Quantum friction between metals in the hydrodynamic regime

Abstract

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