{
  "id": "1704.01628",
  "version": "v1",
  "published": "2017-04-05T19:42:25.000Z",
  "updated": "2017-04-05T19:42:25.000Z",
  "title": "Kinetic energy of a trapped Fermi gas at finite temperature",
  "authors": [
    "Jacek Grela",
    "Satya N. Majumdar",
    "Gregory Schehr"
  ],
  "comment": "5 pages + 9 pages of supplementary material, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the statistics of the kinetic (or equivalently potential) energy for $N$ non-interacting fermions in a $1d$ harmonic trap of frequency $\\omega$, at finite temperature $T$. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature $T$ and for any $N$, using a non-trivial mapping to an integrable Calogero-Moser-Sutherland model. As a function of temperature $T$, and for large $N$, we identify: (i) a quantum regime, for $T \\sim \\hbar \\omega$, where quantum fluctuations dominate and (ii) a thermal regime, for $T \\sim N \\hbar \\omega$, governed by thermal fluctuations. We show how the mean, the variance as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as temperature increases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-05T19:42:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "trapped fermi gas",
      "finite temperature",
      "thermal regime",
      "quantum fluctuations dominate",
      "large deviation function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}