The deviation of the energy position of a delocalized state from the center of Landau level is studied in the framework of the Chalker-Coddington model.It is demonstrated that introducing a weak Landau level mixing results in a shift of the delocalized state up in energy. The mechanism of a levitation is a neighboring -Landau level -assisted resonant tunneling which "shunts" the saddle-points. The magnitude of levitation is shown to be independent of the Landau level number.

We study the falloff of the wave function of an electron in a strong magnetic field and a onedimensional periodic potential with period larger than the magnetic length. If the energy of an electron state is far away from the center of the Landau level, the falloff is described by a simple exponent, i.e. , the logarithm of the wave function depends linearly on the tunneling distance. The characteristic length is proportional to the inverse period of potential and is linear in the reciprocal magnetic field.