Possible coexistence of localized and extended states in the quantum Hall effect

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Abstract
We study the system of a single electron in the plane, subject to a strong transverse magnetic field and an impurity potential, within a subspace scrP^ pertaining to a single Landau level. It is shown that dilute impurities build a potential V which is active only in a subspace P of scrP^. The complementary subspace scrP^-P, the null eigenspace of V, is an infinite-dimensional space of extended states. In other words, there is more than just one extended state available for conductance.