Casimir problem of spherical dielectrics: Numerical evaluation for general permittivities
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN: 1063-651X, Vol: 66, Issue: 2, Page: 026119
2002
- 43Citations
- 4Captures
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Article Description
The 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 63, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index [formula presented] 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 [formula presented] 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. © 2002 The American Physical Society.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=41349121381&origin=inward; http://dx.doi.org/10.1103/physreve.66.026119; http://www.ncbi.nlm.nih.gov/pubmed/12241249; https://link.aps.org/doi/10.1103/PhysRevE.66.026119; http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevE.66.026119/fulltext; http://link.aps.org/article/10.1103/PhysRevE.66.026119
American Physical Society (APS)
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