Casimir friction between dense polarizable media (Q280472)

Summary: The present paper -- a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity (cf. [\textit{J. S. Hø{y}e} and \textit{I. Brevik}, Int. J. Mod. Phys. A 27, No.~15, 1260011, 14 p. (2012; Zbl 1247.74006)]) -- extends the analysis, so as to include dense media. The situation becomes, in this case, more complex, due to induced dipolar correlations, both within planes and between planes. We show that the structure of the problem can be simplified by regarding the two half-planes as a generalized version of a pair of particles. It turns out that macroscopic parameters, such as permittivity, suffice to describe the friction, also in the finite density case. The expression for the friction force per unit surface area becomes mathematically well-defined and finite at finite temperature. We give numerical estimates and compare them with those obtained earlier by \textit{J. B. Pendry} [``Shearing the vacuum -- quantum friction'', J. Phys. Condens. Matter 9, 10301-10320 (1997), \url{doi:10.1088/0953-8984/9/47/001}] and by \textit{A. I. Volokitin} and \textit{B. N. Persson} [``Theory of friction: the contribution from fluctuating electromagnetic field'', J. Phys. Condens. Matter 11, 345--359 (1999), \url{doi:10.1088/0953-8984/11/2/003}]. We also show in an appendix how the statistical methods that we are using correspond to the field theoretical methods more commonly in use.