Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional   lattice II
  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. 
A. R. Kolovsky, I. Chesnokov, and G. Mantica
quant-ph