{
  "id": "1604.08843",
  "version": "v1",
  "published": "2016-04-29T14:15:29.000Z",
  "updated": "2016-04-29T14:15:29.000Z",
  "title": "Extrapolation methods and Bethe ansatz for the asymmetric exclusion process",
  "authors": [
    "Sylvain Prolhac"
  ],
  "comment": "20 pages, 2 figures, 1 table",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous results for the totally asymmetric model $q=0$, precise conjectures are formulated for asymptotics at finite density $\\rho=N/L$ of ASEP eigenstates close to the stationary state. The conjectures are checked with high precision using extrapolation methods on finite size Bethe ansatz numerics. For weak asymmetry $1-q\\sim1/\\sqrt{L}$, double extrapolation combined with an integer relation algorithm gives an exact expression for the spectral gap up to $10$-th order in the asymmetry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-29T14:15:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymmetric exclusion process",
      "extrapolation methods",
      "one-dimensional asymmetric simple exclusion process",
      "finite size bethe ansatz numerics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160408843P"
    }
  }
}