{
  "id": "1401.5960",
  "version": "v2",
  "published": "2014-01-23T12:45:23.000Z",
  "updated": "2014-03-24T19:48:57.000Z",
  "title": "The Ground State Energy of a Dilute Bose Gas in Dimension n >3",
  "authors": [
    "Anders Aaen"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially symmetric two-body potential $V$. In the limit of low density $\\rho$, the ground state energy per particle in the thermodynamic limit is shown to be $(n-2)|\\mathbb S^{n-1}|a^{n-2}\\rho$, where $|\\mathbb S^{n-1}|$ denotes the surface measure of the unit sphere in $\\mathbb{R}^n$ and $a$ is the scattering length of $V$. Furthermore, for smooth and compactly supported two-body potentials, we derive upper bounds to the ground state energy with a correction term $(1+C\\gamma)8\\pi^4a^6\\rho^2|\\ln(a^4\\rho)|$ in dimension $n=4$, where $\\gamma:=\\int V(x)|x|^{-2}\\, dx$, and a correction term which is $\\mathcal{O}(\\rho^2)$ in higher dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-24T19:48:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state energy",
      "dilute bose gas",
      "correction term",
      "radially symmetric two-body potential",
      "spatial dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5960A"
    }
  }
}