T^3/7hopping conductivity in a class of disordered systems

We present a new mechanism which induces a thermally activated hopping-conductivity law exp[−(T0/T)^α], with α close to 1/2 without Coulomb interactions. In fact αŠ=Š3/7 independently of the dimension. We argue that this mechanism solves some old puzzles for systems not too far from percolation threshold such as granular materials and should apply to various systems as long as intercluster tunnelling is negligible. The result relies on the superlocalization property of wave functions on incipient percolation clusters.