{
  "id": "1105.1695",
  "version": "v1",
  "published": "2011-05-09T15:18:53.000Z",
  "updated": "2011-05-09T15:18:53.000Z",
  "title": "Full Counting Statistics in the Resonant-Level Model",
  "authors": [
    "Denis Bernard",
    "Benjamin Doyon"
  ],
  "comment": "31 pages, 1 figure",
  "journal": "J. Math. Phys. 53, 122302 (2012)",
  "categories": [
    "math-ph",
    "cond-mat.str-el",
    "math.MP"
  ],
  "abstract": "We derive the large deviation function, which provides the large-time full counting statistics for the charge transfer, in the non-equilibrium steady state of the resonant-level model. The general form of this function in free fermion models, in terms of transmission coefficients, was proposed by Levitov and Lesovik in 1993 using a particular measurement set-up involving an interacting spin. It was later suggested to hold as well for a proper quantum mechanical measurement of the transferred charge. We give a precise proof of both statements in the resonant-level model. We first give a full description of the model and its steady state. That is, we explain how the decoupled system prepared with a charge differential evolves, with the impurity coupling, towards the Hershfield non-equilibrium density matrix, in the sense of averages of finitely-supported operators. We describe how this holds both for the usual resonant-level model with a point-like impurity, and for a regularised model with an impurity spread on a finite region, shedding light on subtleties associated to the point-like impurity. We then prove Levitov-Lesovik formula by recasting the problem into calculating averages of finitely-supported operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-09T15:18:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.30.Fk",
      "03.65.Ta"
    ],
    "keywords": [
      "hershfield non-equilibrium density matrix",
      "large deviation function",
      "finitely-supported operators",
      "proper quantum mechanical measurement",
      "charge differential evolves"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "doi": "10.1063/1.4763471",
      "year": 2012,
      "month": "Dec",
      "volume": 53,
      "number": 12,
      "pages": 2302
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMP....53l2302B"
    }
  }
}