Asymmetric Bethe Ansatz
Steven G. Jackson, Hélène Perrin, Gregory E. Astrakharchik, Maxim Olshanii
SciPost Phys. Core 7, 062 (2024) · published 12 September 2024
- doi: 10.21468/SciPostPhysCore.7.3.062
- Submissions/Reports
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 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.
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Steven Glenn Jackson,
- 2 Hélène Perrin,
- 3 Grigori E. Astrakharchik,
- 1 Maxim Olshanii
- 1 University of Massachusetts Boston
- 2 Laser Physics Laboratory / Laser Physics Laboratory [LPL]
- 3 Universitat Politècnica de Catalunya [UPC]