Macroscopic approach to the Casimir friction force

V. V. Nesterenko, A. V. Nesterenko

*Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
*

**Abstract**
The general formula is derived for the vacuum friction
force between two parallel perfectly flat planes
bounding two material media separated by a vacuum gap
and moving relative to each other with a constant
velocity . The material media are
described in the framework of macroscopic
electrodynamics whereas the nonzero temperature and
dissipation are taken into account by making use of
the Kubo formulae from non-equilibrium statistical
thermodynamics. The formula obtained provides a
rigorous basis for calculation of the vacuum friction
force within the quantum field theory
methods in the condensed matter physics. The revealed
v-dependence of the vacuum friction force proves to
be the following: for zero temperature (T=0) it is
proportional to (v/c)^{3} and for T>0 this force is
linear in v/c.