dorsal/arxiv
View SchemaCasimir Problem in Spherical Dielectrics: A Quantum Statistical Mechanical Approach
| Authors | I. Brevik, J. B. Aarseth, J. S. Høye |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0111037 |
| URL | https://arxiv.org/abs/quant-ph/0111037 |
Abstract
The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. Whereas F has recently been evaluated for the special case of metals (refractive index n=\infty), here analogous results are presented for dielectrics, and shown graphically when n=2.0. Our calculational method relies upon 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. 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 physical input, invoke the actual dispersion relations. The result of our analysis, based upon adoption of the Drude dispersion relation as the most correct one at low frequencies, is that the zero-frequency TE mode does not contribute for a metal. Accordingly, F turns out in this case to be only one half of the conventional value.
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"abstract": "The Casimir mutual free energy F for a system of two dielectric concentric\nnonmagnetic spherical bodies is calculated, at arbitrary temperatures. Whereas\nF has recently been evaluated for the special case of metals (refractive index\nn=\\infty), here analogous results are presented for dielectrics, and shown\ngraphically when n=2.0. Our calculational method relies upon quantum\nstatistical mechanics. The Debye expansions for the Riccati-Bessel functions\nwhen carried out to a high order are found to be very useful in practice\n(thereby overflow/underflow problems are easily avoided), and also to give\naccurate results even for the lowest values of l. Another virtue of the Debye\nexpansions is that the limiting case of metals becomes quite amenable to an\nanalytical treatment in spherical geometry. We first discuss the zero-frequency\nTE mode problem from a mathematical viewpoint and then, as physical input,\ninvoke the actual dispersion relations. The result of our analysis, based upon\nadoption of the Drude dispersion relation as the most correct one at low\nfrequencies, is that the zero-frequency TE mode does not contribute for a\nmetal. Accordingly, F turns out in this case to be only one half of the\nconventional value.",
"arxiv_id": "quant-ph/0111037",
"authors": [
"I. Brevik",
"J. B. Aarseth",
"J. S. H\u00f8ye"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "Casimir Problem in Spherical Dielectrics: A Quantum Statistical Mechanical Approach",
"url": "https://arxiv.org/abs/quant-ph/0111037"
},
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