Lifshitz theory of Casimir forces at finite temperature

• 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 non-zero 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 novel method. Moreover, we show that the Mellin transform technique and theory of generalized zeta 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.

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