Quantum Cherenkov radiation at the motion of a small neutral particle parallel to the surface of a transparent dielectric

Quantum Cherenkov radiation and quantum friction at the motion of a small neutral particle parallel to the surface of a transparent dielectric with the refractive index $n$ have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, $v>v_c=c/n$. The friction force in the particle-plate configuration has been derived from the friction force in the plate-plate configuration under the assumption that one of the plates is significantly decharged. A decrease in the kinetic energy of the particle near the threshold velocity is due to its radiation and near the speed of light is determined by the heat power absorbed by the particle in the rest frame. The powers of quantum and classical Cherenkov radiation can be comparable in the relativistic case.