Electronic friction for a slow impurity in an inhomogeneous metallic system

The stopping power of a metal for a slow structureless impurity varies linearly with projectile velocity. We show that the coefficient of this linear behavior (friction coefficient) is determined exactly in a static ensemble Kohn-Sham scheme, by extension of the Shifted Fermi Surface procedure originally derived for an homogeneous jellium. We prove that the friction coefficient is determined only by local characteristics of the system. The error incurred when adding a spurious non-local contribution is illustrated for a simple 1D model.