Anderson Transition for Classical Transport in Composite Materials.

Abstract

The Anderson transition in solids and optics is a wave phenomenon where disorder induces localization of the wave functions. We find here that the hallmarks of the Anderson transition are exhibited by classical transport at a percolation threshold-without wave interference or scattering effects. As long range order or connectedness develops, the eigenvalue statistics of a key random matrix governing transport cross over toward universal statistics of the Gaussian orthogonal ensemble, and the field eigenvectors delocalize. The transition is examined in resistor networks, human bone, and sea ice structures.