Abstract
The localization of the electron states and dc-conductivity of the one dimensional Anderson model are investigated with various numerical procedures. It is found that the eigenstates are always exponentially localized and that in the center of the band the localization length is proportional to the inverse square of the disorder. The dc-conductivity, as obtained by using the Kubo-Greenwood formula, obeys the central limit theorem for any finite imaginary frequency, with a variance, which is inversely proportional to the squareroot of the number of states contributing to the transport. There is no exponential length dependence of the Kubo-Greenwood conductivity within this model. The conductivity tends to zero only in the limit of vanishing imaginary frequency.
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Czycholl, G., Kramer, B. & MacKinnon, A. Conductivity and localization of electron states in one dimensional disordered systems: Further numerical results. Z. Physik B - Condensed Matter 43, 5–11 (1981). https://doi.org/10.1007/BF01295469
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DOI: https://doi.org/10.1007/BF01295469