Perturbative test of single parameter scaling for 1D random media
Mathematical Physics
2007-05-23 v2 Disordered Systems and Neural Networks
math.MP
Abstract
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single parameter scaling holds to lowest order perturbation theory in the disorder strength. However, it is generically violated at higher order. This is explicitely exhibited for the Anderson model.
Cite
@article{arxiv.math-ph/0405019,
title = {Perturbative test of single parameter scaling for 1D random media},
author = {R. Schrader and H. Schulz-Baldes and A. Sedrakyan},
journal= {arXiv preprint arXiv:math-ph/0405019},
year = {2007}
}
Comments
minor corrections to previous version, to appear in Annales H. Poincare