Level curvature and metal-insulator transition in 3d Anderson model

The level curvature in the Anderson model on a cubic lattice is numerically investigated as an indicator of the metallic-insulator transition. It is shown that the mean curvature obeys a scaling law in the whole range of the disorder parameter. In the metallic regime, the distribution of rescaled curvatures is found to be well described by a formula proposed by Zakrzewski and Delande for random matrices, implying a relation similar to that by Thouless. In the localized regime the distribution of curvatures is approximated by a log-normal distribution.