{
  "id": "2208.02458",
  "version": "v1",
  "published": "2022-08-04T05:02:38.000Z",
  "updated": "2022-08-04T05:02:38.000Z",
  "title": "Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature",
  "authors": [
    "Manas Kulkarni",
    "Pierre Le Doussal",
    "Satya N. Majumdar",
    "Gregory Schehr"
  ],
  "comment": "18 pages, 7 figures, 1 table",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\\Omega$ and in the presence of an additional repulsive central potential $\\gamma/r^2$. The average density at zero temperature was recently studied in Phys. Rev. A $\\textbf{103}$, 033321 (2021) and an interesting multi-layered \"wedding cake\" structure with a \"hole\" at the center was found for the density in the large $N$ limit. In this paper, we study the average density at finite temperature. We demonstrate how this \"wedding-cake\" structure is modified at finite temperature. These large $N$ results warrant going much beyond the standard Local Density Approximation. We also generalize our results to a wide variety of trapping potentials and demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the \"wedding-cake\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-04T05:02:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite temperature",
      "noninteracting fermions",
      "average density",
      "density profile",
      "standard local density approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}