Universal superdiffusive modes in charged two dimensional liquids

Using a hydrodynamic approach, we show that charge diffusion in two dimensional Coulomb interacting liquids with broken momentum conservation is intrinsically anomalous. The relaxation governed by an overdamped, superdiffusive plasmon mode. We demonstrate the diffusing particles follow L\'evy flight trajectories, and study collective modes under influence of magnetic fields. latter are shown to slow down process. results argued be relevant electron solids, as well plasmas.