We study the Casimir-Lifshitz interaction out of thermal equilibrium, when the interacting objects are at different temperatures. The analysis is focused on the surface-surface, surface-rarefied body, and surface-atom configurations. A systematic investigation of the contributions to the force coming from the propagating and evanescent components of the electromagnetic radiation is performed. The large distance behaviors of such interactions is discussed, and both analytical and numerical results are compared with the equilibrium ones. A detailed analysis of the crossing between the surface-surface and the surface-rarefied body, and finally the surface-atom force is shown, and a complete derivation and discussion of the recently predicted nonadditivity effects and asymptotic behaviors is presented.

Precise optical properties of metals are very important for accurate prediction of the Casimir force acting between two metallic plates. Therefore we measured ellipsometrically the optical responses of Au films in a wide range of wavelengths from $0.14\text{to}33\mu \mathrm{m}$. The films at various thicknesses were deposited at different conditions on silicon or mica substrates. Considerable variation of the frequency dependent dielectric function from sample to sample was found. Detailed analysis of the dielectric functions was performed to check the Kramers-Kronig consistency, and extract the Drude parameters of the films. It was found that the plasma frequency varies in the range from $6.8\text{to}8.4\mathrm{eV}$. It is suggested that this variation is related with the film density. X-ray reflectivity measurements support qualitatively this conclusion. The Casimir force is evaluated for the dielectric functions corresponding to our samples, and for that typically used in the precise prediction of the force. The force for our films was found to be 5%–14% smaller at a distance of $100\mathrm{nm}$ between the plates. Noise in the optical data is responsible for the force variation within 1%. It is concluded that prediction of the Casimir force between metals with a precision better than 10% must be based on the material optical response measured from visible to mid-infrared range.

It is shown that a graphene layer on top of a dielectric slab can dramatically influence the ability of this dielectric for radiative heat exchange turning a poor heat emitter/absorber into a good one and vice versa. The effect of graphene is related to thermally excited plasmons. The frequency of these resonances lies in the terahertz region and can be tuned by varying the Fermi level through doping or gating. It makes possible the fast modulation of the heat flux by electrical means, which opens up new possibilities for very fast manipulations with the heat flux. The heat transfer between two dielectrics covered with graphene can be larger than that between best known materials and becomes especially efficient below the room temperature.

We demonstrate here a controllable variation in the Casimir force. Changes in the force of up to $20\%$ at separations of $~$ $100$ nm between Au and Ag-In-Sb-Te (AIST) surfaces were achieved on crystallization of an amorphous sample of AIST. This material is well known for its structural transformation, which produces a significant change in the optical properties and is exploited in optical data storage systems. The finding paves the way to the control of forces in nanosystems, such as micro- or nanoswitches, by stimulating the phase-change transition via localized heat sources.

The surface impedance approach is discussed in connection with the precise calculation of the Casimir force between metallic plates. It allows us to take into account the nonlocal connection between the current density and electric field inside of metals. In general, a material has to be described by two impedances $Z_s(\omega ,q)$ and $Z_p(\omega ,q)$ corresponding to two different polarization states. In contrast with the approximate Leontovich impedance they depend not only on frequency $\omega$ but also on the wave vector along the plate $q$. In this paper only the nonlocal effects happening at frequencies $\omega <{\omega }_p$ (plasma frequency) are analyzed. We refer to all of them as the anomalous skin effect. The impedances are calculated for the propagating and evanescent fields in the Boltzmann approximation. It is found that $Z_p$ significantly deviates from the local impedance as a result of the Thomas-Fermi screening. The nonlocal correction to the Casimir force is calculated at zero temperature. This correction is small but observable at small separations between bodies. The same theory can be used to find more significant nonlocal contribution at $\omega \sim {\omega }_p$ due to the plasmon excitation.

We investigate the force acting between two parallel plates held at different temperatures. The force reproduces, as limiting cases, the well-known Casimir-Lifshitz surface-surface force at thermal equilibrium and the surface-atom force out of thermal equilibrium recently derived by M. Antezza et al., Phys. Rev. Lett. 95, 113202 (2005). The asymptotic behavior of the force at large distances is explicitly discussed. In particular when one of the two bodies is a rarefied gas the force is not additive, being proportional to the square root of the density. Nontrivial crossover regions at large distances are also identified.