{
  "id": "1505.04923",
  "version": "v1",
  "published": "2015-05-19T09:29:28.000Z",
  "updated": "2015-05-19T09:29:28.000Z",
  "title": "Quantum canonical ensemble: a projection operator approach",
  "authors": [
    "Wim Magnus",
    "Fons Brosens"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "Fixing the number of particles $N$, the quantum canonical ensemble imposes a constraint on the occupation numbers of single-particle states. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary $N$ since, unlike the case of the grand-canonical ensemble, traces in the $N$-particle Hilbert space fail to factorize into simple traces over single-particle states. In this paper we introduce a projection operator that enables a constraint-free computation of the partition function and its derived quantities, at the price of an angular or contour integration. Being applicable to both bosonic and fermionic non-interacting systems in arbitrary dimensions, the projection operator approach provides closed-form expressions for the partition function $Z_N$ and the Helmholtz free energy $F_{\\! N}$ as well as for two- and four-point correlation functions. While appearing only as a secondary quantity in the present context, the chemical potential potential emerges as a by-product from the relation $\\mu_N = F_{\\! N+1} - F_{\\! N}$, as illustrated for a two-dimensional fermion gas with $N$ ranging between 2 and 500.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T09:29:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projection operator approach",
      "quantum canonical ensemble",
      "partition function",
      "particle hilbert space fail",
      "single-particle states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}