Casimir friction between dense polarizable media

Abstract

The present paper-a continuation of our recent series of papers on Casimirfriction for a pair of particles at low relative particle velocity-extends the analysis, so asto include dense media. The situation becomes, in this case, more complex, due to induceddipolar correlations, both within planes and between planes. We show that the structure ofthe problem can be simplified by regarding the two half-planes as a generalized version ofa pair of particles. It turns out that macroscopic parameters, such as permittivity, suffice todescribe the friction, also in the finite density case. The expression for the friction force perunit surface area becomes mathematically well-defined and finite at finite temperature. Wegive numerical estimates and compare them with those obtained earlier by Pendry (1997) andby Volokitin and Persson (2007). We also show in an appendix how the statistical methodsthat we are using correspond to the field theoretical methods more commonly in use. © 2013 by the authors.