Perturbative test of single parameter scaling for 1D random media

Details Perturbative test of single parameter scaling for 1D random media Perturbative test of single parameter scaling for 1D random media

2004-05-07

arxiv.org/abs/math-ph/0405019v2

Annales Henri Poincare 5 (2004) 1159 - 1180

Physics

Mathematical Physics

minor corrections to previous version, to appear in Annales H. Poincare

Scientific paper

10.1007/s00023-004-0195-3

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.

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