Casimir Force Between Real Boundaries: Contributions of Mechanical and Electrical Imperfections

Abstract

In this report the corrections to the Casimir force due to non-ideality of the geometrical and electrical properties of the boundary bodies are discussed. Such corrections must be taken into account in experiments on measuring the Casimir force and in some applications of the Casimir effect (e.g., in obtaining of constraints on the parameters of hypothetical long-range interactions [1, 2]). At first the known results were reminded on the Casimir force between the dielectrical plates [3] and the plates made of real metal [4] . The corrections due to the penetration of zero oscillations into the metal were calculated up to the second order in the relative penetration depth. Both the cases of normal and anomalous skin effects were considered. Also the corrections due to the dielectrical layers on the surfaces of real metal were demonstrated. The most important subject of the report is the presentation of the new general perturbative approach to the calculation of the corrections to the Casimir force for configurations with small deviations from the plane parallel geometry [5, 6] . Here all the corrections are obtained up to the fourth order in the relative deviations amplitudes. The cases of nonparallel plates, of plates with a large scale unevenness and of plates with short scale distortions which may be both periodical and nonperiodical are considered. The continuous transition is traced numerically between the cases of large scale and short scale deviations. The developed approach was applied in [7] to configurations of a spherical lens above a plane and of two crossed cylinders which are used in experiments on Casimir force measurements.