  We study the critical dynamics of matter waves at the 3D Anderson mobility
edge in cold-atom disorder quench experiments. General scaling arguments are
supported by precision numerics for the spectral function, diffusion
coefficient, and localization length in isotropic blue-detuned speckle
potentials. We discuss signatures of critical slowdown in the time-dependent
central column density of a spreading wave packet, and evaluate the prospects
of observing anomalous diffusion right at criticality.
