Surface impedance and the Casimir force

Abstract

The impedance boundary condition is used to calculate the Casimir force in configurations of two parallel plates and a shpere (spherical lens) above a plate at both zero and nonzero temperature. The impedance approach allows one to find the Casimir force between the realistic test bodies regardless of the electromagnetic fluctuations inside the media. Although this approach is an approximate one, it has wider areas of application than the Lifshitz theory of the Casimir force. The general formulas of the impedance approach to the theory of the Casimir force are given and the formal substitution is found for connecting it with the Lifshitz formula. The range of micrometer separations between the test bodies which is interesting from the experimental point of view is investigated in detail. It is shown that at zero temperature the results obtained on the basis of the surface impedance method are in agreement with those obtained in framework of the Lifshitz theory within a fraction of a percent. The temperature correction to the Casimir force from the impedance method coincides with that from the Lifshitz theory up to four significant figures. The case of millimeter separations which corresponds to the normal skin effect is also considered. At zero temperature the obtained results have good agreement with the Lifshitz theory. At nonzero temperature the impedance approach is not subject to the interpretation problems peculiar to the zero-frequency term of the Lifshitz formula in dissipative media.