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

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

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.6838484

Related papers

Bose-Einstein condensates with spin and orbital angular momentum coupling

Kuei Sun, Chunlei Qu, Chuanwei Zhang

Bulletin of the American Physical Society•Mar 2, 2015•0 citations

Spin - orbital angular momentum coupled Bose-Einstein condensate

Chunlei Qu, Kuei Sun, Chuanwei Zhang

Bulletin of the American Physical Society•Mar 6, 2015•1 citation

Ground States and Dynamics of Spin-Orbit-Coupled Bose--Einstein Condensates

Weizhu Bao, Yongyong Cai

We study analytically and asymptotically, as well as numerically, ground states and dynamics of two-component spin-orbit-coupled Bose--Einstein condensates (BECs) modeled by the coupled Gross--Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynamical properties become very rich and complicated. For the ground states, we establish existence and nonexistence results under different parameter regimes and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either nonperiodic or with different frequency than the trapping frequency when the external trapping potential is taken as harmonic and/or the initial data is chosen as a stationary state (e.g., ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclassical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.

arXiv:1407.5815•SIAM Journal on Applied Mathematics•Jan 1, 2015•45 citations

Efficient numerical methods for computing ground states and dynamics of dipolar Bose–Einstein condensates

Weizhu Bao, Yongyong Cai, Hanquan Wang

arXiv:1001.2372•Journal of Computational Physics•Jul 9, 2010•144 citations

An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose–Einstein condensates

Weizhu Bao, Hanquan Wang

arXiv:cond-mat/0609678•Journal of Computational Physics•Feb 22, 2006•144 citations

Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates.

Weizhu Bao null, Yongyong Cai

In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical methods for computing ground states and dynamics. Then we extend these results to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems and/or general spin-F (F>=3) BEC are discussed.

arXiv:1709.03840•Communications in Computational Physics•Jun 1, 2018•57 citations
We study analytically and asymptotically, as well as numerically, ground states and dynamics of two-component spin-orbit-coupled Bose--Einstein condensates (BECs) modeled by the coupled Gross--Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynamical properties become very rich and complicated. For the ground states, we establish existence and nonexistence results under different parameter regimes and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either nonperiodic or with different frequency than the trapping frequency when the external trapping potential is taken as harmonic and/or the initial data is chosen as a stationary state (e.g., ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclassical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.
In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical methods for computing ground states and dynamics. Then we extend these results to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems and/or general spin-F (F>=3) BEC are discussed.