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Asymmetric Bethe Ansatz
by Steven G. Jackson, Hélène Perrin, Gregory E. Astrakharchik, Maxim Olshanii
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Submission summary
| Authors (as registered SciPost users): | Maxim Olshanii |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2311.15155v4 (pdf) |
| Date accepted: | 2024-09-04 |
| Date submitted: | 2024-08-26 03:28 |
| Submitted by: | Olshanii, Maxim |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The recently proposed exact quantum solution for two $\delta$-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 $\delta$-well. Finally, we show that the exact solution of the Liu-Qi-Zhang-Chen problem is a particular instance of the the Asymmetric BA.
Author comments upon resubmission
List of changes
* New section on an explicit derivation for spatially odd bound states for two $\delta$ interacting bosons in a $\delta$ potential.
* A pedestrian explanation for how the conventional Bethe Ansatz works.
Published as SciPost Phys. Core 7, 062 (2024)