Casimir-Lifshitz force out of thermal equilibrium and asymptotic non-additivity

Mauro Antezza, Lev P. Pitaevskii, Sandro Stringari, Vitaly B. Svetovoy

Published 2006-07-07, updated 2006-11-30Version 2

We investigate the force acting between two parallel plates held at different temperatures. The force reproduces, as limiting cases, the well known Casimir-Lifshitz surface-surface force at thermal equilibrium and the surface-atom force out of thermal equilibrium recently derived by M. Antezza \emph{et al.}, Phys. Rev. Lett. {\bf 95}, 113202 (2005). The asymptotic behavior of the force at large distances is explicitly discussed. In particular when one of the two bodies is a rarefied gas the force is not additive, being proportional to the square root of the density. Nontrivial cross-over regions at large distances are also identified.