Localization Exponents of Waves in Percolation Systems

Abstract

The asymptotic behavior of localized wave functions of fractons and electrons in bond-percolation systems is investigated numerically by calculating the system-size dependence of the conductance. It is found that two-dimensional (2d) fracton wave functions are superlocalized with d_φ=1.26±0.02, where d_φ is the exponent indicating the strength of localization, while localized electronic states in 2d percolation systems decay exponentially (d_φ=1).