Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integrals. The local properties of the vacuum are investigated in various asymptotic regions of the parameters. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. It is shown that the interaction forces between the separate parts of the boundary are always attractive. The generalization to the case of a scalar field with Neumann boundary condition is discussed.     

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.     

Vacuum energy-momentum tensor in models with non-trivial topology in the presence of boundaries

The vacuum expectation value of the energy-momentum tensor for a scalar field in models with the compact subspace of an arbitrary geometry in the presence of parallel plates is investigated. The field operator on the plates obeys Robin boundary conditions with constant coefficients. Depending on the values of the coefficients, the vacuum energy density can be either positive or negative. As an example, the case of one-dimensional internal space is considered.     

Higgs characterisation at NLO in QCD: CP properties of the top-quark Yukawa interaction

We evaluate the Wightman function, the mean field squared and the vacuum expectation value of the energy–momentum tensor for a scalar field with the Robin boundary condition on a spherical shell in the background of a constant negative curvature space. For the coefficient in the boundary condition there is a critical value above which the scalar vacuum becomes unstable. In both the interior and the exterior regions, the vacuum expectation values are decomposed into the boundary-free and sphere-induced contributions. For the latter, rapidly convergent integral representations are provided. In the region inside the sphere, the eigenvalues are expressed in terms of the zeros of the combination of the associated Legendre function and its derivative and the decomposition is achieved by making use of the Abel–Plana type summation formula for the series over these zeros. The sphere-induced contribution to the vacuum expectation value of the field squared is negative for the Dirichlet boundary condition and positive for the Neumann one. At distances from the sphere larger than the curvature scale of the background space the suppression of the vacuum fluctuations in the gravitational field corresponding to the negative curvature space is stronger compared with the case of the Minkowskian bulk. In particular, the decay of the vacuum expectation values with the distance is exponential for both massive and massless fields. The corresponding results are generalized for spaces with spherical bubbles and for cosmological models with negative curvature spaces.     

Casimir Effect in Hemisphere Capped Tubes

In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2 + 1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.     

Wightman function and vacuum polarization in models with non-trivial topology in the presence of boundaries

Wightman function and the vacuum expectation value of the scalar field squared are studied in models with a compact subspace in the presence of parallel plane boundaries, on which the field obeys Robin boundary conditions. By means of the generalized Abel-Plana summation formula we have explicitly extracted from the vacuum expectation values the parts induced by the boundaries. As a simple example, a one-dimensional internal space is considered compactified on a circle.     

Surface vacuum energy and stresses for a brane in de Sitter spacetime

Vacuum expectation values of the surface energy–momentum tensor is investigated for a massless scalar field obeying mixed boundary condition on a brane in de Sitter bulk. To generate the corresponding vacuum surface densities we use the conformal relation between de Sitter and Rindler spacetimes.     

Casimir Effect for Two Parallel Plates Through a Gupta-Bleuler Type Quantization on the Static Domain Wall Background

In this paper, Casimir energy-momentum tensor for a conformally coupled scalar field in the presence of two parallel plates with Dirichlet boundary condition on background of planar domain wall is investigated. We show that by utilizing a Gupta-Bleuler type quantization approach, one can obtain finite result for the vacuum expectation values of the energy-momentum tensor. In addition, we calculate the pressures on the plates and energy density between two plates and show that they satisfy the standard thermodynamical relations.     

Vacuum correlators of the electromagnetic field and the Casimir-Polder forces in the field of a cosmic string

Vacuum correlators of the electric and magnetic fields are calculated in the geometry of a cosmic string. Formulas for the vacuum expectation values for the squares of field components are derived. The forces acting on an atom due to the vacuum fluctuations (Casimir-Polder forces) are investigated. For atoms with isotropic tensor of polarizability these forces are attractive with respect to the string. In the anisotropic case, depending on the eigenvalues of the polarizability tensor, the Casimir-Polder forces can be either attractive or repulsive.     

Vacuum quantum effect for curved boundaries in static Robertson–Walker space–time

The energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=−1 static Robertson–Walker space–time is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k=−1 Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in Robertson–Walker space from the corresponding Rindler counterpart by the conformal transformation.     

