{
  "id": "2208.04584",
  "version": "v1",
  "published": "2022-08-09T07:54:07.000Z",
  "updated": "2022-08-09T07:54:07.000Z",
  "title": "Derivation of the Ginzburg-Landau Theory for Interacting Fermions in a Trap",
  "authors": [
    "Andrea Calignano",
    "Michele Correggi"
  ],
  "comment": "Contribution to the proceedings of the intensive period \"INdAM Quantum Meetings (IQM22)\" (https://sites.google.com/view/iqm22), pdfLaTex, 21 pages",
  "categories": [
    "math-ph",
    "cond-mat.supr-con",
    "math.MP"
  ],
  "abstract": "We study a dilute gas of interacting fermions at temperature $T=0$ and chemical potential $\\mu \\in \\mathbb{R}$. The particles are trapped by an external potential, and they interact via a microscopic attractive two-body potential with a two-body bound state. We prove the emergence of the macroscopic Ginzburg-Landau theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-09T07:54:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interacting fermions",
      "derivation",
      "vanishing micro-to-macro scale parameter",
      "bcs energy functional",
      "macroscopic ginzburg-landau theory"
    ],
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}