Temperature effect in the Casimir attraction of a thin metal film

摘要

The Casimir effect for conductors at arbitrary temperatures is theoreticallystudied. By using the analytical properties of the Green functions and applyingthe Abel-Plan formula to Lifshitz's equation, the Casimir force is presented assum of a temperature dependent and vacuum contributions of the fluctuatingelectromagnetic field. The general results are applied to the system consistingof a bulk conductor and a thin metal film. It is shown that a characteristicfrequency of the thermal fluctuations in this system is proportional to thesquare root of a thickness of the metal film. For the case of the sufficientlyhigh temperatures when the thermal fluctuations play the main role in theCasimir interaction, this leads to the growth of the effective dielectricpermittivity of the film and to a disappearance of the dependence of Casimir'sforce on the sample thickness.