{
  "id": "math-ph/0002014",
  "version": "v1",
  "published": "2000-02-06T12:16:52.000Z",
  "updated": "2000-02-06T12:16:52.000Z",
  "title": "The Ground State Energy of a Dilute Two-dimensional Bose Gas",
  "authors": [
    "Elliott H. Lieb",
    "Jakob Yngvason"
  ],
  "categories": [
    "math-ph",
    "cond-mat",
    "math.MP"
  ],
  "abstract": "The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be $E_0/N = (2\\pi \\hbar^2\\rho /m){|\\ln (\\rho a^2)|^{-1}}$, to leading order, with a relative error at most ${\\rm O} (|\\ln (\\rho a^2)|^{-1/5})$. Here $N$ is the number of particles, $\\rho =N/V$ is the particle density and $a$ is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, $E_0$ is not simply $N(N-1)/2$ times the energy of two particles in a large box of volume (area, really) $V$. It is much larger.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-06T12:16:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "35Q55",
      "46N50"
    ],
    "keywords": [
      "dilute two-dimensional bose gas",
      "ground state energy",
      "two-body potential",
      "thermodynamic limit",
      "three-dimensional case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.ph...2014L"
    }
  }
}