{
  "id": "cond-mat/0610255",
  "version": "v2",
  "published": "2006-10-10T08:30:55.000Z",
  "updated": "2006-10-20T09:14:51.000Z",
  "title": "Mixing, ergodicity and slow relaxation phenomena",
  "authors": [
    "Ismael V. L. Costa",
    "Mendeli H. Vainstein",
    "Luciano C. Lapas",
    "Adriano A. Batista",
    "Fernando A. Oliveira"
  ],
  "comment": "6 pages, 1 figure. Corrected last citation. Proceedings of LAWNP05",
  "journal": "Physica A, 371 (2006) 130-134",
  "doi": "10.1016/j.physa.2006.04.096",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-20T09:14:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "slow relaxation phenomena",
      "ergodicity",
      "necessary condition",
      "lee recurrence relations method",
      "fluctuation-dissipation theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}