Scattering at the Anderson transition: Power-law banded random matrix model

We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal-insulator transition. We focus on the scaling of Wigner delay times τ and resonance widths Γ . We find that the typical values of τ and Γ (calculated as the geometric mean) scale with the system size L as τ^typ∝L^D₁ and Γ^typ∝L^-(2-D₂) , where D₁ is the information dimension and D₂ is the correlation dimension of eigenfunctions of the corresponding closed system.