Erratum: Exact surface impedance formulation of the Casimir force: Application to spatially dispersive metals [Phys. Rev. A<b>68</b>, 052103 (2003)]

It is well known that, beginning in 2000, the behaviour of the thermal correction to the Casimir force between real metals has been hotly debated. As was shown by several research groups, the Lifshitz theory, which provides the theoretical foundation for the calculation of both the van der Waals and Casimir forces, leads to different results depending on the model of metal conductivity used. To resolve these controversies, theoretical considerations based on the principles of thermodynamics and new experimental tests were invoked. We analyse the present status of the problem (in particular, the advantages and disadvantages of the approaches based on the surface impedance and on the Drude model dielectric function) using rigorous analytical calculations of the entropy of a fluctuating field. We also discuss the results of a new precise experiment on the determination of the Casimir pressure between two parallel plates by means of a micromechanical torsional oscillator.

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“…(This is in fact the case as long as |ε(ω)| 1.) Some authors (see, e.g., [12,27]) introduce the so-called 'exact' impedances…”

Section: Do the 'Exact' Impedances Lead To The Same Results As The Drumentioning

confidence: 99%

Present status of controversies regarding the thermal Casimir force

Mostepanenko

Bezerra

Decca

et al. 2006

J. Phys. A: Math. Gen.

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“…The contribution of the surface plasmon for Au of about 2% at a separation z = λ p = 137 nm, obtained in recent Ref. [49], is explained by the use in [49] of the spatially nonlocal dielectric permittivity in the frequency region of infrared optics where it is in fact local [41,42,46] (we would like to point out that at the separation z = λ p the characteristic frequency of the Casimir effect is equal not to ω p , as one might expect, but ω p /(4π)]. As a result, the surface plasmons do not give any contribution to the Casimir force in the experimental configuration of Ref.…”

Section: Experimental Precision In the Casimir Force Measure-mentmentioning

confidence: 99%

Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision

2004

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We compare theory and experiment in the Casimir force measurement between gold surfaces performed with the atomic force microscope. Both random and systematic experimental errors are found leading to a total absolute error equal to 8.5 pN at 95% confidence. In terms of the relative errors, experimental precision of 1.75% is obtained at the shortest separation of 62 nm at 95% confidence level (at 60% confidence the experimental precision of 1% is confirmed at the shortest separation). An independent determination of the accuracy of the theoretical calculations of the Casimir force and its application to the experimental configuration is carefully made. Special attention is paid to the sample-dependent variations of the optical tabulated data due to the presence of grains, contribution of surface plasmons, and errors introduced by the use of the proximity force theorem. Nonmultiplicative and diffraction-type contributions to the surface roughness corrections are examined. The electric forces due to patch potentials resulting from the polycrystalline nature of the gold films are estimated. The finite size and thermal effects are found to be negligible. The theoretical accuracy of about 1.69% and 1.1% are found at a separation 62 nm and 200 nm, respectively. Within the limits of experimental and theoretical errors very good agreement between experiment and theory is confirmed characterized by the root mean square deviation of about 3.5 pN within all measurement range. The conclusion is made that the Casimir force is stable relative to variations of the sample-dependent optical and electric properties, which opens new opportunities to use the Casimir effect for diagnostic purposes.

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“…Reflection properties of metals can be described with the surface impedances Z s (ω, q) and Z p (ω, q) [31,32], which can be expressed via the nonlocal dielectric functions. For the anomalous skin effect these impedances were found in [30] (see also [27]).…”

Section: Entropy In the Low-temperature Limitmentioning

confidence: 99%

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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Erratum: Exact surface impedance formulation of the Casimir force: Application to spatially dispersive metals [Phys. Rev. A68, 052103 (2003)]

Cited by 41 publications

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Present status of controversies regarding the thermal Casimir force

Present status of controversies regarding the thermal Casimir force

Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision

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

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