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

Disordered Systems and Neural Networks