  We study the quantum dynamics of a charged particle in a two-dimensional
lattice, subject to constant and homogeneous electric and magnetic fields. We
find that different regimes characterize these motions, depending on a
combination of conditions, corresponding to weak and strong electric field
intensities, rational or irrational directions of the electric field with
respect to the lattice, and small or large values of the magnetic (Peierls)
phase.
