Using a fully relativistic theory we study the quantum Vavilov-Cherenkov radiation and quantum friction occurring during relative sliding of two transparent dielectric plates with the refractive index $n$. These phenomena occur above the threshold velocity $v_c=2nc/(n^2+1)$. Close to the threshold velocity they are dominated by the contribution from $s$-polarized electromagnetic waves, which agrees with the approximate (relativistic) theory by Pendry [J. B. Pendry, J. Mod. Opt. 45, 2389 (1998)]. However, in the ultrarelativistic case $\left(v\to c\right)$, the contributions from both polarizations are strongly enhanced in comparison with the approximate theory, and a new contribution occurs from the mixing of the electromagnetic waves with different polarizations. The numerical results are supplemented by an analytical treatment close to the threshold velocity and the light velocity.

• Received 19 November 2015

DOI:https://doi.org/10.1103/PhysRevB.93.035407