Temperature dependence of the Casimir effect between metallic mirrors

TLDR

The study calculates the Casimir force and free energy for plane metallic mirrors at nonzero temperature. The authors perform numerical evaluations treating temperature and conductivity effects simultaneously, then compare the results with an approximation that multiplies independent corrections. They find that the deviation between exact and approximated results is a temperature‑dependent function with an analytical expression, enabling simple estimations accurate to within 1 %.

Abstract

We calculate the Casimir force and free energy for plane metallic mirrors at nonzero temperature. Numerical evaluations are given with temperature and conductivity effects treated simultaneously. The results are compared with the approximation where both effects are treated independently and the corrections simply multiplied. The deviation between the exact and approximated results takes the form of a temperature dependent function for which an analytical expression is given. The knowledge of this function allows simple estimations that are accurate below the 1% level.