Quantum Cherenkov radiation at the relative sliding of two transparent plates

Quantum Cherenkov radiation and quantum friction at the relative sliding of two transparent plates with the refractive index $n$ have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, $v>v_c=2nc/(n^2+1)$. The contribution from $s$-polarized electromagnetic waves dominates near the threshold velocity. However, in the ultrarelativistic case ($v\to c$), contributions from both polarizations are much larger than those in a nonrelativistic theory and a new contribution from the mixing of waves with different polarizations appears. The numerical results are supplemented by analytical calculations near the threshold velocity and the speed of light.