dorsal/arxiv
View SchemaMicroscopic theory of the Casimir effect
| Authors | Luca Valeri, Gunter Scharf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502115 |
| URL | https://arxiv.org/abs/quant-ph/0502115 |
Abstract
Based on the photon-exciton Hamiltonian a microscopic theory of the Casimir problem for dielectrics is developed. Using well-known many-body techniques we derive a perturbation expansion for the energy which is free from divergences. In the continuum limit we turn off the interaction at a distance smaller than a cut-off distance $a$ to keep the energy finite. We will show that the macroscopic theory of the Casimir effect with hard boundary conditions is not well defined because it ignores the finite distance between the atoms, hence is including infinite self-energy contributions. Nevertheless for disconnected bodies the latter do not contribute to the force between the bodies. The Lorentz-Lorenz relation for the dielectric constant that enters the force is deduced in our microscopic theory without further assumptions. The photon Green's function can be calculated from a Dyson type integral equation. The geometry of the problem only enters in this equation through the region of integration which is equal to the region occupied by the dielectric. The integral equation can be solved exactly for various plain and spherical geometries without using boundary conditions. This clearly shows that the Casimir force for dielectrics is due to the forces between the atoms. Convergence of the perturbation expansion and the metallic limit are discussed. We conclude that for any dielectric function the transverse electric (TE) mode does not contribute to the zero-frequency term of the Casimir force.
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"abstract": "Based on the photon-exciton Hamiltonian a microscopic theory of the Casimir\nproblem for dielectrics is developed. Using well-known many-body techniques we\nderive a perturbation expansion for the energy which is free from divergences.\nIn the continuum limit we turn off the interaction at a distance smaller than a\ncut-off distance $a$ to keep the energy finite. We will show that the\nmacroscopic theory of the Casimir effect with hard boundary conditions is not\nwell defined because it ignores the finite distance between the atoms, hence is\nincluding infinite self-energy contributions. Nevertheless for disconnected\nbodies the latter do not contribute to the force between the bodies. The\nLorentz-Lorenz relation for the dielectric constant that enters the force is\ndeduced in our microscopic theory without further assumptions.\n The photon Green\u0027s function can be calculated from a Dyson type integral\nequation. The geometry of the problem only enters in this equation through the\nregion of integration which is equal to the region occupied by the dielectric.\nThe integral equation can be solved exactly for various plain and spherical\ngeometries without using boundary conditions. This clearly shows that the\nCasimir force for dielectrics is due to the forces between the atoms.\n Convergence of the perturbation expansion and the metallic limit are\ndiscussed. We conclude that for any dielectric function the transverse electric\n(TE) mode does not contribute to the zero-frequency term of the Casimir force.",
"arxiv_id": "quant-ph/0502115",
"authors": [
"Luca Valeri",
"Gunter Scharf"
],
"categories": [
"quant-ph"
],
"title": "Microscopic theory of the Casimir effect",
"url": "https://arxiv.org/abs/quant-ph/0502115"
},
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