Probing the eigenfunction fractality using Wigner delay times -: art. no. 064108

We study numerically the distribution of scattering phases P(Phi) and of Wigner delay times P(tau(W)) for the power-law banded random matrix (PBRM) model at criticality with one channel attached to it. We find that 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 similar to L-q+1(-qD), 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.