  We show that rotational angles of electrons moving in two dimensions (2D) in
a perpendicular magnetic field can be synchronized by an external microwave
field which frequency is close to the Larmor frequency. The synchronization
eliminates collisions between electrons and thus creates a regime with zero
diffusion corresponding to the zero-resistance states observed in experiments
with high mobility 2D electron gas (2DEG). For long range Coulomb interactions
electrons form a rotating hexagonal Wigner crystal. Possible relevance of this
effect for planetary rings is discussed.
