Retarded dispersion forces in dielectrics at finite temperatures

Abstract

The long-range dispersion forces in a non-uniform dielectric at finite temperature are deduced from the frequency-dependent susceptibility of the electric field and the dielectric constant at imaginary frequency by a method which gives the main results of Lifshitz's treatment and does not use quantum field theory. The fluctuation-dissipation theorem allows one to express the dispersion free energy of an atom in terms of its electric polarizability, and to derive the image force on an atom near a metal surface, or the dispersion force between two atoms in vacuo at any temperature. By considering the relation between the force on an atom outside a dielectric and the state of the field inside the dielectric we derive an expression for the long-range dispersion part of the free energy of the medium, and find the force between two dissolved atoms in a dielectric fluid. The forces are equivalent to a system of Maxwell stresses which can be calculated from the field susceptibilities. A simple classical treatment of the susceptibility then gives the Lifshitz force between two parallel plates of dielectric at close distances.