Scaling properties of localization in random band matrices: A σ-model approach

Yan V. Fyodorov and Alexander D. Mirlin
Phys. Rev. Lett. 67, 2405 – Published 28 October 1991
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Abstract

We reduce a random-band-matrix (RBM) problem to a one-dimensional, nonlinear, supersymmetric, σ model. This reduction becomes exact in the limit b→∞, b being the effective bandwidth. We prove that b2/N, N being the matrix size, is the relevant scaling parameter. When the mean value of diagonal elements increases linearly along the diagonal an extra scaling parameter arises. These conclusions are in agreement with recent numerical results.

  • Received 21 May 1991

DOI:https://doi.org/10.1103/PhysRevLett.67.2405

©1991 American Physical Society

Authors & Affiliations

Yan V. Fyodorov and Alexander D. Mirlin

  • Universität Gesamthochschule Essen, D-4300 Essen 1, Germany
  • Leningrad Nuclear Physics Institute, 188350 Gatchina, Leningrad District, U.S.S.R

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Vol. 67, Iss. 18 — 28 October 1991

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