Casimir force between two ideal-conductor walls revisited

Abstract

The high-temperature aspects of the Casimir force between two neutral conducting walls are studied. The mathematical model of "inert" ideal-conductor walls, considered in the original formulations of the Casimir effect, is based on the universal properties of the electromagnetic radiation in the vacuum between the conductors, with zero boundary conditions for the tangential components of the electric field on the walls. This formulation seems to be in agreement with experiments on metallic conductors at room temperature. At high temperatures or large distances, at least, fluctuations of the electric field are present in the bulk and at the surface of a particle system forming the walls, even in the high-density limit: "living" ideal conductors. This makes the enforcement of the inert boundary conditions inadequate. Within a hierarchy of length scales, the high-temperature Casimir force is shown to be entirely determined by the thermal fluctuations in the conducting walls, modelled microscopically by classical Coulomb fluids in the Debye-H\"{u}ckel regime. The semi-classical regime, in the framework of quantum electrodynamics, is studied in the companion letter by P.R.Buenzli and Ph.A.Martin, cond-mat/0506363, Europhys.Lett.72, 42 (2005).