Superlocalization of waves and electrons and hopping conductivity on classical and superconductive fractals

We have found an unexpected paradoxical situation in the percolation transition: the superconductive behavior below and above the threshold. We have found also the two different density of states ds=4/3 and dv=1.05 and the inverse localization lengths for fractons with the scalar and vector interactions, respectively. In this concept the wave functions of electrons or waves on an incipient percolation cluster and fractal dilute structure exhibit superlocalization behavior of the form ψ(r)∝exp[−rdφ] with values of dφ1=1.73 and dφ2=2.4 for the former and the latter. Applications of these results for thermally activated hopping conductivity σ(t)∝exp[−(T0/T)β] between impurities on a random fractal structure give the values of β=2/5 for the scalar and β=1/2 (Mottʹs law) for the vector interactions, respectively. Band states are localized in classical and superlocalized in superconductive percolations.