Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D6 Symmetry

• Published in: iScience Vol. 22; pp. 181 - 194
• Main Authors: Liu, Yanxia, Qi, Fan, Zhang, Yunbo, Chen, Shu
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 20.12.2019; Elsevier
• Subjects: Cold Atom; Mathematical Method in Physics; Mathematical Physics; Mathematical Physics; Mathematical Method in Physics; Cold Atom
• ISSN: 2589-0042; 2589-0042
• DOI: 10.1016/j.isci.2019.11.018

We show that a system consisting of two interacting particles with mass ratio 3 or 1/3 in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group D6, which enforces the momentums after a series of scattering and reflection processes to fulfill the D6 symmetry. Starting from a two-body elastic collision model in a hard-wall box, we demonstrate how a finite momentum distribution is related to the D2n symmetry for permitted mass ratios. For a quantum system with mass ratio 3, we obtain exact eigenenergies and eigenstates by solving Bethe-type-ansatz equations for arbitrary interaction strength. A many-body excited state of the system is found to be independent of the interaction strength, i.e., the wave function looks exactly the same for non-interacting two particles or in the hard-core limit. [Display omitted] •At nonergodicity points, the permitted momentums fulfill the D2n symmetry•The Bethe Ansatz method is extended to solve the mass-imbalanced quantum system•We exactly solve the interacting two-particle system in a hard-wall with mass ratio 3 Cold Atom; Mathematical Physics; Mathematical Method in Physics