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 of normalized decay rates of quasimodes 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- part of which we exploit to estimate the critical exponent of the localization transition. Finite-size scaling analysis of small- percentiles of yields an estimate . 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.
3 More- Received 23 May 2016
- Revised 1 August 2016
DOI:https://doi.org/10.1103/PhysRevB.94.064202
©2016 American Physical Society