Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent $D_{6}$ symmetry

Yanxia Liu; Fan Qi; Yunbo Zhang; Shu Chen

doi:10.1016/j.isci.2019.11.018

paper

Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent $D_{6}$ symmetry

arXiv:1903.08449 · doi:10.1016/j.isci.2019.11.018

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 $D_{6}$ , which enforces the momentums after a series of scattering and reflection processes to fulfill the $D_{6}$ 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 $D_{2 n}$ 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.

33 pages, 5 figures

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

Abstract

Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent $D_{6}$ symmetry