Asymmetric Bethe Ansatz
The recently proposed exact quantum solution for two \delta δ -function-interacting particles with a mass-ratio 3\!:\!1 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 conditio...
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Published in | SciPost physics core Vol. 7; no. 3; p. 062 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
SciPost
12.09.2024
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Online Access | Get full text |
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Summary: | The recently proposed exact quantum solution for two \delta δ -function-interacting particles with a mass-ratio 3\!:\!1 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 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 \delta 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. |
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ISSN: | 2666-9366 2666-9366 |
DOI: | 10.21468/SciPostPhysCore.7.3.062 |