Dynamical localization for Bloch electrons in Magnetic and Electric Fields

We study the time evolution of wave packets of noninteracting electrons in a two-dimensional periodic system in the presence of magnetic and electric fields. The model includes consistently the coupling between Landau levels as well as the periodic and external field contributions. It is shown that the electric field produces localization along its longitudinal direction, this effect is a physical consequence of the quantization of the energy levels with respect to the longitudinal quasi-momentum. For incommensurate orientations of $\mathbf{E}$ relative to the lattice the wave packet becomes localized in both directions.