Vacuum Polarization of a Massless Scalar Field in the Background of a Global Monopole with Finite Core

In this paper we analyze the vacuum polarization effects of a massless scalar field in the background of a global monopole considering a inner structure to it. Specifically we investigate the effect of its structure on the vacuum expectation value of the square of the field operator, , admitting a non-minimal coupling between the field with the geometry: $\xi {\cal{R}}\hat{\Phi}^2$. Also we calculate the corrections on the vacuum expectation value of the energy-momentum tensor, , due to the inner structure of the monopole. In order to develop these analysis, we calculate the Euclidean Green function associated with the system for points in the region outside the core. As we shall see, for specific value of the coupling parameter $\xi$, the corrections caused by the inner structure of the monopole can provide relevant contributions on these vacuum polarizations.Comment: Accepted for publication in Classical and Quantum Gravity. Added references. 22 pages, 1 figur

Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of a nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate is suggested which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur

New features of the thermal Casimir force at small separations

The difference of the thermal Casimir forces at different temperatures between real metals is shown to increase with a decrease of the separation distance. This opens new opportunities for the demonstration of the thermal dependence of the Casimir force. Both configurations of two parallel plates and a sphere above a plate are considered. Different approaches to the theoretical description of the thermal Casimir force are shown to lead to different measurable predictions.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let

Higher order conductivity corrections to the Casimir force

The finite conductivity corrections to the Casimir force in two configurations are calculated in the third and fourth orders in relative penetration depth of electromagnetic zero oscillations into the metal. The obtained analytical perturbation results are compared with recent computations. Applications to the modern experiments are discussed.Comment: 15 pages, 4 figure

Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii

The impact of imperfections, which are always present on surfaces of lenses with centimeter-size curvature radii, on the Casimir force in the lens-plate geometry is investigated. It is shown that the commonly used formulation of the proximity force approximation is inapplicable for spherical lenses with surface imperfections, such as bubbles and pits. More general expressions for the Casimir force are derived that take surface imperfections into account. Using these expressions we show that surface imperfections can both increase and decrease the magnitude of the Casimir force up to a few tens of percent when compared with the case of a perfectly spherical lens. We demonstrate that the Casimir force between a perfectly spherical lens and a plate described by the Drude model can be made approximately equal to the force between a sphere with some surface imperfection and a plate described by the plasma model, and vice versa. In the case of a metallic sphere and semiconductor plate, approximately the same Casimir forces are obtained for four different descriptions of charge carriers in the semiconductor if appropriate surface imperfections on the lens surface are present. The conclusion is made that there is a fundamental problem in the interpretation of measurement data for the Casimir force, obtained by using spherical lenses of centimeter-size radii, and their comparison with theory.Comment: 28 pages, 7 figures, 1 table. To appear in Phys. Rev.

Gravitating Magnetic Monopole in the Global Monopole Spacetime

In this paper we study the regular self-gravitating 't Hooft-Polyakov magnetic monopole in a global monopole spacetime. We show that for the large distance, the structure of the manifold corresponds to the Reissner-Nordstr\"{o}m spacetime with a solid angle deficit factor. Although we analyze static and spherically symmetric solutions, it is not possible to solve analytically the system of coupled differential equations and only numerical evaluations can provide detailed information about the behavior of this system at the neighborhood of the defect's core. So, for this reason we solve numerically the set of differential equations for the metric tensor and for the matter fields for different values of the Higgs field vacuum expectation value, $\eta$, and the self-coupling constant, $\lambda$.Comment: 26 pages, 6 figures, LaTex forma

Casimir and van der Waals force between two plates or a sphere (lens) above a plate made of real metals

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated accounting for the finite conductivity of the metals. The simple formalism of surface modes is briefly presented which allows the possibility to obtain the generalization of Lifshitz results for the case of two semi-spaces covered by the thin layers. Additional clarifications of the regularization procedure provides the means to obtain reliable results not only for the force but also for the energy density. This, in turn, leads to the value of the force for the configuration of a sphere (lens) above a plate both of which are covered by additional layers. The Casimir interaction between Al and Au test bodies is recalculated using the optical tabulated data for the complex refractive index of these metals. The computations turn out to be in agreement with the perturbation theory up to the fourth order in relative penetration depth of electromagnetic zero point oscillations into the metal. The disagreements between the results recently presented in the literature are resolved. The Casimir force between Al bodies covered by the thin Au layers is computed and the possibility to neglect spatial dispersion effects is discussed as a function the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure non-retarded van der Waals force law between Al and Au bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2--4) nm. New, more exact, values of the Hamaker constant for Al and Au are determined.Comment: 5 figure

Temperature correction to the Casimir force in cryogenic range and anomalous skin effect

Temperature correction to the Casimir force is considered for real metals at low temperatures. With the temperature decrease the mean free path for electrons becomes larger than the field penetration depth. In this condition description of metals with the impedance of anomalous skin effect is shown to be more appropriate than with the permittivity. The effect is crucial for the temperature correction. It is demonstrated that in the zero frequency limit the reflection coefficients should coincide with those of ideal metal if we demand the entropy to be zero at T=0. All the other prescriptions discussed in the literature for the $n=0$ term in the Lifshitz formula give negative entropy. It is shown that the temperature correction in the region of anomalous skin effect is not suppressed as it happens in the plasma model. This correction will be important in the future cryogenic measurements of the Casimir force.Comment: 12 pages, 2 figures, to be published in Phys. Rev.

Thermal correction to the Casimir force, radiative heat transfer, and an experiment

The low-temperature asymptotic expressions for the Casimir interaction between two real metals described by Leontovich surface impedance are obtained in the framework of thermal quantum field theory. It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude model attains at zero temperature a positive value which depends on the parameters of a system, i.e., the Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test, whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates. The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer predicted from this impedance is several times less than previous predictions due to different contributions from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula is discussed. It is concluded that new measurements of radiative heat transfer are required to find out the adequate description of a metal in the theory of electromagnetic fluctuations.Comment: 19 pages, 4 figures. svjour.cls is used, to appear in Eur. Phys. J.