On the Temperature Dependence of the Casimir Effect

The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences with the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being consistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on {\it ad hoc} assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.Comment: 14 pages, 3 eps figures, revtex4. New version includes clarifications and new reference. Accepted for publication in Phys. Rev.

What is the Temperature Dependence of the Casimir Effect?

There has been recent criticism of our approach to the Casimir force between real metallic surfaces at finite temperature, saying it is in conflict with the third law of thermodynamics and in contradiction with experiment. We show that these claims are unwarranted, and that our approach has strong theoretical support, while the experimental situation is still unclear.Comment: 6 pages, REVTeX, final revision includes two new references and related discussio

Analytical and Numerical Demonstration of How the Drude Dispersive Model Satisfies Nernst's Theorem for the Casimir Entropy

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersive model, assuming the relaxation is nonzero at zero temperature (which is the case when impurities are present), gives consistent results for the Casimir free energy at low temperatures. Specifically, we find that the free energy consists essentially of two terms, one leading term proportional to T^2, and a next term proportional to T^{5/2}. Both these terms give rise to zero Casimir entropy as T -> 0, thus in accordance with Nernst's theorem.Comment: 11 pages, 4 figures; minor changes in the discussion. Contribution to the QFEXT07 proceedings; matches version to be published in J. Phys.

Calculation of the Casimir Force between Similar and Dissimilar Metal Plates at Finite Temperature

The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu, or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T=300 K and T=350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.Comment: 23 latex pages, 12 figures. Introductory section expanded, 4 new references. To appear in J. Phys. A: Math. Ge

Casimir Force on Real Materials - the Slab and Cavity Geometry

We analyse the potential of the geometry of a slab in a planar cavity for the purpose of Casimir force experiments. The force and its dependence on temperature, material properties and finite slab thickness are investigated both analytically and numerically for slab and walls made of aluminium and teflon FEP respectively. We conclude that such a setup is ideal for measurements of the temperature dependence of the Casimir force. By numerical calculation it is shown that temperature effects are dramatically larger for dielectrics, suggesting that a dielectric such as teflon FEP whose properties vary little within a moderate temperature range, should be considered for experimental purposes. We finally discuss the subtle but fundamental matter of the various Green's two-point function approaches present in the literature and show how they are different formulations describing the same phenomenon.Comment: 24 pages, 11 figures; expanded discussion, one appendix added, 1 new figure and 10 new references. To appear in J. Phys. A: Math. Theo

Thermal corrections to the Casimir effect

The Casimir effect, reflecting quantum vacuum fluctuations in the electromagnetic field in a region with material boundaries, has been studied both theoretically and experimentally since 1948. The forces between dielectric and metallic surfaces both plane and curved have been measured at the 10 to 1 percent level in a variety of room-temperature experiments, and remarkable agreement with the zero-temperature theory has been achieved. In fitting the data various corrections due to surface roughness, patch potentials, curvature, and temperature have been incorporated. It is the latter that is the subject of the present article. We point out that, in fact, no temperature dependence has yet been detected, and that the experimental situation is still too fluid to permit conclusions about thermal corrections to the Casimir effect. Theoretically, there are subtle issues concerning thermodynamics and electrodynamics which have resulted in disparate predictions concerning the nature of these corrections. However, a general consensus has seemed to emerge that suggests that the temperature correction to the Casimir effect is relatively large, and should be observable in future experiments involving surfaces separated at the few micrometer scale.Comment: 21 pages, 9 eps figures, uses iopart.cls. Final version to be published in New Journal of Physics, contains Conclusion and clarified remark

Casimir energy and entropy between dissipative mirrors

We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T->0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.Comment: 8 pages, 1 figur

Present status of controversies regarding the thermal Casimir force

It is well known that, beginning in 2000, the behavior 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, the theoretical considerations based on the principles of thermodynamics and new experimental tests were invoked. We analyze 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.Comment: 14 pages, 1 figure, iopart.cls is used, to appear in J. Phys. A (special issue: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005