{
  "id": "2003.04351",
  "version": "v1",
  "published": "2020-03-09T18:34:00.000Z",
  "updated": "2020-03-09T18:34:00.000Z",
  "title": "Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells",
  "authors": [
    "O. Olendski"
  ],
  "comment": "7 figures",
  "categories": [
    "quant-ph",
    "cond-mat.mes-hall",
    "physics.data-an"
  ],
  "abstract": "A comparative analysis of the Dirichlet and Neumann boundary conditions (BCs) of the one-dimensional (1D) quantum well extracts similarities and differences of the R\\'{e}nyi $R(\\alpha)$ as well as Tsallis $T(\\alpha)$ entropies between these two geometries. It is shown, in particular, that for either BC the dependencies of the R\\'{e}nyi position components on the parameter $\\alpha$ are the same for all orbitals but the lowest Neumann one for which the corresponding functional $R$ is not influenced by the variation of $\\alpha$. Lower limit $\\alpha_{TH}$ of the semi infinite range of the dimensionless R\\'{e}nyi/Tsallis coefficient where {\\em momentum} entropies exist crucially depends on the {\\em position} BC and is equal to one quarter for the Dirichlet requirement and one half for the Neumann one. At $\\alpha$ approaching this critical value, the corresponding momentum functionals do diverge. The gap between the thresholds $\\alpha_{TH}$ of the two BCs causes different behavior of the R\\'{e}nyi uncertainty relations as functions of $\\alpha$. For both configurations, the lowest-energy level at $\\alpha=1/2$ does saturate either type of the entropic inequality thus confirming an earlier surmise about it. It is also conjectured that the threshold $\\alpha_{TH}$ of one half is characteristic of any 1D non-Dirichlet system. Other properties are discussed and analyzed from the mathematical and physical points of view.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-09T18:34:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann one-dimensional quantum wells",
      "tsallis entropies",
      "semi infinite range",
      "1d non-dirichlet system",
      "neumann boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}