{
  "id": "cond-mat/0304392",
  "version": "v1",
  "published": "2003-04-17T09:37:53.000Z",
  "updated": "2003-04-17T09:37:53.000Z",
  "title": "Self-consistent equation for an interacting Bose gas",
  "authors": [
    "Philippe A. Martin",
    "Jaroslaw Piasecki"
  ],
  "comment": "33 pages, 6 figures, submitted to Phys.Rev. E",
  "doi": "10.1103/PhysRevE.68.016113",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential $V(r)$ such that $0<\\int d\\br V(r) = a<\\infty$. Expressing the partition function by the Feynman-Kac functional integral yields a classical-like polymer representation of the quantum gas. With Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation $\\rho (\\mu)=F(\\mu-a\\rho(\\mu))$ between the density $\\rho $ and the chemical potential $\\mu$, valid in the range of convergence of Mayer series. The function $F$ is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling $V_{\\gamma}(\\br)=\\gamma^{3}V(\\gamma r)$ we prove that in the mean-field limit $\\gamma\\to 0$ only tree diagrams contribute and function $F$ reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of Mayer series (vicinity of Bose-Einstein condensation) and study dominant corrections to mean field. At lowest order, the form of function $F$ is shown to depend on single polymer partition function for which we derive lower and upper bounds and on the resummation of ring diagrams which can be analytically performed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-17T09:37:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interacting bose gas",
      "self-consistent equation",
      "single polymer partition function",
      "self-consistent relation",
      "mayer graph summation techniques"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}