Reply to “Comment on ‘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.77.023102

Cited by 34 publications

(8 citation statements)

References 6 publications

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“…Thus, they pointed out that the Drude model combined with the Lifshitz formula violates the Nernst heat theorem for a perfect crystal lattice and is in contradiction with quantum statistical physics. Høye et al (2008) have argued that the Drude model combined with the Lifshitz formula is thermodynamically consistent in the case of a perfect crystal lattice also. To justify this statement they introduced the definition of a perfect lattice as the limiting case of a crystal lattice with nonzero residual relaxation γ res when γ res → 0.…”

Section: Real Metalsmentioning

confidence: 99%

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The Casimir force between real materials: Experiment and theory

2009

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Section: Real Metalsmentioning

confidence: 99%

“…Specifically, the relaxation parameter turns out to be temperature-dependent and vanishes with vanishing temperature. The definition of a perfect lattice introduced by Høye et al (2008) violates lattice symmetry properties.…”

Section: Real Metalsmentioning

confidence: 99%

The Casimir force between real materials: Experiment and theory

2009

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“…[8,9,10,11,12,13,14]). The zero-temperature contribution to the force, originating from quantum fluctuations of the electromagnetic field, is well understood.…”

Section: Problems Linked To Lifshitz's Theory For the Casimir Forcementioning

confidence: 99%

“…In spite of intensive studies on the Casimir effect, it is surprising that such an important problem as the temperature dependence of this effect is still unclear and is still an issue of lively discussion (see, e.g., Refs. [8,9,10,11,12,13,14]). The zero-temperature contribution to the force, originating from quantum fluctuations of the electromagnetic field, is well understood.…”

Section: Problems Linked To Lifshitz's Theory For the Casimir Forcementioning

confidence: 99%

Temperature dependence of the Casimir force for bulk lossy media

et al. 2010

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We discuss the limitations of the applicability of the Lifshitz formula to describe the temperature dependence of the Casimir force between two bulk lossy metals. These limitations follow from the finite sizes of the interacting bodies. Namely, Lifshitz's theory is not applicable when the characteristic wavelengths of the fluctuating fields, responsible for the temperature-dependent terms in the Casimir force, is longer than the sizes of the samples. As a result of this, the widely discussed linearly decreasing temperature dependence of the Casimir force can be observed only for dirty and/or large metal samples at high enough temperatures. This solves the problem of the inconsistency between the Nernst theorem and the "linearly decreasing temperature dependence" of the Casimir free energy, because this linear dependence is not valid when T → 0.

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“…In this limit, modes with frequencies above k B T /h 'freeze' to their ground state, do not contribute to the entropy, and a unique ground state for the system remains at T = 0. We have checked that the free energies at low T due to eddy currents alone and in the full Lifshitz theory [16,17] coincide in their first two terms (T 2 and T 5/2 ). Another scenario emerges with a T -dependent scattering rate when the ratio ξ L (T )/T vanishes as T → 0.…”

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confidence: 99%

Casimir Interaction from Magnetically Coupled Eddy Currents

Intravaia

Henkel

2009

Phys. Rev. Lett.

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We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasi-static magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state. Spatially diffusive transport is a basic physical phenomenon that has been studied with a wealth of methods. For example, the equation for heat conduction was solved by J. Fourier by his transformation that provided later the framework for quantum field theory. Remarkably, the Fourier modes of the diffusion equation itself,do not fit into a simple quantum field theory because they have purely imaginary frequencies. The quantization of (over)damped modes can be done, however, with an alternative approach, the 'system+bath' paradigm of dissipative quantum dynamics. In this picture, the observables relevant to a mode (specified, e.g., in Fourier space by its wavevector q) are damped in time because they strongly couple to a system with infinitely many degrees of freedom that are not directly accessible ('bath') [1]. The additional fluctuations the bath couples into the system, compensate at equilibrium for dissipative loss[2], even at zero temperature. This implies that a quantity like the zero-point energy of a damped mode is no longer given by the usual 1 2h ω q and must be redefined and reinterpreted. Indeed, the ground state of the combined system+bath is, in general, entangled : the corresponding interaction Hamiltonian is responsible for the change in the zero-point energy relative to the decoupled system [3,4]. Clearly this has an impact on all phenomena connected with fluctuation energy, for which the paradigmatic example is the Casimir effect [5].In this letter we discuss a specific example of 'diffusive modes': eddy (Foucault) currents in two metallic plates [6]. We address their quantum and thermal fluctuations and their role in the electromagnetic Casimir interaction [5]. Similar to the approach of Ref.[7], we isolate the contribution of eddy currents among all other modes. We show that these modes quantitatively reproduce the "unusual features" of the Casimir force between good conductors at finite temperature (as predicted by Lifshitz theory), that have been intensely debated for several years [8,9].To begin with, consider a metallic bulk described by a local dielectric function in Drude form:(Ω: plasma frequency, γ: damping rate). This system allows for a continuum of damped, chargeless modes with a (transverse) current density and (dominantly) magnetic fields at frequencies of order γ or below: they are called 'eddy' or 'Foucault currents' and are at the base of phenomena like magnetic braking or the familiar induction...

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Reply to “Comment on ‘Analytical and numerical verification of the Nernst theorem for metals’ ”

Cited by 34 publications

References 6 publications

The Casimir force between real materials: Experiment and theory

The Casimir force between real materials: Experiment and theory

Temperature dependence of the Casimir force for bulk lossy media

Casimir Interaction from Magnetically Coupled Eddy Currents

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