{
  "id": "1610.08912",
  "version": "v1",
  "published": "2016-10-12T13:51:22.000Z",
  "updated": "2016-10-12T13:51:22.000Z",
  "title": "Ground state energy of the $δ$-Bose gas at weak coupling from double extrapolation",
  "authors": [
    "Sylvain Prolhac"
  ],
  "comment": "7 pages, 1 figure, 2 tables",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the ground state energy $e(\\gamma)$ of the $\\delta$-Bose gas with repulsive interaction in the weak coupling regime $\\gamma\\to0$, where previous analytical studies gave the expansion $e(\\gamma)\\simeq\\gamma-4\\gamma^{3/2}/3\\pi+(1/6-1/\\pi^{2})\\gamma^{2}$. Using a numerical solution of the Bethe equations for a finite number $N$ of particles and finite strength $\\gamma$ of the interaction, we obtain very accurate numerics for the next orders after extrapolating on $N$ and $\\gamma$. The coefficient of $\\gamma^{5/2}$ in the expansion is found approximately equal to $-0.00158769986550594499$. This value is supported by a numerical solution of the Lieb-Liniger integral equation discretized with $M$ points followed by extrapolation on $M$ and $\\gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-12T13:51:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state energy",
      "bose gas",
      "double extrapolation",
      "lieb-liniger integral equation",
      "numerical solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}