Dynamical properties of the Anderson localization model in the short-time critical regime

We studied the transport properties of the Anderson localization model for a disordered metal using a new numerical method in which the time evolution of the current in response to a constant electric field which is turned on abruptly at t=0 is calculated directly. We report results on the current response of a sample of ${128}^2$ sites in the one-orbital-per-site Anderson model near the metal-insulator transition. We find the current response out to times of the order of 1000 times the inverse bandwidth. We discuss scaling and the values of the critical exponents ν and z (usually thought to be 3).