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We review the theory of the Casimir effect using scattering techniques. After years of theoretical efforts, this formalism is now largely mastered so that the accuracy of theory-experiment comparisons is determined by the level of precision…
The impedance boundary condition is used to calculate the Casimir force in configurations of two parallel plates and a shpere (spherical lens) above a plate at both zero and nonzero temperature. The impedance approach allows one to find the…
We consider the Casimir interaction between a cylinder and a hollow cylinder, both conducting, with parallel axis and slightly different radii. The Casimir force, which vanishes in the coaxial situation, is evaluated for both small and…
The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is calculated. The calculation is performed in the framework of covariant perturbation theory with the boundary conditions implemented as…
We consider experiments on measuring the Casimir interaction which have been performed in the last four years. The emphasis is made on measuring differences in the Casimir pressures under a transition of the plate metal from normal to…
We consider the Casimir force including all important corrections to it for the configuration used in a recent experiment employing an atomic force microscope. We calculate the long-range hypothetical forces due to the exchange of light and…
We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly…
In a previous work we formulated a model of semitransparent dielectric surfaces, coupled to the electromagnetic field by means of an effective potential. Here we consider a setup with two dissimilar mirrors, and compute exactly the…
The Casimir effect in graphene systems is reviewed with emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for…
We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from…
Isoelectronic differential force measurements provide a unique opportunity to probe controversial features of the thermal Casimir effect, that are still much debated in the current literature. Isolectronic setups offer two major advantages…
We describe experimental and related theoretical work on the measurement of the Casimir force using semiconductor test bodies. This field of research started in 2005 and several important and interesting results have already been obtained.…
Patch potentials arising from the polycrystalline structure of material samples may contribute significantly to measured signals in Casimir force experiments. Most of these experiments are performed in the sphere-plane geometry, yet, up to…
We develop a spectral representation formalism to calculate the Casimir force in the non-retarded limit, between a spherical particle and a substrate, both with arbitrary local dielectric properties. This spectral formalism allows one to do…
Within the scattering theoretical approach, the Casimir force is obtained numerically by an evaluation of the round trip of an electromagnetic wave between the objects involved. Recently [Hartmann M et al. 2017, Phys. Rev. Lett. 119 043901]…
For non-reciprocal objects in vacuum, the Casimir interaction can become repulsive. Here, we present a comprehensive study for idealized non-reciprocal materials known as perfect electromagnetic conductors (PEMC). The system consists of two…
We review recent developments in the Casimir effect which arises in quantization volumes restricted by material boundaries and in spaces with non-Euclidean topology. The starting point of our discussion is the novel exact solution for the…
The Casimir force between a pair of parallell plates filled with ionic particles is considered. We use a statistical mechanical approach and consider the classical high temperature limit. In this limit the ideal metal result with no…
Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field theoretical methods, we investigate the Casimir interaction between two spherical particles and between a…
The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects' electromagnetic response, the necessary calculations in quantum field theory are most naturally…