Assuming that the force constants scale as σ(λx) = λ –α σ(x), we construct the model of elastic (linear) excitations on a fractal (fractons). We show that the fractons on a specific class of fractals, “net fractals”, can be assumed to be log-scale phonons. Further, we discuss the model of fracton mediated superconductivity in the “net fractal” systems). We show that with the use of logarithmic coordinates, the fracton mediated superconductivity can be described within a model which is reminiscent of the conventional BCS formulation.
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