{
  "id": "nucl-th/0007064",
  "version": "v1",
  "published": "2000-07-27T17:37:03.000Z",
  "updated": "2000-07-27T17:37:03.000Z",
  "title": "Universal trend of the information entropy of a fermion in a mean field",
  "authors": [
    "C. P. Panos",
    "S. E. Massen",
    "C. G. Koutroulos"
  ],
  "comment": "9 pages, latex, 6 figures",
  "journal": "Phys.Rev. C63 (2001) 064307",
  "doi": "10.1103/PhysRevC.63.064307",
  "categories": [
    "nucl-th",
    "quant-ph"
  ],
  "abstract": "We calculate the information entropy of single-particle states in position-space $S_{r}$ and momentum-space $S_{k}$ for a nucleon in a nucleus, a $\\Lambda$ particle in a hypernucleus and an electron in an atomic cluster. It is seen that $S_{r}$ and $S_{k}$ obey the same approximate functional form as functions of the number of particles, $S_{r}$ ({\\rm or} $S_{k}) = a+bN^{1/3}$ in all of the above many-body systems in position- and momentum- space separately. The net information content $S_{r}+S_{k}$ is a slowly varying function of $N$ of the same form as above. The entropy sum $S_{r}+S_{k}$ is invariant to uniform scaling of coordinates and a characteristic of the single-particle states of a specific system. The order of single-particle states according to $S_r +S_k$ is the same as their classification according to energy keeping the quantum number $n$ constant. The spin-orbit splitting is reproduced correctly. It is also seen that $S_{r}+S_{k}$ enhances with excitation of a fermion in a quantum-mechanical system. Finally, we establish a relationship of $S_r +S_k$ with the energy of the corresponding single-particle state i.e. $S_r +S_k = k \\ln (\\mu E +\\nu)$. This relation holds for all the systems under consideration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-07-27T17:37:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "information entropy",
      "mean field",
      "single-particle state",
      "universal trend",
      "net information content"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. C"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 530990
    }
  }
}