Localization of waves in fractals: Spatial behavior

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Abstract
Localization of a quantum particle on two-dimensional percolating networks is investigated numerically. Solving the time-dependent Schrödinger equation for particular initial wave packets we study the spatial behavior of eigenstates for two tight-binding models: the quantum percolation model and the fracton model. At the lower band edge of the fracton model localization lengths agree with theoretical scaling predictions. We address the question concerning the existence of superlocalization. Our results show no indication for superlocalized behavior of eigenstates.