The Casimir force at high temperature

Abstract

The standard expression of the high-temperature Casimir force between perfect\nconductors is obtained by imposing macroscopic boundary conditions on the\nelectromagnetic field at metallic interfaces. This force is twice larger than\nthat computed in microscopic classical models allowing for charge fluctuations\ninside the conductors. We present a direct computation of the force between two\nquantum plasma slabs in the framework of non relativistic quantum\nelectrodynamics including quantum and thermal fluctuations of both matter and\nfield. In the semi-classical regime, the asymptotic force at large slab\nseparation is identical to that found in the above purely classical models,\nwhich is therefore the right result. We conclude that when calculating the\nCasimir force at non-zero temperature, fluctuations inside the conductors can\nnot be ignored.\n