Speaker: Dr. Yong-Jun Yuan, Beijing Computational Science Research Center

Abstract: An efficient and accurate numerical method is proposed to compute the ground state of spin-2 Bose-Einstein Condensates (BECs) by using the normalized gradient flow or imaginary time method. In order to do this, on one hand, a splitting scheme is applied to the continuous normalized gradient flow (CNGF) to avoid solving an integral-differential equation, and the five projection constants in the second step of the splitting scheme (i.e., projection step) can be completely and uniquely determined by introducing the three normalization conditions derived from the relations between the chemical potentials and the other two physical conditions given by the conservation of total mass and total magnetization. On the other hand, the ground state structure of a corresponding spatial uniform spin-2 BEC is verified so that efficient initial data can be selected to compute ground states of the original spin-2 BEC. The back-Euler finite difference method is proposed to discretize the normalized gradient flow, which is much efficient and simple. Extensive numerical results on ground states of spin-2 BECs with ferromagnetic/nematic/cyclic interaction and harmonic/optical lattice potential in one/two dimensions are reported to demonstrate the efficiency of our method and interesting physics.

Date&Time: October 31, 2014 (Friday), 14:30–15:30
Location: 606 Conference Room