Weak disorder expansion for localization lengths of quasi-1D systems

Abstract

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.

arXiv comment4 pages with 5 .eps figures included

References in corpus (3)

• Random-Matrix Theory of Quantum Transport
• Critical properties of the metal-insulator transition in anisotropic systems
• Perturbation theory for Lyapunov exponents of an Anderson model on a strip

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