The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities

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dc.creatorBrevik, I.
dc.creatorAarseth, J. B.
dc.creatorHøye, J. S.
dc.date2002-01-29
dc.date2002-06-27
dc.date.accessioned2026-07-07T12:17:06Z
dc.date.available2026-07-07T12:17:06Z
dc.descriptionThe Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The present paper is a continuation of an earlier investigation [Phys. Rev. E {\bf 63}, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index n=infinity). Here, analogous results are presented for dielectrics, for some chosen values of n. Our basic calculational method stems from quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l down to l=1. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as a physical input, invoke the actual dispersion relations. The result of our analysis, based upon the adoption of the Drude dispersion relation at low frequencies, is that the zero-frequency TE mode does not contribute for a real metal. Accordingly, F turns out in this case to be only one half of the conventional value at high temperatures. The applicability of the Drude model in this context has however been questioned recently, and we do not aim at a complete discussion of this issue here. Existing experiments are low-temperature experiments, and are so far not accurate enough to distinguish between the different predictions. We also calculate explicitly the contribution from the zero-frequency mode for a dielectric. For a dielectric, this zero-frequency problem is absent.
dc.description23 pages, LaTeX, 7 ps figures; expanded discussion, especially in Sec. 5. To appear in Phys. Rev. E
dc.identifierhttps://arxiv.org/abs/quant-ph/0201137
dc.identifierhttp://arxiv.org/abs/quant-ph/0201137
dc.identifierPhys.Rev.E66:026119,2002
dc.identifierdoi:10.1103/PhysRevE.66.026119
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212010
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleThe Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities
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