Analytical and numerical verification of the Nernst theorem for metals

Høye, Johan S.; Brevik, Iver; Ellingsen, Simen Å.; Aarseth, J. B.

doi:10.1103/physreve.75.051127

Cited by 101 publications

(133 citation statements)

References 31 publications

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“…The situation is summarized in recent reviews [31,32]. In particular, the lack of a thermodynamic inconsistency has been conclusively demonstrated [33,34], by showing that the free energy for a Casimir system made from real metal plates with impurities has a quadratic temperature dependence at low temperature. Further evidence for the validity of the notion of excluding the TE zero mode for metals comes from the recent work of Buenzli and Martin [35], corroborating earlier work by these authors and others [36,37], who show from a microscopic viewpoint that the high-temperature behavior of the Casimir force is half that of an ideal metal, a rather conclusive demonstration that the TE zero mode is not present.…”

Section: Introductionmentioning

confidence: 99%

Casimir energies: Temperature dependence, dispersion, and anomalies

Brevik

Milton

2008

Phys. Rev. E

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Assuming the conventional Casimir setting with two thick parallel perfectly conducting plates of large extent with a homogeneous and isotropic medium between them, we discuss the physical meaning of the electromagnetic field energy W disp when the intervening medium is weakly dispersive but nondissipative. The presence of dispersion means that the energy density contains terms of the form d[ωε(ω)]/dω and d[ωµ(ω)]/dω. We find that, as W disp refers thermodynamically to a non-closed physical system, it is not to be identified with the internal thermodynamic energy U following from the free energy F , or the electromagnetic energy W , when the last-mentioned quantities are calculated without such dispersive derivatives. To arrive at this conclusion, we adopt a model in which the system is a capacitor, linked to an external self-inductance L such that stationary oscillations become possible. Therewith the model system becomes a non-closed one. As an introductory step, we review the meaning of the nondispersive energies, F, U, and W . As a final topic, we consider an anomaly connected with local surface divergences encountered in Casimir energy calculations for higher spacetime dimensions, D > 4, and discuss briefly its dispersive generalization. This kind of application is essentially a generalization of the treatment of Alnes et al. [J. Phys. A: Math. Theor. 40, F315 (2007)] to the case of a medium-filled cavity between two hyperplanes.

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Section: Introductionmentioning

confidence: 99%

Casimir energies: Temperature dependence, dispersion, and anomalies

Brevik

Milton

2008

Phys. Rev. E

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“…A similar calculation is subsequently performed for the TE mode, which extends that of Ref. [23] in several ways: We allow for the conductivity to be small; we work out one further order of the temperature correction to the free energy; and we allow, for generality, the permittivity to have a finite dielectric constant term in addition to the Drude-type dielectric response due to free charges.…”

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confidence: 99%

Temperature correction to Casimir-Lifshitz free energy at low temperatures: Semiconductors

Ellingsen¹,

Brevik²,

Høye³

et al. 2008

Phys. Rev. E

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The Casimir force and free energy at low temperatures have been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is new. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the analytic results. . The zero-temperature Casimir-Lifshitz theory seems to have been confirmed to 1% accuracy over a range from 100 nm to a micrometer [4,5,6,7,8,9,10,11,12].

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“…Ideal crystals can be seen as the limit of no relaxation ν → 0. We have shown very accurately, both analytically and numerically [2] -cf. also Refs.…”

mentioning

confidence: 87%

“…[2] was that the relaxation frequency ν stays finite at any temperature including T = 0. At low temperatures we expect ν to be smaller than at room temperature; this changes our results quantitatively but not qualitatively.…”

mentioning

confidence: 99%