What happens to the quantum Hall effect when magnetic-field-induced spin-density wave moves

The influence of the motion of a magnetic-field-induced spin-density wave (FISDW) on the quantum Hall effect in a quasi-one-dimensional conductor is studied theoretically. In the ideal case of a free FISDW, it is found that the counterflow of the FISDW precisely cancels the quantum Hall current, so the resultant Hall conductivity is zero. In real systems, the Hall conductivity should vanish at the high frequencies, where the pinning and the damping can be neglected, and the dynamics of the FISDW is dominated by inertia.