2016/05/31 by S. E. Skipetrov · 35 citations
Engineering · Mathematics · Physics and Astronomy · #Anderson localization #Condensed matter physics #Exponent #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Random lasers and scattering media #Renormalization group #Scalar (mathematics) #Scaling #Scaling law #Statistical physics #Terahertz technology and applications #Transition point #Universality (dynamical systems) #cond-mat.dis-nn #physics.optics
paper · pdf · doi:10.1103/physrevb.94.064202
published in Physical review. B./Physical review. B 94(6) (American Physical Society) · 11 pages, 10 figures, revised manuscript
openalex created_date 2016/06/24 · arxiv created 2016/08/04 · openalex publication_date 2016/08/23 · arxiv updated 2016/08/30 · openalex updated_date 2026/08/05
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 \ensuremathν of the localization transition. Finite-size scaling analysis of small-q percentiles gq of p(g) yields an estimate \ensuremathν\ensuremath≃1.55\ifmmode±\else\textpm\fi0.07. 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.