Perturbative test of single parameter scaling for 1D random media
Schrader R, Schulz-Baldes H, Sedrakyan A (2004)
Publication Type: Journal article
Publication year: 2004
Journal
Publisher: Institute Henri Poincaré
Book Volume: 5
Pages Range: 1159-1180
URI: http://de.arxiv.org/abs/cond-mat/0405125
DOI: 10.1007/s00023-004-0195-3
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 explicitly exhibited for the Anderson model.
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APA:
Schrader, R., Schulz-Baldes, H., & Sedrakyan, A. (2004). Perturbative test of single parameter scaling for 1D random media. Annales Henri Poincaré, 5, 1159-1180. https://dx.doi.org/10.1007/s00023-004-0195-3
MLA:
Schrader, Robert, Hermann Schulz-Baldes, and Ara Sedrakyan. "Perturbative test of single parameter scaling for 1D random media." Annales Henri Poincaré 5 (2004): 1159-1180.
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