**Abstract:**
We consider the quantum dynamics of a single particle in the plane
under the influence of a constant perpendicular magnetic and a crossed
electric potential field. For a class of smooth and small potentials we
prove that the Hamiltonian is unitarily equivalent to an effective
Hamiltonian which commutes with the observable of kinetic energy. Further we
discuss the derived quantum network percolation model suggested by Chalker
and Coddington. For the restriction to a cylinder of perimeter 2M we prove
simplicity of the Lyapunov exponents, finiteness of the localization
length and compute the mean Lyapunov exponent by a Thouless formula.