Scattering at the Anderson transition: Power--law banded random matrix model

Abstract

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

6 pages, 8 figures