Low density expansion for Lyapunov exponents

Details Low density expansion for Lyapunov exponents Low density expansion for Lyapunov exponents

2006-07-12

arxiv.org/abs/math-ph/0607027v1

Mathematical Physics of Quantum Mechanics, Eds. Asch, Joye, Springer 2006

Physics

Mathematical Physics

Scientific paper

In some quasi-one-dimensional weakly disordered media, impurities are large and rare rather than small and dense. For an Anderson model with a low density of strong impurities, a perturbation theory in the impurity density is developed for the Lyapunov exponent and the density of states. The Lyapunov exponent grows linearly with the density. Anomalies of the Kappus-Wegner type appear for all rational quasi-momenta even in lowest order perturbation theory.

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