  This paper studies the quantum dynamics of a charged particle in a 2D square
lattice, under the influence of electric and magnetic fields, the former being
aligned with one of the lattice axes and the latter perpendicular to the
lattice plane. While in free space these dynamics consist of uniform motions in
the direction orthogonal to the electric field vector, we find that, in a
lattice, this directed drift takes place only for specific initial conditions
and for electric field magnitudes smaller than a critical value. Otherwise, the
quantum wave--packet spreads ballistically in both directions orthogonal to the
electric field. We quantify this ballistic spreading and identify the subspace
of initial conditions insuring directed transport with the drift velocity. We
also describe the effect of disorder in the system.
