Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent D₆ symmetry

2019/03/31 by Yanxia Liu, Fan Qi, Yunbo Zhang +1 · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1016/j.isci.2019.11.018

published as iScience 22, 181-194 (2019) · 33 pages, 5 figures

arxiv created 2019/12/10 · arxiv updated 2019/12/11

Abstract

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 D_2n 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.

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