  It is now possible to study experimentally the combined effect of disorder
and interactions in cold atom physics. Motivated by these developments we
investigate the dynamics around the metal-insulator transition (MIT) in a
one-dimensional (1D) Fermi gas with short-range interactions in a quasiperiodic
potential by the time-dependent density-matrix renormalization group (tDMRG)
technique. By tuning disorder and interactions we study the MIT from the weakly
to the strongly interacting limit. The MIT is not universal as time evolution,
well described by a process of anomalous diffusion, depends qualitatively on
the interaction strength. By using scaling ideas we relate the parameter that
controls the diffusion process with the critical exponent that describes the
divergence of the localization length. In the limit of strong interactions
theoretical arguments suggest that the motion at the MIT tends to ballistic and
critical exponents approach mean-field predictions.
