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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 randommatrix (PBRM) model at criticality with one channel attached to it. We findthat ${\cal P}(\Phi)$ is insensitive to the position of the channel andundergoes a transition towards uniformity as the bandwidth $b$ of the PBRMmodel increases. The inverse moments of Wigner delay times scale as$<\tau_W^{-q} >\sim L^{- q D_{q+1}}$, where $D_q$ are the multifractaldimensions of the eigenfunctions of the corresponding closed system and $L$ isthe system size. The latter scaling law is sensitive to the position of thechannel.Comment: 5 pages, 4 figure

Probing the eigenfunction fractality using Wigner delay times