Analytic approach to the thermal Casimir force between metal and dielectric

Journal Article · Fri Feb 15 04:00:00 EST 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.04.005· OSTI ID:21077681

Geyer, B ^[1]; Klimchitskaya, G L ^[1]; Mostepanenko, V M ^[1]

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1. Center of Theoretical Studies and Institute for Theoretical Physics, Leipzig University, Augustusplatz 10/11, D-04109 Leipzig (Germany)

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.

• OSTI ID: 21077681
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 323; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
CALCULATION METHODS
CASIMIR EFFECT
DIELECTRIC MATERIALS
ENTROPY
FREE ENERGY
FREQUENCY DEPENDENCE
METALS
NERNST HEAT THEOREM
PERMITTIVITY
PERTURBATION THEORY
PLATES
QUANTUM FIELD THEORY
SEMICONDUCTOR MATERIALS
TEMPERATURE DEPENDENCE
THERMODYNAMICS