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 $\tau$ and resonance widths $\mathrm{\Gamma }$. We found that the typical values of $\tau$ and $\mathrm{\Gamma }$ (calculated as the geometric mean) scale with the system size $L$ as ${\tau }^{typ}\propto L^{D_1}$ and $\Gamma^{\tiny typ} \propto L^{-(2-D_2)}$,where$D_1$istheinformationdimensionand$D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.