Abstract
We study theE-dependence of the Lyapounov exponent <γ(E)> of an electron with energyE in the one dimensional Anderson model with off diagonal disorder. In the neighbourhood of the band centre we find for nonzero disorder <Reγ(E)>∼log−1 E→0 forE→0, but all even moments of Reγ(E) diverge logarithmically. As the probability of Re γ(E)=0 decreases to zero forE→0 we conclude that the electron is always exponentially localised.
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Markoš, P. The one dimensional anderson model with off diagonal disorder: band centre anomaly. Z. Physik B - Condensed Matter 73, 17–21 (1988). https://doi.org/10.1007/BF01312150
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DOI: https://doi.org/10.1007/BF01312150