{
  "id": "1408.7043",
  "version": "v1",
  "published": "2014-08-29T14:54:30.000Z",
  "updated": "2014-08-29T14:54:30.000Z",
  "title": "Electric Conductivity from the solution of the Relativistic Boltzmann Equation",
  "authors": [
    "A. Puglisi",
    "S. Plumari",
    "V. Greco"
  ],
  "comment": "9 pages, 9 figures",
  "categories": [
    "hep-ph",
    "nucl-th"
  ],
  "abstract": "We present numerical results of electric conductivity $\\sigma_{el}$ of a fluid obtained solving the Relativistic Transport Boltzmann equation in a box with periodic boundary conditions. We compute $\\sigma_{el}$ using two methods: the definition itself, i.e. applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in Relaxation Time Approximation (RTA) where the relaxation time for $\\sigma_{el}$ is determined by the transport cross section $\\sigma_{tr}$, i.e. the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the 2-body scatterings: isotropic and anisotropic cross-section, and massless and massive particles. We find that the RTA underestimates considerably $\\sigma_{el}$; for example at screening masses $m_D \\sim \\,T$ such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasi-particle model, tuned to lQCD thermodynamics, as well as the case of a pQCD gas with running coupling. Also for these cases more directly related to the description of the QGP system, we find that RTA significantly underestimate the $\\sigma_{el}$ by about a $60-80\\%$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-29T14:54:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12.38.Mh",
      "25.75.Nq",
      "47.75.+f",
      "52.25.Fi"
    ],
    "keywords": [
      "relativistic boltzmann equation",
      "relativistic transport boltzmann equation",
      "collisional momentum transfer",
      "transport cross section",
      "differential cross section"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevD.90.114009",
      "journal": "Physical Review D",
      "year": 2014,
      "month": "Dec",
      "volume": 90,
      "number": 11,
      "pages": 114009
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1312992,
      "adsabs": "2014PhRvD..90k4009P"
    }
  }
}