Finite-size scaling analysis of localization transition for scalar waves in a three-dimensional ensemble of resonant point scatterers

Abstract : We use the random Green's matrix model to study the scaling properties of the localization transition for scalar waves in a three-dimensional (3D) ensemble of resonant point scatterers. We show that the probability density p(g) of normalized decay rates of quasimodes g is very broad at the transition and in the localized regime and that it does not obey a single-parameter scaling law for finite system sizes that we can access. The single-parameter scaling law holds, however, for the small-g part of p(g) which we exploit to estimate the critical exponent ν of the localization transition. Finite-size scaling analysis of small-q percentiles g_q of p(g) yields an estimate ν≃1.55±0.07. This value is consistent with previous results for the Anderson transition in the 3D orthogonal universality class and suggests that the localization transition under study belongs to the same class.