org/intro/article_detail/eajam/10896.html} }
TY - JOUR T1 - Ground States of Two-Component Bose-Einstein Condensates with an Internal Atomic Josephson Junction JO - East Asian Journal on Applied Mathematics VL - 1 SP - 49 EP - 81 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.190310.170510a UR - https://global-sci.org/intro/article_detail/eajam/10896.html KW - Bose-Einstein condensate, coupled Gross-Pitaevskii equations, two-component, ground state, normalized gradient flow, internal atomic Josephson junction, energy. AB -

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.

Weizhu Bao & Yongyong Cai. (1970). Ground States of Two-Component Bose-Einstein Condensates with an Internal Atomic Josephson Junction. East Asian Journal on Applied Mathematics. 1 (1). 49-81. doi:10.4208/eajam.190310.170510a
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