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Ground states of spin-1 BEC with attractive mean-field interaction trapped in harmonic potential in \({\mathbb {R}}^2\)

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Abstract

We investigate the ground states of spin-1 Bose–Einstein condensate trapped in harmonic potential in \({\mathbb {R}}^2\) with attractive mean-field interaction constant \(c_0\) and spin-exchange interaction constant \(c_1\), two conserved quantities, the number of atoms N and the total magnetization M are involved in. The existence and nonexistence of the ground states have been analyzed according to the relations among \(c_0\), \(c_1\) and M. As \((c_{0}\), \(c_{1})\) approaches the thresholds, the asymptotic behavior of the ground states are presented in details, and the energy estimates, mass concentration and vanishing phenomena are described rigorously.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, China

    Yuzhen Kong & Dun Zhao

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Qingxuan Wang

Authors
  1. Yuzhen Kong
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  2. Qingxuan Wang
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  3. Dun Zhao
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Correspondence to Dun Zhao.

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Communicated by M. Struwe.

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This work is supported by NSFC under the Grant Nos. 12075102, 11971212 and 11801519.

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Kong, Y., Wang, Q. & Zhao, D. Ground states of spin-1 BEC with attractive mean-field interaction trapped in harmonic potential in \({\mathbb {R}}^2\). Calc. Var. 60, 152 (2021). https://doi.org/10.1007/s00526-021-02015-4

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