Superlocalization of Electrons and Waves in Fractal Media

摘要: We show that impurity quantum states and Anderson localized exhibit "superlocalization" in fractal media, is their wave function decays faster than exponentially with distance. More precisely, the at large distances like exp [- |x|a] a > 1. In specific case of percolation problem concentration pc, we argue ≈ 1.9 for d = 3. Analogous results hold waves. Applications are suggested to disordered amorphous materials porous materials.