Single Parameter Scaling in One-Dimensional Localization Revisited

Lev I. Deych; A. A. Lisyansky; B. L. Altshuler

doi:10.1103/PhysRevLett.84.2678

Single Parameter Scaling in One-Dimensional Localization Revisited

Lev I. Deych, A. A. Lisyansky, and B. L. Altshuler

Phys. Rev. Lett. 84, 2678 – Published 20 March 2000

Abstract

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned $δ$ functions with random strength.

Received 10 September 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.2678

Authors & Affiliations

Lev I. Deych¹, A. A. Lisyansky², and B. L. Altshuler³

¹Physics Department, Seton Hall University, South Orange, New Jersey 07052
²Physics Department, Queens College of CUNY, Flushing, New York 11367
³Physics Department, Princeton University and NEC Research Institute, Princeton, New Jersey 08540