The Casimir force between metallic mirrors

We analyze the possibility to measure small thermal effects in the Casimir force between metal test bodies in configurations of a sphere above a plate and two parallel plates. For sphere-plate geometry used in many experiments we investigate the applicability of the proximity force approximation (PFA) to calculate thermal effects in the Casimir force and its gradient. It is shown that for real metals the two formulations of the PFA used in the literature lead to relative diff...

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 ...

We compute the Casimir interaction between a plane and a sphere, the configuration employed in the most precise experiments. The scattering formula is developed by taking a suitably chosen plane-wave and multipole basis and is valid for arbitrary values of the sphere radius, inter-plate distance, temperature and arbitrary dielectric functions for both sphere and plate. Our analytical and numerical results for metallic surfaces show a non-trivial interplay between the effects ...

We investigate the thermal Casimir interaction between two magnetodielectric plates made of real materials. On the basis of the Lifshitz theory, it is shown that for diamagnets and for paramagnets in the broad sense (with exception of ferromagnets) the magnetic properties do not influence the magnitude of the Casimir force. For ferromagnets, taking into account the realistic dependence of magnetic permeability on frequency, we conclude that the impact of magnetic properties o...

Within the framework of the Drude dispersive model, we predict an unusual non-monotonous temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk...

We derive modified reflection coefficients for electromagnetic waves in the THz and far infrared range. The idea is based on hydrodynamic boundary conditions for metallic conduction electrons. The temperature-dependent part of the Casimir pressure between metal plates is evaluated. The results should shed light on the "thermal anomaly" where measurements deviate from the standard fluctuation electrodynamics for conducting metals.

The new approach to the theoretical description of the thermal Casimir force between real metals is presented. It uses the plasma-like dielectric permittivity that takes into account the interband transitions of core electrons. This permittivity precisely satisfies the Kramers-Kronig relations. The respective Casimir entropy is positive and vanishes at zero temperature in accordance with the Nernst heat theorem. The physical reasons why the Drude dielectric function, when sub...

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...

It has been known that the Lifshitz theory of the Casimir force comes into conflict with the measurement data if the response of conduction electrons in metals to electromagnetic fluctuations is described by the well tested dissipative Drude model. The same theory is in a very good agreement with measurements of the Casimir force from graphene whose spatially nonlocal electromagnetic response is derived from the first principles of quantum electrodynamics. Here, we propose th...

Starting from the Lifshitz formula for the Casimir force between parallel plates we calculate the difference between the forces at two different settings, one in which the temperature is $T_1=350$ K, the other when $T_2=300$ K. As material we choose gold, and make use of the Drude dispersion relation. Our results, which are shown graphically, should be directly comparable to experiment. As an analogous calculation based upon the plasma dispersion relation leads to a different...