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Self-bound states induced by the Lee–Huang–Yang effect in non-\(\mathcal{PT}\mathcal{}\)-symmetric complex potentials

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Abstract

We numerically investigate the existence and stability of self-bound states forming in a one-dimensional binary bosonic condensate confined in non-parity-time (\(\mathcal{PT}\mathcal{}\))-symmetric complex potentials under the influence of the Lee–Huang–Yang (LHY) correction. The linear spectrum of the non-\(\mathcal{PT}\mathcal{}\)-symmetric complex potentials may undergo phase transition where the eigenspectrum changes from partially complex to all real through the adjustment of the phase transition parameter. Below the phase transition, it is shown that the fundamental and dipole self-bound states can exist in different regions bifurcating from different discrete eigenvalues in the linear spectrum. The fundamental and dipole self-bound states are completely stable for the general case (i.e., \(\sigma =1\), with \(\sigma \) being the relative strength of the cubic self-interaction between atoms with respect to the quadratic LHY correction). Above the phase transition, the self-bound states are not stable for \(\sigma =1\) regardless of the value of the condensate norm. However, the fundamental self-bound states in the large condensate are able to become stable by decreasing \(\sigma \) to relatively small values.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 12175315 and 12165008. The Scientific Research Fund of Hunan Provincial Education Department of China under Grant Nos. 20B162, 20A136, and 19A069. The Hunan Provincial Natural Science Foundation under Grant Nos. 2019JJ40060 and 2019JJ30044. The Undergraduate Innovation and Entrepreneurship Training Program of Hunan province under Grant No. S202211528077.

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Authors and Affiliations

  1. Department of Physics, Hunan Institute of Technology, Hengyang, 421002, China

    Zheng Zhou & Yimin Shi

  2. Department of Physics, Jishou University, Jishou, 416000, China

    Fuqiu Ye

  3. Department of Physics, Hunan Institute of Science and Technology, Yueyang, 414006, China

    Hao Chen

  4. College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China

    Shiqing Tang

  5. School of Electronic Information and Electrical Engineering, Xiangnan University, Chenzhou, 423000, China

    Haiming Deng

  6. Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, 410004, China

    Honghua Zhong

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  1. Zheng Zhou
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Zhou, Z., Shi, Y., Ye, F. et al. Self-bound states induced by the Lee–Huang–Yang effect in non-\(\mathcal{PT}\mathcal{}\)-symmetric complex potentials. Nonlinear Dyn 110, 3769–3778 (2022). https://doi.org/10.1007/s11071-022-07797-6

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