• Milestone

New method for a scaling theory of localization

P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher
Phys. Rev. B 22, 3519 – Published 15 October 1980
An article within the collection: Physical Review B 50th Anniversary Milestones
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Abstract

We base a scaling theory of localization on an expression for conductivity of a system of random elastic scatterers in terms of its scattering properties at a fixed energy. This expression, proposed by Landauer, is first derived and generalized to a system of indefinite size and number of scattering channels (a "wire"), and then an exact scaling theory for the one-dimensional chain is given. It is shown that the appropriate scaling variable is f(ρ)=ln(1+ρ) where ρ is the dimensionless resistance, which has the property of "additive mean," and that scaling leads to a well-behaved probability distribution of this variable and to a very simple scaling law not previously given in the literature.

  • Received 13 February 1980

DOI:https://doi.org/10.1103/PhysRevB.22.3519

©1980 American Physical Society

Collections

This article appears in the following collection:

Physical Review B 50th Anniversary Milestones

These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.

Authors & Affiliations

P. W. Anderson*

  • Bell Laboratories, Murray Hill, New Jersey 07974

D. J. Thouless

  • Yale University, New Haven, Connecticut 06520

E. Abrahams

  • Serin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854

D. S. Fisher

  • Bell Laboratories, Murray Hill, New Jersey 07974

  • *Also at Princeton University, Princeton, New Jersey 08540.

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Issue

Vol. 22, Iss. 8 — 15 October 1980

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