A. S. Kotanjyan

Repulsive Casimir–Polder forces from cosmic strings

We investigate the Casimir–Polder force acting on a polarizable microparticle in the geometry of a straight cosmic string. In order to develop this analysis we evaluate the electromagnetic field Green tensor on the imaginary frequency axis. The expression for the Casimir–Polder force is derived in the general case of anisotropic polarizability. In dependence on the eigenvalues for the polarizability tensor and of the orientation of its principal axes, the Casimir–Polder force can be either repulsive or attractive. Moreover, there are situations where the force changes the sign with separation. We show that for an isotropic polarizability tensor the force is always repulsive. At large separations between the microparticle and the string, the force varies inversely with the fifth power of the distance. In the non-retarded regime, corresponding to separations smaller than the relevant transition wavelengths, the force decays with the inverse fourth power of the distance. In the case of anisotropic polarizability, the dependence of the Casimir–Polder potential on the orientation of the polarizability tensor principal axes also leads to a moment of force acting on the particle.

Electromagnetic two-point functions and Casimir densities for a conducting plate in de Sitter spacetime ✩

Abstract We evaluate the two-point function for the electromagnetic field tensor in ( D + 1 ) -dimensional de Sitter spacetime assuming that the field is prepared in Bunch–Davies vacuum state. This two-point function is used for the investigation of the vacuum expectation values (VEVs) of the field squared and the energy–momentum tensor in the presence of a conducting plate. The VEVs are decomposed into the boundary-free and plate-induced parts. For the latter, closed form analytical expressions are given in terms of the hypergeometric function. For 3 ≤ D ≤ 8 the plate-induced part in the VEV of the electric field squared is positive everywhere, whereas for D ≥ 9 it is positive near the plate and negative at large distances. The VEV of the energy–momentum tensor, in addition to the diagonal components, contains an off-diagonal component which corresponds to the energy flux along the direction normal to the plate. Simple asymptotic expressions are provided at small and large distances from the plate compared with the de Sitter curvature scale. For D ≥ 4 , all the diagonal components of the plate-induced vacuum energy–momentum tensor are negative and the energy flux is directed from the plate.

Electromagnetic Casimir effect for conducting plates in de Sitter spacetime

Two-point functions, the mean field squared and the vacuum expectation value (VEV) of the energy–momentum tensor are investigated for the electromagnetic field in the geometry of parallel plates on background of -dimensional dS spacetime. We assume that the field is prepared in the Bunch–Davies vacuum state and on the plates a boundary condition is imposed that is a generalization of the perfectly conducting boundary condition for an arbitrary number of spatial dimensions. It is shown that for the background gravitational field essentially changes the behavior of the VEVs at separations between the plates larger than the curvature radius of dS spacetime. At large separations, the Casimir forces are proportional to the inverse fourth power of the distance for all values of spatial dimension . For this behavior is in sharp contrast with the case of plates in Minkowski bulk where the force decays as the inverse power of the distance.

Casimir–Polder potential for a metallic cylinder in cosmic string spacetime

Abstract Casimir–Polder potential is investigated for a polarizable microparticle in the geometry of a straight cosmic string with a metallic cylindrical shell. The electromagnetic field Green tensor is evaluated on the imaginary frequency axis. The expressions for the Casimir–Polder potential is derived in the general case of anisotropic polarizability for the both interior and exterior regions of the shell. The potential is decomposed into pure string and shell-induced parts. The latter dominates for points near the shell, whereas the pure string part is dominant near the string and at large distances from the shell. For the isotropic case and in the region inside the shell the both pure string and shell-induced parts in the Casimir–Polder force are repulsive with respect to the string. In the exterior region the shell-induced part of the force is directed toward the cylinder whereas the pure string part remains repulsive with respect to the string. At large distances from the shell the total force is repulsive.

SYNCHROTRON RADIATION INSIDE A DIELECTRIC CYLINDER

We investigate the electromagnetic fields generated by a charged particle rotating inside a dielectric cylinder immersed into a homogeneous medium. The expressions for the bound modes of the radiation field are derived in both interior and exterior regions. The radiation intensity for the modes propagating inside the cylinder is evaluated by using two different ways: by evaluating the work done by the radiation field on the charge and by evaluating the energy flux through the cross-section of the cylinder. The relation between these two quantities is discussed. We investigate the relative contributions of the bound modes and the modes propagating at large distances from the cylinder to the total radiation intensity. Numerical examples are given for a dielectric cylinder in the vacuum. It is shown that the presence of the cylinder can lead to the considerable increase of the synchrotron radiation intensity.

Electromagnetic quantum effects in anti-de Sitter spacetime

The two-point functions of the vector potential and of the field tensor for the electromagnetic field in the background of anti-de Sitter (AdS) spacetime are evaluated in an arbitrary number of spatial dimensions. First, we consider the two-point functions in the boundary-free geometry and then generalize the results in the presence of a reflecting boundary parallel to the AdS horizon. By using the expressions for the two-point functions of the field tensor, we investigate the vacuum expectation values of the electric field squared and of the energy–momentum tensor. Simple asymptotic expressions are provided near the AdS boundary and horizon.

Synchrotron and Smith-Purcell radiations from a charge rotating around a cylindrical grating

Abstract We study the radiation for a charge rotating around a diffraction grating on a cylindrical surface with metallic strips parallel to the cylinder axis. The effect of the grating on the radiation intensity is approximated by the surface currents induced on the strips by the field of the rotating charge. The expressions are derived for the vector potential and for the angular density of the radiation intensity on a given harmonic. We show that the behavior of the radiation intensity on large harmonics can be essentially different from that for a charge rotating in the vacuum. For the geometry of diffraction grating the radiation intensity on higher harmonics does not vanish for small angles with respect to the cylinder axis. For given characteristics of the charge, by the choice of the parameters of the diffraction grating, one can have highly directional radiation near the normal to the plane of the charge rotation. With decreasing energy, the relative contribution of the synchrotron radiation decreases and the Smith-Purcell part is dominant.

The study of undulator radiation of transversal oscillator

We study the radiation intensity for a charged transversal oscillator moving around a dielectric cylinder. Similar to the case of coaxial circular motion, under certain conditions for the parameters of the trajectory and dielectric cylinder, strong narrow peaks appear in the angular distribution of the radiation intensity in the exterior medium for a given harmonic. Comparing to the case of a uniform coaxial circular motion, for a transversal oscillator new peaks may appear. The oscillations serve as a mechanism for the control of the spectral-angular characteristics of the radiation intensity

Radiation from a longitudinal oscillator moving along a circular trajectory

Radiation intensity is investigated for a charged longitudinal oscillator moving along a helical trajectory around a dielectric cylinder immersed into a homogeneous medium. The influence of the longitudinal oscillations one on the characteristics of the angular distribution of the radiation intensity in the exterior medium is discussed. It is shown that the presence of oscillations serves as a mechanism to control the location and the height of the radiation peaks.

Conformal representations of the general scalar-tensor theory and cosmological models

The article is a review of cosmological models describing the accelerated expansion of the Universe built by using various conformal representations of the modified Jordan-Brans-Dicke (JBD) theory.