{
  "id": "2305.00834",
  "version": "v1",
  "published": "2023-05-01T14:03:47.000Z",
  "updated": "2023-05-01T14:03:47.000Z",
  "title": "Hilbert-Schmidt Estimates for Fermionic 2-Body Operators",
  "authors": [
    "Martin Ravn Christiansen"
  ],
  "comment": "8 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the 2-body operator $\\gamma_2^\\Psi$ of a fermionic $N$-particle state $\\Psi$ obeys $||\\gamma_2^\\Psi||_{HS} \\leq \\sqrt{5} N$, which complements the bound of Yang that $||\\gamma_2^\\Psi||_{op} \\leq N$. This estimate furthermore resolves a conjecture of Carlen-Lieb-Reuvers (arXiv:1403.3816) concerning the entropy of the normalized 2-body operator. We also prove that the Hilbert-Schmidt norm of the truncated 2-body operator $\\gamma_2^{\\Psi,T}$ obeys the inequality $||\\gamma_2^{\\Psi,T}||_{HS} \\leq \\sqrt{5 N \\, \\mathrm{tr}(\\gamma_1^\\Psi (1 - \\gamma_1^\\Psi))}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-01T14:03:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert-schmidt estimates",
      "particle state",
      "hilbert-schmidt norm",
      "complements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}