Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Computer Physics Communications

Projection gradient method for energy functional minimization with a constraint and its application to computing the ground state of spin–orbit-coupled Bose–Einstein condensates

Hanquan Wang, Zhiguo Xu

Published May 28, 2014• 5 citations
Publisher
DOI
10.1016/j.cpc.2014.05.007

Related papers

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

Hanquan Wang

Journal of Computational Physics•Jun 18, 2014•31 citations

An accelerated projected gradient flow method for computing the ground states of rotating two-dimensional Bose-Einstein condensates with Lee-Hang-Yang correction

Kaizhi Tang, Zixu Feng, Qingzhou Shu +1 more

Communications in Nonlinear Science and Numerical Simulation•Apr 24, 2026•0 citations

Efficient and accurate numerical methods for computing ground states and dynamics of spin--orbital-angular-momentum coupled Bose-Einstein condensates on unbounded domains

Yongyong Cai, Yingkai Li, Yong Wu

•Jan 1, 2026•0 citations

The Numerical Study of the Ground States of Spin-1 Bose-Einstein Condensates with Spin-Orbit-Coupling

Yongjun Yuan, Zhiguo Xu, Qinglin Tang +1 more

A projection gradient method for computing the ground state of the spin-orbit-coupled spin-1 Bose-Einstein condensate at extremely low temperatures is proposed. The continuous gradient flows are discretised by a second-order finite difference method in space and the Crank-Nicolson method in time. Our discretisation preserves the total mass conservation and the energy diminishing property. Numerical results show the efficiency of the method.

East Asian Journal on Applied Mathematics•Sep 17, 2018•7 citations

A Mass and Magnetization Conservative and Energy-Diminishing Numerical Method for Computing Ground State of Spin-1 Bose–Einstein Condensates

Weizhu Bao, Hanquan Wang

In this paper, a mass (or normalization) and magnetization conservative and energy-diminishing numerical method is presented for computing the ground state of spin-1 (or $F=1$ spinor) Bose–Einstein condensates (BECs). We begin with the coupled Gross–Pitaevskii equations, and the ground state is defined as the minimizer of the energy functional under two constraints on the mass and magnetization. By constructing a continuous normalized gradient flow (CNGF) which is mass and magnetization conservative and energy-diminishing, the ground state can be computed as the steady state solution of the CNGF. The CNGF is then discretized by the Crank–Nicolson finite difference method with a proper way to deal with the nonlinear terms, and we prove that the discretization is mass and magnetization conservative and energy-diminishing in the discretized level. Numerical results of the ground state and their energy of spin-1 BECs are reported to demonstrate the efficiency of the numerical method.

SIAM Journal on Numerical Analysis•Jan 1, 2007•48 citations

A Regularized Newton Method for Computing Ground States of Bose–Einstein Condensates

Xinming Wu, Zaiwen Wen, Weizhu Bao

arXiv:1504.02891•Journal of Scientific Computing•Mar 15, 2017•64 citations
In this paper, a mass (or normalization) and magnetization conservative and energy-diminishing numerical method is presented for computing the ground state of spin-1 (or F=1F=1F=1 spinor) Bose–Einstein condensates (BECs). We begin with the coupled Gross–Pitaevskii equations, and the ground state is defined as the minimizer of the energy functional under two constraints on the mass and magnetization. By constructing a continuous normalized gradient flow (CNGF) which is mass and magnetization conservative and energy-diminishing, the ground state can be computed as the steady state solution of the CNGF. The CNGF is then discretized by the Crank–Nicolson finite difference method with a proper way to deal with the nonlinear terms, and we prove that the discretization is mass and magnetization conservative and energy-diminishing in the discretized level. Numerical results of the ground state and their energy of spin-1 BECs are reported to demonstrate the efficiency of the numerical method.