Lifshitz theory of Casimir forces at finite temperature

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Abstract
We reexamine the Casimir and Lifshitz theories of intermolecular forces at nonzero temperature. For dilute media and atomic interactions, the limits of validity of the London–van der Waals potential between atoms at finite temperature are established by a detailed asymptotic analysis. In the retarded limit, the Casimir-Polder interaction potential is shown to be rigorously correct only in the limit of zero temperature. At any nonzero temperature a different analytic form obtains and is derived. We then consider Casimir forces between perfectly conducting plates. Existing results for the case of intervening vacuum are recovered by a different method. Moreover, we show that the Mellin transform technique and theory of generalized ζ functions allows a detailed asymptotic treatment of a system of perfectly conducting plates with an intervening electron plasma, useful in the modeling of forces between metal plates, where the finite metallic skin depth is an important consideration.