{
  "id": "1902.08047",
  "version": "v1",
  "published": "2019-02-21T13:45:09.000Z",
  "updated": "2019-02-21T13:45:09.000Z",
  "title": "Non-cooperative Equilibria of Fermi Systems With Long Range Interactions",
  "authors": [
    "J. -B. Bru",
    "W. de Siqueira Pedra"
  ],
  "comment": "This manuscript has been originally published in 2013 in Memoirs of the AMS (volume 224, no. 1052). This postprint is a corrected version of this publication, but the historical part has not been updated and thus runs until 2013. We are also very grateful to S\\'ebastien Breteaux for pointing out several mistakes and suggesting various improvements on the text",
  "journal": "Memoirs of the AMS 224 (2013), no. 1052. Print ISBN: 978-0-8218-8976-3",
  "doi": "10.1090/S0065-9266-2012-00666-6",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We define a Banach space $\\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\\mathfrak{m}\\in \\mathcal{M}_{1}$. In particular, we give a first answer to an old open problem in mathematical physics - first addressed by Ginibre in 1968 within a different context - about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\\mathfrak{m}\\in \\mathcal{M}_{1}$, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show that the thermodynamics of long range models $\\mathfrak{m}\\in \\mathcal{M}_{1}$ is governed by the non-cooperative equilibria of a zero-sum game, called here the thermodynamic game.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-21T13:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C10",
      "82C20",
      "82C22",
      "47D06",
      "58D25",
      "82C70",
      "82C44",
      "34G10"
    ],
    "keywords": [
      "long range interactions",
      "non-cooperative equilibria",
      "fermi systems",
      "old open problem",
      "long range models"
    ],
    "tags": [
      "journal article",
      "monograph"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Mem. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}