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Title: A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates

Abstract

In this paper, a projection gradient method is presented for computing ground state of spin-2 Bose–Einstein condensates (BEC). We first propose the general projection gradient method for solving energy functional minimization problem under multiple constraints, in which the energy functional takes real functions as independent variables. We next extend the method to solve a similar problem, where the energy functional now takes complex functions as independent variables. We finally employ the method into finding the ground state of spin-2 BEC. The key of our method is: by constructing continuous gradient flows (CGFs), the ground state of spin-2 BEC can be computed as the steady state solution of such CGFs. We discretized the CGFs by a conservative finite difference method along with a proper way to deal with the nonlinear terms. We show that the numerical discretization is normalization and magnetization conservative and energy diminishing. Numerical results of the ground state and their energy of spin-2 BEC are reported to demonstrate the effectiveness of the numerical method.

Authors:
 [1]
  1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan Province, 650221 (China)
Publication Date:
OSTI Identifier:
22382119
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 274; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; FINITE DIFFERENCE METHOD; GROUND STATES; LIMITING VALUES; MAGNETIZATION; MINIMIZATION; NONLINEAR PROBLEMS; SPIN; STEADY-STATE CONDITIONS

Citation Formats

Wang, Hanquan, and Yunnan Tongchang Scientific Computing and Data Mining Research Center, Kunming, Yunnan Province, 650221. A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates. United States: N. p., 2014. Web. doi:10.1016/J.JCP.2014.06.015.
Wang, Hanquan, & Yunnan Tongchang Scientific Computing and Data Mining Research Center, Kunming, Yunnan Province, 650221. A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates. United States. https://doi.org/10.1016/J.JCP.2014.06.015
Wang, Hanquan, and Yunnan Tongchang Scientific Computing and Data Mining Research Center, Kunming, Yunnan Province, 650221. 2014. "A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates". United States. https://doi.org/10.1016/J.JCP.2014.06.015.
@article{osti_22382119,
title = {A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates},
author = {Wang, Hanquan and Yunnan Tongchang Scientific Computing and Data Mining Research Center, Kunming, Yunnan Province, 650221},
abstractNote = {In this paper, a projection gradient method is presented for computing ground state of spin-2 Bose–Einstein condensates (BEC). We first propose the general projection gradient method for solving energy functional minimization problem under multiple constraints, in which the energy functional takes real functions as independent variables. We next extend the method to solve a similar problem, where the energy functional now takes complex functions as independent variables. We finally employ the method into finding the ground state of spin-2 BEC. The key of our method is: by constructing continuous gradient flows (CGFs), the ground state of spin-2 BEC can be computed as the steady state solution of such CGFs. We discretized the CGFs by a conservative finite difference method along with a proper way to deal with the nonlinear terms. We show that the numerical discretization is normalization and magnetization conservative and energy diminishing. Numerical results of the ground state and their energy of spin-2 BEC are reported to demonstrate the effectiveness of the numerical method.},
doi = {10.1016/J.JCP.2014.06.015},
url = {https://www.osti.gov/biblio/22382119}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 274,
place = {United States},
year = {Wed Oct 01 00:00:00 EDT 2014},
month = {Wed Oct 01 00:00:00 EDT 2014}
}