{
  "id": "2009.07251",
  "version": "v1",
  "published": "2020-09-15T17:37:20.000Z",
  "updated": "2020-09-15T17:37:20.000Z",
  "title": "Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap",
  "authors": [
    "Manas Kulkarni",
    "Satya N. Majumdar",
    "Gregory Schehr"
  ],
  "comment": "Main text: 6 pages, 3 figures. Supplemental material: 15 pages, 7 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\\Omega$ in the presence of an additional repulsive central potential $\\gamma/r^2$. We find that, in the large $N$ limit, the bulk density has a rich and nontrivial profile -- with a hole at the center of the trap and surrounded by a multi-layered \"wedding cake\" structure. The number of layers depends on $N$ and on the two parameters $\\Omega$ and $\\gamma$ leading to a rich phase diagram. Zooming in on the edge of the $k^{\\rm th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\\rm th}$ Hermite polynomial. Interestingly, in the large $k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-15T17:37:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rotating two-dimensional trap",
      "noninteracting fermions",
      "multilayered density profile",
      "quantum spin chains",
      "rich phase diagram"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}