Perturbation theory for Lyapunov exponents of an Anderson model on a strip

Details Perturbation theory for Lyapunov exponents of an Anderson model on a strip Perturbation theory for Lyapunov exponents of an Anderson model on a strip

2004-05-07

arxiv.org/abs/math-ph/0405018v1

Physics

Mathematical Physics

to appear in GAFA

Scientific paper

It is proven that the inverse localization length of an Anderson model on a strip of width $L$ is bounded above by $L/\lambda^2$ for small values of the coupling constant $\lambda$ of the disordered potential. For this purpose, a formalism is developed in order to calculate the bottom Lyapunov exponent associated with random products of large symplectic matrices perturbatively in the coupling constant of the randomness.

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