Two dimensional electron gas driven by strong alternating electric field

2D Fermi liquid driven by uniform alternating electric field at zero temperature may remain in quantum coherent non-equilibrium state. We develop a quasistatic approximation for strong and slow ac-fields and solve the problem of driven disordered 2D electron gas in high non-overlapping Landau levels. The broadening of Landau level has the Lorentz form and is inversely proportional to the amplitude of the ac-field. In the absence of electron-phonon interaction the electron distribution function is constant within the last Landau level and the diagonal dc-conductivity is zero. For weak electron-phonon interaction the dc-conductivity is anisotropic. A kinetic transition from the phonon cooling to the phonon heating is predicted.