{
  "id": "1204.5169",
  "version": "v1",
  "published": "2012-04-24T11:50:48.000Z",
  "updated": "2012-04-24T11:50:48.000Z",
  "title": "Conductance of Finite Systems and Scaling in Localization Theory",
  "authors": [
    "I. M. Suslov"
  ],
  "comment": "Latex, 24 pages, 16 figures included",
  "journal": "Zh.Eksp.Teor.Fiz. 142, 1020 (2012) [ J.Exp.Theor.Phys. 115, 897 (2012)]",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al, 1979). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D(\\omega,q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Woelfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann - Low functions \\beta(g) for space dimensions d=1,2,3 are calculated. In contrast to the previous attempt by Vollhardt and Woelfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of \\beta(g) in 1/g coincides with results of the \\sigma-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d=2+\\epsilon looks incompatible with the physical essence of the problem. The obtained results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law \\sigma\\propto -i\\omega for conductivity are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-24T11:50:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conductance",
      "localization theory",
      "self-consistent theory",
      "finite systems plays",
      "shell model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1134/S1063776112110143",
      "journal": "Soviet Journal of Experimental and Theoretical Physics",
      "year": 2012,
      "month": "Nov",
      "volume": 115,
      "number": 5,
      "pages": 897
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JETP..115..897S"
    }
  }
}