{
  "id": "2007.15661",
  "version": "v1",
  "published": "2020-07-30T18:00:03.000Z",
  "updated": "2020-07-30T18:00:03.000Z",
  "title": "Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble",
  "authors": [
    "Hatem Barghathi",
    "Jiangyong Yu",
    "Adrian Del Maestro"
  ],
  "comment": "17 pages, 4 figures. For associated code and data repository see: https://github.com/DelMaestroGroup/CanonicalEnsembleTheory-paper-code",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas"
  ],
  "abstract": "We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functions, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-30T18:00:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "canonical ensemble",
      "non-interacting fermions",
      "occupation numbers",
      "auxiliary partition functions",
      "particle number counting statistics"
    ],
    "tags": [
      "github project"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}