Three and four identical fermions near the unitary limit
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866915635092520960 |
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| author | Higgins, Michael D. Greene, Chris H. |
| author_facet | Higgins, Michael D. Greene, Chris H. |
| contents | This work analyzes the three and four equal-mass fermionic systems near and at the $s$- and $p$-wave unitary limits using hyperspherical methods. The unitary regime addressed here is where the two-body dimer energy is at zero energy. For fermionic systems near the $s$-wave unitary limit, the hyperradial potentials in the $N$-body continuum exhibit a universal long-range $R^{-3}$ behavior governed by the $s$-wave scattering length alone. The implications of this behavior on the low energy phase shift are discussed. At the $p$-wave unitary limit, the four-body system is studied through a qualitative look at the structure of the hyperradial potentials at unitarity for the $L^π=0^{+}$ symmetry. A quantitative analysis shows that there are tetramer states in the lowest hyperradial potentials for these systems. Correlations are made between these tetramers and the corresponding trimers in the two-body fragmentation channels. Universal properties related to the four-body recombination process $\mathrm{A+A+A+A}\leftrightarrow \mathrm{A_3+A}$ are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04564 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Three and four identical fermions near the unitary limit Higgins, Michael D. Greene, Chris H. Atomic Physics Quantum Physics This work analyzes the three and four equal-mass fermionic systems near and at the $s$- and $p$-wave unitary limits using hyperspherical methods. The unitary regime addressed here is where the two-body dimer energy is at zero energy. For fermionic systems near the $s$-wave unitary limit, the hyperradial potentials in the $N$-body continuum exhibit a universal long-range $R^{-3}$ behavior governed by the $s$-wave scattering length alone. The implications of this behavior on the low energy phase shift are discussed. At the $p$-wave unitary limit, the four-body system is studied through a qualitative look at the structure of the hyperradial potentials at unitarity for the $L^π=0^{+}$ symmetry. A quantitative analysis shows that there are tetramer states in the lowest hyperradial potentials for these systems. Correlations are made between these tetramers and the corresponding trimers in the two-body fragmentation channels. Universal properties related to the four-body recombination process $\mathrm{A+A+A+A}\leftrightarrow \mathrm{A_3+A}$ are discussed. |
| title | Three and four identical fermions near the unitary limit |
| topic | Atomic Physics Quantum Physics |
| url | https://arxiv.org/abs/2205.04564 |