TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.3.062
TI  - Asymmetric Bethe Ansatz
PY  - 2024/09/12
UR  - https://scipost.org/SciPostPhysCore.7.3.062
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 3
SP  - 062
A1  - Jackson, Steven Glenn
AU  - Perrin, Hélène
AU  - Astrakharchik, Grigori E.
AU  - Olshanii, Maxim
AB  - 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 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.
ER  -

@Article{10.21468/SciPostPhysCore.7.3.062,
	title={{Asymmetric Bethe Ansatz}},
	author={Steven G. Jackson and Hélène Perrin and Gregory E. Astrakharchik and Maxim Olshanii},
	journal={SciPost Phys. Core},
	volume={7},
	pages={062},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.3.062},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.3.062},
}