Weak-disorder expansion for localization lengths of quasi-1D systemsR. A. Römer1 and H. Schulz-Baldes2
1 Department of Physics and Centre for Scientific Computing, University of Warwick Coventry CV4 7AL, UK
2 Institut für Mathematik - Strasse des 17. Juni 136, Technische Universität Berlin 10623 Berlin, Germany
received 20 July 2004; accepted 19 August 2004
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength.
72.15.Rn - Localization effects (Anderson or weak localization).
73.20.Fz - Weak or Anderson localization.
73.23.-b - Electronic transport in mesoscopic systems.
© EDP Sciences 2004