Quantum friction between metals in the hydrodynamic regime

In this work, we study the phenomenon of quantum friction in a system consisting on an atom moving at constant speed parallel to metallic plate. We use hydrodynamic model describe degrees freedom clean metal without internal dissipation. polarizable as two-level with unique ($l=0$) ground state and threefold degenerate ($l=1$) excited state. show that frictional force is present even absence intrinsic damping metal, but there threshold relative velocity gives rise such force. particular, find for occur, must move larger than effective sound material, condition can be reached near empty or filled bands, where Fermi (which proportional speed) becomes low. provide analytical arguments result holds all orders perturbation theory.