Skip to main content
SpringerLink
Log in

Limiting profiles of two-component attractive Bose-Einstein condensates passing an obstacle

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

This paper is concerned with ground states of two-component trapped Bose-Einstein condensates passing an obstacle in ℝ2, where the intraspecies interactions are attractive and the interspecies interactions are repulsive. We address the classification on the existence and non-existence of ground states. The limiting profiles of ground states are also studied by the energy analysis and the elliptic partial differential equation theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bao W Z, Cai Y Y. Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction. East Asian J Appl Math, 2011, 1: 49–81

    Article  MathSciNet  MATH  Google Scholar 

  2. Cao D M, Peng S J, Yan S S. Singularly Perturbed Methods for Nonlinear Elliptic Problems. Cambridge: Cambridge University Press, 2021

    Book  MATH  Google Scholar 

  3. Carlen E A, Frank R L, Lieb E H. Stability estimates for the lowest eigenvalue of a Schrödinger operator. Geom Funct Anal, 2014, 24: 63–84

    Article  MathSciNet  MATH  Google Scholar 

  4. Carusotto I, Hu S X, Collins L A, et al. Bogoliubov-Čerenkov radiation in a Bose-Einstein condensate flowing against an obstacle. Phys Rev Lett, 2006, 97: 260403

    Article  Google Scholar 

  5. Deng Y B, Guo Y J, Xu L S. Limit behavior of attractive Bose-Einstein condensates passing an obstacle. J Differential Equations, 2021, 272: 370–398

    Article  MathSciNet  MATH  Google Scholar 

  6. El G A, Gammal A, Kamchatnov A M. Generation of oblique dark solitons in supersonic flow of Bose-Einstein condensate past an obstacle. Nuclear Phys A, 2007, 790: 771–775

    Article  Google Scholar 

  7. Frisch T, Pomeau Y, Rica S. Transition to dissipation in a model of superflow. Phys Rev Lett, 1992, 69: 1644–1647

    Article  Google Scholar 

  8. Gidas B, Ni W M, Nirenberg L. Symmetry of positive solutions of nonlinear elliptic equations in ℝn. Math Anal Appl, 1981, 7: 369–402

    MathSciNet  MATH  Google Scholar 

  9. Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order. Berlin-Heidelberg-New York: Springer, 1997

    MATH  Google Scholar 

  10. Guo Y J, Li S, Wei J C, et al. Ground states of two-component attractive Bose-Einstein condensates I: Existence and uniqueness. J Funct Anal, 2019, 276: 183–230

    Article  MathSciNet  MATH  Google Scholar 

  11. Guo Y J, Luo Y, Zhang Q. Minimizers of mass critical Hartree energy functionals in bounded domains. J Differential Equations, 2018, 265: 5177–5211

    Article  MathSciNet  MATH  Google Scholar 

  12. Guo Y J, Seiringer R. On the mass concentration for Bose-Einstein condensates with attractive interactions. Lett Math Phys, 2014, 104: 141–156

    Article  MathSciNet  MATH  Google Scholar 

  13. Guo Y J, Wang Z Q, Zeng X Y, et al. Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials. Nonlinearity, 2018, 31: 957–979

    Article  MathSciNet  MATH  Google Scholar 

  14. Guo Y J, Zeng X Y, Zhou H S. Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials. Ann Inst H Poincaré Anal Non Linéaire, 2016, 33: 809–828

    Article  MathSciNet  MATH  Google Scholar 

  15. Guo Y J, Zeng X Y, Zhou H S. Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions. Discrete Contin Dyn Syst, 2017, 37: 3749–3786

    Article  MathSciNet  MATH  Google Scholar 

  16. Guo Y J, Zeng X Y, Zhou H S. Blow-up behavior of ground states for a nonlinear Schrödinger system with attractive and repulsive interactions. J Differential Equations, 2018, 264: 1411–1441

    Article  MathSciNet  MATH  Google Scholar 

  17. Han Q, Lin F H. Elliptic Partial Differential Equations. Courant Lecture Notes, vol. 1. New York: Courant Inst Math Sci, 2011

    MATH  Google Scholar 

  18. Jia H F, Li G B, Luo X. Stable standing waves for cubic nonlinear Schrödinger systems with partial confinement. Discrete Contin Dyn Syst, 2020, 40: 2739–2766

    Article  MathSciNet  MATH  Google Scholar 

  19. Stießberger J S, Zwerger W. Critical velocity of superfluid flow past large obstacles in Bose-condensates. Phys Rev A, 2000, 62: 061601

    Article  Google Scholar 

  20. Xu L S. Ground states of two-component Bose-Einstein condensates passing an obstacle. J Math Phys, 2020, 61: 061501

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11931012), the Fundamental Research Funds for the Central Universities (Grant No. CCNU22LJ002) and Excellent Doctoral Dissertation Program at Central China Normal University in China (Grant No. 2020YBZZ055).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China

    Yinbin Deng, Yujin Guo & Liangshun Xu

Authors
  1. Yinbin Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yujin Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liangshun Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yinbin Deng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, Y., Guo, Y. & Xu, L. Limiting profiles of two-component attractive Bose-Einstein condensates passing an obstacle. Sci. China Math. 66, 1767–1788 (2023). https://doi.org/10.1007/s11425-022-2006-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-022-2006-1

Keywords

MSC(2020)

Search

Navigation