Close Search Advanced
Journals
Resources
About Us
Open Access

A Two-Parameter Continuation Method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices

A Two-Parameter Continuation Method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices
Preview
Add to basket

Year:    2013

Communications in Computational Physics, Vol. 13 (2013), Iss. 2 : pp. 442–460

Abstract

We study efficient spectral-collocation and continuation methods (SCCM) for rotating two-component Bose-Einstein condensates (BECs) and rotating two-component BECs in optical lattices, where the second kind Chebyshev polynomials are used as the basis functions for the trial function space. A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations (GPEs), where the classical tangent vector is split into two constraint conditions for the bordered linear systems. Numerical results on rotating two-component BECs and rotating two-component BECs in optical lattices are reported. The results on the former are consistent with the published numerical results.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.110711.170212a

Communications in Computational Physics, Vol. 13 (2013), Iss. 2 : pp. 442–460

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:   

  1. An efficient split-step compact finite difference method for the coupled Gross–Pitaevskii equations

    Wei, Xinxin | Zhang, Luming | Wang, Shanshan | Liao, Feng

    International Journal of Computer Mathematics, Vol. 96 (2019), Iss. 12 P.2334

    https://doi.org/10.1080/00207160.2018.1557326 [Citations: 2]

  2. Pseudo-Arclength Continuation Algorithms for Binary Rydberg-Dressed Bose-Einstein Condensates

    Sriburadet, Sirilak | Wang, Y.-S. | Chien, C.-S. | Shih, Y.

    Communications in Computational Physics, Vol. 19 (2016), Iss. 4 P.1067

    https://doi.org/10.4208/cicp.151214.021015a [Citations: 3]

  3. A preconditioned Riemannian conjugate gradient method for computing the ground states of arbitrary-angle rotating Bose-Einstein condensates

    Shu, Qingzhou | Tang, Qinglin | Zhang, Shaobo | Zhang, Yong

    Journal of Computational Physics, Vol. 512 (2024), Iss. P.113130

    https://doi.org/10.1016/j.jcp.2024.113130 [Citations: 0]

  4. Second-Order Flows for Computing the Ground States of Rotating Bose-Einstein Condensates

    Chen, Haifan | Dong, Guozhi | Liu, Wei | Xie, Ziqing

    SSRN Electronic Journal , Vol. (2022), Iss.

    https://doi.org/10.2139/ssrn.4109828 [Citations: 0]

  5. BEC2HPC: A HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation

    Gaidamour, Jérémie | Tang, Qinglin | Antoine, Xavier

    Computer Physics Communications, Vol. 265 (2021), Iss. P.108007

    https://doi.org/10.1016/j.cpc.2021.108007 [Citations: 7]

  6. Multi-parameter continuation and collocation methods for rotating multi-component Bose–Einstein condensates

    Chen, S.-Y. | Wang, Y.-S. | Jeng, B.-W. | Chien, C.-S.

    International Journal of Computer Mathematics, Vol. 92 (2015), Iss. 4 P.850

    https://doi.org/10.1080/00207160.2014.915959 [Citations: 2]

  7. A New Preconditioned Nonlinear Conjugate Gradient Method in Real Arithmetic for Computing the Ground States of Rotational Bose–Einstein Condensate

    Zhang, Tianqi | Xue, Fei

    SIAM Journal on Scientific Computing, Vol. 46 (2024), Iss. 3 P.A1764

    https://doi.org/10.1137/23M1590317 [Citations: 0]

  8. Continuation and preconditioned imaginary time evolution methods for boson–fermion mixtures

    Jeng, B.-W. | Sriburadet, Sirilak

    Journal of Computational and Applied Mathematics, Vol. 381 (2021), Iss. P.113019

    https://doi.org/10.1016/j.cam.2020.113019 [Citations: 1]

  9. Spectral collocation and a two-level continuation scheme for dipolar Bose–Einstein condensates

    Jeng, B.-W. | Chien, C.-S. | Chern, I.-L.

    Journal of Computational Physics, Vol. 256 (2014), Iss. P.713

    https://doi.org/10.1016/j.jcp.2013.09.018 [Citations: 4]

  10. Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose–Einstein condensates

    Antoine, Xavier | Duboscq, Romain

    Journal of Computational Physics, Vol. 258 (2014), Iss. P.509

    https://doi.org/10.1016/j.jcp.2013.10.045 [Citations: 53]

  11. An efficient spectral method for computing dynamics of rotating two-component Bose–Einstein condensates via coordinate transformation

    Ming, Ju | Tang, Qinglin | Zhang, Yanzhi

    Journal of Computational Physics, Vol. 258 (2014), Iss. P.538

    https://doi.org/10.1016/j.jcp.2013.10.044 [Citations: 14]

  12. Second-order flows for computing the ground states of rotating Bose-Einstein condensates

    Chen, Haifan | Dong, Guozhi | Liu, Wei | Xie, Ziqing

    Journal of Computational Physics, Vol. 475 (2023), Iss. P.111872

    https://doi.org/10.1016/j.jcp.2022.111872 [Citations: 4]

  13. Efficient spectral computation of the stationary states of rotating Bose–Einstein condensates by preconditioned nonlinear conjugate gradient methods

    Antoine, Xavier | Levitt, Antoine | Tang, Qinglin

    Journal of Computational Physics, Vol. 343 (2017), Iss. P.92

    https://doi.org/10.1016/j.jcp.2017.04.040 [Citations: 61]

  14. A two-parameter continuation method for computing numerical solutions of spin-1 Bose–Einstein condensates

    Wang, Y.-S. | Chien, C.-S.

    Journal of Computational Physics, Vol. 256 (2014), Iss. P.198

    https://doi.org/10.1016/j.jcp.2013.08.056 [Citations: 8]

  15. A two-parameter continuation algorithm using radial basis function collocation method for rotating Bose–Einstein condensates

    Shih, Yin-Tzer | Tsai, Chih-Ching

    Journal of Computational Physics, Vol. 252 (2013), Iss. P.37

    https://doi.org/10.1016/j.jcp.2013.06.018 [Citations: 0]

  16. 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

    Wang, Hanquan | Xu, Zhiguo

    Computer Physics Communications, Vol. 185 (2014), Iss. 11 P.2803

    https://doi.org/10.1016/j.cpc.2014.05.007 [Citations: 4]

  17. Efficient spectral collocation and continuation methods for symmetry-breaking solutions of rotating Bose–Einstein condensates

    Chen, S.-Y. | Li, Z.-C. | Wang, Y.-S. | Chien, C.-S.

    International Journal of Computer Mathematics, Vol. 90 (2013), Iss. 3 P.651

    https://doi.org/10.1080/00207160.2012.736615 [Citations: 1]

  18. Acceleration of the imaginary time method for spectrally computing the stationary states of Gross–Pitaevskii equations

    Antoine, Xavier | Besse, Christophe | Duboscq, Romain | Rispoli, Vittorio

    Computer Physics Communications, Vol. 219 (2017), Iss. P.70

    https://doi.org/10.1016/j.cpc.2017.05.008 [Citations: 11]

  19. Stability analysis and continuation for the coupled Gross–Pitaevskii equations

    Sriburadet, Sirilak | Shih, Yin-Tzer | Chien, C.-S.

    Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 3 P.807

    https://doi.org/10.1016/j.camwa.2019.03.003 [Citations: 2]