{
  "id": "1404.1315",
  "version": "v2",
  "published": "2014-04-04T17:10:56.000Z",
  "updated": "2014-08-13T18:03:31.000Z",
  "title": "Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states",
  "authors": [
    "Sylvain Prolhac"
  ],
  "comment": "31 pages, 10 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles. Bethe ansatz shows that these eigenstates are characterized by four finite sets of positive half-integers, or equivalently by two integer partitions. Each corresponding eigenvalue is found to be equal to the value at its saddle point of a function indexed by the four sets. Our derivation of the large $L$ asymptotics relies on a version of the Euler-Maclaurin formula with square root singularities at both ends of the summation range.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-13T18:03:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "totally asymmetric simple exclusion process",
      "first excited states",
      "periodic lattice"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/47/37/375001",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2014,
      "month": "Sep",
      "volume": 47,
      "number": 37,
      "pages": 375001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JPhA...47K5001P"
    }
  }
}