We study numerically the distribution of scattering phases ${ \cal P}(\Phi)$ and of Wigner delay times ${ \cal P}(\tau_W)$ for the power-law banded random matrix (PBRM) model at criticality with one channel attached to it. We find that ${ \cal P}(\Phi)$ is insensitive to the position of the channel and undergoes a transition towards uniformity as the bandwidth $b$ of the PBRM model increases. The inverse moments of Wigner delay times scale as $<\tau_W^{ -q} >\sim L^{ - q D_{ q+1}}$, where $D_q$ are the multifractal dimensions of the eigenfunctions of the corresponding closed system and $L$ is the system size. The latter scaling law is sensitive to the position of the channel.
Categories: cond-mat.mes-hall