{
  "id": "1903.08449",
  "version": "v1",
  "published": "2019-03-20T11:25:31.000Z",
  "updated": "2019-03-20T11:25:31.000Z",
  "title": "Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent $D_{2n}$ symmetry",
  "authors": [
    "Yanxia Liu",
    "Fan Qi",
    "Yunbo Zhang",
    "Shu Chen"
  ],
  "comment": "10 pages, 5 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We show that a system consisting of two interacting particles with unequal masses in a hard-wall box can be exactly solved by using Bethe ansatz, when the mass ratio takes some specific values. The ansatz is based on finite superpositions of plane waves associated with a dihedral group $D_{2n}$, which enforces the momentums after a series of scattering and reflection processes to fulfill the $D_{2n}$ 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 and gives the condition of permitted mass ratios corresponding to classical superintegrable points. For a quantum system with mass ratio $3$, we obtain exact eigenenergies and eigenstates by solving Bethe 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-20T11:25:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exactly solvable model",
      "hard-wall trap",
      "mass-imbalanced atoms",
      "mass ratio",
      "hard-wall box"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}