Casimir Energies: Temperature Dependence, Dispersion, and Anomalies

Assuming the conventional Casimir setting with two thick parallel perfectly conducting plates of large extent with a homogeneous and isotropic medium between them, we discuss the physical meaning of the electromagnetic field energy $W_{\rm disp}$ when the intervening medium is weakly dispersive but nondissipative. The presence of dispersion means that the energy density contains terms of the form $d[\omega\epsilon(\omega)] /d\omega$ and $d[\omega\mu(\omega)] /d\omega$. We find that, as $W_{\rm disp}$ refers thermodynamically to a non-closed physical system, it is {\it not} to be identified with the internal thermodynamic energy $U$ following from the free energy $F$, or the electromagnetic energy $W$, when the last-mentioned quantities are calculated without such dispersive derivatives. To arrive at this conclusion, we adopt a model in which the system is a capacitor, linked to an external self-inductance $L$ such that stationary oscillations become possible. Therewith the model system becomes a non-closed one. As an introductory step, we review the meaning of the nondispersive energies, $F, U,$ and $W$. As a final topic, we consider an anomaly connected with local surface divergences encountered in Casimir energy calculations for higher spacetime dimensions, $D>4$, and discuss briefly its dispersive generalization. This kind of application is essentially a generalization of the treatment of Alnes {\it et al.} [J. Phys. A: Math. Theor. {\bf 40}, F315 (2007)] to the case of a medium-filled cavity between two hyperplanes.Comment: 15 pages, no figures; slight revision of discussio

Casimir effect with rough metallic mirrors

We calculate the second order roughness correction to the Casimir energy for two parallel metallic mirrors. Our results may also be applied to the plane-sphere geometry used in most experiments. The metallic mirrors are described by the plasma model, with arbitrary values for the plasma wavelength, the mirror separation and the roughness correlation length, with the roughness amplitude remaining the smallest length scale for perturbation theory to hold. From the analysis of the intracavity field fluctuations, we obtain the Casimir energy correction in terms of generalized reflection operators, which account for diffraction and polarization coupling in the scattering by the rough surfaces. We present simple analytical expressions for several limiting cases, as well as numerical results that allow for a reliable calculation of the roughness correction in real experiments. The correction is larger than the result of the Proximity Force Approximation, which is obtained from our theory as a limiting case (very smooth surfaces).Comment: 16 page

Casimir interaction between plane and spherical metallic surfaces

We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the non trivial situation where the sphere radius $R$, the plane-sphere distance $L$ and the plasma wavelength $\lambda_\P$ have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of $L/R$. For metallic nanospheres where $R, L$ and $\lambda_\P$ have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation (PFA) and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments performed with spheres of large radius $R\gg L$.Comment: 4 pages, new presentation (highlighting the novelty of the results) and added references. To appear in Physical Review Letter

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

Movement and Fluctuations of the Vacuum

Quantum fields possess zero-point or vacuum fluctuations which induce mechanical effects, namely generalised Casimir forces, on any scatterer. Symmetries of vacuum therefore raise fundamental questions when confronted with the principle of relativity of motion in vacuum. The specific case of uniformly accelerated motion is particularly interesting, in connection with the much debated question of the appearance of vacuum in accelerated frames. The choice of Rindler representation, commonly used in General Relativity, transforms vacuum fluctuations into thermal fluctuations, raising difficulties of interpretation. In contrast, the conformal representation of uniformly accelerated frames fits the symmetry properties of field propagation and quantum vacuum and thus leads to extend the principle of relativity of motion to uniform accelerations. Mirrors moving in vacuum with a non uniform acceleration are known to radiate. The associated radiation reaction force is directly connected to fluctuating forces felt by motionless mirrors through fluctuation-dissipation relations. Scatterers in vacuum undergo a quantum Brownian motion which describes irreducible quantum fluctuations. Vacuum fluctuations impose ultimate limitations on measurements of position in space-time, and thus challenge the very concept of space-time localisation within a quantum framework. For test masses greater than Planck mass, the ultimate limit in localisation is determined by gravitational vacuum fluctuations. Not only positions in space-time, but also geodesic distances, behave as quantum variables, reflecting the necessary quantum nature of an underlying geometry.Comment: 17 pages, to appear in Reports on Progress in Physic