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Lifshitz transitions are topological transitions of a Fermi surface, whose signatures typically appear in the conduction properties of a host metal. Here, we demonstrate, using an extended Falicov- Kimball model of a two-flavor fermion…

We generalize the derivative expansion (DE) approach to the interaction between almost-flat smooth surfaces, to the case of surfaces which are optimally described in cylindrical coordinates. As in the original form of the DE, the obtained…

I investigate the finite temperature Casimir effect for a charged and massless scalar field satisfying mixed (Dirichlet-Neumann) boundary conditions on a pair of plane parallel plates of infinite size. The effect of a uniform magnetic…

The frequency spectrum of the Casimir force between two plates separated by vacuum as it appears in the Lifshitz formalism is reexamined and generalised as compared to previous works to allow for imperfectly reflecting plates. As previously…

In this work, we investigate the violation of Lorentz symmetry through the Casimir effect. The Casimir effect is one of the most intriguing aspects of modern physics, representing a macroscopic quantum-origin force between two neutral…

Due to their collective nature Casimir forces can strongly depend on the geometrical shape of the interacting objects. We study the effect of strong periodic shape deformations of two ideal metal plates on their quantum interaction. A…

Using the recently derived representation for the polarization tensor in (2+1)-dimensional space-time allowing an analytic continuation to the entire plane of complex frequencies, we obtain simple analytic expressions for the reflection…

The Casimir force acting between two test bodies made of different metals is considered. The finiteness of the conductivity of the metals is taken into account perturbatively up to the fourth order of the relative penetration depths of…

The Casimir effect refers to the existence of a macroscopic force between conducting plates in vacuum due to quantum fluctuations of fields. These forces play an important role, among other things, in the design of nano-scale mechanical…

We review modern achievements and problems in physics of the van der Waals and Casimir forces which arise due to zero-point and thermal fluctuations of the electromagnetic field between closely spaced material surfaces. This subject…

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…

It has been known that the fundamental Lifshitz theory, which is based on first principles of thermal quantum field theory, experiences difficulties when compared with precise measurements of the Casimir force. We analyze the…

We calculate the Casimir energy for scalar and gauge fields in interaction with zero-width mirrors, including quantum effects due to the matter fields inside the mirrors. We consider models where those fields are either scalar or fermionic,…

Several problems at the interface between the field-theoretical description of the Casimir effect and experiments on measuring the Casimir force are discussed. One of these problems is connected with the definition of the Casimir free…

We use a functional approach to evaluate the Casimir free energy for a self-interacting scalar field in $d+1$ dimensions, satisfying Dirichlet boundary conditions on two parallel planes. When the interaction is turned off, exact results for…

We derive an expression for the Casimir force between slabs with arbitrary dielectric properties characterized by their reflection coefficients. The formalism presented here is applicable to media with a local or a non-local dielectric…

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…

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 free energy and pressure of thin metal films deposited on metallic plates are considered using the Lifshitz theory and the Drude and plasma model approaches to the role of conduction electrons. The bound electrons are taken into…

We study the Casimir pressure between two similar plates of finite thickness kept at different temperatures in the case when the dielectric permittivity of the plates depends on temperature. It is suggested to consider the dielectric…