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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.11330 |
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| _version_ | 1866914928584032256 |
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| author | Givois, J. Tononi, A. Petrov, D. S. |
| author_facet | Givois, J. Tononi, A. Petrov, D. S. |
| contents | We study binding of $N$ identical heavy fermions by a light atom in two dimensions assuming zero-range attractive heavy-light interactions. By using the mean-field theory valid for large $N$ we show that the $N+1$ cluster is bound when the mass ratio exceeds $1.074N^2$. The mean-field theory, being scale invariant in two dimensions, predicts only the shapes of the clusters leaving their sizes and energies undefined. By taking into account beyond-mean-field effects we find closed-form expressions for these quantities. We also discuss differences between the Thomas-Fermi and Hartree-Fock approaches for treating the heavy fermions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11330 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Heavy-light $N+1$ clusters of two-dimensional fermions Givois, J. Tononi, A. Petrov, D. S. Quantum Gases We study binding of $N$ identical heavy fermions by a light atom in two dimensions assuming zero-range attractive heavy-light interactions. By using the mean-field theory valid for large $N$ we show that the $N+1$ cluster is bound when the mass ratio exceeds $1.074N^2$. The mean-field theory, being scale invariant in two dimensions, predicts only the shapes of the clusters leaving their sizes and energies undefined. By taking into account beyond-mean-field effects we find closed-form expressions for these quantities. We also discuss differences between the Thomas-Fermi and Hartree-Fock approaches for treating the heavy fermions. |
| title | Heavy-light $N+1$ clusters of two-dimensional fermions |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2310.11330 |