{
  "id": "2012.07633",
  "version": "v1",
  "published": "2020-12-11T11:33:16.000Z",
  "updated": "2020-12-11T11:33:16.000Z",
  "title": "Remarks on thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures",
  "authors": [
    "Andrés G. Jirón Vicente",
    "Luis B. Castro",
    "Angel E. Obispo",
    "Luis E. Arroyo Meza"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "cond-mat.mes-hall",
    "hep-th",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In a recent paper published in this Journal, Khordad and collaborators [J Low Temp Phys (2018) 190:200] have studied the thermodynamics properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. In that meritorious research the energy of system was obtained by solving the Schr\\\"{o}dinger equation. The radial equation was mapped into a confluent hypergeometric differential equation and the differential equation associated to $z$ coordinate was mapped into a biconfluent Heun differential equation. In this paper, it is pointed out a misleading treatment on the solution of the biconfluent Heun equation. It is shown that the energy $E_{z}$ can not be labeled with $n_{z}$ and this fact jeopardizes the results of this system. We calculate the partition function with the correct energy spectrum and recalculate the specific heat and entropy as a function of low and high temperatures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-11T11:33:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high temperatures",
      "thermodynamic properties",
      "confluent hypergeometric differential equation",
      "biconfluent heun differential equation",
      "gaas double ring-shaped quantum dot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}