SciPost Submission Page
Asymmetric Bethe Ansatz
by Steven G. Jackson, Hélène Perrin, Gregory E. Astrakharchik, Maxim Olshanii
Submission summary
| Ontological classification |
| 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
We are truly grateful to both the Editors and the referees for investing their valuable time and energy into making our paper better. We do agree that SciPost Core is the most suitable venue for our manuscript.
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.
