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 - <p style="text-align: justify;">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.</p>