Exact Solution for Two $δ$-Interacting Bosons on a Ring in the Presence of a $δ$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917087855771648 |
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| author | Olshanii, Maxim Albert, Mathias Aupetit-Diallo, Gianni Vignolo, Patrizia Jackson, Steven G. |
| author_facet | Olshanii, Maxim Albert, Mathias Aupetit-Diallo, Gianni Vignolo, Patrizia Jackson, Steven G. |
| contents | In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a $δ$-function barrier. Only half of the Hilbert space--namely, the two-body states that are odd under point inversion about the position of the barrier--is accessible to this method. The other half is presumably non-integrable. We consider benchmarking the recently proposed $1/g$ expansion about the hard-core boson point [A. G. Volosniev, D. V. Fedorov, A. S. Jensen, M. Valiente, N. T. Zinner, Nature Communications 5, 5300 (2014)] as one application of our results. Additionally, we find that when the $δ$-barrier is converted to a $δ$-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its non-interacting counterpart while its eigenstates display features of a strongly interacting system. We discuss this phenomenon in the "Summary and Future Research" section of our paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Solution for Two $δ$-Interacting Bosons on a Ring in the Presence of a $δ$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States Olshanii, Maxim Albert, Mathias Aupetit-Diallo, Gianni Vignolo, Patrizia Jackson, Steven G. Mathematical Physics Quantum Gases Quantum Physics In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a $δ$-function barrier. Only half of the Hilbert space--namely, the two-body states that are odd under point inversion about the position of the barrier--is accessible to this method. The other half is presumably non-integrable. We consider benchmarking the recently proposed $1/g$ expansion about the hard-core boson point [A. G. Volosniev, D. V. Fedorov, A. S. Jensen, M. Valiente, N. T. Zinner, Nature Communications 5, 5300 (2014)] as one application of our results. Additionally, we find that when the $δ$-barrier is converted to a $δ$-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its non-interacting counterpart while its eigenstates display features of a strongly interacting system. We discuss this phenomenon in the "Summary and Future Research" section of our paper. |
| title | Exact Solution for Two $δ$-Interacting Bosons on a Ring in the Presence of a $δ$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States |
| topic | Mathematical Physics Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2508.17371 |