Anderson Orthogonality Catastrophe in Disordered Systems

We study the Anderson orthogonality catastrophe (AOC) in finite conductors with diffusive disorder. The disorder averaged logarithm of $\chi$, the overlap between the ground states before and after adding a static impurity, is found to depend nonmonotonically on the disorder. In two dimensions $<\ln\chi^{-1}> \propto \ln^2 N$ in the weak disorder limit, thus showing a stronger dependence on the number of electrons $N$ than in the canonical AOC. A very broad tail of the distribution of $\chi$, found numerically, is a signature of the importance of a few-level statistics at the Fermi energy.