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

The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches

The Casimir free energy for a system of two dielectric concentric nonmagnetic spherical bodies is calculated with use of a quantum statistical mechanical method, at arbitrary temperature. By means of this rather novel method, which turns out to be quite powerful (we have shown this to be true in other situations also), we consider first an explicit evaluation of the free energy for the static case, corresponding to zero Matsubara frequency ($n=0$). Thereafter, the time-dependent case is examined. For comparison we consider the calculation of the free energy with use of the more commonly known field theoretical method, assuming for simplicity metallic boundary surfaces.Comment: 31 pages, LaTeX, one new reference; version to appear in Phys. Rev.

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.

The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities

The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The present paper is a continuation of an earlier investigation [Phys. Rev. E {\bf 63}, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index n=infinity). Here, analogous results are presented for dielectrics, for some chosen values of n. Our basic calculational method stems from quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l down to l=1. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as a physical input, invoke the actual dispersion relations. The result of our analysis, based upon the adoption of the Drude dispersion relation at low frequencies, is that the zero-frequency TE mode does not contribute for a real metal. Accordingly, F turns out in this case to be only one half of the conventional value at high temperatures. The applicability of the Drude model in this context has however been questioned recently, and we do not aim at a complete discussion of this issue here. Existing experiments are low-temperature experiments, and are so far not accurate enough to distinguish between the different predictions. We also calculate explicitly the contribution from the zero-frequency mode for a dielectric. For a dielectric, this zero-frequency problem is absent.Comment: 23 pages, LaTeX, 7 ps figures; expanded discussion, especially in Sec. 5. To appear in Phys. Rev.

Casimir Force on a Micrometer Sphere in a Dip: Proposal of an Experiment

The attractive Casimir force acting on a micrometer-sphere suspended in a spherical dip, close to the wall, is discussed. This setup is in principle directly accessible to experiment. The sphere and the substrate are assumed to be made of the same perfectly conducting material.Comment: 11 pages, 1 figure; 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