The vibrational dynamics of a general Vicsek fractal with nearest-neighbor interactions has been solved exactly. The most surprising finding of this paper is that the nondegenerate modes are all extended in nature. Furthermore, the nondegenerate modes occur side by side with the persistent degenerate modes, which are superlocalized. There is no single demarcation frequency separating the extended states from the localized states as one would expect in a three-dimensional disordered system.
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Jayanthi et al. (1993) studied this question.
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