  We theoretically study the frictional damping of a small probe object on a
coated planar surface, analyzing the resulting phonon modes via a theory of
viscoelasticity. Three different types of excitations are found to contribute
to friction in distinct ways: traveling (3D) spherical waves, traveling (2D)
surface waves, and evanescent waves. While traveling waves transport energy
away from the probe, determined by long range elastic properties (wavelength),
evanescent waves transform energy into heat in a near-field range,
characterized by the size of the probe. Thus, fundamentally different behaviors
are predicted, depending on coating thickness and material properties.
