Microscopic origin of universality in Casimir forces

Abstract

The microscopic mechanisms for universality of Casimir forces between macroscopic conductors are displayed in a model of classical charged fluids. The model consists of two slabs in empty space at distance $d$ containing classical charged particles in thermal equilibrium (plasma, electrolyte). A direct computation of the average force per unit surface yields, at large distance, the usual form of the Casimir force in the classical limit (up to a factor 2 due to the fact that the model does not incorporate the magnetic part of the force). Universality originates from perfect screening sum rules obeyed by the microscopic charge correlations in conductors. If one of the slabs is replaced by a macroscopic dielectric medium, the result of Lifshitz theory for the force is retrieved. The techniques used are Mayer expansions and integral equations for charged fluids.