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Unusual wave functions in the Aubry model in 1-d

Wave functions are currently classified as extended or localized. In the Aubry model intermediate "critical" states have been reported for a potential strength value λ = 2 and for an incommensurate modulation. We show here novel "packeted" states for λ ≠ 2 and for both commensurate and incommensurate modulations that appear at band edges. Packeted structures have also been observed in disordered models for certain values of the parameters.