Analytic approach to the thermal Casimir force between metal and dielectric

Details Analytic approach to the thermal Casimir force between metal and dielectric Analytic approach to the thermal Casimir force between metal and dielectric

2007-04-28

arxiv.org/abs/0704.3818v1

Annals of Physics, v.323, p.291-316 (2008).

Physics

Quantum Physics

34 pages, 3 figures, elsart.cls is used, to appear in Ann. Phys. (N.Y.), 2007

Scientific paper

10.1016/j.aop.2007.04.005

The analytic asymptotic expressions for the Casimir free energy, pressure and entropy at low temperature in the configuration of one metal and one dielectric plate are obtained. For this purpose we develop the perturbation theory in a small parameter proportional to the product of the separation between the plates and the temperature. This is done using both the simplified model of an ideal metal and of a dielectric with constant dielectric permittivity and for the realistic case of the metal and dielectric with frequency-dependent dielectric permittivities. The analytic expressions for all related physical quantities at high temperature are also provided. The obtained analytic results are compared with numerical computations and good agreement is found. We demonstrate for the first time that the Lifshitz theory, when applied to the configuration of metal-dielectric, satisfies the requirements of thermodynamics if the static dielectric permittivity of a dielectric plate is finite. If it is infinitely large, the Lifshitz formula is shown to violate the Nernst heat theorem. The implications of these results for the thermal quantum field theory in Matsubara formulation and for the recent measurements of the Casimir force between metal and semiconductor surfaces are discussed.

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