Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons

We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1/t.