Quantum friction and van der Waals friction in particle-plate and plate-plate configurations: nonlocal effects

Within the nonrelativistic approximation of fluctuation electrodynamics, using the specular reflection model and nonlocal permittivity of the metal, we have obtained simple analytical expressions for friction forces in particle – plate and plate – plate systems at relative motion of bodies at a constant velocity. It has been shown that at distances of about 1–10 nm for an Au nanoparticle (or gold plate) moving near another (identical) plate at rest, dissipative forces prove to be 2–4 orders of magnitude higher than when using the local Drude dielectric function.