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

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.     

Three-dimensional analysis of a vacuum window connected towaveguide

For an effective additional heating system in the experimental tokamak-type system the pillbox-type vacuum window is proposed to isolate each part. L.J.B. Bergeron's formulation (1941) of the pillbox-type vacuum window connected to cylindrical waveguides is described, and the fundamental characteristics of the electromagnetic field within this system are shown. Local heating at the surface of the dielectric disk may be decreased by reducing circumferential dependence by using cylindrical waveguides. A unified analysis involving the pillbox window and both the input-side waveguide and the output-side one has been performed using the presented method. The results obtained present the complex variations of the distribution of the field in the overall analyzed region as a function of the length of the pillbox window. These results illustrate the characteristics of the three-dimensional analysis. The analyzed model is described; in particular, the boundary conditions of the conductor are explained. The numerical results of the field distributions are shown by the longitudinal magnetic field variations and the electric field variations in the various cross sections in the pillbox window     

Letter: Casimir Stress for Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in the de Sitter background for a massless scalar field satisfying Dirichlet boundary conditions on the cylinder is calculated. The metric is written in conformally flat form to make maximal use of the Minkowski space calculations. In the framework of a toy model, we have considered the quantum vacuum effect in the evolution of a domain wall between a cylindrical or in fact circle region around the z axis in which vacuum is _in and the remaining part of space where vacuum is _out .     

Spontaneous breaking of anti-de sitter supersymmetry

We compute the one-loop effective potential of the Wess-Zumino model in Anti-de Sitter space. The effect of the background geometry is determined exactly. After the renormalization of the kinetic action and the insertion of a linear counterterm in the superpotential, we solve the quantum-corrected equations of motion, obtaining the vacuum solutions in the semiclassical approximation. The vacuum expectation values of theA andB fields are shifted by finite terms which depend upon the boundary conditions for the field propagators. Despite this result, we show with complete generality that supersymmetry is preserved to the one-loop order at each classically supersymmetric extremum of the effective potential.     

Acoustic scattering by a cylindrical shell with symmetric line constraints in the heavy fluid-loading limit

A cylindrical shell, modelled using Donnell-Mushtari thin shell theory, is reinforced by two internal rigid plates attached to the shell along lines parallel to the shell axis. A circumferential mode expansion is used to obtain numerical results for the scattered sound field due to the presence of the reaction forces along the attachment lines. In the heavy fluid-loading limit, which is appropriate for low and mid-frequency ranges for practical underwater structures, asymptotic analysis is presented which allows the peak frequencies in the scattered field due to the reaction forces to be expressed (to leading order) in terms of the geometry and the shell and fluid parameters. These predictions agree well with results obtained by numerically evaluating the infinite sums needed to calculate the reaction forces and hence the scattered field.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

Free vibration analysis of a hanged clamped-free cylindrical shell partially submerged in fluid: The effect of external wall,internal shaft,and flat bottom

The free flexural vibration of a hanged clamped-free cylindrical shell with various boundary conditions partially submerged in a fluid is investigated. Specifically, the effects of the boundary conditions such as the existence of the external wall, internal shaft, and bottom on the natural vibration characteristics of the partially submerged cylindrical shell are investigated both theoretically and experimentally. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion. The theoretical predictions were in good agreement with the experimental results validating the theoretical approach developed in this study. The effects of the external wall, internal shaft, and bottom on the natural vibration characteristics can be neglected when its boundaries are not very close to the shell structure.     

Vibration and stability of a circular cylindrical shell subjected to a torque

An analysis is presented for the vibration and stability of a circular cylindrical shell subjected to a torque. The displacements of a circular shell are written in a series of beam eigenfunctions satisfying the boundary conditions. The kinetic and strain energies of the shell are evaluated analytically, and the frequency eauation of the shell is derived by the Ritz method. The method is applied to circular cylindrical shells under two types of boundary conditions at the edges; the natural frequencies and the divergence torques are calculated numerically, and the effects of the thickness ratio, length ratio and edge conditions on the vibration and stability are studied.     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.