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 (In chi(-1))proportional toln(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.