{
  "id": "1701.00949",
  "version": "v1",
  "published": "2017-01-04T10:17:03.000Z",
  "updated": "2017-01-04T10:17:03.000Z",
  "title": "Identical Wells, Symmetry Breaking, and the Near-Unitary Limit",
  "authors": [
    "N. L. Harshman"
  ],
  "comment": "6 pages, 1 figure, accepted in Few-Body Systems",
  "categories": [
    "quant-ph",
    "cond-mat.quant-gas"
  ],
  "abstract": "Energy level splitting from the unitary limit of contact interactions to the near unitary limit for a few identical atoms in an effectively one-dimensional well can be understood as an example of symmetry breaking. At the unitary limit in addition to particle permutation symmetry there is a larger symmetry corresponding to exchanging the $N!$ possible orderings of $N$ particles. In the near unitary limit, this larger symmetry is broken, and different shapes of traps break the symmetry to different degrees. This brief note exploits these symmetries to present a useful, geometric analogy with graph theory and build an algebraic framework for calculating energy splitting in the near unitary limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-04T10:17:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetry breaking",
      "near-unitary limit",
      "identical wells",
      "larger symmetry",
      "brief note exploits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}