dorsal/arxiv
View SchemaThermal quantum field theory and the Casimir interaction between dielectrics
| Authors | B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510054 |
| URL | https://arxiv.org/abs/quant-ph/0510054 |
| DOI | 10.1103/PhysRevD.72.085009 |
| Journal | Phys.Rev. D72 (2005) 085009 |
Abstract
The Casimir and van der Waals interaction between two dissimilar thick dielectric plates is reconsidered on the basis of thermal quantum field theory in Matsubara formulation. We briefly review two main derivations of the Lifshitz formula in the framework of thermal quantum field theory without use of the fluctuation-dissipation theorem. A set of special conditions is formulated under which these derivations remain valid in the presence of dissipation. The low-temperature behavior of the Casimir and van der Waals interactions between dissimilar dielectrics is found analytically from the Lifshitz theory for both an idealized model of dilute dielectrics and for real dielectrics with finite static dielectric permittivities. The free energy, pressure and entropy of the Casimir and van der Waals interactions at low temperatures demonstrate the same universal dependence on the temperature as was previously discovered for ideal metals. The entropy vanishes when temperature goes to zero proving the validity of the Nernst heat theorem. This solves the long-standing problem on the consistency of the Lifshitz theory with thermodynamics in the case of dielectric plates. The obtained asymptotic expressions are compared with numerical computations for both dissimilar and similar real dielectrics and found to be in excellent agreement. The role of the zero-frequency term in Matsubara sum is investigated in the case of dielectric plates. It is shown that the inclusion of conductivity in the model of dielectric response leads to the violation of the Nernst heat theorem. The applications of this result to the topical problems of noncontact atomic friction and the Casimir interaction between real metals are discussed.
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"abstract": "The Casimir and van der Waals interaction between two dissimilar thick\ndielectric plates is reconsidered on the basis of thermal quantum field theory\nin Matsubara formulation. We briefly review two main derivations of the\nLifshitz formula in the framework of thermal quantum field theory without use\nof the fluctuation-dissipation theorem. A set of special conditions is\nformulated under which these derivations remain valid in the presence of\ndissipation. The low-temperature behavior of the Casimir and van der Waals\ninteractions between dissimilar dielectrics is found analytically from the\nLifshitz theory for both an idealized model of dilute dielectrics and for real\ndielectrics with finite static dielectric permittivities. The free energy,\npressure and entropy of the Casimir and van der Waals interactions at low\ntemperatures demonstrate the same universal dependence on the temperature as\nwas previously discovered for ideal metals. The entropy vanishes when\ntemperature goes to zero proving the validity of the Nernst heat theorem. This\nsolves the long-standing problem on the consistency of the Lifshitz theory with\nthermodynamics in the case of dielectric plates. The obtained asymptotic\nexpressions are compared with numerical computations for both dissimilar and\nsimilar real dielectrics and found to be in excellent agreement. The role of\nthe zero-frequency term in Matsubara sum is investigated in the case of\ndielectric plates. It is shown that the inclusion of conductivity in the model\nof dielectric response leads to the violation of the Nernst heat theorem. The\napplications of this result to the topical problems of noncontact atomic\nfriction and the Casimir interaction between real metals are discussed.",
"arxiv_id": "quant-ph/0510054",
"authors": [
"B. Geyer",
"G. L. Klimchitskaya",
"V. M. Mostepanenko"
],
"categories": [
"quant-ph",
"cond-mat.mtrl-sci",
"hep-th"
],
"doi": "10.1103/PhysRevD.72.085009",
"journal_ref": "Phys.Rev. D72 (2005) 085009",
"title": "Thermal quantum field theory and the Casimir interaction between dielectrics",
"url": "https://arxiv.org/abs/quant-ph/0510054"
},
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