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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.15155 |
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| _version_ | 1866913524149649408 |
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| author | Jackson, Steven G. Perrin, Hélène Astrakharchik, Gregory E. Olshanii, Maxim |
| author_facet | Jackson, Steven G. Perrin, Hélène Astrakharchik, Gregory E. Olshanii, Maxim |
| contents | The recently proposed exact quantum solution for two $δ$-function-interacting particles with a mass-ratio $3\!:\!1$ in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary condition for a Bethe Ansatz integrability, the condition being that the system must be reducible to a superposition of semi-transparent mirrors that is invariant under all the reflections it generates. In this article, we found a way to relax this condition: some of the semi-transparent mirrors of a known self-invariant mirror superposition can be replaced by the perfectly reflecting ones, thus breaking the self-invariance. The proposed name for the method is \emph{Asymmetric Bethe Ansatz} (Asymmetric BA). As a worked example, we study in detail the bound states of the nominally non-integrable system comprised of a bosonic dimer in a $δ$-well. Finally, we show that the exact solution of the Liu-Qi-Zhang-Chen problem is a particular instance of the the Asymmetric BA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15155 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymmetric Bethe Ansatz Jackson, Steven G. Perrin, Hélène Astrakharchik, Gregory E. Olshanii, Maxim Mathematical Physics Quantum Gases Quantum Physics The recently proposed exact quantum solution for two $δ$-function-interacting particles with a mass-ratio $3\!:\!1$ in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary condition for a Bethe Ansatz integrability, the condition being that the system must be reducible to a superposition of semi-transparent mirrors that is invariant under all the reflections it generates. In this article, we found a way to relax this condition: some of the semi-transparent mirrors of a known self-invariant mirror superposition can be replaced by the perfectly reflecting ones, thus breaking the self-invariance. The proposed name for the method is \emph{Asymmetric Bethe Ansatz} (Asymmetric BA). As a worked example, we study in detail the bound states of the nominally non-integrable system comprised of a bosonic dimer in a $δ$-well. Finally, we show that the exact solution of the Liu-Qi-Zhang-Chen problem is a particular instance of the the Asymmetric BA. |
| title | Asymmetric Bethe Ansatz |
| topic | Mathematical Physics Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2311.15155 |