Localization by pseudorandom potentials in one dimension

Localization in one dimension in the presence of a pseudorandom potential is investigated. The localization length of the tight-binding model Vₙ{u}ₙ$+${u}ₙ₊₁$+${u}_{n{{-}}1}$=${Eu}ₙ$ with ${V}ₙ=λ cosπαn{{{}}}^{{ν}}is calculated numerically and in perturbation theory for λ1, for generic values of α and ν. The similarity between the potential{V}ₙ$ and random potentials increases with {ν}. It is found that for {ν}{≥}2 all the states are localized and the localization length is equal to that of the corresponding random model while for 0<{ν}{≤}1 there are extended states. The intermediate regime 1<{ν}<2 is discussed as well.