Temperature correction to the Casimir force in cryogenic range and anomalous skin effect

Svetovoy, V. B.; Lokhanin, M. V.

doi:10.1103/physreva.67.022113

Cited by 56 publications

(66 citation statements)

References 41 publications

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“…It was argued [23] that S is going to zero with T only if the plasma model is used for the n = 0 term. We stressed [25,27] that to analyse the low-temperature behaviour one has to take into consideration the anomalous skin effect. Description of nonlocal metals can be done with two nonlocal dielectric functions [26] or equivalently with two impedances [30], which are known in the theory of metals.…”

Section: Discussionmentioning

confidence: 99%

“…For this reason the results based on the Leontovich approximation [25,34] must be reconsidered. The impedance Z s at a low-temperature approaches its local limit, for which s polarization does not contribute to the n = 0 term in (2).…”

Section: Entropy In the Low-temperature Limitmentioning

confidence: 99%

“…We would like to emphasize that at low-temperatures the anomalous skin effect plays an important role [25] and must be taken into account in any reasonable calculations. Because ω τ decreases fast with the temperature, at a sufficiently low-temperature inevitably the mean free path l = v F /ω τ (T ) for electrons becomes much larger than the field penetration depth δ.…”

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confidence: 99%

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The Casimir free energy in high- and low-temperature limits

Svetovoy

Esquivel

2006

J. Phys. A: Math. Gen.

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The problem with the temperature dependence of the Casimir force is investigated. We analyse high-temperature limit analytically making calculations at real frequencies. The purpose is to answer the question why there is no continuous transition between real and ideal metals and why the result does not depend on the relaxation frequency. It is found that the contribution of evanescent s polarized fields is finite even for an infinitely small relaxation frequency (plasma model) and exactly cancels the contribution of propagating fields. For the ideal metal the evanescent fields do not contribute at all. The lowtemperature limit is analysed to establish behaviour of the entropy at T → 0. It is stressed that the nonlocal effects are important in this limit because the mean free path for electrons becomes larger than the field penetration depth. In this limit v F /a plays the role of the relaxation frequency, where v F is the Fermi velocity and a is the distance between plates. It is indicated that the Leontovich approximate impedance cannot be used for calculations because it is good for the description of propagating but not evanescent fields. It is found that due to nonlocality the Casimir entropy approaches zero at T → 0 when s polarization does not contribute to the classical part of the Casimir force.

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Section: Discussionmentioning

confidence: 99%

Section: Entropy In the Low-temperature Limitmentioning

confidence: 99%

mentioning

confidence: 99%

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The Casimir free energy in high- and low-temperature limits

Svetovoy

Esquivel

2006

J. Phys. A: Math. Gen.

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“…Moreover, for small separations L, as well as for small film thicknesses D < 25 − 30 nm and/or at cryogenic temperatures non-local effects become important also in the normal state [19], and indeed it has been advocated that space dispersion should be taken into account, for example, to evaluate the influence of thin metal coatings, that are used to protect the plates in most of the current experiments on the Casimir effect (see [3] and last of Refs. [19]. The influence of space dispersion on the Casimir effect at room temperature is studied also in the recent paper [20]).…”

Section: Calculation Of the Variation Of Casimir Energy In The Smentioning

confidence: 99%

Variations of Casimir energy from a superconducting transition

et al. 2005

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We consider a five-layer Casimir cavity, including a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the microwave region) of the reflection coefficient of the film produces a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and thus causes a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The proposed scheme might also help clarifying the current controversy about the magnitude of the contribution to Casimir free energy from the TE zero mode, as we find that alternative treatments of this mode strongly affect the shift of critical field.

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“…conductivity run into serious troubles which have been the subject of much controversy [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The key contradiction is on whether the term of the Lifshitz formula [34,35] related to the zero Matsubara frequency for the perpendicular polarized modes of an electromagnetic field contributes to the physical quantities and, if so, how much would its contribution be.…”

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confidence: 99%

Surface-impedance approach solves problems with the thermal Casimir force between real metals

2003

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The surface impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity depending only on frequency is shown to be inapplicable in the frequency region where a real current may arise leading to Joule heating of the metal. The standard concept of a fluctuating electromagnetic field on such frequencies meets difficulties when used as a model for the zero-point oscillations or thermal photons in the thermal equilibrium inside metals. Instead, the surface impedance permits not to consider the electromagnetic oscillations inside the metal but taking the realistic material properties into account by means of the effective boundary condition. An independent derivation of the Lifshitz-type formulas for the Casimir free energy and force between two metal plates is presented within the impedance approach. It is shown that they are free of the contradictions with thermodynamics which are specific to the usual Lifshitz formula for dielectrics in combination with the Drude model. We demonstrate that in the impedance approach the zero-frequency contribution is uniquely fixed by the form of impedance function and does not need any of the ad hoc prescriptions intensively discussed in the recent literature. As an example, the computations of the Casimir free energy between two gold plates (or the Casimir force acting between a plate and a sphere) are performed at different separations and temperatures specific for the regions of the anomalous skin effect and infrared optics. The results are in good agreement with those obtained by the use of the tabulated optical data for the complex refraction index and plasma model. It is argued that the surface impedance approach lays a reliable theoretical framework for the future measurements of the thermal Casimir force.

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Temperature correction to the Casimir force in cryogenic range and anomalous skin effect

Cited by 56 publications

References 41 publications

The Casimir free energy in high- and low-temperature limits

The Casimir free energy in high- and low-temperature limits

Variations of Casimir energy from a superconducting transition

Surface-impedance approach solves problems with the thermal Casimir force between real metals

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