  The surface roughness correction to the near-field heat transfer between two
rough bulk materials is discussed by using second-order perturbation theory.
The results allow for estimating the impact of surface roughness to the heat
transfer in recent experiments between two plates and between a microsphere and
a plate (using the Derjaguin approximation). Furthermore, we show that the
proximity approximation for describing rough surfaces is valid for distances
much smaller than the correlation length of the surface roughness even if the
heat transfer is dominated by the coupling of surface modes.

Mesoscale and Nanoscale Physics;Quantum Physics