Friction forces arising from fluctuating thermal fields

We calculate the damping of a classical oscillator induced by the electromagnetic field generated by thermally fluctuating currents in the environment. The fluctuation-dissipation theorem is applied to derive the linear-velocity damping coefficient γ. It turns out that γ is the result of fourth-order correlation functions. The theory is applied to a particle oscillating parallel to a flat substrate and numerical values for γ are evaluated for particle and substrate materials made of silver and glass. We find that losses are much higher for dielectric materials than for metals because of the higher resistivity. We predict that measurements performed on metal films are strongly affected by the underlying dielectric substrate and we show that our theory reproduces existing theoretical results in the nonretarded limit. The theory provides an explanation for the observed distance-dependent damping in shear-force microscopy and it gives guidance for future experiments. Also, the theory should be of importance for the design of nanoscale mechanical systems and for understanding the trade-offs of miniaturization.